Produced by Marius Masi, Don Kretz and the Online
Distributed Proofreading Team at http://www.pgdp.net







Transcriber's notes:

(1) Numbers following letters (without space) like C2 were originally
      printed in subscript. Letter subscripts are preceded by an
      underscore, like C_n.

(2) Characters following a carat (^) were printed in superscript.

(3) Side-notes were relocated to function as titles of their respective
      paragraphs.

(4) Macrons and breves above letters and dots below letters were not
      inserted.

(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
      letters.

(6) The following typographical errors have been corrected:

    ARTICLE MADISON, JAMES: "On the 26th of December 1785 Jefferson's
      Bill for establishing religious freedom in Virginia, which had been
      introduced by Madison, was passed. In the Virginia House of
      Delegates, as in the Continental Congress ..." 'Virginia' amended
      from 'Viginia'.

    ARTICLE MADRAS: "... the college of agriculture at Coimbatore; the
      teachers' college at Saidapet; the school of arts at Madras; and
      the military orphanage at Ootacamund, in memory of Sir Henry
      Lawrence." 'orphanage' amended from 'ophanage'.

    ARTICLE MAGNETISM: "... the ratio of magnetization to magnetizing
      force remained sensibly constant at 6.4, which may therefore with
      great probability be assumed to represent the initial value ..."
      'which' amended from 'wihch'.

    ARTICLE MAGNETISM: "From experiments of both classes it appears
      that for a given field there is a certain value of the load for
      which the magnetization is a maximum, the maximum occurring at a
      smaller load the stronger the field." 'occurring' amended from
      'occuring'.

    ARTICLE MAGNETISM: "Recent researches have shown that other
      important changes in its properties occur at the same critical
      temperature." 'important' amended from 'imporant'.

    ARTICLE MAGNETISM: "Wills found that the susceptibility was
      constant in fields ranging from 4200 to 15,000." 'susceptibility'
      amended from 'suceptibility'.

    ARTICLE MAGNETISM, TERRESTRIAL: "As explained above, a would
      represent the range in a year of no sun-spots, while 100 b would
      represent the excess over this shown by the range in a year when
      Wolf's sun-spot frequency is 100." "Wolf's" amended from
      "Wolfer's".




          ENCYCLOPAEDIA BRITANNICA

  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
           AND GENERAL INFORMATION

              ELEVENTH EDITION


           VOLUME XVII, SLICE III

  McKinley, William to Magnetism, Terrestrial




ARTICLES IN THIS SLICE:


  McKINLEY, WILLIAM                 MADISON (Wisconsin, U.S.A.)
  McKINNEY (Texas, U.S.A.)          MADOU, JEAN BAPTISTE
  MACKINTOSH, SIR JAMES             MADOZ, PASCUAL
  MACKLIN, CHARLES                  MADRAS (Indian presidency)
  MACK VON LEIBERICH, KARL          MADRAS (Indian city)
  McLANE, LOUIS                     MADRAZO Y KUNT, DON FEDERICO DE
  MACLAREN, CHARLES                 MADRID (province of Spain)
  MACLAREN, IAN                     MADRID (the capital of Spain)
  MACLAURIN, COLIN                  MADRIGAL
  M'LENNAN, JOHN FERGUSON           MADURA (island)
  MACLEOD, HENRY DUNNING            MADURA (city)
  MACLEOD, NORMAN                   MADVIG, JOHAN NICOLAI
  MACLISE, DANIEL                   MAECENAS, GAIUS
  MACLURE, WILLIAM                  MAECIANUS, LUCIUS VOLUSIUS
  MacMAHON, MARIE EDMÉ MAURICE DE   MAELDUIN, VOYAGE OF
  McMASTER, JOHN BACH               MAELIUS, SPURIUS
  MACMILLAN                         MAELSTROM
  MACMONNIES, FREDERICK WILLIAM     MAENADS
  MACNAGHTEN, SIR WILLIAM HAY       MAENIUS, GAIUS
  MacNALLY, LEONARD                 MAERLANT, JACOB VAN
  MACNEE, SIR DANIEL                MAES, NICOLAS
  MACNEIL, HERMON ATKINS            MAESTRO
  McNEILE, HUGH                     MAETERLINCK, MAURICE
  MACNEILL, HECTOR                  MAFEKING
  MACOMB                            MAFFEI, FRANCESCO SCIPIONE
  MACOMER                           MAFIA
  MACON, NATHANIEL                  MAFRA
  MÂCON (town of France)            MAGADHA
  MACON (Georgia, U.S.A.)           MAGALDÁN
  MACPHERSON, SIR DAVID LEWIS       MAGALLANES
  MACPHERSON, JAMES                 MAGAZINE
  McPHERSON, JAMES BIRDSEYE         MAGDALA
  MACQUARIE                         MAGDEBURG
  MACRAUCHENIA                      MAGEE, WILLIAM
  MACREADY, WILLIAM CHARLES         MAGEE, WILLIAM CONNOR
  MACROBIUS, AMBROSIUS THEODOSIUS   MAGELLAN, FERDINAND
  MACROOM                           MAGELLANIC CLOUDS
  MACUGNAGA                         MAGENTA
  MacVEAGH, WAYNE                   MAGGIORE, LAGO
  MADÁCH, IMRE                      MAGIC
  MADAGASCAR                        MAGIC SQUARE
  MADAN, MARTIN                     MAGINN, WILLIAM
  MADDALONI                         MAGISTRATE
  MADDEN, SIR FREDERIC              MAGLIABECHI, ANTONIO DA MARCO
  MADDER                            MAGLIANI, AGOSTINO
  MADEC, RENÉ-MARIE                 MAGNA CARTA
  MADEIRA                           MAGNA GRAECIA
  MADELENIAN                        MAGNATE
  MADELEY                           MAGNES
  MADHAVA ACHARYA                   MAGNESIA
  MADI                              MAGNESITE
  MADISON, JAMES                    MAGNESIUM
  MADISON (Indiana, U.S.A.)         MAGNETISM
  MADISON (New Jersey, U.S.A.)      MAGNETISM, TERRESTRIAL




McKINLEY, WILLIAM (1843-1901), twenty-fifth president of the United
States, was born in Niles, Trumbull county, Ohio, on the 29th of January
1843. His ancestors on the paternal side were Scotch-Irish who lived at
Dervock, Co. Antrim, and spelled the family name "McKinlay." His
great-great-grandfather settled in York county, Pennsylvania, about
1743, and from Chester county, Pennsylvania, his great-grandfather,
David McKinley, who served as a private during the War of Independence,
moved to Ohio in 1814. David's son James had gone in 1809 to Columbiana
county, Ohio. His son William McKinley (b. 1807), like his father an
iron manufacturer, was married in 1829 to Nancy Campbell Allison, and to
them were born nine children, of whom William, the president, was the
seventh. In 1852 the family removed to Poland, Mahoning county, where
the younger William was placed at school. At seventeen he entered the
junior class of Allegheny College, at Meadville, Pennsylvania; but he
studied beyond his strength, and returned to Poland, where for a time he
taught in a neighbouring country school. When the Civil War broke out in
1861 he promptly enlisted as a private in the 23rd Ohio Volunteer
Infantry. He saw service in West Virginia, at South Mountain, where this
regiment lost heavily, and at Antietam, where he brought up hot coffee
and provisions to the fighting line; for this he was promoted second
lieutenant on the 24th of September 1862. McKinley was promoted first
lieutenant in February 1864, and for his services at Winchester was
promoted captain on the 25th of July 1864. He was on the staff of
General George Crook at the battles of Opequan, Fisher's Hill, and Cedar
Creek in the Shenandoah valley, and on the 14th of March 1865 was
brevetted major of volunteers for gallant and meritorious services. He
also served on the staff of General Rutherford B. Hayes, who spoke
highly of his soldierly qualities. He was mustered out with his regiment
on the 26th of July 1865. Four years of army life had changed him from a
pale and sickly lad into a man of superb figure and health.

After the war McKinley returned to Poland, and bent all his energy upon
the study of law. He completed his preparatory reading at the Albany
(N.Y.) law school, and was admitted to the bar at Warren, Ohio, in March
1867. On the advice of an elder sister, who had been for several years a
teacher in Canton, Stark county, Ohio, he began his law practice in that
place, which was to be his permanent home. He identified himself
immediately with the Republican party, campaigned in the Democratic
county of Stark in favour of negro suffrage in 1867, and took part in
the campaign work on behalf of Grant's presidential candidature in 1868.
In the following year he was elected prosecuting attorney on the
Republican ticket; in 1871 he failed of re-election by 45 votes, and
again devoted himself to his profession, while not relaxing his interest
in politics.

In 1875 he first became known as an able campaign speaker by his
speeches favouring the resumption of specie payments, and in behalf of
Rutherford B. Hayes, the Republican candidate for governor of Ohio. In
1876 he was elected by a majority of 3304 to the national House of
Representatives. Conditions both in Ohio and in Congress had placed him,
and were to keep him for twenty years, in an attitude of aggressive and
uncompromising partisanship. His Congressional district was naturally
Democratic, and its boundaries were changed two or three times by
Democratic legislatures for the purpose of so grouping Democratic
strongholds as to cause his defeat. But he overcame what had threatened
to be adverse majorities on all occasions from 1876 to 1890, with the
single exception of 1882, when, although he received a certificate of
election showing that he had been re-elected by a majority of 8, and
although he served nearly through the long session of 1883-1884, his
seat was contested and taken (May 28, 1884) by his Democratic opponent,
Jonathan H. Wallace. McKinley reflected the strong sentiment of his
manufacturing constituency in behalf of a high protective tariff, and he
soon became known in Congress (where he particularly attracted the
attention of James G. Blaine) as one of the most diligent students of
industrial policy and question affecting national taxation. In 1878 he
took part in the debates over the Wood Tariff Bill, proposing lower
import duties; and in the same year he voted for the Bland-Allison
Silver Bill. In December 1880 he was appointed a member of the Ways and
Means committee, succeeding General James A. Garfield, who had been
elected president in the preceding month, and to whose friendship, as to
that of Rutherford B. Hayes, McKinley owed much in his earlier years in
Congress. He was prominent in the debate which resulted in the defeat of
the Democratic Morrison Tariff Bill in 1884, and, as minority leader of
the Ways and Means committee, in the defeat of the Mills Bill for the
revision of the tariff in 1887-1888. In 1889 he became chairman of the
Ways and Means committee and Republican leader in the House of
Representatives, after having been defeated by Thomas B. Reed on the
third ballot in the Republican caucus for speaker of the House. On the
16th of April 1890 he introduced from the Ways and Means committee the
tariff measure known commonly as the McKinley Bill, which passed the
House on the 21st of May, passed the Senate (in an amended form, with a
reciprocity clause, which McKinley had not been able to get through the
House) on the 10th of September, was passed as amended, by the House,
and was approved by the president on the 1st of October 1890. The
McKinley Bill reduced revenues by its high and in many cases almost
prohibitive duties; it put sugar on the free list with a discriminating
duty of (1/10)th of one cent a pound on sugar imported from countries
giving a bounty for sugar exported, and it gave bounties to American
sugar growers; it attempted to protect many "infant" industries such as
the manufacture of tin-plate; under its provision for reciprocal trade
agreements (a favourite project of James G. Blaine, who opposed many of
the "protective" features of the Bill) reciprocity treaties were made
with Germany, France, Italy, and Belgium, which secured a market in
those countries for American pork. Abroad, where the Bill made
McKinley's name known everywhere, there was bitter opposition to it and
reprisals were threatened by several European states. In the United
States the McKinley Tariff Bill was one of the main causes of the
Democratic victory in the Congressional elections of 1890, in which
McKinley himself was defeated by an extraordinary Democratic gerrymander
of his Congressional district. In November 1891 he was elected governor
of Ohio with a plurality of more than 21,000 votes in a total of 795,000
votes cast. He was governor of Ohio in 1892-1895, being re-elected in
1893. His administration was marked by no important events, except that
he had on several occasions in his second term to call out the militia
of the state to preserve order; but it may be considered important
because of the training it gave him in executive as distinguished from
legislative work.

McKinley had been prominent in national politics even before the passage
of the tariff measure bearing his name. In 1888 in the National
Republican Convention in Chicago he was chairman of the committee on
resolutions (i.e. the platform committee) and was leader of the
delegation from Ohio, which had been instructed for John Sherman; after
James G. Blaine withdrew his name there was a movement, begun by
Republican congressmen, to nominate McKinley, who received 16 votes on
the seventh ballot, but passionately refused to be a candidate,
considering that his acquiescence would be a breach of faith toward
Sherman. In 1892 McKinley was the permanent president of the National
Republican Convention which met in Minneapolis and which renominated
Benjamin Harrison on the first ballot, on which James G. Blaine received
182(5/6) votes, and McKinley, in spite of his efforts to the contrary,
received 182 votes. In 1894 he made an extended campaign tour before the
Congressional elections, and spoke even in the South. In 1896 he seemed
for many reasons the most "available" candidate of his party for the
presidency: he had no personal enemies in the party; he had carried the
crucial state of Ohio by a large majority in 1893; his attitude on the
coinage question had never been so pronounced as to make him unpopular
either with the radical silver wing or with the conservative
"gold-standard" members of the party. The campaign for his nomination
was conducted with the greatest adroitness by his friend, Marcus A.
Hanna, and in the National Republican Convention held in St Louis in
June he was nominated for the presidency on the first ballot by 661½ out
of a total of 906 votes. The convention adopted a tariff plank drafted
by McKinley, and, of far greater immediate importance, a plank, which
declared that the Republican party was "opposed to the free coinage of
silver, except by international agreement with the leading commercial
nations of the world, which we pledge ourselves to promote, and until
such agreement can be obtained the existing gold standard must be
preserved." This "gold standard" plank drove out of the Republican party
the Silver Republicans of the West, headed by Senator Henry M. Teller of
Colorado. The Republican convention nominated for the vice-presidency
Garrett A. Hobart of New Jersey. The National Democratic Convention
declared for the immediate opening of the mints to the free and
unlimited coinage of silver at the ratio with gold of 16 to 1; and it
nominated for the presidency William Jennings Bryan of Nebraska, who
also received the nomination of the People's party and of the National
Silver party. There was a secession from the Democratic party of
conservatives who called themselves the National Democratic party, who
were commonly called Gold Democrats, and who nominated John M. Palmer
(1817-1900) of Illinois for president. In this re-alignment of parties
McKinley, who had expected to make the campaign on the issue of a high
protective tariff, was diverted to the defence of the gold standard as
the main issue. While his opponent travelled throughout the country
making speeches, McKinley remained in Canton, where he was visited by
and addressed many Republican delegations. The campaign was
enthusiastic: the Republican candidate was called the "advance agent of
prosperity"; "Bill McKinley and the McKinley Bill" became a campaign
cry; the panic of 1893 was charged to the repeal of the McKinley tariff
measure; and "business men" throughout the states were enlisted in the
cause of "sound money" to support McKinley, who was elected in November
by a popular vote of 7,106,779 to 6,502,925 for Bryan, and by an
electoral vote of 271 to 176.

McKinley was inaugurated president of the United States on the 4th of
March 1897. The members of his cabinet were: secretary of state, John
Sherman (whose appointment created a vacancy in the Senate to which
Marcus A. Hanna was elected), who was succeeded in April 1898 by William
R. Day, who in turn was followed in September 1898 by John Hay;
secretary of the treasury, Lyman J. Gage, a Gold Democrat; secretary of
war, Russell A. Alger, who was succeeded in 1899 by Elihu Root;
secretary of the navy, John D. Long; attorney-general, Joseph McKenna,
succeeded in January 1898 by John William Griggs; postmaster-general,
James A. Gary, succeeded in April 1898 by Charles Emory Smith; secretary
of the interior, Cornelius N. Bliss, succeeded in February 1899 by Ethan
Allen Hitchcock; and secretary of agriculture, James Wilson. (For the
political history of McKinley's administration see UNITED STATES:
_History_). Immediately after his inauguration the president summoned
Congress to assemble in an extra session on the 15th of March. The
Democratic tariff in 1893 had been enacted as part of the general
revenue measure, which included an income-tax. The income-tax having
been declared unconstitutional by the Supreme Court, the measure had
failed to produce a sufficient revenue, and it had been necessary to
increase the public debt. McKinley's message to the new Congress dwelt
upon the necessity of an immediate revision of the tariff and revenue
system of the country, and the so-called Dingley Tariff Bill was
accordingly passed through both houses, and was approved by the
president on the 24th of July.

The regular session of Congress which opened in December was occupied
chiefly with the situation in Cuba. President McKinley showed himself
singularly patient and self-controlled in the midst of the popular
excitement against Spain and the clamour for intervention by the United
States in behalf of the Cubans; but finally, on the 23rd of March, he
presented an ultimatum to the Spanish government, and on the 25th of
April, on his recommendation. Congress declared war upon Spain. During
the war itself he devoted himself with great energy to the mastery of
military details; but there was bitter criticism of the war department
resulting in the resignation of the secretary of war, Russell A. Alger
(q.v.). The signing of a peace protocol on the 12th of August was
followed by the signature at Paris on the 10th of December of articles
of peace between the United States and Spain. After a long discussion
the peace treaty was ratified by the United States Senate on the 6th of
February 1899; and in accordance with its terms Porto Rico, the
Philippine Archipelago, and Guam were transferred by Spain to the United
States, and Cuba came under American jurisdiction pending the
establishment there of an independent government. Two days before the
ratification of the peace treaty, a conflict took place between armed
Filipinos under the leadership of Emilio Aguinaldo and the American
forces that were in possession of Manila. The six months that had
elapsed between the signing of the peace protocol and the ratification
of the treaty had constituted a virtual interregnum, Spain's authority
having been practically destroyed in the Philippines and that of the
United States not having begun. In this period a formidable native
Filipino army had been organized and a provisional government created.
The warfare waged by these Filipinos against the United States, while
having for the most part a desultory and guerilla character, was of a
very protracted and troublesome nature. Sovereignty over the Filipinos
having been accepted by virtue of the ratification of the Paris treaty,
President McKinley was not at liberty to do otherwise than assert the
authority of the United States and use every endeavour to suppress the
insurrection. But there was bitter protest against this "imperialism,"
both within the party by such men as Senators George F. Hoar and Eugene
Hale, and Thomas B. Reed and Carl Schurz, and, often for purely
political reasons, from the leaders of the Democratic party. In the
foreign relations of the United States, as directed by President
McKinley, the most significant change was the cordial understanding
established with the British government, to which much was contributed
by his secretary of state, John Hay, appointed to that portfolio when he
was ambassador to the court of St James, and which was due to some
extent to the friendliness of the British press and even more markedly
of the British navy in the Pacific during the Spanish War. Other
important foreign events during McKinley's administration were: the
annexation of the Hawaiian Islands (see HAWAII) in August 1898, and the
formation of the Territory of Hawaii in April 1900; the cessation in
1899 of the tripartite (German, British, and French) government of the
Samoan Islands, and the annexation by the United States of those of the
islands east of 171°, including the harbour of Pago-Pago; the
participation of American troops in the march of the allies on Pekin in
August 1900, and the part played by McKinley's secretary of state, John
Hay, in securing a guarantee of the integrity of the Chinese empire. In
1900 McKinley was unanimously renominated by the National Republican
Convention which met in Philadelphia on the 19th of June, and which
nominated Theodore Roosevelt, governor of New York, for the
vice-presidency. The Republican convention demanded the maintenance of
the gold standard, and pointed to the fulfilment of some of the most
important of the pledges given by the Republican party four years
earlier. The intervening period had been one of very exceptional
prosperity in the United States, foreign commerce having reached an
unprecedented volume, and agriculture and manufactures having made
greater advancement than in any previous period of the country's
history. The tendency towards the concentration of capital in great
industrial corporations had been active to an extent previously undreamt
of, with incidental consequences that had aroused much apprehension; and
the Democrats accused President McKinley and the Republican party of
having fostered the "trusts." But the campaign against McKinley and the
Republican party was not only "anti-trust" but "anti-imperialistic."
William Jennings Bryan, renominated by the Democratic party in July (and
in May by the Fusion People's party) on a free silver platform, declared
that imperialism was the "paramount issue" and made a second vigorous
campaign; and the opposition to McKinley's re-election, whether based on
opposition to his economic or to his foreign policy, was not entirely
outside of his own party. As the result of the polling in November, 292
Republican presidential electors were chosen, and 155 Democratic
electors, elected in Colorado, Idaho, Montana, Nevada, and the Southern
states, represented the final strength of the Bryan and Stevenson
ticket. The Republican popular vote was 7,207,923, and the Democratic
6,358,133. Since 1872 no president had been re-elected for a second
consecutive term.

In the term of Congress immediately following the presidential election
it was found possible to reduce materially the war taxes which had been
levied on the outbreak of the Spanish-American War. Arrangements were
perfected for the termination of the American military occupation of
Cuba and the inauguration of a Cuban Republic as a virtual protectorate
of the United States, the American government having arranged with the
Cuban constitutional convention for the retention of certain naval
stations on the Cuban coast. In the Philippines advanced steps had been
taken in the substitution of civil government for military occupation,
and a governor-general, Judge William H. Taft, had been appointed and
sent to Manila. Prosperity at home was great, and foreign relations were
free from complications. The problems which had devolved upon McKinley's
administration had been far advanced towards final settlement. He
retained without change the cabinet of his first administration. After
an arduous and anxious term, the president had reached a period that
promised to give him comparative repose and freedom from care. He had
secured, through the co-operation of Congress, the permanent
reorganization of the army and a very considerable development of the
navy. In these circumstances. President McKinley, accompanied by the
greater part of his cabinet, set forth in the early summer on a tour to
visit the Pacific coast, where he was to witness the launching of the
battleship "Ohio" at San Francisco. The route chosen was through the
Southern states, where many stops were made, and where the president
delivered brief addresses. The heartiness of the welcome accorded him
seemed to mark the disappearance of the last vestige of sectional
feeling that had survived the Civil War, in which McKinley had
participated as a young man. After his return he spent a month in a
visit at his old home in Canton, Ohio, and at the end of this visit, by
previous arrangement, he visited the city of Buffalo, New York, in order
to attend the Pan-American exposition and deliver a public address. This
address (Sept. 5, 1901) was a public utterance designed by McKinley to
affect American opinion and public policy, and apparently to show that
he had modified his views upon the tariff. It declared that henceforth
the progress of the nations must be through harmony and co-operation, in
view of the fast-changing conditions of communication and trade, and it
maintained that the time had come for wide-reaching modifications in the
tariff policy of the United States, the method preferred by McKinley
being that of commercial reciprocity arrangements with various nations.
On the following day, the 6th of September 1901, a great reception was
held for President McKinley in one of the public buildings of the
exposition, all sorts and conditions of men being welcome. Advantage of
this opportunity was taken by a young man of Polish parentage, by name
Leon Czolgosz, to shoot at the president with a revolver at close range.
One of the two bullets fired penetrated the abdomen. After the world had
been assured that the patient was doing well and would recover, he
collapsed and died on the 14th. The assassin, who, it was for a time
supposed, had been inflamed by the editorials and cartoons of the
demagogic opposition press, but who professed to hold the views of that
branch of anarchists who believe in the assassination of rulers and
persons exercising political authority, was promptly seized, and was
convicted and executed in October 1901. McKinley's conduct and
utterances in his last days revealed a loftiness of personal character
that everywhere elicited admiration and praise. Immediately after his
death Vice-President Roosevelt took the oath of office, announcing that
it would be his purpose to continue McKinley's policy, while also
retaining the cabinet and the principal officers of the government.
McKinley's funeral took place at Canton, Ohio, on the 19th of September,
the occasion being remarkable for the public manifestations of mourning,
not only in the United States, but in Great Britain and other countries;
in Canton a memorial tomb has been erected.

Though he had not the personal magnetism of James G. Blaine, whom he
succeeded as a leader of the Republican party and whose views of
reciprocity he formally adopted in his last public address, McKinley had
great personal suavity and dignity, and was thoroughly well liked by his
party colleagues. As a politician he was always more the people's
representative than their leader, and that he "kept his ear to the
ground" was the source of much of his power and at the same time was his
greatest weakness: his address at Buffalo the day before his
assassination seems to voice his appreciation of the change in popular
sentiment regarding the tariff laws of the United States and is the more
remarkable as coming from the foremost champion for years of a form of
tariff legislation devised to stifle international competition. His
apparently inconsistent record on the coinage question becomes
consistent if considered in the same way, as the expression of the
gradually changing views of his constituency. And it may not be fanciful
to suggest that the obvious growth of McKinley in breadth and power
during his term as president was due to his being the representative of
a larger constituency, less local and less narrow-minded. He was an able
but far from brilliant campaign speaker. His greatest administrative
gift was a fine intuition in choosing men to serve him. McKinley's
private life was irreproachable; and very fine was his devotion to his
wife, Ida Saxton (d. 1907), whom he had married in Canton in 1871, who
was throughout his political career a confirmed invalid. He was from his
early manhood a prominent member of the Methodist Episcopal Church.

  His _Speeches and Addresses_ were printed in two volumes (New York,
  1893 and 1901).




McKINNEY, a city and the county-seat of Collin county, Texas, U.S.A.,
about 30 m. N. by E. of Dallas. Pop. (1890), 2489; (1900), 4342 (917
negroes); (1910) 4714. It is served by the Missouri, Kansas & Texas and
the Houston & Texas Central railways, and by the Dallas & Sherman
inter-urban (electric) line, the central power plant of which is
immediately north of the city. McKinney is in a fine farming region;
there are also manufactures. The municipal water supply is obtained from
artesian wells. The first settlement in Collin county was made about 10
m. north of what is now McKinney in 1841. McKinney was named, as was the
county, in honour of Collin McKinney, a pioneer in the region and a
signer of the Declaration of the Independence of Texas. It was settled
in 1844, was laid out and became the county-seat in 1846, and was first
chartered as a city in 1874.




MACKINTOSH, SIR JAMES (1765-1832), Scottish publicist, was born at
Aldourie, 7 m. from Inverness, on the 24th of October 1765. He came of
old Highland families on both sides. He went in 1780 to college at
Aberdeen, where he made a friend of Robert Hall, afterwards the famous
preacher. In 1784 he proceeded for the study of medicine to Edinburgh,
where he participated to the full in the intellectual ferment, but did
not quite neglect his medical studies, and took his degree in 1787.

In 1788 Mackintosh removed to London, then agitated by the trial of
Warren Hastings and the king's first lapse into insanity. He was much
more interested in these and other political events than in his
professional prospects; and his attention was specially directed to the
events and tendencies which caused or preceded the Revolution in France.
In 1789 he married his first wife, Catherine Stuart, whose brother
Daniel afterwards became editor of the _Morning Post_. His wife's
prudence was a corrective to his own unpractical temperament, and his
efforts in journalism became fairly profitable. Mackintosh was soon
absorbed in the question of the time; and in April 1791, after long
meditation, he published his _Vindiciae Gallicae_, a reply to Burke's
_Reflections on the French Revolution_. It was the only worthy answer to
Burke that appeared. It placed the author in the front rank of European
publicists, and won him the friendship of some of the most distinguished
men of the time, including Burke himself. The success of the _Vindiciae_
finally decided him to give up the medical for the legal profession. He
was called to the bar in 1795, and gained a considerable reputation
there as well as a tolerable practice. In 1797 his wife died, and next
year he married Catherine Allen, sister-in-law of Josiah and John
Wedgwood, through whom he introduced Coleridge to the _Morning Post_. As
a lawyer his greatest public efforts were his lectures (1799) at
Lincoln's Inn on the law of nature and nations, of which the
introductory discourse was published, and his eloquent defence (1803) of
Jean Gabriel Peltier, a French refugee, tried at the instance of the
French government for a libel against the first consul. In 1803 he was
knighted, and received the post of recorder at Bombay. The spoilt child
of London society was not at home in India, and he was glad to return to
England, where he arrived in 1812.

He courteously declined the offer of Perceval to resume political life
under the auspices of the dominant Tory party, though tempting prospects
of office in connexion with India were opened up. He entered parliament
in the Whig interest as member for Nairn. He sat for that county, and
afterwards for Knaresborough, till his death. In London society, and in
Paris during his occasional visits, he was a recognized favourite for
his genial wisdom and his great conversational power. On Mme de Stael's
visit to London he was the only Englishman capable of representing his
country in talk with her. His parliamentary career was marked by the
same wide and candid liberalism as his private life. He opposed the
reactionary measures of the Tory government, supported and afterwards
succeeded Romilly in his efforts for reforming the criminal code, and
took a leading part both in Catholic emancipation and in the Reform
Bill. But he was too little of a partisan, too widely sympathetic and
candid, as well as too elaborate, to be a telling speaker in parliament,
and was consequently surpassed by more practical men whose powers were
incomparably inferior. From 1818 to 1824 he was professor of law and
general politics in the East India Company's College at Haileybury.

In the midst of the attractions of London society and of his
parliamentary avocations Mackintosh felt that the real work of his life
was being neglected. His great ambition was to write a history of
England. His studies both in English and foreign speculation led him to
cherish the design also of making some worthy contribution to
philosophy. It was not till 1828 that he set about the first task of his
literary ambition. This was the _Dissertation on the Progress of Ethical
Philosophy_, prefixed to the seventh edition of the _Encyclopaedia
Britannica_. The dissertation, written mostly in ill-health and in
snatches of time taken from his parliamentary engagements, was published
in 1831. It was severely attacked in 1835 by James Mill in his _Fragment
on Mackintosh_. About the same time he wrote for the _Cabinet
Cyclopaedia_ a "History of England from the Earliest Times to the Final
Establishment of the Reformation." His more elaborate _History of the
Revolution_, for which he had made great researches and collections, was
not published till after his death. Already a privy councillor,
Mackintosh was appointed commissioner for the affairs of India under the
Whig administration of 1830. He died on the 30th of May 1832.

Mackintosh was undoubtedly one of the most cultured and catholic-minded
men of his time. His studies and sympathies embraced almost every human
interest, except pure science. But the width of his intellectual
sympathies, joined to a constitutional indecision and _vis inertiae_,
prevented him from doing more enduring work. _Vindiciae Gallicae_ was
the verdict of a philosophic Liberal on the development of the French
Revolution up to the spring of 1791, and though the excesses of the
revolutionists compelled him a few years after to express his entire
agreement with the opinions of Burke, its defence of the "rights of man"
is a valuable statement of the cultured Whig's point of view at the
time. The _History of the Revolution in England_, breaking off at the
point where William of Orange is preparing to intervene in the affairs
of England, is chiefly interesting because of Macaulay's admiring essay
on it and its author.

  A _Life_, by his son R. J. Mackintosh, was published in 1836.




MACKLIN, CHARLES (c. 1699-1797), Irish actor and playwright, whose
real name was McLaughlin, was born in Ireland, and had an adventurous
youth before coming to Bristol, where he made his first appearance on
the stage as Richmond in _Richard III_. He was at Lincoln's Inn Fields
about 1725, and by 1733 was at Drury Lane, where the quarrel between the
manager and the principal actors resulted in his getting better parts.
When the trouble was over and these were taken from him, he went to the
Haymarket, but he returned in 1734 to Drury Lane and acted there almost
continuously until 1748. Then for two seasons he and his wife (d. _c._
1758), an excellent actress, were in Dublin under Sheridan, then back in
London at Covent Garden. He played a great number of characters,
principally in comedy, although Shylock was his greatest part, and Iago
and the Ghost in _Hamlet_ were in his repertory. At the end of 1753
Macklin bade farewell to the stage to open a tavern, near the theatre,
where he personally supervised the serving of dinner. He also delivered
an evening lecture, followed by a debate, which was soon a hopeless
subject of ridicule. The tavern failed, and Macklin returned to the
stage, and played for a number of years in London and Dublin. His quick
temper got him into constant trouble. In a foolish quarrel over a wig in
1735 he killed a fellow actor in the green-room at Drury Lane, and he
was constantly at law over his various contracts and quarrels. The
bitterest of these arose on account of his appearing as Macbeth at
Covent Garden in 1772. The part was usually played there by William
Smith, and the public would not brook a change. A few nights later the
audience refused to hear Macklin as Shylock, and shouted their wish, in
response to the manager's question, to have him discharged. This was
done in order to quell the riot. His lawsuit, well conducted by himself,
against the leaders of the disturbance resulted in an award of £600 and
costs, but Macklin magnanimously elected instead that the defendants
should take £100 in tickets at three benefits--for himself, his daughter
and the management. He returned to Covent Garden, but his appearances
thereafter were less frequent, ending in 1789, when as Shylock, at his
benefit, he was only able to begin the play, apologize for his wandering
memory, and retire. He lived until the 11th of July 1797, and his last
years were provided for by a subscription edition of two of his best
plays, _The Man of the World_ and _Love in a Maze_. Macklin's daughter,
Mary Macklin (_c._ 1734-1781), was a well-known actress in her day.

  See Edward A. Parry, _Charles Macklin_ (1891).




MACK VON LEIBERICH, KARL, FREIHERR (1752-1828), Austrian soldier, was
born at Nenslingen, in Bavaria, on the 25th of August 1752. In 1770 he
joined an Austrian cavalry regiment, in which his uncle, Leiberich, was a
squadron commander, becoming an officer seven years later. During the
brief war of the Bavarian Succession he was selected for service on the
staff of Count Kinsky, under whom, and subsequently under the
commander-in-chief Field Marshal Count Lacy, he did excellent work. He
was promoted first lieutenant in 1778, and captain on the
quartermaster-general's staff in 1783. Count Lacy, then the foremost
soldier of the Austrian army, had the highest opinion of his young
assistant. In 1785 Mack married Katherine Gabrieul, and was ennobled
under the name of Mack von Leiberich. In the Turkish war he was employed
on the headquarter staff, becoming in 1788 major and personal
aide-de-camp to the emperor, and in 1789 lieutenant-colonel. He
distinguished himself greatly in the storming of Belgrade. Shortly after
this, disagreements between Mack and Loudon, now commander-in-chief, led
to the former's demanding a court-martial and leaving the front. He was,
however, given a colonelcy (1789) and the order of Maria Theresa, and in
1790 Loudon and Mack, having become reconciled, were again on the field
together. During these campaigns Mack received a severe injury to his
head, from which he never fully recovered. In 1793 he was made
quartermaster-general (chief of staff) to Prince Josias of Saxe-Coburg,
commanding in the Netherlands; and he enhanced his reputation by the
ensuing campaign. The young Archduke Charles, who won his own first
laurels in the action of the 1st of March 1793, wrote after the battle,
"Above all we have to thank Colonel Mack for these successes." Mack
distinguished himself again on the field of Neerwinden; and had a leading
part in the negotiations between Coburg and Dumouriez. He continued to
serve as quartermaster-general, and was now made titular chief
(_Inhaber_) of a cuirassier regiment. He received a wound at Famars, but
in 1794 was once more engaged, having at last been made a major-general.
But the failure of the allies, due though it was to political and
military factors and ideas, over which Mack had no control, was ascribed
to him, as their successes of March-April 1793 had been, and he fell into
disfavour in consequence. In 1797 he was promoted lieutenant field
marshal, and in the following year he accepted, at the personal request
of the emperor, the command of the Neapolitan army. But with the
unpromising material of his new command he could do nothing against the
French revolutionary troops, and before long, being in actual danger of
being murdered by his men, he took refuge in the French camp. He was
promised a free pass to his own country, but Napoleon ordered that he
should be sent to France as a prisoner of war. Two years later he escaped
from Paris in disguise. The allegation that he broke his parole is false.
He was not employed for some years, but in 1804, when the war party in
the Austrian court needed a general to oppose the peace policy of the
Archduke Charles, Mack was made quartermaster-general of the army, with
instructions to prepare for a war with France. He did all that was
possible within the available time to reform the army, and on the opening
of the war of 1805 he was made quartermaster-general to the titular
commander-in-chief in Germany, the Archduke Ferdinand. He was the real
responsible commander of the army which opposed Napoleon in Bavaria, but
his position was ill-defined and his authority treated with slight
respect by the other general officers. For the events of the Ulm campaign
and an estimate of Mack's responsibility for the disaster, see NAPOLEONIC
CAMPAIGNS. After Austerlitz, Mack was tried by a court-martial, sitting
from February 1806 to June 1807, and sentenced to be deprived of his
rank, his regiment, and the order of Maria Theresa, and to be imprisoned
for two years. He was released in 1808, and in 1819, when the ultimate
victory of the allies had obliterated the memory of earlier disasters, he
was, at the request of Prince Schwarzenberg, reinstated in the army as
lieutenant field marshal and a member of the order of Maria Theresa. He
died on the 22nd of October 1828 at S. Pölten.

  See Schweigerd, _Oesterreichs Helden_ (Vienna, 1854); Würzbach,
  _Biogr. Lexikon d. Kaiserthums Oesterr._ (Vienna, 1867); Ritter von
  Rittersberg, _Biogr. d. ausgezeichneten Feldherren d. oest. Armee_
  (Prague, 1828); Raumer's _Hist. Taschenbuch_ (1873) contains Mack's
  vindication. A short critical memoir will be found in _Streffleur_ for
  January 1907.




McLANE, LOUIS (1786-1857), American political leader, was born in
Smyrna, Delaware, on the 28th of May 1786, son of Allan McLane
(1746-1829), a well-known Revolutionary soldier. He was admitted to the
bar in 1807. He entered politics as a Democrat, and served in the
Federal House of Representatives in 1817-1827 and in the Senate in
1827-1829. He was minister to England in 1829-1831, and secretary of the
treasury in Jackson's cabinet from 1831 (when in his annual report he
argued for the United States Bank) until May 1833, when he was
transferred to the state department. He retired from the cabinet in June
1834. He was president of the Baltimore & Ohio railway in 1837-1847,
minister to England in 1845-1846, and delegate to the Maryland
constitutional convention of 1850-1851. He died in Baltimore, Maryland,
on the 7th of October 1857.

His son, ROBERT MILLIGAN MCLANE (1815-1898), graduated at West Point in
1837, resigned from the army in 1843, and practised law in Baltimore. He
was a Democratic representative in Congress in 1847-1851 and again in
1879-1883, governor of Maryland in 1884-1885, U.S. commissioner to China
in 1853-1854, and minister to Mexico in 1859-1860 and to France in
1885-1889.

  See R. M. McLane's _Reminiscences_, 1827-1897 (privately printed,
  1897).




MACLAREN, CHARLES (1782-1866), Scottish editor, was born at Ormiston,
Haddingtonshire, on the 7th of October 1782, the son of a farmer and
cattle-dealer. He was almost entirely self-educated, and when a young
man became a clerk in Edinburgh. In 1817, with others, he established
the _Scotsman_ newspaper in Edinburgh and at first acted as its editor.
Offered a post as clerk in the custom house, he resigned his editorial
position, resuming it in 1820, and resigning it again in 1845. In 1820
Maclaren was made editor of the sixth edition of the _Encyclopaedia
Britannica_. From 1864-1866 he was president of the Geological Society
of Edinburgh, in which city he died on the 10th of September 1866.




MACLAREN, IAN, the pseudonym of JOHN WATSON (1850-1907), Scottish author
and divine. The son of John Watson, a civil servant, he was born at
Manningtree, Essex, on the 3rd of November 1850, and was educated at
Stirling and at Edinburgh University, afterwards studying theology at
New College, Edinburgh, and at Tübingen. In 1874 he entered the ministry
of the Free Church of Scotland and became assistant minister of Barclay
Church, Edinburgh. Subsequently he was minister at Logiealmond in
Perthshire and at Glasgow, and in 1880 he became minister of Sefton Park
Presbyterian church, Liverpool, from which he retired in 1905. In 1896
he was Lyman Beecher lecturer at Yale University, and in 1900 he was
moderator of the synod of the English Presbyterian church. While
travelling in America he died at Mount Pleasant, Iowa, on the 6th of May
1907. Ian Maclaren's first sketches of rural Scottish life, _Beside the
Bonnie Briar Bush_ (1894), achieved extraordinary popularity and were
followed by other successful books, _The Days of Auld Lang Syne_ (1895),
_Kate Carnegie and those Ministers_ (1896) and _Afterwards and other
Stories_ (1898). Under his own name Watson published several volumes of
sermons, among them being _The Upper Room_ (1895); _The Mind of the
Master_ (1896) and _The Potter's Wheel_ (1897).

  See Sir W. Robertson Nicoll, _Ian Maclaren_ (1908).




MACLAURIN, COLIN (1698-1746), Scottish mathematician, was the son of a
clergyman, and born at Kilmodan, Argyllshire. In 1709 he entered the
university of Glasgow, where he exhibited a decided genius for
mathematics, more especially for geometry; it is said that before the
end of his sixteenth year he had discovered many of the theorems
afterwards published in his _Geometria organica_. In 1717 he was elected
professor of mathematics in Marischal College, Aberdeen, as the result
of a competitive examination. Two years later he was admitted F.R.S. and
made the acquaintance of Sir Isaac Newton. In 1719 he published his
_Geometria organica, sive descriptio linearum curvarum universalis_. In
it Maclaurin developed several theorems due to Newton, and introduced
the method of generating conics which bears his name, and showed that
many curves of the third and fourth degrees can be described by the
intersection of two movable angles. In 1721 he wrote a supplement to the
_Geometria organica_, which he afterwards published, with extensions, in
the _Philosophical Transactions_ for 1735. This paper is principally
based on the following general theorem, which is a remarkable extension
of Pascal's hexagram: "If a polygon move so that each of its sides
passes through a fixed point, and if all its summits except one describe
curves of the degrees _m_, _n_, _p_, &c., respectively, then the free
summit moves on a curve of the degree _2mnp_... which reduces to _mnp_
... when the fixed points all lie on a right line." In 1722 Maclaurin
travelled as tutor and companion to the eldest son of Lord Polwarth, and
after a short stay in Paris resided for some time in Lorraine, where he
wrote an essay on the percussion of bodies, which obtained the prize of
the French Academy of Sciences for the year 1724. The following year he
was elected professor of mathematics in the university of Edinburgh on
the urgent recommendation of Newton. After the death of Newton, in 1728,
his nephew, John Conduitt, applied to Maclaurin for his assistance in
publishing an account of Newton's life and discoveries. This Maclaurin
gladly undertook, but the death of Conduitt put a stop to the project.

In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the
prize offered by the French Academy of Sciences for an essay on tides.
His _Treatise on Fluxions_ was published at Edinburgh in 1742, in two
volumes. In the preface he states that the work was undertaken in
consequence of the attack on the method of fluxions made by George
Berkeley in 1734. Maclaurin's object was to found the doctrine of
fluxions on geometrical demonstration, and thus to answer all objections
to its method as being founded on false reasoning and full of mystery.
The most valuable part of the work is that devoted to physical
applications, in which he embodied his essay on the tides. In this he
showed that a homogeneous fluid mass revolving uniformly round an axis
under the action of gravity ought to assume the form of an ellipsoid of
revolution. The importance of this investigation in connexion with the
theory of the tides, the figure of the earth, and other kindred
questions, has always caused it to be regarded as one of the great
problems of mathematical physics. Maclaurin was the first to introduce
into mechanics, in this discussion, the important conception of
_surfaces of level_; namely, surfaces at each of whose points the total
force acts in the normal direction. He also gave in his _Fluxions_, for
the first time, the correct theory for distinguishing between maxima and
minima in general, and pointed out the importance of the distinction in
the theory of the multiple points of curves. In 1745, when the rebels
were marching on Edinburgh, Maclaurin took a most prominent part in
preparing trenches and barricades for its defence. The anxiety, fatigue
and cold to which he was thus exposed, affecting a constitution
naturally weak, laid the foundation of the disease to which he
afterwards succumbed. As soon as the rebel army got possession of
Edinburgh Maclaurin fled to England, to avoid making submission to the
Pretender. He accepted the invitation of T. Herring, then archbishop of
York, with whom he remained until it was safe to return to Edinburgh. He
died of dropsy on the 14th of June 1746, at Edinburgh. Maclaurin was
married in 1733 to Anne, daughter of Walter Stewart, solicitor-general
for Scotland. His eldest son John, born in 1734, was distinguished as an
advocate, and appointed one of the judges of the Scottish court of
session, with the title of Lord Dreghorn. He inherited an attachment to
scientific discovery, and was one of the founders of the Royal Society
of Edinburgh, in 1782.

  After Maclaurin's death his account of Newton's philosophical
  discoveries was published by Patrick Murdoch, and also his algebra in
  1748. As an appendix to the latter appeared his _De linearum
  geometricarum proprietatibus generalibus tractatus_, a treatise of
  remarkable elegance. Of the more immediate successors of Newton in
  Great Britain Maclaurin is probably the only one who can be placed in
  competition with the great mathematicians of the continent of Europe
  at the time.     (B. W.)




M'LENNAN, JOHN FERGUSON (1827-1881), Scottish ethnologist, was born at
Inverness on the 14th of October 1827. He studied at King's college,
Aberdeen, where he graduated with distinction in 1849, thence proceeding
to Cambridge, where he remained till 1855 without taking a degree. He
was called to the Scottish bar in 1857, and in 1871 was appointed
parliamentary draughtsman for Scotland. In 1865 he published _Primitive
Marriage_, in which, arguing from the prevalence of the symbolical form
of capture in the marriage ceremonies of primitive races, he developed
an intelligible picture of the growth of the marriage relation and of
systems of kinship (see FAMILY) according to natural laws. In 1866 he
wrote in the _Fortnightly Review_ (April and May) an essay on "Kinship
in Ancient Greece," in which he proposed to test by early Greek facts
the theory of the history of kinship set forth in _Primitive Marriage_;
and three years later appeared a series of essays on "Totemism" in the
same periodical for 1869-1870 (the germ of which had been contained in
the paper just named), which mark the second great step in his
systematic study of early society. A reprint of _Primitive Marriage_,
with "Kinship in Ancient Greece" and some other essays not previously
published, appeared in 1876, under the title of _Studies in Ancient
History_. The new essays in this volume were mostly critical, but one of
them, in which perhaps his guessing talent is seen at its best, "The
Divisions of the Irish Family," is an elaborate discussion of a problem
which has long puzzled both Celtic scholars and jurists; and in another,
"On the Classificatory System of Relationship," he propounded a new
explanation of a series of facts which, he thought, might throw light
upon the early history of society, at the same time putting to the test
of those facts the theories he had set forth in _Primitive Marriage_.
Papers on "The Levirate and Polyandry," following up the line of his
previous investigations (_Fortnightly Review_, 1877), were the last work
he was able to publish. He died of consumption on the 14th of June 1881
at Hayes Common, Kent.

  Besides the works already cited, M'Lennan wrote a _Life of Thomas
  Drummond_ (1867). The vast materials which he had accumulated on
  kinship were edited by his widow and A. Platt, under the title
  _Studies in Ancient History: Second Series_ (1896).




MACLEOD, HENRY DUNNING (1821-1902), Scottish economist, was born in
Edinburgh, and educated at Eton, Edinburgh University, and Trinity
College, Cambridge, where he graduated in 1843. He travelled in Europe,
and in 1849 was called to the English bar. He was employed in Scotland
on the work of poor-law reform, and devoted himself to the study of
economics. In 1856 he published his _Theory and Practice of Banking_, in
1858 _Elements of Political Economy_, and in 1859 _A Dictionary of
Political Economy_. In 1873 appeared his _Principles of Economist
Philosophy_, and other books on economics and banking were published
later. Between 1868 and 1870 he was employed by the government in
digesting and codifying the law of bills of exchange. He died on the
16th of July 1902. Macleod's principal contribution to the study of
economics consists in his work on the theory of credit, to which he was
the first to give due prominence.

  For a judicious discussion of the value of Macleod's writings, see an
  article on "The Revolt against Orthodox Economics" in the _Quarterly
  Review_ for October 1901 (No. 388).




MACLEOD, NORMAN (1812-1872), Scottish divine, son of Rev. Norman Macleod
(1783-1862), and grandson of Rev. Norman Macleod, minister of Morven,
Argyllshire, was born at Campbeltown on the 3rd of June 1812. In 1827 he
became a student at Glasgow University, and in 1831 went to Edinburgh to
study divinity under Dr Thomas Chalmers. On the 18th of March 1838 he
became parish minister at Loudoun, Ayrshire. At this time the troubles
in the Scottish Church were already gathering to a head (see FREE CHURCH
OF SCOTLAND). Macleod, although he had no love for lay patronage, and
wished the Church to be free to do its proper work, clung firmly to the
idea of a national Established Church, and therefore remained in the
Establishment when the disruption took place. He was one of those who
took a middle course in the non-intrusion controversy, holding that the
fitness of those who were presented to parishes should be judged by the
presbyteries--the principle of Lord Aberdeen's Bill. On the secession of
1843 he was offered many different parishes, and having finally settled
at Dalkeith, devoted himself to parish work and to questions affecting
the Church as a whole. He was largely instrumental in the work of
strengthening the Church. In 1847 he became one of the founders of the
Evangelical Alliance, and from 1849 edited the _Christian Instructor_
(Edinburgh). In 1851 he was called to the Barony church, Glasgow, in
which city the rest of his days were passed. There the more liberal
theology rapidly made way among a people who judged it more by its
fruits than its arguments, and Macleod won many adherents by his
practical schemes for the social improvement of the people. He
instituted temperance refreshment rooms, a congregational penny savings
bank, and held services specially for the poor. In 1860 Macleod was
appointed editor of the new monthly magazine _Good Words_. Under his
control the magazine, which was mainly of a religious character, became
widely popular. His own literary work, nearly all of which originally
appeared in its pages--sermons, stories, travels, poems--was only a
by-product of a busy life. By far his best work was the spontaneous and
delightful _Reminiscences of a Highland Parish_ (1867). While _Good
Words_ made his name known, and helped the cause he had so deeply at
heart, his relations with the queen and the royal family strengthened
yet further his position in the country. Never since Principal Carstairs
had any Scottish clergyman been on such terms with his sovereign. In
1865 he risked an encounter with Scottish Sabbatarian ideas. The
presbytery of Glasgow issued a pastoral letter on the subject of Sunday
trains and other infringements of the Sabbath. Macleod protested
against the grounds on which its strictures were based. For a time,
owing partly to a misleading report of his statement, he became "the man
in all Scotland most profoundly distrusted." But four years later the
Church accorded him the highest honour in her power by choosing him as
moderator of her general assembly. In 1867, along with Dr Archibald
Watson, he was sent to India, to inquire into the state of the missions.
He undertook the journey in spite of failing health, and seems never to
have recovered from its effects. He returned resolved to devote the rest
of his days to rousing the Church to her duty in the sphere of foreign
missions, but his health was now broken, and his old energy flagged. He
died on the 16th of June 1872, and was buried at Campsie. He was one of
the greatest of Scottish religious leaders, a man of wide sympathy and
high ideals. His Glasgow church was named after him the "Macleod Parish
Church," and the "Macleod Missionary Institute" was erected by the
Barony church in Glasgow. Queen Victoria gave two memorial windows to
Crathie church as a testimony of her admiration for his work.

  See _Memoir of Norman Macleod_, by his brother, Donald Macleod (1876).




MACLISE, DANIEL (1806-1870), Irish painter, was born at Cork, the son of
a Highland soldier. His education was of the plainest kind, but he was
eager for culture, fond of reading, and anxious to become an artist. His
father, however, placed him, in 1820, in Newenham's Bank, where he
remained for two years, and then left to study in the Cork school of
art. In 1825 it happened that Sir Walter Scott was travelling in
Ireland, and young Maclise, having seen him in a bookseller's shop, made
a surreptitious sketch of the great man, which he afterwards
lithographed. It was exceedingly popular, and the artist became
celebrated enough to receive many commissions for portraits, which he
executed, in pencil, with very careful treatment of detail and
accessory. Various influential friends perceived the genius and promise
of the lad, and were anxious to furnish him with the means of studying
in the metropolis; but with rare independence he refused all aid, and by
careful economy saved a sufficient sum to enable him to leave for
London. There he made a lucky hit by a sketch of the younger Kean,
which, like his portrait of Scott, was lithographed and published. He
entered the Academy schools in 1828, and carried off the highest prizes
open to the students. In 1829 he exhibited for the first time in the
Royal Academy. Gradually he began to confine himself more exclusively to
subject and historical pictures, varied occasionally by portraits of
Campbell, Miss Landon, Dickens, and other of his literary friends. In
1833 he exhibited two pictures which greatly increased his reputation,
and in 1835 the "Chivalric Vow of the Ladies and the Peacock" procured
his election as associate of the Academy, of which he became full member
in 1840. The years that followed were occupied with a long series of
figure pictures, deriving their subjects from history and tradition and
from the works of Shakespeare, Goldsmith and Le Sage. He also designed
illustrations for several of Dickens's Christmas books and other works.
Between the years 1830 and 1836 he contributed to _Fraser's Magazine_,
under the pseudonym of Alfred Croquis, a remarkable series of portraits
of the literary and other celebrities of the time--character studies,
etched or lithographed in outline, and touched more or less with the
emphasis of the caricaturist, which were afterwards published as the
_Maclise Portrait Gallery_ (1871). In 1858 Maclise commenced one of the
two great monumental works of his life, the "Meeting of Wellington and
Blücher," on the walls of Westminster Palace. It was begun in fresco, a
process which proved unmanageable. The artist wished to resign the task;
but, encouraged by Prince Albert, he studied in Berlin the new method of
"water-glass" painting, and carried out the subject and its companion,
the "Death of Nelson," in that medium, completing the latter painting in
1864. The intense application which he gave to these great historic
works, and various circumstances connected with the commission, had a
serious effect on the artist's health. He began to shun the company in
which he formerly delighted; his old buoyancy of spirits was gone; and
when, in 1865, the presidentship of the Academy was offered to him he
declined the honour. He died of acute pneumonia on the 25th of April
1870. His works are distinguished by powerful intellectual and
imaginative qualities, but most of them are marred by harsh and dull
colouring, by metallic hardness of surface and texture, and by frequent
touches of the theatrical in the action and attitudes of the figures.
His fame rests most securely on his two greatest works at Westminster.

  A memoir of Maclise, by his friend W. J. O'Driscoll, was published in
  1871.




MACLURE, WILLIAM (1763-1840), American geologist, was born at Ayr in
Scotland in 1763. After a brief visit to New York in 1782 he began
active life as a partner in a London firm of American merchants. In 1796
business affairs took him to Virginia, U.S.A., which he thereafter made
his home. In 1803 he visited France as one of the commissioners
appointed to settle the claims of American citizens on the French
government; and during the few years then spent in Europe he applied
himself with enthusiasm to the study of geology. On his return home in
1807 he commenced the self-imposed task of making a geological survey of
the United States. Almost every state in the Union was traversed and
mapped by him, the Alleghany Mountains being crossed and recrossed some
fifty times. The results of his unaided labours were submitted to the
American Philosophical Society in a memoir entitled _Observations on the
Geology of the United States explanatory of a Geological Map_, and
published in the Society's _Transactions_ (vol. iv. 1809, p. 91)
together with the first geological map of that country. This antedates
William Smith's geological map of England by six years. In 1817 Maclure
brought before the same society a revised edition of his map, and his
great geological memoir was issued separately, with some additional
matter, under the title _Observations on the Geology of the United
States of America_. Subsequent survey has corroborated the general
accuracy of Maclure's observations. In 1819 he visited Spain, and
attempted, unsuccessfully, to establish an agricultural college near the
city of Alicante. Returning to America in 1824, he settled for some
years at New Harmony, Indiana, and sought to develop his scheme of the
agricultural college. Failing health ultimately constrained him to
relinquish the attempt, and to seek (in 1827) a more congenial climate
in Mexico. There, at San Angel, he died on the 23rd of March 1840.

  See S. G. Morton, "Memoir of William Maclure," _Amer. Journ. Sci._,
  vol. xlvii. (1844), p. 1.




MacMAHON, MARIE EDMÉ PATRICE MAURICE DE, duke of Magenta (1808-1893),
French marshal and president of the French republic, was born on the
13th of July 1808 at the château of Sully, near Autun. He was descended
from an Irish family which went into exile with James II. Educated at
the military school of St Cyr, in 1827 he entered the army, and soon saw
active service in the first French campaign in Algeria, where his
ability and bravery became conspicuous. Being recalled to France, he
gained renewed distinction in the expedition to Antwerp in 1832. He
became captain in 1833, and in that year returned to Algeria. He led
daring cavalry raids across plains infested with Bedouin, and especially
distinguished himself at the siege of Constantine in 1837. From then
until 1855 he was almost constantly in Algeria, and rose to the rank of
general of division. During the Crimean War MacMahon was given the
command of a division, and in September 1855 he successfully conducted
the assault upon the Malakoff works, which led to the fall of
Sebastopol. After his return to France honours were showered upon him,
and he was made a senator. Desiring a more active life, however, and
declining the highest command in France, he was once more sent out, at
his own request, to Algeria, where he completely defeated the Kabyles.
After his return to France he voted as a senator against the
unconstitutional law for general safety, which was brought forward in
consequence of Orsini's abortive attempt on the emperor's life. MacMahon
greatly distinguished himself in the Italian campaign of 1859. Partly
by good luck and partly by his boldness and sagacity in pushing forward
without orders at a critical moment at the battle of Magenta, he enabled
the French to secure the victory. For his brilliant services MacMahon
received his marshal's baton and was created duke of Magenta. In 1861 he
represented France at the coronation of William I. of Prussia, and in
1864 he was nominated governor-general of Algeria. MacMahon's action in
this capacity formed the least successful episode of his career.
Although he did institute some reforms in the colonies, complaints were
so numerous that twice in the early part of 1870 he sent in his
resignation to the emperor. When the ill-fated Ollivier cabinet was
formed the emperor abandoned his Algerian schemes and MacMahon was
recalled.

War being declared between France and Prussia in July 1870, MacMahon was
appointed to the command of the Alsace army detachment (see
FRANCO-GERMAN WAR). On the 6th of August MacMahon fought the battle of
Wörth (q.v.). His courage was always conspicuous on the field, but the
two-to-one numerical superiority of the Germans triumphed. MacMahon was
compelled to fall back upon Saverne, and thence to Toul. Though he
suffered further losses in the course of his retreat, his movements were
so ably conducted that the emperor confided to him the supreme command
of the new levies which he was mustering at Châlons, and he was directed
to effect a junction with Bazaine. This operation he undertook against
his will. He had an army of 120,000 men, with 324 guns; but large
numbers of the troops were disorganized and demoralized. Early on the
1st of September the decisive battle of Sedan began. MacMahon was
dangerously wounded in the thigh, whereupon General Ducrot, and soon
afterwards General de Wimpffen, took command. MacMahon shared the
captivity of his comrades, and resided at Wiesbaden until the conclusion
of peace.

In March 1871 MacMahon was appointed by Thiers commander-in-chief of the
army of Versailles; and in that capacity he suppressed the Communist
insurrection, and successfully conducted the second siege of Paris. In
the following December he was invited to become a candidate for Paris in
the elections to the National Assembly, but declined nomination. On the
resignation of Thiers as president of the Republic, on the 24th of May
1873, MacMahon was elected to the vacant office by an almost unanimous
vote, being supported by 390 members out of 392. The duc de Broglie was
empowered to form a Conservative administration, but the president also
took an early opportunity of showing that he intended to uphold the
sovereignty of the National Assembly. On the 5th of November 1873
General Changarnier presented a motion in the Assembly to confirm
MacMahon's powers for a period of ten years, and to provide for a
commission of thirty to draw up a form of constitutional law. The
president consented, but in a message to the Assembly he declared in
favour of a confirmation of his own powers for seven years, and
expressed his determination to use all his influence in the maintenance
of Conservative principles. After prolonged debates the Septennate was
adopted on the 19th of November by 378 votes to 310. There was no _coup
d'état_ in favour of "Henri V.," as had been expected, and the president
resolved to abide by "existing institutions." One of his earliest acts
was to receive the finding of the court-martial upon his old comrade in
arms, Marshal Bazaine, whose death sentence he commuted to one of twenty
years' imprisonment in a fortress. Though MacMahon's life as president
of the Republic was of the simplest possible character, his term of
office was marked by many brilliant displays, while his wife was a
leader in all works of charity and benevolence.

The president was very popular in the rural districts of France, through
which he made a successful tour shortly after the declaration of the
Septennate. But in Paris and other large cities his policy soon caused
great dissatisfaction, the Republican party especially being alienated
by press prosecutions and the attempted suppression of Republican ideas.
Matters were at a comparative deadlock in the National Assembly, until
the accession of some Orleanists to the Moderate Republican party in
1875 made it possible to pass various constitutional laws. In May 1877,
however, the constitutional crisis became once more acute. A peremptory
letter of censure from MacMahon to Jules Simon caused the latter to
resign with his colleagues. The duc de Broglie formed a ministry, but
Gambetta carried a resolution in the Chamber of Deputies in favour of
parliamentary government. The president declined to yield, and being
supported by the Senate, he dissolved the Chamber, by decree, on the
25th of June. The prosecution of Gambetta followed for a speech at
Lille, in which he had said "the marshal must, if the elections be
against him, _se soumettre ou se démettre_." In a manifesto respecting
the elections, the president referred to his successful government and
observed, "I cannot obey the injunctions of the demagogy; I can neither
become the instrument of Radicalism nor abandon the post in which the
constitution has placed me." His confidence in the result of the
elections was misplaced. Notwithstanding the great pressure put upon the
constituencies by the government, the elections in October resulted in
the return of 335 Republicans and only 198 anti-Republicans, the latter
including 30 MacMahonists, 89 Bonapartists, 41 Legitimists, and 38
Orleanists. The president endeavoured to ignore the significance of the
elections, and continued his reactionary policy. As a last resort he
called to power an extra-parliamentary cabinet under General Rochebouet,
but the Republican majority refused to vote supplies, and after a brief
interval the president was compelled to yield, and to accept a new
Republican ministry under Dufaure. The prolonged crisis terminated on
the 14th of December 1877, and no further constitutional difficulties
arose in 1878. But as the senatorial elections, held early in 1879, gave
the Republicans an effective working majority in the Upper Chamber, they
now called for the removal of the most conspicuous anti-Republicans
among the generals and officials. The president refused to supersede
them, and declined to sanction the law brought in with this object.
Perceiving further resistance to be useless, however, MacMahon resigned
the presidency on the 30th of January 1879, and Jules Grévy was elected
as his successor.

MacMahon now retired into private life. Relieved from the cares of
state, his simple and unostentatious mode of existence enabled him to
pass many years of dignified repose. He died at Paris on the 17th of
October 1893, in his eighty-sixth year. A fine, tall, soldierly man, of
a thoroughly Irish type, in private life MacMahon was universally
esteemed as generous and honourable; as a soldier he was brave and able,
without decided military genius; as a politician he was patriotic and
well-intentioned, but devoid of any real capacity for statecraft.
     (G. B. S.)




McMASTER, JOHN BACH (1852-   ), American historian, was born in Brooklyn,
New York, on the 29th of June 1852. He graduated from the college of the
City of New York in 1872, worked as a civil engineer in 1873-1877, was
instructor in civil engineering at Princeton University in 1877-1883,
and in 1883 became professor of American history in the university of
Pennsylvania. He is best known for his _History of the People of the
United States from the Revolution to the Civil War_ (1883 sqq.), a
valuable supplement to the more purely political writings of Schouler,
Von Holst and Henry Adams.




MACMILLAN, the name of a family of English publishers. The founders of
the firm were two Scotsmen, Daniel Macmillan (1813-1857) and his younger
brother Alexander (1818-1896). Daniel was a native of the Isle of Arran,
and Alexander was born in Irvine on the 3rd of October 1818. Daniel was
for some time assistant to the bookseller Johnson at Cambridge, but
entered the employ of Messrs Seeley in London in 1837; in 1843 he began
business in Aldersgate Street, and in the same year the two brothers
purchased the business of Newby in Cambridge. They did not confine
themselves to bookselling, but published educational works as early as
1844. In 1845 they became the proprietors of the more important business
of Stevenson, in Cambridge, the firm being styled Macmillan, Barclay &
Macmillan. In 1850 Barclay retired and the firm resumed the name of
Macmillan & Co. Daniel Macmillan died at Cambridge on the 27th of June
1857. In that year an impetus was given to the business by the
publication of Kingsley's _Two Years Ago_. A branch office was opened in
1858 in Henrietta Street, London, which led to a great extension of
trade. These premises were surrendered for larger ones in Bedford
Street, and in 1897 the buildings in St Martin's Street were opened.
Alexander Macmillan died in January 1896. By his great energy and
literary associations, and with the aid of his partners, there had been
built up in little over half a century one of the most important
publishing houses in the world. Besides the issue of many important
series of educational and scientific works, they published the works of
Kingsley, Huxley, Maurice, Tennyson, Lightfoot, Westcott, J. R. Green,
Lord Roberts, Lewis Carroll, and of many other well-known authors. In
1898 they took over the old-established publishing house of R. Bentley &
Son, and with it the works of Mrs Henry Wood, Miss Rhoda Broughton, _The
Ingoldsby Legends_, and also _Temple Bar_ and the _Argosy_. In 1893 the
firm was converted into a limited liability company, its chairman being
Frederick Macmillan (b. 1851), who was knighted in 1909. The American
firm of the Macmillan Company, of which he was also a director, is a
separate business.

  See Thomas Hughes, _Memoir of Daniel Macmillan_ (1882); _A
  Bibliographical Catalogue of Macmillan & Co's Publications from 1843
  to 1889_ (1891), with portraits of the brothers Daniel and Alexander
  after Lowes Dickinson and Hubert Herkomer; also articles in _Le Livre_
  (September 1886), _Publishers' Circular_ (January 14, 1893), the
  _Bookman_ (May 1901), &c.




MACMONNIES, FREDERICK WILLIAM (1863-   ) American sculptor and painter,
was born at Brooklyn, New York, on the 20th of September 1863. His
mother was a niece of Benjamin West. At the age of sixteen MacMonnies
was received as an apprentice in the studio of Augustus St Gaudens, the
sculptor, where he remained for five years. In 1884 he went to Paris and
thence to Munich, where he painted for some months. Returning to Paris
next year he became the most prominent pupil of Falguière. His "Diana"
brought him a mention at the Salon of 1889. Three life-sized figures of
angels for the church of St Paul, New York, were followed by his "Nathan
Hale," in the City Hall Park, New York, and a portrait of James S. T.
Stranahan, for Brooklyn. This last brought him a "second medal" in the
Salon of 1891, the first time an American sculptor had been so honoured.
In 1893 he was chosen to design and carry out the Columbian Fountain for
the Chicago World's Fair, which placed him instantly in the front rank.
His largest work is a decoration for the Memorial Arch to Soldiers and
Sailors, in Prospect Park, Brooklyn, consisting of three enormous groups
in bronze. In Prospect Park, Brooklyn, MacMonnies has also a large
"Horse Tamer," a work of much distinction. A "Winged Victory" at the
U.S. military academy at West Point, New York, is of importance; and his
"Bacchante," an extraordinary combination of realism and imagination,
rejected by the Boston Public Library, is now at the Metropolitan Museum
of Art, New York. He also became well known as a painter, mainly of
portraits. In 1888 he married Mary Fairchild, a figure painter of
distinction, but in 1909 they were divorced and she married Will H. Low.




MACNAGHTEN, SIR WILLIAM HAY, BART. (1793-1841), Anglo-Indian
diplomatist, was the second son of Sir Francis Macnaghten, Bart., judge
of the supreme courts of Madras and Calcutta. He was born in August
1793, and educated at Charterhouse. He went out to Madras as a cadet in
1809, but was appointed in 1816 to the Bengal Civil Service. He early
displayed a great talent for languages, and also published several
treatises on Hindu and Mahommedan law. His political career began in
1830 as secretary to Lord William Bentinck; and in 1837 he became one of
the most trusted advisers of the governor-general, Lord Auckland, with
whose policy of supporting Shah Shuja against Dost Mahommed, the
reigning amir of Kabul, Macnaghten was closely identified. As political
agent at Kabul he came into conflict with the military authorities and
subsequently with his subordinate Sir Alexander Burnes. Macnaghten
attempted to placate the Afghan chiefs with heavy subsidies, but when
the drain on the Indian exchequer became too great, and the allowances
were reduced, this policy led to an outbreak. Burnes was murdered on the
2nd of November 1841; and owing to the incapacity of the aged General
Elphinstone the British army in Kabul degenerated into a leaderless mob.
Macnaghten tried to save the situation by negotiating with the Afghan
chiefs and, independently of them, with Dost Mahommed's son, Akbar Khan,
by whom he was assassinated on the 23rd of December 1841; the disastrous
retreat from Kabul and the massacre of the British army in the Kurd
Kabul pass followed. These events threw doubt on Macnaghten's capacity
for dealing with the problems of Indian diplomacy, though his
fearlessness and integrity were unquestioned. He had been created a
baronet in 1840, and four months before his death was nominated to the
governorship of Bombay.




MacNALLY, LEONARD (1752-1820), Irish informer, was born in Dublin, the
son of a merchant. In 1776 he was called to the Irish, and in 1783 to
the English bar. He supported himself for some time in London by writing
plays and editing the _Public Ledger_. Returning to Dublin, he entered
upon a systematic course of informing against the members of the
revolutionary party, for whom his house had become the resort. He also
betrayed to the government prosecutors political clients whom he
defended eloquently in the courts. He made a fine defence for Robert
Emmet and cheered him in his last hours, although before appearing in
court he had sold, for £200, the contents of his brief to the lawyers
for the Crown. After living a professed Protestant all his life, he
received absolution on his deathbed from a Roman Catholic priest. He
died on the 13th of February 1820.




MACNEE, SIR DANIEL (1806-1882), Scottish portrait painter, was born at
Fintry in Stirlingshire. At the age of thirteen he was apprenticed,
along with Horatio Macculloch and Leitch the water-colour painter, to
John Knox, a landscapist of some repute. He afterwards worked for a year
as a lithographer, was employed by the Smiths of Cumnock to paint the
ornamental lids of their planewood snuff-boxes, and, having studied in
Edinburgh at the "Trustees' Academy," supporting himself meanwhile by
designing and colouring book illustrations for Lizars the engraver, he
established himself as an artist in Glasgow, where he became a
fashionable portrait painter. He was in 1829 admitted a member of the
Royal Scottish Academy; and on the death of Sir George Harvey in 1876 he
was elected president, and received the honour of knighthood. From this
period till his death, on the 18th of January 1882, he resided in
Edinburgh, where his genial social qualities and his inimitable powers
as a teller of humorous Scottish anecdote rendered him popular.




MACNEIL, HERMON ATKINS (1866- ), American sculptor, was born at Chelsea,
Massachusetts. He was an instructor in industrial art at Cornell
University in 1886-1889, and was then a pupil of Henri M. Chapu and
Falguière in Paris. Returning to America, he aided Philip Martiny in the
preparation of sketch models for the Columbian exposition, and in 1896
he won the Rinehart scholarship, passing four years (1896-1900) in Rome.
In 1906 he became a National Academician. His first important work was
"The Moqui Runner," which was followed by "A Primitive Chant," and "The
Sun Vow," all figures of the North-American Indian. A "Fountain of
Liberty," for the St Louis exposition, and other Indian themes came
later; his "Agnese" and his "Beatrice," two fine busts of women, also
deserve mention. His principal work is the sculpture for a large
memorial arch, at Columbus, Ohio, in honour of President McKinley. In
1909 he won in competition a commission for a large soldiers' and
sailors' monument in Albany, New York. His wife, Carol Brooks MacNeil,
also a sculptor of distinction, was a pupil of F. W. MacMonnies.




McNEILE, HUGH (1795-1879), Anglican divine, younger son of Alexander
McNeile (or McNeill), was born at Ballycastle, Co. Antrim, on the 15th
of July 1795. He graduated at Trinity College, Dublin, in 1810. His
handsome presence, and his promise of exceptional gifts of oratory, led
a wealthy uncle, Major-General Daniel McNeill, to adopt him as his heir;
and he was destined for a parliamentary career. During a stay at
Florence, Hugh McNeile became temporarily intimate with Lord Byron and
Madame de Staël. On returning home, he determined to abandon the
prospect of political distinction for the clerical profession, and was
disinherited. In 1820 he was ordained, and after holding the curacy of
Stranorlar, Co. Donegal, for two years, was appointed to the living of
Albury, Surrey, by Henry Drummond.

Edward Irving endeavoured, not without success at first, to draw McNeile
into agreement with his doctrine and aims. Irving's increasing
extravagance, however, soon alienated McNeile. His preaching now
attracted much attention; in London he frequently was heard by large
congregations. In 1834 he accepted the incumbency of St Jude's,
Liverpool, where for the next thirty years he wielded great political as
well as ecclesiastical influence. He repudiated the notion that a
clergyman should be debarred from politics, maintaining at a public
meeting that "God when He made the minister did not unmake the citizen."
In 1835 McNeile entered upon a long contest, in which he was eventually
successful, with the Liverpool corporation, which had been captured by
the Whigs, after the passing of the Municipal Reform Act. A proposal was
carried that the elementary schools under the control of the corporation
should be secularized by the introduction of what was known as the Irish
National System. The threatened withdrawal of the Bible as the basis of
denominational religious teaching was met by a fierce agitation led by
McNeile, who so successfully enlisted public support that before the new
system could be introduced every child was provided for in new Church of
England schools established by public subscriptions. At the same time he
conducted a campaign which gradually reduced the Whig element in the
council, till in 1841 it almost entirely disappeared. To his influence
was also attributed the defeat of the Liberal parliamentary candidates
in the general election of 1837, followed by a long period of
Conservative predominance in Liverpool politics. McNeile had the Irish
Protestant's horror of Romanism, which he constantly denounced in the
pulpit and on the platform; and Macaulay, speaking in the House of
Commons on the Maynooth endowment in April 1845, singled him out for
attack as the most powerful representative of uncompromising Protestant
opinion in the country. As the Tractarian movement in the Church of
England developed, he became one of its most zealous opponents and the
most conspicuous leader of the evangelical party. In 1840 he published a
volume of _Lectures on the Church of England_, and in 1846 (the year
after Newman's secession to Rome) _The Church and the Churches_, in
which he maintained with much dialectical skill the evangelical doctrine
of the "invisible Church" in opposition to the teaching of Newman and
Pusey. Hugh McNeile was in close sympathy with the philanthropic work as
well as the religious views of the 7th earl of Shaftesbury, who more
than once tried to persuade Lord Palmerston to raise him to the
episcopal bench. But although Palmerston usually followed the advice of
Shaftesbury in the appointment of bishops, he would not consent to the
elevation to the House of Lords of so powerful a political opponent as
McNeile, whom Lord John Russell had accused of frustrating for thirty
years the education policy of the Liberal party. In 1860 he was
appointed a canon of Chester; and in 1868 Disraeli appointed him dean of
Ripon. This preferment he resigned in 1875, and he lived in retirement
at Bournemouth till his death on the 28th of January 1879. McNeile
married, in 1822, Anne, daughter of William Magee, archbishop of Dublin,
and aunt of William Connor Magee, archbishop of York, by whom he had a
large family.

Although a vehement controversialist, Hugh McNeile was a man of simple
and sincere piety of character. Sir Edward Russell, an opponent alike of
his religious and his political opinions, bears witness to the deep
spirituality of his teaching, and describes him as an absolutely unique
personality. "He made himself leader of the Liverpool people, and always
led with calm and majesty in the most excited times. His eloquence was
grave, flowing, emphatic--had a dignity in delivery, a perfection of
elocution, that only John Bright equalled in the latter half of the
19th century. Its fire was solemn force. McNeile's voice was probably
the finest organ ever heard in public oratory. His action was as
graceful as it was expressive. He ruled an audience."

  See J. A. Picton, _Memorials of Liverpool_, vol. i. (1873); Sir Edward
  Russell, "The Religious Life of Liverpool," in the _Sunday Magazine_
  (June 1905); Charles Bullock, _Hugh McNeile and Reformation Truth_.
       (R. J. M.)




MACNEILL, HECTOR (1746-1818), Scottish poet, was born near Roslin,
Midlothian, on the 22nd of October 1746, the son of an impoverished army
captain. He went to Bristol as a clerk at the age of fourteen, and soon
afterwards was despatched to the West Indies. From 1780 to 1786 he acted
as assistant secretary on board the flagships of Admiral Geary and Sir
Richard Bickerton (1727-1792). Most of his later life was spent in
Scotland, and it was in the house of a friend at Stirling that he wrote
most of his songs and his _Scotland's Skaith, or the History of Will and
Jean_ (1795), a narrative poem intended to show the deteriorating
influences of whisky and pothouse politics. A sequel, _The Waes of War_,
appeared next year. In 1800 he published _The Memoirs of Charles
Macpherson, Esq._, a novel understood to be a narrative of his own
hardships and adventures. A complete edition of the poems he wished to
own appeared in 1812. His songs "Mary of Castlecary," "Come under my
plaidy," "My boy Tammy," "O tell me how for to woo," "I lo'ed ne'er a
lassie but ane," "The plaid amang the hether," and "Jeanie's black e'e,"
are notable for their sweetness and simplicity. He died at Edinburgh on
the 15th of March 1818.




MACOMB, a city and the county-seat of McDonough county, Illinois,
U.S.A., in the W. part of the state, about 60 m. S.W. of Peoria. Pop.
(1890), 4052; (1900), 5375 (232 foreign-born); (1910), 5774. Macomb is
served by the Chicago, Burlington & Quincy, and the Macomb & Western
Illinois railways. The city is the seat of the Western Illinois state
normal school (opened in 1902), and has a Carnegie library and a city
park. Clay is found in the vicinity, and there are manufactures of
pottery, bricks, &c. The city was founded in 1830 as the county-seat of
McDonough county, and was called Washington by the settlers, but the
charter of incorporation, also granted in 1830, gave it the present name
in honour of General Alexander Macomb. Macomb was first chartered as a
city in 1856.




MACOMER, a village of Sardinia in the province of Cagliari, from which
it is 95 m. N.N.W. by rail, and the same distance S.W. of Golfo degli
Aranci. Pop. (1901), 3488. It is situated 1890 ft. above sea-level on
the southern ascent to the central plateau (the Campeda) of this part of
Sardinia; and it is the junction of narrow-gauge lines branching from
the main line eastwards to Nuoro and westwards to Bosa. The old parish
church of S. Pantaleone has three Roman mile-stones in front of it,
belonging to the Roman high-road from Carales to Turris Libisonis. The
modern high-road follows the ancient. The district, especially the
Campeda, is well fitted for grazing and horse and cattle breeding, which
is carried on to a considerable extent. It is perhaps richer in
_nuraghi_ than any other part of Sardinia.




MACON, NATHANIEL (1758-1837), American political leader, was born at
Macon Manor, Warren county, North Carolina, on the 17th of December
1758. He studied at the college of New Jersey (now Princeton University)
from 1774 to 1776, when the institution was closed on account of the
outbreak of the War of Independence; served for a short time in a New
Jersey militia company; studied law at Bute Court-house, North Carolina,
in 1777-1780, at the same time managing his tobacco plantation; was a
member of a Warren county militia company in 1780-1782, and served in
the North Carolina Senate in 1781-1785. In 1786 he was elected to the
Continental Congress, but declined to serve. In 1791-1815 he was a
member of the national House of Representatives, and in 1815-1828 of the
United States Senate. Macon's point of view was always local rather than
national. He was essentially a North Carolinian first, and an American
afterwards; and throughout his career he was an aggressive advocate of
state sovereignty and an adherent of the doctrines of the "Old
Republicans." He at first opposed the adoption of the Federal
constitution of 1787, as a member of the faction led by Willie Jones
(1731-1801) of Halifax, North Carolina, but later withdrew his
opposition. In Congress he denounced Hamilton's financial policy,
opposed the Jay Treaty (1795) and the Alien and Sedition Acts, and
advocated a continuance of the French alliance of 1778. His party came
into power in 1801, and he was Speaker of the house from December 1801
to October 1807. At first he was in accord with Jefferson's
administration; he approved the Louisiana Purchase, and as early as 1803
advocated the purchase of Florida. For a number of years, however, he
was politically allied with John Randolph.[1] As speaker, in spite of
strong opposition, he kept Randolph at the head of the important
committee on Ways and Means from 1801 to 1806; and in 1805-1808, with
Randolph and Joseph H. Nicholson (1770-1817) of Maryland, he was a
leader of the group of about ten independents, called the "Quids," who
strongly criticized Jefferson and opposed the presidential candidature
of Madison. By 1809, however, Macon was again in accord with his party,
and during the next two years he was one of the most influential of its
leaders. In December 1809 he introduced resolutions which combined the
ideas of Peter Early (1773-1817) of Georgia, David R. Williams
(1776-1830) of South Carolina, and Samuel W. Dana (1757-1830) of
Connecticut with his own. The resolutions recommended the complete
exclusion of foreign war vessels from United States ports and the
suppression of illegal trade carried on by foreign merchants under the
American flag. The substance of these resolutions was embodied in the
"Macon Bill, No. 1," which passed the House but was defeated in the
Senate. On the 7th of April 1810 Macon reported from committee the
"Macon Bill, No. 2," which had been drawn by John Taylor (1770-1832) of
South Carolina, and was not actively supported by him. This measure
(amended) became law on the 1st of May, and provided for the repeal of
the Non-Intercourse Act of 1809, authorized the president, "in case
either Great Britain or France shall before the 3rd day of March next so
revoke or modify her edicts as that they shall cease to violate the
neutral commerce of the United States," to revive non-intercourse
against the other, and prohibited British and French vessels of war from
entering American waters. In 1812 Macon voted for the declaration of war
against Great Britain, and later was chairman of the Congressional
committee which made a report (July 1813) condemning Great Britain's
conduct of the war. He opposed the Bank Act of 1816, the "internal
improvements" policy of Calhoun (in the early part of his career) and
Clay, and the Missouri Compromise, his speech against the last being
especially able. In 1824 Macon received the electoral vote of Virginia
for the vice-presidency, and in 1826-1828 was president pro tempore of
the Senate. He was president of the North Carolina constitutional
convention in 1835, and was an elector on the Van Buren ticket in 1836.
He died at his home, Buck Springs, Warren county, North Carolina, on the
29th of June 1837.

  See William E. Dodd, _The Life of Nathaniel Macon_ (Raleigh, N.C.,
  1903); E. M. Wilson, _The Congressional Career of Nathaniel Macon_
  (Chapel Hill, N.C., 1900).


FOOTNOTE:

  [1] Their names are associated in Randolph-Macon College, named in
    their honour in 1830.




MÂCON, a town of east-central France, capital of the department of
Saône-et-Loire, 45 m. N. of Lyons on the Paris-Lyon railway. Pop.
(1906), 16,151. Mâcon is situated on the right bank of the Saône facing
the plain of the Bresse; a bridge of twelve arches connects it with the
suburb of St Laurent on the opposite bank. The most prominent building
is the modern Romanesque church of St Pierre, a large three-naved
basilica, with two fine spires. Of the old cathedral of St Vincent (12th
and 13th centuries), destroyed at the Revolution, nothing remains but
the Romanesque narthex, now used as a chapel, the façade and its two
flanking towers. The hôtel de ville contains a library, a theatre and
picture-gallery. Opposite to it stands a statue of the poet Alphonse
Lamartine, a native of the town. Mâcon is the seat of a prefecture, and
has tribunals of first instance and of commerce, and a chamber of
commerce. There are lycées and training colleges. Copper-founding is an
important industry; manufactures include casks, mats, rope and utensils
for the wine-trade. The town has a large trade in wine of the district,
known as Mâcon. It is a railway centre of considerable importance, being
the point at which the line from Paris to Marseilles is joined by that
from Mont Cenis and Geneva, as well as by a branch from Moulins.

Mâcon (_Matisco_) was an important town of the Aedui, but under the
Romans it was supplanted by Autun and Lyons. It suffered a succession of
disasters at the hands of the Germans, Burgundians, Vandals, Huns,
Hungarians and even of the Carolingian kings. In the feudal period it
was an important countship which in 1228 was sold to the king of France,
but more than once afterwards passed into the possession of the dukes of
Burgundy, until the ownership of the French crown was established in the
time of Louis XI. In the 16th century Mâcon became a stronghold of the
Huguenots, but afterwards fell into the hands of the League, and did not
yield to Henry IV. until 1594. The bishopric, created by King
Childebert, was suppressed in 1790.




MACON, a city and the county-seat of Bibb county, Georgia, U.S.A., in
the central part of the state, on both sides of the Ocmulgee river (at
the head of navigation), about 90 m. S.S.E. of Atlanta. Pop. (1900),
23,272, of whom 11,550 were negroes; (1910 census) 40,665. Macon is,
next to Atlanta, the most important railway centre in the state, being
served by the Southern, the Central of Georgia, the Georgia, the Georgia
Southern & Florida, the Macon Dublin & Savannah, and the Macon &
Birmingham railways. It was formerly an important river port, especially
for the shipment of cotton, but lost this commercial advantage when
railway bridges made the river impassable. It is, however, partially
regaining the river trade in consequence of the compulsory substitution
of drawbridges for the stationary railway bridges. The city is the seat
of the Wesleyan female college (1836), which claims to be the first
college in the world chartered to grant academic degrees to women;
Mercer university (Baptist), which was established in 1833 as Mercer
Institute at Penfield, became a university in 1837, was removed to Macon
in 1871, and controls Hearn Academy (1839) at Cave Spring and Gibson
Mercer Academy (1903) at Bowman; the state academy for the blind (1852),
St Stanislaus' College (Jesuit), and Mt de Sales Academy (Roman
Catholic) for women. There are four orphan asylums for whites and two
for negroes, supported chiefly by the Protestant Episcopal and Methodist
Churches, and a public hospital. Immediately east of Macon are two large
Indian mounds, and there is a third mound 9 m. south of the city.
Situated in the heart of the "Cotton Belt," Macon has a large and
lucrative trade; it is one of the most important inland cotton markets
of the United States, its annual receipts averaging about 250,000 bales.
The city's factory products in 1905 were valued at $7,297,347 (33.8%
more than in 1900). In the vicinity are large beds of kaolin, 30 m.
wide, reaching nearly across the state, and frequently 35 to 70 ft. in
depth. Macon is near the fruit-growing region of Georgia, and large
quantities of peaches and of garden products are annually shipped from
the city.

Macon (named in honour of Nathaniel Macon) was surveyed in 1823 by order
of the Georgia legislature for the county-seat of Bibb county, and
received its first charter in 1824. It soon became the centre of trade
for Middle Georgia; in 1833 a steamboat line to Darien was opened, and
in the following year 69,000 bales of cotton were shipped by this route.
During the Civil War the city was a centre for Confederate commissary
supplies and the seat of a Treasury depository. In July 1864 General
George Stoneman (1822-1894) with 500 men was captured near the city by
the Confederate general, Howell Cobb. Macon was finally occupied by
Federal troops under General James H. Wilson (b. 1837) on the 20th of
April 1865. In 1900-1910 the area of the city was increased by the
annexation of several suburbs.




MACPHERSON, SIR DAVID LEWIS (1818-1896), Canadian financier and
politician, was born at Castle Leathers, near Inverness, Scotland, on
the 12th of September 1818. In 1835 he emigrated to Canada, settling in
Montreal, where he built up a large fortune by "forwarding" merchandise.
In 1853 he removed to Toronto, and in the same year obtained the
contract for building a line of railway from Toronto to Sarnia, a
project from which sprang the Grand Trunk railway, in the construction
of which line he greatly increased his wealth. In 1864 he was elected to
the Canadian parliament as member of the Legislative Council for
Saugeen, and on the formation of the Dominion, in 1867, was nominated to
the Senate. In the following years he published a number of pamphlets on
economic subjects, of which the best-known is _Banking and Currency_
(1869). In 1880 he was appointed Speaker of the Senate, and from October
1883 till 1885 was minister of the interior in the Conservative cabinet.
In 1884 he was knighted by Queen Victoria. He died on the 16th of August
1896.




MACPHERSON, JAMES (1736-1796), Scottish "translator" of the Ossianic
poems, was born at Ruthven in the parish of Kingussie, Inverness, on the
27th of October 1736. He was sent in 1753 to King's College, Aberdeen,
removing two years later to Marischal College. He also studied at
Edinburgh, but took no degree. He is said to have written over 4000
lines of verse while a student, but though some of this was published,
notably _The Highlander_ (1758), he afterwards tried to suppress it. On
leaving college he taught in the school of his native place. At Moffat
he met John Home, the author of _Douglas_, for whom he recited some
Gaelic verses from memory. He also showed him MSS. of Gaelic poetry,
supposed to have been picked up in the Highlands, and, encouraged by
Home and others, he produced a number of pieces translated from the
Gaelic, which he was induced to publish at Edinburgh in 1760 as
_Fragments of Ancient Poetry collected in the Highlands of Scotland_. Dr
Hugh Blair, who was a firm believer in the authenticity of the poems,
got up a subscription to allow Macpherson to pursue his Gaelic
researches. In the autumn he set out to visit western Inverness, the
islands of Skye, North and South Uist and Benbecula. He obtained MSS.
which he translated with the assistance of Captain Morrison and the Rev.
A. Gallie. Later in the year he made an expedition to Mull, when he
obtained other MSS. In 1761 he announced the discovery of an epic on the
subject of Fingal, and in December he published _Fingal, an Ancient Epic
Poem in Six Books, together with Several Other Poems composed by Ossian,
the Son of Fingal, translated from the Gaelic Language_, written in the
musical measured prose of which he had made use in his earlier volume.
_Temora_ followed in 1763, and a collected edition, _The Works of
Ossian_, in 1765.

The genuineness of these so-called translations from the works of a
3rd-century bard was immediately challenged in England, and Dr Johnson,
after some local investigation, asserted (_Journey to the Western
Islands of Scotland_, 1775) that Macpherson had only found fragments of
ancient poems and stories, which he had woven into a romance of his own
composition. Macpherson is said to have sent Johnson a challenge, to
which Johnson replied that he was not to be deterred from detecting what
he thought a cheat by the menaces of a ruffian. Macpherson never
produced his originals, which he refused to publish on the ground of the
expense. In 1764 he was made secretary to General Johnstone at
Pensacola, West Florida, and when he returned, two years later, to
England, after a quarrel with Johnstone, he was allowed to retain his
salary as a pension. He occupied himself with writing several historical
works, the most important of which was _Original Papers, containing the
Secret History of Great Britain from the Restoration to the Accession of
the House of Hanover; to which are prefixed Extracts from the Life of
James II., as written by himself_ (1775). He enjoyed a salary for
defending the policy of Lord North's government, and held the lucrative
post of London agent to Mahommed Ali, nabob of Arcot. He entered
parliament in 1780, and continued to sit until his death. In his later
years he bought an estate, to which he gave the name of Belville, in his
native county of Inverness, where he died on the 17th of February 1796.

After Macpherson's death, Malcolm Laing, in an appendix to his _History
of Scotland_ (1800), propounded the extreme view that the so-called
Ossianic poems were altogether modern in origin, and that Macpherson's
authorities were practically non-existent. For a discussion of this
question see CELT: _Scottish Gaelic Literature_. Much of Macpherson's
matter is clearly his own, and he confounds the stories belonging to
different cycles. But apart from the doubtful morality of his
transactions he must still be regarded as one of the great Scottish
writers. The varied sources of his work and its worthlessness as a
transcript of actual Celtic poems do not alter the fact that he produced
a work of art which by its deep appreciation of natural beauty and the
melancholy tenderness of its treatment of the ancient legend did more
than any single work to bring about the romantic movement in European,
and especially in German, literature. It was speedily translated into
many European languages, and Herder and Goethe (in his earlier period)
were among its profound admirers. Cesarotti's Italian translation was
one of Napoleon's favourite books.

  AUTHORITIES.--For Macpherson's life, see _The Life and Letters of
  James Macpherson ..._ (1894, new ed., 1906), by T. Bailey Saunders,
  who has laboured to redeem his character from the suspicions generally
  current with English readers. The antiquity of the Ossianic poems was
  defended in the introduction by Archibald Clerk to his edition of the
  _Poems of Ossian_ (1870). Materials for arriving at a decision by
  comparison with undoubtedly genuine fragments of the Ossianic legend
  are available in _The Book of the Dean of Lismore_, Gaelic verses,
  collected by J. McGregor, dean of Lismore, in the early 16th century
  (ed. T. McLauchlan, 1862); the _Leabhar na Feinne_ (1871) of F. J.
  Campbell, who also discusses the subject in _Popular Tales of the
  Western Highlands_, iv. (1893). See also L. C. Stern, "Die ossianische
  Heldenlieder" in _Zeitschrift für vergleichende Litteratur-geschichte_
  (1895; Eng. trans. by J. L. Robertson in _Trans. Gael. Soc. of
  Inverness_, xxii., 1897-1898); Sir J. Sinclair, _A Dissertation on the
  Authenticity of the Poems of Ossian_ (1806); _Transactions of the
  Ossianic Society_ (Dublin, 1854-1861); _Cours de littérature
  celtique_, by Arbois de Jubainville, editor of the _Revue celtique_
  (1883, &c.); A. Nutt, _Ossian and the Ossianic Literature_ (1899),
  with a valuable bibliographical appendix; J. S. Smart, _James
  Macpherson: an Episode in Literature_ (1905).




McPHERSON, JAMES BIRDSEYE (1828-1864), American soldier, was born at
Sandusky, Ohio, on the 14th of November 1828. He entered West Point at
the age of twenty-one, and graduated (1853) at the head of his class,
which included Sheridan, Schofield and Hood. He was employed at the
military academy as instructor of practical military engineering (1853).
A year later he was sent to engineer duty at New York, and in 1857,
after constructing Fort Delaware, he was sent as superintending engineer
to San Francisco, becoming 1st lieutenant in 1858. He was promoted
captain during the first year of the Civil War, and towards the close of
1861 became lieutenant-colonel and aide-de-camp to General Halleck, who
in the spring of 1862 sent him to General Grant as chief engineer. He
remained with Grant during the Shiloh campaign, and acted as engineer
adviser to Halleck during the siege operations against Corinth in the
summer of 1862. In October he distinguished himself in command of an
infantry brigade at the battle of Corinth, and on the 8th of this month
was made major-general of volunteers and commander of a division. In the
second advance on Vicksburg (1863) McPherson commanded the XVII. corps,
fought at Port Gibson, Raymond and Jackson, and after the fall of
Vicksburg was strongly recommended by Grant for the rank of
brigadier-general in the regular army, to which he was promoted on the
1st of August 1863. He commanded at Vicksburg until the following
spring. He was about to go on leave of absence in order to be married in
Baltimore when he received his nomination to the command of the Army of
the Tennessee, Grant's and Sherman's old army, which was to take part
under Sherman's supreme command in the campaign against Atlanta (1864).
This nomination was made by Sherman and entirely approved by Grant, who
had the highest opinion of McPherson's military and personal qualities.
He was in command of his army at the actions of Resaca, Dallas, Kenesaw
Mountain and the battles about Atlanta. On the 22nd of July, when the
Confederates under his old classmate Hood made a sudden and violent
attack on the lines held by the Army of the Tennessee, McPherson rode
up, in the woods, to the enemy's firing line and was killed. He was one
of the most heroic figures of the American Civil War, and Grant is
reported to have said when he heard of McPherson's death, "The country
has lost one of its best soldiers, and I have lost my best friend."




MACQUARIE, a British island in the South Pacific Ocean, in 54° 49´ S.
and 159° 49´ E. It is about 20 m. long, and covered with a grassy
vegetation, with some trees or shrubs in the sheltered places which
afford food to a parrot of the genus _Cyanorhamphus_, allied to those of
the Auckland Islands. Although it has no settled population, Macquarie
is constantly visited by sailors in quest of the seals which abound in
its waters.




MACRAUCHENIA, a long-necked and long-limbed, three-toed South American
ungulate mammal, typifying the suborder _Litopterna_ (q.v.).




MACREADY, WILLIAM CHARLES (1793-1873), English actor, was born in London
on the 3rd of March 1793, and educated at Rugby. It was his intention to
go up to Oxford, but in 1809 the embarrassed affairs of his father, the
lessee of several provincial theatres, called him to share the
responsibilities of theatrical management. On the 7th of June 1810 he
made a successful first appearance as Romeo at Birmingham. Other
Shakespearian parts followed, but a serious rupture between father and
son resulted in the young man's departure for Bath in 1814. Here he
remained for two years, with occasional professional visits to other
provincial towns. On the 16th of September 1816, Macready made his first
London appearance at Covent Garden as Orestes in _The Distressed
Mother_, a translation of Racine's _Andromaque_ by Ambrose Philips.
Macready's choice of characters was at first confined chiefly to the
romantic drama. In 1818 he won a permanent success in Isaac Pocock's
(1782-1835) adaptation of Scott's _Rob Roy_. He showed his capacity for
the highest tragedy when he played Richard III. at Covent Garden on the
25th of October 1819. Transferring his services to Drury Lane, he
gradually rose in public favour, his most conspicuous success being in
the title-rôle of Sheridan Knowles's _William Tell_ (May 11, 1825). In
1826 he completed a successful engagement in America, and in 1828 his
performances met with a very flattering reception in Paris. On the 15th
of December 1830 he appeared at Drury Lane as Werner, one of his most
powerful impersonations. In 1833 he played in _Antony and Cleopatra_, in
Byron's _Sardanapalus_, and in _King Lear_. Already Macready had done
something to encourage the creation of a modern English drama, and after
entering on the management of Covent Garden in 1837 he introduced Robert
Browning's _Strafford_, and in the following year Bulwer's _Lady of
Lyons_ and _Richelieu_, the principal characters in which were among his
most effective parts. On the 10th of June 1838 he gave a memorable
performance of _Henry V._, for which Stanfield prepared sketches, and
the mounting was superintended by Bulwer, Dickens, Forster, Maclise, W.
J. Fox and other friends. The first production of Bulwer's _Money_ took
place under the artistic direction of Count d'Orsay on the 8th of
December 1840, Macready winning unmistakable success in the character of
Alfred Evelyn. Both in his management of Covent Garden, which he
resigned in 1839, and of Drury Lane, which he held from 1841 to 1843, he
found his designs for the elevation of the stage frustrated by the
absence of adequate public support. In 1843-1844 he made a prosperous
tour in the United States, but his last visit to that country, in 1849,
was marred by a riot at the Astor Opera House, New York, arising from
the jealousy of the actor Edwin Forrest, and resulting in the death of
seventeen persons, who were shot by the military called out to quell the
disturbance. Macready took leave of the stage in a farewell performance
of _Macbeth_ at Drury Lane on the 26th of February 1851. The remainder
of his life was spent in happy retirement, and he died at Cheltenham on
the 27th of April 1873. He had married, in 1823, Catherine Frances
Atkins (d. 1852). Of a numerous family of children only one son and one
daughter survived. In 1860 he married Cecile Louise Frederica Spencer
(1827-1908), by whom he had a son.

Macready's performances always displayed fine artistic perceptions
developed to a high degree of perfection by very comprehensive culture,
and even his least successful personations had the interest resulting
from thorough intellectual study. He belonged to the school of Kean
rather than of Kemble; but, if his tastes were better disciplined and in
some respects more refined than those of Kean, his natural temperament
did not permit him to give proper effect to the great tragic parts of
Shakespeare, _King Lear_ perhaps excepted, which afforded scope for his
pathos and tenderness, the qualities in which he specially excelled.
With the exception of a voice of good compass and capable of very varied
expression, Macready had no especial physical gifts for acting, but the
defects of his face and figure cannot be said to have materially
affected his success.

  See _Macready's Reminiscences_, edited by Sir Frederick Pollock, 2
  vols. (1875); _William Charles Macready_, by William Archer (1890).




MACROBIUS, AMBROSIUS THEODOSIUS, Roman grammarian and philosopher,
flourished during the reigns of Honorius and Arcadius (395-423). He
himself states that he was not a Roman, but there is no certain evidence
whether he was of Greek or perhaps African descent. He is generally
supposed to have been praetorian praefect in Spain (399), proconsul of
Africa (410), and lord chamberlain (422). But the tenure of high office
at that date was limited to Christians, and there is no evidence in the
writings of Macrobius that he was a Christian. Hence the identification
is more than doubtful, unless it be assumed that his conversion to
Christianity was subsequent to the composition of his books. It is
possible, but by no means certain, that he was the Theodosius to whom
Avianus dedicates his fables.

The most important of his works is the _Saturnalia_, containing an
account of the discussions held at the house of Vettius Praetextatus (c.
325-385) during the holiday of the Saturnalia. It was written by the
author for the benefit of his son Eustathius (or Eustachius), and
contains a great variety of curious historical, mythological, critical
and grammatical disquisitions. There is but little attempt to give any
dramatic character to the dialogue; in each book some one of the
personages takes the leading part, and the remarks of the others serve
only as occasions for calling forth fresh displays of erudition. The
first book is devoted to an inquiry as to the origin of the Saturnalia
and the festivals of Janus, which leads to a history and discussion of
the Roman calendar, and to an attempt to derive all forms of worship
from that of the sun. The second book begins with a collection of _bons
mots_, to which all present make their contributions, many of them being
ascribed to Cicero and Augustus; a discussion of various pleasures,
especially of the senses, then seems to have taken place, but almost the
whole of this is lost. The third, fourth, fifth and sixth books are
devoted to Virgil, dwelling respectively on his learning in religious
matters, his rhetorical skill, his debt to Homer (with a comparison of
the art of the two) and to other Greek writers, and the nature and
extent of his borrowings from the earlier Latin poets. The latter part
of the third book is taken up with a dissertation upon luxury and the
sumptuary laws intended to check it, which is probably a dislocated
portion of the second book. The seventh book consists largely of the
discussion of various physiological questions. The value of the work
consists solely in the facts and opinions quoted from earlier writers,
for it is purely a compilation, and has little in its literary form to
recommend it. The form of the _Saturnalia_ is copied from Plato's
_Symposium_ and Gellius's _Noctes atticae_; the chief authorities (whose
names, however, are not quoted) are Gellius, Seneca the philosopher,
Plutarch (_Quaestiones conviviales_), Athenaeus and the commentaries of
Servius (excluded by some) and others on Virgil. We have also two books
of a commentary on the _Somnium Scipionis_ narrated by Cicero in his _De
republica_. The nature of the dream, in which the elder Scipio appears
to his (adopted) grandson, and describes the life of the good after
death and the constitution of the universe from the Stoic point of view,
gives occasion for Macrobius to discourse upon many points of physics in
a series of essays interesting as showing the astronomical notions then
current. The moral elevation of the fragment of Cicero thus preserved to
us gave the work a popularity in the middle ages to which its own merits
have little claim. Of a third work, _De differentiis et societatibus
graeci latinique verbi_, we only possess an abstract by a certain
Johannes, identified with Johannes Scotus Erigena (9th century).

  See editions by L. von Jan (1848-1852, with bibliog. of previous
  editions, and commentary) and F. Eyssenhardt (1893, Teubner text); on
  the sources of the _Saturnalia_ see H. Linke (1880) and G. Wissowa
  (1880). The grammatical treatise will be found in Jan's edition and H.
  Keil's _Grammatici latini_, v.; see also G. F. Schömann, _Commentatio
  macrobiana_ (1871).




MACROOM, a market town in the western part of county Cork, Ireland, on
the river Sullane, an affluent of the Lee, 24½ m. W. of Cork by the Cork
& Macroom railway, of which it is the terminus. Pop. (1901), 3016.
Besides a fine Roman Catholic church, a court house and barracks,
Macroom possesses a modernized castle, which is said to have been
founded by King John, though it is more probably attributable to Norman
invaders. It was besieged more than once in the 17th century, and is
said to have been the birthplace of Admiral Sir William Penn, whose more
famous son founded Pennsylvania. Here some rebels of 1798 were executed
and their heads exhibited on the spikes of the castle gate. Macroom has
trade in corn-milling, leather-work and dairy produce, and is a good
centre for salmon and trout fishing. It is governed by an urban district
council.




MACUGNAGA, a village of Piedmont, Italy, in the province of Novara, 20
m. W.S.W. of Piedimulera, which is 7 m. S. of Domodossola by rail. Pop.
(1901), 798. It is situated 4047 ft. above sea-level, and is 10 m. N.E.
of the highest summit of Monte Rosa. It is frequented as a summer
resort.




MacVEAGH, WAYNE (1833-   ), American lawyer and diplomatist, was born
near Phoenixville, Chester county, Pa., on the 19th of April 1833. He
graduated at Yale in 1853, was admitted to the bar in 1856, and was
district attorney of Chester county in 1859-1864. He held commands in
militia forces raised to meet threatened Confederate invasions of
Pennsylvania (1862-63). He became a leader in the Republican party, and
was a prominent opponent of his father-in-law, Simon Cameron, in the
fight within the party in 1871. MacVeagh was minister to Turkey in
1870-1871; was a member of the state constitutional convention of
1872-1873; was chairman of the "MacVeagh Commission," sent in 1877 by
President Hayes to Louisiana, which secured the settlement of the
contest between the two existing state governments and thus made
possible the withdrawal of Federal troops from the state; and was
attorney-general of the United States in 1881 under President Garfield,
but resigned immediately after Garfield's death. In 1892 he supported
Grover Cleveland, the Democratic nominee for the presidency, and from
1893 to 1897 was ambassador to Italy. He returned to the Republican
party in 1896. In 1903 he was chief counsel of the United States before
the Hague tribunal in the case regarding the claims of Germany, Great
Britain and Italy against the republic of Venezuela.




MADÁCH, IMRE (1829-1864), Hungarian dramatist, was born at
Alsó-Sztregova. He took part in the great revolution of 1848-49 and was
imprisoned; on his return to his small estate in the county of Nógrád,
he found that his family life had meanwhile been completely wrecked.
This only increased his natural tendency to melancholy, and he withdrew
from public life till 1861, devoting his time mainly to the composition
of his chief work, _Az ember tragoediája_ ("The Tragedy of Man"). John
Arany, then at the height of his fame as a poet, at once recognized the
great merits of that peculiar drama, and Madách enjoyed a short spell of
fame before his untimely death of heart-disease in 1864. In _The Tragedy
of Man_ Madách takes us from the hour when Adam and Eve were innocently
walking in the Garden of Eden to the times of the Pharaohs; then to the
Athens of Miltiades; to declining Rome; to the period of the crusades;
into the study of the astronomer Kepler; thence into the horrors of the
French Revolution; into greed-eaten and commerce-ridden modern London;
nay, into the ultra-Socialist state of the future, when all the former
ideals of man will by scientific formulae be shown up in their
hollowness; still further, the poet shows the future of ice-clad earth,
when man will be reduced to a degraded brute dragging on the misery of
his existence in a cave. In all these scenes, or rather anticipatory
dreams, Adam, Eve and the arch-fiend Lucifer are the chief and
constantly recurring _personae dramatis_. In the end, Adam, despairing
of his race, wants to commit suicide, when at the critical moment Eve
tells him that she is going to be a mother. Adam then prostrates himself
before God, who encourages him to hope and trust. The diction of the
drama is elevated and pure, and although not meant for the stage, it has
proved very effective at several public performances.

  Concerning Madách there is an ample literature, consisting mostly of
  elaborate articles by Charles Szász (1862), Augustus Greguss (1872),
  B. Alexander (1871), M. Palágyi (1890), and others.




MADAGASCAR, an island in the Indian Ocean, and after New Guinea and
Borneo the largest island in the world, about 260 m. distant, at the
nearest point, from the S.E. coast of Africa, from which it is separated
by the Mozambique Channel. Since 1896 Madagascar has been a French
colony. It is 995 m. in length from N. to S., and about 250 m. in
average breadth, although near the centre it is nearly 360 m. across;
its area is about 228,000 sq. m., or not quite four times the extent of
England and Wales. It lies mainly between 44° and 50° E. Its
northernmost point, Cape Ambro, in 12° S., inclines 16° to the E. from
the longitude of Cape St Mary, the southernmost point, in 25° 35´ S., so
that the main axis of the island runs from N.N.E. to S.S.W. In its broad
structure Madagascar consists of an elevated mountainous region, from
3000 to 5000 ft. in altitude, occupying from two-fifths to a half of the
centre and the eastern side of the island, around which are extensive
plains at a much less elevation above the sea, and most developed on the
western and north-west sides. But this lower region is broken up by
masses of hills, with several elevated plateaus, especially in the
south-west and south.

  _Physical Features._--Madagascar has a very regular and compact form,
  with few indentations considering its great extent of shore-line. In
  general outline it has a strong resemblance to the impression of a
  human foot--the left side. Along two-thirds of its eastern side the
  coast is almost a straight line, without any inlet, Tamatàve, the
  chief port on this side of the island, being only protected by coral
  reefs. North of this line, however, is Antongil Bay, a deep and wide
  inlet running northwards for about 50 m.; farther north is Port
  Louquez, and at almost the extreme point of the island is Diégo-Suarez
  Bay, one of the finest harbours in the world. But the north-western
  side of Madagascar is broken up by a number of inlets, some of them
  land-locked and of considerable size. South of Cape St Andrew, the
  north-west angle of the island, the coast-line is unbroken until the
  estuary of the river Onilàhy, or St Augustine's Bay, is reached.
  Rounding the southern end of the island, there is no other inlet save
  the small bay north of Fort Dauphin, at the southern end of the
  straight line of coast already mentioned.

  The islands around Madagascar are few and unimportant. The largest are
  Ste Marie, near the eastern coast, a narrow island about 35 m. long,
  and Nossi-bé (q.v.), larger and more compact in form, opposite
  Ampàsindàva Bay on the N.W. coast. Except the Minnow group, north of
  Nossi-bé, the rest are merely rocky islets, chiefly of coral.

  The shores of the greater portion of the southern half of the island
  are low and flat, but in the northern half the coast is often bold and
  precipitous, the high land occasionally approaching the sea. On the
  eastern side the plains vary from 10 to 50 m. in breadth, but on the
  western side they exceed in some localities 100 m. From these
  coast-plains the ground rises by successive ranges of hills to the
  high interior land. This elevated region is broken in all directions
  by mountains, from which the crystalline rocks show most frequently as
  huge bosses, and in certain regions present very varied and
  picturesque outlines, resembling Titanic castles, cathedrals, domes,
  pyramids and spires. The highest mountain mass is centrally situated
  as regards the length of the island, but more to the eastern side.
  This is the ancient extinct volcano Ankàratra, three of the highest
  points varying in elevation from 7284 to 8635 ft. above the sea, and
  from 4000 to 5000 ft. above the general level of the surrounding
  country. The loftiest of these is named Tsi-àfa-jàvona, i.e. "That
  which the mists cannot climb." It had been supposed that Ankàratra was
  the highest point in the island, but in 1903 it was found that Ambòro,
  in the northern province of Antankàrana, is about 9490 ft. in
  altitude. Besides these highest points there are a considerable number
  of mountains in the central provinces of Imèrina and Bétsiléo and the
  intervening and surrounding districts; and in the Bàra country the
  Isàlo range has been compared to the "Church Buttes" and other
  striking features of the scenery of Utah. One of the finest of the
  Madagascar mountains is an isolated mass near the northern point of
  the island called Ambòhitra. This is 4460 ft. high, and rising from
  land little above the sea-level, is well seen far out to sea.

  In the elevated region of Madagascar are many fertile plains and
  valleys, the former being the dried-up beds of ancient lakes. Among
  these are Bètsimitàtatra in Imèrina, and Tsiènimparìhy in Bétsiléo,
  supplying a large proportion of the rice required for the capitals of
  these two provinces. Still more spacious valleys are the Antsihànaka
  country and the Ankày district, between the two eastern lines of
  forest. The extensive coast plains on the western side of the island
  are chiefly in Ibòina (N.W.) and in Ménabé (S. of the Tsìribìhina
  River); those on the east are widest in the Taifàsy country (S.E.).
  The water-parting for six-sevenths of the whole length of the island
  is much nearer the eastern than the western side, averaging from 80 to
  90 m. from the sea. There are no arid districts, except in the extreme
  south-west and towards the southern point of the island. The general
  surface of the interior highland consists of bare rolling moor-like
  country, with a great amount of red clay-like soil, while the valleys
  have a rich humus of bluish-black alluvium.

  The chief rivers flow to the west and north-west sides of the island.
  The eastern streams are all less in size, except the Mangòro, which
  flows parallel with the coast. Few of them therefore are of much
  service for navigation, except for the light-draught native canoes;
  and all of them are more or less closed at their outlets by sand-bars.
  Beginning at the south-eastern point and going northwards, the
  principal rivers are the Mànanàra, Mànampàtrana, Màtitànana,
  Mànanjàry, Mangòro, with its great affluent Onivé, Vòhitra, Màningòry,
  and the Antànambàlana at the head of Antongil Bay. On the N.W. coast,
  going southwards, are the Sofià and Màhajàmba, falling into Màhajàmba
  Bay, the Bétsiboka with the Ikòpa--the great drains of the northern
  central provinces, forming unitedly the second largest river of the
  island and falling into Bèmbatòka Bay--the Màhavàry, Mànambòlo,
  Tsìribìhina or Onimàinty, the third largest river, with its
  tributaries the Kìtsàmby, Màhajìlo and Manìa, the Mòrondàva, Mangòky,
  probably the largest river in the country, with its important
  tributaries the Matsìatra, Mànantànana and Rànomàitso, the Fiherènana
  and Onilàhy. On the south coast are four considerable streams, the
  largest of which is the Mènaràndra. Of the western rivers the
  Bètsibòka can be ascended by small steamers for about 100 m., and the
  Tsìribìhina is also navigable for a considerable distance. The former
  is about 300 m. long; the latter somewhat less, but by its affluents
  spreads over a greater extent of country, as also does the Mangòky.
  The rivers are all crossed frequently by rocky bars, which often form
  grand waterfalls. The eastern rivers cut their way through the
  ramparts of the high land by magnificent gorges amidst dense forest,
  and descend by a succession of rapids and cataracts. The Màtitànana,
  whose falls were first seen by the writer in 1876, descends at one
  plunge some 400 ft.; and on the Vòhitra River, whose valley is
  followed by the railway, there are also many fine waterfalls.

  On the eastern side of Madagascar the contest between the fresh water
  of the rivers and the sea has caused the formation of a chain of
  lagoons for nearly 300 m. In many places these look like a river
  following the coast-line, but frequently they spread out into
  extensive sheets of water. By cutting about 30 m. of canal to connect
  them, a continuous waterway could be formed for 270 m. along the
  coast. This has already been done for about 55 m. between Ivòndrona
  and Andòvorànto, a service of small steamers forming part of the
  communication between the coast and the capital. Besides these
  lagoons, there are few lakes of any size in Madagascar, although there
  were some very extensive lakes in a recent geological epoch. Of the
  largest of these, the Alàotra Lake in the Antsihànaka plain is the
  relic; it is about 25 m. long. Next comes Kinkòny, near Maròambitsy
  Bay (N.W. coast), about 16 m. long, and then Itàsy, in western
  Imèrina, about half as large. There is also a salt lake,
  Tsimànampetsòtsa (S.W. coast), about as large as Alàotra.

  There is now no active volcano in Madagascar, but a large number of
  extinct cones are found, some apparently of very recent formation.
  Some miles south of Diégo-Suarez is a huge volcanic mountain,
  Ambòhitra, with scores of subsidiary cones on its slopes and around
  its base. About 40 m. south-west of Antanànarìvo there is a still
  larger extinct volcano, Ankàratra, with an extensive lava field
  surrounding it; while near Lake Itàsy are some 200 volcanic cones.
  Another group of extinct volcanoes is in the Vàkinankàratra district,
  S.W. of Ankàratra. Many others exist in other parts of the island (see
  § _Geology_). Slight shocks of earthquake are felt every year, and hot
  springs occur at many places. Several of these are sulphurous and
  medicinal, and have been found efficacious in skin diseases and in
  internal complaints.

  _Geology._--Madagascar may be divided into two very distinct
  geological regions, viz. (I.) the Archean Region, which extends over
  the central and eastern portions of the island and occupies about
  two-thirds of its whole area, and is composed of crystalline schists;
  and (II.) the Western Region, of sedimentary rocks, including the
  remaining third of the island, in the centre of which, however, is an
  isolated patch of Archean rocks, near Cape St Andrew. There are also
  found in both regions numerous masses of igneous rocks, both plutonic
  and volcanic, in some places of considerable extent, which pierce
  through and overflow the earlier formations.

  [Illustration: Map of Madagascar.]

  I. _The Archean Region._[1]--This region, nearly coincident with the
  mountainous upper portion of the island, is chiefly composed of the
  following crystalline rocks: gneiss, which is the most common of them
  all, quartzite and quartz-schist, with occasional beds of crystalline
  limestone and mica-schist, although this latter rock is very rare. The
  gneiss is mostly grey, but occasionally pinkish, its essential
  constituents (felspar and quartz) being almost always associated with
  dark mica (biotite) and hornblende in variable quantity. The rock is
  therefore a hornblende-granitite-gneiss. Granite--more frequently
  granitite--occurs in several places, as well as pyroxene-granulite,
  serpentine, argillate, &c.; and gold is found widely disseminated, as
  well as other metals, but these latter, as far as at present known,
  except iron, are not abundant. The general strike of the rocks is the
  same as that of the trend of the island itself (N.N.E. to S.S.W.),
  but in its western portion the strike is frequently from N.N.W. to
  S.S.E. In both cases the strike of the rocks is coincident with the
  direction of several large valleys, which mark huge faults in the
  crystalline rocks. Almost the whole of this region is covered by a red
  soil, often of great thickness, which resembles and is often described
  as "clay," but is really decomposed rock, chiefly gneiss, reddened
  with oxidized magnetite.

  II. _The Sedimentary Region._--The sedimentary rocks extend
  continuously along the western side of Madagascar, following the
  coast-line; in the north these series of strata are only from 20 to 30
  m. across, but farther south they reach a breadth of nearly 100 m.,
  while opposite the Bétsiléo province they extend nearly half across
  the island. A narrow band, of Cretaceous age, occurs also on the east
  coast, for about 120 m., between Vàtomàndry and Mànanjàry. The
  following formations are represented:--

  1. _Primary._ It is thought that certain beds of slaty rocks, which
  have been recognized at different places, may belong to some of the
  Primary strata. Some siliceous schists of the Permian age were
  discovered in 1908 in the valley of the Sàkamèira, south of the
  Onilàhy, or Augustine river. (S.W. coast). These contain reptilian
  remains, and also clear imprints of leaves of the _Glossopteris
  indica_, as well as other indications of an ancient vegetation. In the
  same region conglomerates have been found containing enormous blocks,
  apparently brought by glacial action, and said to be identical in
  character with those described as existing in the Transvaal. True coal
  has also been obtained in the same district, the deposits varying from
  a third to half a metre in thickness.

  2. _Secondary._ The lowest members of these rest directly upon the
  central mass of crystalline rocks, and consist of sandstones,
  conglomerates and shales, which have been supposed by some to belong
  to the Trias, without, however, the discovery of any fossil necessary
  to confirm this supposition, except some silicified trunks of trees.
  These beds are most probably lower members of the Jurassic series.
  Westward of and above these strata, the Middle and Upper Jurassic
  formations are found (Lias, Lower Oolite, Oxfordian, &c.), with
  well-marked and numerous fossils (_Ammonites_, _Nerinaea_, _Natica_,
  _Astarte_, _Rhynchonella_, _Echinodermata_, &c.); then the Cretaceous
  rocks, both these and the Jurassic series being largely developed, the
  Cretaceous fossils including _Nautilus_, _Belemnites_, _Ostrea_,
  _Gryphaea_, &c., and some very large Ammonites (_Pachydiscus_). The
  Secondary strata show generally a very slight dip westwards and are
  consequently almost horizontal. They do not seem to have been greatly
  disturbed, although faults occur here and there.

  3. _Tertiary._ A small strip of coast of Eocene age is known near
  Tullear (S.W. coast), and rocks of the same period occur in Nòssi-bé,
  at Màhajamba Bay, and at Diégo-Suarez, with Nummulites and other
  foraminifera. Near the latter locality, beds of Oligocene age have
  been noticed, consisting of coarse limestones.

  4. _Quaternary and Recent._ A narrow band of these deposits extends
  along the west coast, from north of Cape St Andrew nearly to the
  extreme southern point of the island. But the most noticeable of these
  are those in the ancient bed of the Alàotra Lake, which formerly
  extended far southwards along the valley of the Mangòro; also those in
  the marshes of Antsìrabè and of Ifànja, in the Ikòpa valley (the great
  rice plain west of the capital), and also in the plain of
  Tsiénimpàrìhy in Bétsiléo, and especially the recent deposits of
  Ampàsambazìmba, north-west of Lake Itàsy, discovered in 1902. These
  beds, rich in subfossil remains, have yielded important additions to
  our knowledge of the extinct fauna of the island. (See §
  _Palaeontology_.)

  _Igneous Rocks._ (1) _Plutonic rocks._--The ancient or plutonic
  igneous rocks (including granite, syenite, diorite, gabbro, porphyry,
  porphyrite, norite and retinite) appear at various points of the two
  previously described regions. In the Archean region the gneiss is very
  often found passing into granite, but certain granitic masses have a
  sufficiently distinct character. In the midst of the sedimentary
  region are two well-recognized masses of plutonic rocks, belonging to
  the syenites, sometimes quartziferous in structure. (2) _Volcanic
  rocks._--Recent volcanic eruptive rocks (including rhyolite, trachyte,
  phonolite, andesite and basalt) have been examined at a number of
  points throughout both the geological regions of the island. In the
  Archean region these are very noticeable near Lake Itàsy, in the
  _massif_ of Ankàratra (an ancient volcano) and in Vàkinankàratra (at
  Bètàfo, Antsìrabé, &c.); while there are numerous outflows of
  doleritic rocks, probably from faults, along the eastern side of the
  island and almost parallel with the coast line. In the sedimentary
  region volcanic rocks are very numerous; the most extensive of these
  is a tract of country, more than 80 m. long, on the west coast, where
  the basalt has overflowed the Cretaceous strata. It must be remembered
  that the geology of Madagascar is still only known in its broad
  features.[2]

  _Minerals and Metals._--The country has considerable mineral wealth.
  Gold is found almost all over the region of crystalline rocks, except
  in and around the Antsihànaka province, the richest auriferous
  districts being a band of country parallel with the east coast and
  spreading at its southern end into the interior; and another tract,
  whose centre is about 100 m. N. of the capital (see § _Industries_,
  &c.). Silver has been detected in certain galenas, and also platinum;
  copper has been found in various localities, as well as zinc, lead,
  nickel, antimony and manganese, but none of these metals has yet been
  discovered in sufficient quantities for profitable working. Iron, on
  the contrary, especially magnetite, is found abundantly and has for
  long been worked by the Malagasy with the simple appliances brought by
  their ancestors from their original home in the Far East. The
  principal seats of the native industry are on the edge of the upper
  forest, where charcoal is easily procured. The following precious
  stones are reported: corundum (rubies and sapphires), beryl, topaz,
  zircon, garnet, amazon-stone, tourmaline, often in large crystals, and
  variously coloured quartz, also often found in crystals of great size.
  Bitumen and petroleum have been found; graphite is plentiful, and
  sulphur, salt, saltpetre and lime are also procured. On the north-west
  coast thin beds of lignite occur, and coal has been found in the
  valley of the Sàkamèira.

  _Palaeontology._--Researches in various parts of the island have
  revealed the existence, in a subfossil state, of the bones of numerous
  birds of the family _Struthidae_. These have been arranged in twelve
  species, belonging to two genera, _Aepyornis_ and _Mullerornis_, which
  varied in size from that of a bustard to birds much exceeding an
  ostrich, and rivalling the recently extinct moa of New Zealand, the
  largest species being about 10 ft. in height. One species of these
  great wingless birds laid an egg which is the largest known, being 12½
  in. by 9½ in. Associated with these remains there have been found
  those of many other birds, including a hawk, a duck, a darter, a
  spoonbill, a heron, a rail and a wild-goose, some of these being much
  larger than any now inhabiting Madagascar. In the same beds the
  remains of two, if not three, species of hippopotamus have been found,
  about two-thirds the size of the living South African species; also
  the bones and carapace, &c., of gigantic tortoises, and the bones of a
  crocodile, now extinct on the coast and rivers, but still living in
  the two chief lakes; also the remains of a river-hog, of a species of
  swine, and of a slender-legged form of zebu-ox. Near the south-west
  coast the skull of a large lemuroid animal was discovered in 1893,
  much longer than that of any living lemur, the animal being probably
  three times the size of any previously known Madagascar lemuroid.
  Later still, in 1899 and subsequently, the bones of two other
  creatures of the same suborder have been discovered, one of them
  indicating an animal much larger than a man. Many of these birds and
  animals were probably contemporaneous with the earliest human
  inhabitants of Madagascar. The remains of two species of Edentata have
  been found, as well as those of several species of small Rodents, also
  of a Carnivore (_Cryptoprocta_), a larger variety of the species still
  living in the island.

  In the deposits of a much more remote era than those already spoken
  of--the Jurassic--the bones of some enormous terrestrial lizards have
  been brought to light, belonging to Sauropodous Dinosaurs of the
  genera _Bothriospondylus_ and _Titanosaurus_, and to a Theropod of the
  genus _Megalosaurus_. In the beds of the Lower Oolite portions of the
  skull of a reptile resembling the gavial of the Ganges had been
  previously discovered, from which a new genus called _Steneosaurus_
  has been founded. Since the French occupation (1895) considerable
  additions have been made to our knowledge of the fossil fauna of
  Madagascar from researches made both on the west and south-west coast
  (at Bèlo and Ambòlisatrana) and in the interior (at Antsìrabè),
  especially in the rich deposits near Tsàrazàza (Ampàsambazimba), to
  the north-west of Lake Itàsy. From these various localities the
  subfossil remains of thirteen or fourteen extinct species of lemuroid
  animals (including the gigantic species already mentioned) have been
  obtained, and have been classified under five new genera: viz.
  _Megaladapis_ (3 sp.), _Palaeopropithecus_ (3 sp.), _Archaeolemur_ (2
  sp.), _Bradylemur_ (1 sp.) and _Hadropithecus_ (1 sp.), together with
  three new species of lemur. Of these, the _Archaeolemurs_ seem to have
  combined the characteristics of lemuroid animals with those of the
  monkeys, while _Hadropithecus_ is pronounced to be the nearest known
  link with them. A list of all the fossils of the island known in 1895,
  but omitting the vertebrates above mentioned, included 140
  species,[3] belonging to the Mollusca, Foraminifera, Echinodermata,
  Actinozoa and Plantae; but the researches of French geologists made
  the total number of Madagascar fossils known in 1907 to be not fewer
  than 280 species.

  _Climate._--In the high interior the climate resembles that of the
  temperate zones, although six-sevenths of the island are within the
  tropics; there is no intense heat, and it is quite cold, occasionally
  touching freezing point, during the nights of the cool season. These
  parts of the country are tolerably healthy for Europeans. But the
  coasts are much hotter, especially on the western side, as is also the
  interior west of the highland region; and from the large amount of
  marsh and lagoon on the coasts, malarial fever is common and
  frequently fatal, both to Europeans and to natives from the interior.
  Epidemics of influenza and fever have been very prevalent of late
  years in the central provinces. The seasons are two--the hot and rainy
  season from November to April, and the cool and dry season during the
  rest of the year; this remark applies chiefly to the interior, for
  rain falls throughout the year on the eastern coast, which is exposed
  to the vapour-laden south-east trade winds. The rainfall diminishes as
  one goes westward and especially south-westward, there being very
  little rain in the south-west corner of the island. No snow is known,
  even on the loftiest mountains, but thin ice is occasionally seen; and
  hail-showers, often very destructive, are frequent in the rainy
  season. Terrific thunderstorms are also common at that period;
  waterspouts are sometimes seen; and as the Indian Ocean cyclone region
  touches the eastern coast, hurricanes occur every few years, at rare
  intervals ascending into the interior highland. The yearly rainfall of
  the Imèrina province (Antanànarìvo) averages about 54½ in.; accurate
  statistics as to that of other parts of the island are not available;
  but on the east coast it appears to be about double that of the
  interior; in the south-east considerably more than that amount; while
  at Mòrondàva (west coast) it is given as about 21 in. annually, and at
  Tullear (south-west coast) as only 10 in. At Tamatàve (east coast) the
  mean annual temperature is given as 76.5°, while at the capital it is
  about 66°; the temperature of Antanànarìvo resembles that of Naples or
  Palermo.[4] The following table gives the mean of two different sets
  of government returns of mean rainfall: Antanànarìvo, 1369 mm.;
  Tamatàve, E. coast, 1863 mm.; Fàrafangàna, S.E. coast, 2803 mm.;
  Diégo-Suarez, N. end of island, 1196 mm.; Mòrondàva, W. coast, 543
  mm.; Tullear, S.W. coast, 273 mm.; Màrovoày, W. interior, 1413 mm.

  _Fauna._--The fauna of Madagascar, while deficient in most of the
  characteristic tropical forms of life, is one of great interest to the
  naturalist from its remote affinities, much of its animal life having
  Asiatic rather than African relationships. The central portions of the
  island, from their generally bare and treeless character, are poor in
  living creatures; but the lower country, and especially the forests
  and coast plains, are fairly well stocked. But it is noticeable that
  many species have a very limited range. Although a continental island,
  it possesses no large quadrupeds--none of the larger carnivorous,
  ungulate, proboscoid or quadrumanous animals; but it is the
  headquarters of the _Lemuroidea_, no fewer than thirty-nine species of
  which are found in its forests and wooded plains. Some of these
  creatures are highly specialized, while the curious aye-aye (_Chiromys
  madagascariensis_), an allied form, is one of the most remarkable
  animals known, forming a genus and family by itself. Its whole
  structure is strangely modified to enable it to procure the
  wood-boring larvae which form its food. Other peculiar animals are
  twenty-three species of the _Centetidae_, a family of the Insectivora
  almost confined to Madagascar; while of the _Carnivora_ there are
  several small creatures belonging to the civets (_Viverridae_). The
  largest of these ferocious animals, also forming a genus and family by
  itself, is the _Cryptoprocta ferox_; it is a plantigrade animal, 3 ft.
  long, but very like an enormous weasel, and attacks other animals with
  the greatest ferocity. The island contains twenty-five species of
  bats, mostly of African, but some of Indian, affinities. African
  humped cattle were introduced several hundred years ago and now exist
  in large herds all over the country. The fat-tailed sheep, goats and
  swine have also been naturalized, as well as all kinds of domestic
  poultry.

  The avi-fauna is much richer than the mammalian, and, although wanting
  the largest birds as well as the most brilliantly coloured, comprises
  two hundred and sixty species, half of which are endemic. Many of the
  birds are remarkable not so much for their shape or colouring as for
  their distant relationships; many belong to peculiar genera, and some
  are so isolated that new families have had to be formed for their
  reception. There is a large variety of perching birds, including
  several species of brilliant plumage--sun-birds, kingfishers, rollers
  and flycatchers, &c.; kites, hawks and owls are numerous, and the
  lakes and marshes abound with water-fowl and herons, ibises, &c.

  The island is free from deadly serpents, but contains two or three
  small species of boa; crocodiles abound in the rivers and lakes; and
  numerous species of lizard, chameleon and tree-frog inhabit the woods.
  Madagascar may be considered as one of the headquarters of the
  _Chamaeleonidae_, for of the fifty known species no fewer than
  twenty-five have already been described from the island. Many of these
  are of curious form, with remarkable developments of the plates of the
  head and projecting horns and spines. There are several peculiar
  tortoises, but the gigantic species are now found alive only on the
  little island of Aldabra, to the north. The insect life comprises many
  brilliantly-coloured beetles, butterflies (about eight hundred species
  of which are known), moths, locusts, spiders and flies, and also
  noxious spiders, with scorpions and centipedes. The river fishes
  belong chiefly to the family _Chromididae_; many of them are of
  brilliant and bizarre appearance, with strongly contrasted colours in
  bands and spots. Those found in the coast waters do not differ
  materially from the widely spread Indian Ocean species.

  As a whole, the Madagascar fauna is marked by a strong individuality,
  which would appear to be the result of long isolation from the other
  zoological "regions." The Asiatic and Malayan affinities of many of
  its animals, as well as the physical conditions of the bed of the
  Indian Ocean, make it highly probable that Madagascar, while once
  forming part of Africa, is the chief relic of a considerable
  archipelago formerly connecting that continent with Asia, its other
  portions being shown by groups of small islands, and by coral atolls
  and shoals, which are gradually disappearing beneath the waves. These
  questions have been fully treated by Dr A. R. Wallace in his
  _Geographical Distribution of Animals_ (vol. i. ch. ix., 1876) and
  _Island Life_, ch. xix. (1880).

  _Flora._--The flora of Madagascar is one of great interest. One of its
  most prominent features is the belt of forest round a large part of
  the island at no great distance from the sea, and generally following
  the coast-line. This forest is densest on the east side, and for about
  120 m. forms a double line, the lower one being much the broader and
  averaging 30 m. across, but attaining a breadth of 60 or 70 m. on the
  north-east, near Antongil Bay. The vegetation on the western side of
  the island is much less dense, often appearing as scattered clumps of
  trees on savannah-like plains rather than continuous forest; while in
  the south-west, where the rainfall is very scanty, the vegetation is
  largely of fleshy-leaved and spiny plants--aloes and cacti (the latter
  introduced), with several species of Euphorbia, as well as numerous
  lianas, one of which (_Intisy_) yields india-rubber. It is estimated
  that there are about 30,000 sq. m. of forest-covered country in
  Madagascar, or about one-eighth of its whole surface. The vegetation
  of the forests, the abundant epiphytes, the tree-mosses, the filmy
  ferns and the viviparous character of many of the ferns, show clearly
  how abundant the rainfall is in the eastern forest region. This
  contains a large variety of hard-wooded and valuable timber trees,
  including species of _Weinmannia_ (_Lalòna_[5]), _Elaeocarpus_
  (_Voànana_), _Dalbergia_ (_Vòambòana_), _Nuxia_ (_Vàlanìrana_),
  _Podocarpus_, a pine, the sole species in the island (_Hètatra_),
  _Tambourissa_ (_Ambòra_), _Neobaronia_ (_Hàrahàra_), _Ocotea_
  (_Varòngy_) and probably ebony, _Diospyros_ sp., &c. The following
  trees are characteristic of Madagascar vegetation, some of them being
  endemic, and others very prominent features in the landscape: the
  traveller's-tree (_Urania speciosa_), with its graceful crown of
  plantain-like leaves growing like an enormous fan at the top of a tall
  trunk, and affording a supply of pure cool water, every part of the
  tree being of some service in building; the Raphia (rofia) palm
  (_Sagus ruffia_); the tall fir-like _Casuarina equisetifolia_ or
  beefwood tree, very prominent on the eastern coast, as well as several
  species of screw-pine (_Pandanus_); the Madagascar spice (_Ravintsara
  madagascariensis_), a large forest tree, with fragrant fruit, leaves
  and bark; a beautiful-leaved species of _Calophyllum_; and the Tangèna
  (_Tanghinia veneniflua_), formerly employed as a poison ordeal. On the
  lagoons and lower reaches of the rivers the Vìha (_Typhonodorum
  lindleyanum_), an arum endemic to Madagascar, grows in great profusion
  to a height of 12 or 13 ft. and has a white spathe more than a foot in
  length; and on the western coast dense thickets of mangrove line the
  creeks and rivers. In the interior rivers is found the curious and
  beautiful lace-leaf plant (_Ouvirandra fenestralis_), with an edible
  tuberous root. On the western side of the island the baobab, the
  tamarind, the ròtra (_Eugenia_ sp.), the rofia palm, and several
  species of fan-palm (_Hyphaene_) and of _Ficus_ are prominent; and the
  mango (introduced) grows to a large tree. In the generally bare
  interior highlands, large trees, species of _Ficus_ (_Amòntana_,
  _Aviàvy_, _Nònoka_, _Adàbo_, &c.), often mark the position of the old
  towns; and some of these, as Ambòhimànga, Vòhilèna, &c., are
  surrounded by remnants of the original forest, which formerly covered
  large portions of the interior. The most prominent tree in the central
  province is now the Cape-lilac (_Melia azederach_) introduced about
  1825; and since the French conquest several species of eucalyptus have
  been planted in vast numbers by the road sides. These have given quite
  a new aspect to the vegetation, while bright colour is imparted by
  species of _Bougainvillea_ and _Poinsettia_. In the eastern forests
  palms, bamboos, lianas and tree-ferns, as well as species of
  _Dracaena_, are found.

  Although flowers growing on the ground or on shrubs are not
  conspicuous for number or beauty, there are many fine flowering trees,
  such as _Poinciana regia_, presenting a mass of scarlet flowers;
  _Colvillia racemosa_, with yellow flowers; _Astrapaea Wallichii_,
  striking attention from its abundant flowers; and species of
  _Cryptostegia_, a purple-flowered creeper, and _Strongylodon_, another
  creeper with cream-coloured blossoms. Among attractive plants are
  species of _Hibiscus, Euphorbia, Buddleia, Ixora, Kitchingia,
  Clematis_, &c. On the east coast two orchids, species of _Angraecum_,
  with large white waxy flowers, one with an extraordinarily long spur
  or nectary, attract the attention of every traveller during June and
  July by their abundance and beauty. Some 320 species o£ fern have been
  collected, and there are large numbers of spiny and prickly plants, as
  well as numerous grasses, reeds and rushes, many of them of great
  service in the native manufactures of mats, hats, baskets, &c.

  The Rev R. Baron divides the flora into three distinctly marked
  "regions," which run in a longitudinal direction, following
  approximately the longer axis of the island, and are termed
  respectively eastern, western and central. The central includes the
  elevated highland of the interior, while the eastern and western
  include the forest belts and most of the wooded country and coast
  plains. Of the 4100 known plants--of which about three-fourths are
  endemic--composing the Madagascar flora, there are 3492 Dicotyledons,
  248 Monocotyledons and 360 Acotyledons. Of these, the orders most
  largely represented (together with their species) are: Leguminosae,
  346; Filices, 318; Compositae, 281; Euphorbiaceae, 228; Orchideae,
  170; Cyperaceae, 160; Rubiaceae, 147; Acanthaceae, 131; Gramineae,
  130. The number of endemic genera now known is 148. Of the 3178
  species of plants whose localities have been determined, 35% are
  peculiar to the eastern region, 27.5% to the central, and 22% to the
  western. One natural order, Chlaenaceae, is strictly confined to
  Madagascar. "A small proportion of the species are Asian, but not
  African; and the flora of the mountains corresponds closely with that
  of the great ranges of the tropical zone of Africa." "The general plan
  of the flora follows thoroughly the same lines as that of the tropical
  regions of the Old World."

  Among the food-giving plants are rice--the staff of life to the
  majority of the Malagasy--in many varieties, maize, millet, manioc,
  yams, sweet-potatoes, arrowroot, which is largely used by the western
  tribes--as well as numerous vegetables, many of them of foreign
  introduction. The fruits--the majority of which are introduced--are
  the banana, peach, loquat, pineapple, mango, melon, grape, quince,
  plum, apple, mulberry, orange, lemon, citron, guava, Chinese-guava,
  Cape-gooseberry, fig, raspberry, tomato, &c. Several spices are grown,
  including ginger, capsicum, &c.; sugar-cane, coffee, indigo, vanilla,
  tobacco, cotton, hemp, gourds, dye-woods, gums, mulberry and other
  trees and plants for silk-culture, are also among the vegetable
  productions; gum-copal was formerly, and india-rubber is still, an
  important article of export.

_Provinces and Towns._--The island may be divided into districts or
provinces, which in the main indicate tribal divisions. Of these tribal
territories the following may be distinguished, taking them in three
main divisions, from north to south: (1) _Eastern_: Antankàrana,
occupying the northern peninsula; the country of the Bétsimisàraka, who
inhabit a long extent of the coast plains, about 500 m. in length;
parallel with this for about a third of it, and between the two lines of
forest, is the Bézànozàno country. South again are the districts of the
Taimbahòaka, the Taimòro, the Taifàsy and the Taisàka; and at the
south-eastern corner are the Tanòsy. (2) _Central_: the districts of
Tsimihèty and the Sihànaka; Imèrina, the Hòva province; the Bétsiléo;
the Tanàla or foresters; the Bàra; and the emigrant Tanòsy. (3)
_Western_: the people from almost the northern to the southern
extremities of the island are known as Sàkalàva, but consist of a number
of distinct tribes--the Tibòina, the Màilaka, the Taménabé, and the
Fiherènana, &c. South of these last are the Màhafàly, with the Tandròy
at the extreme south. There are no distinctly marked boundaries between
any of these tribal territories; and west of Imèrina and Bétsiléo there
is a considerable extent of country with hardly any population, a kind
of "no-man's-land." There are numerous subdivisions of most of the
tribes.

The capital, Antanànarìvo (pop. 69,000), in the highlands of Imèrina,
and Tamatàve (pop. 4600), on the east coast and the chief seaport, are
separately described. Majunga (properly Mojangà, pop. 5300) on the
north-west coast, just north of 16° S., and Diégo-Suarez, are important
ports for foreign trade, the latter being also a fortified naval and
military station. Other ports and towns are Màhanòro, Mànanjàry (S.E.
coast, pop. 4500), Tullear (S.W. coast), and Fianàrantsòa (pop. 6200),
the chief town of the Bétsiléo. There are very few places besides these
with as many as 2000 people.

_Inhabitants._--The population is somewhat under two and three-quarter
millions,[6] including some 10,000 or 11,000 Europeans, and a smaller
number of Indian, Arab, and other Asiatics, mostly small traders found
in the seaports, the Chinese being found in every town of any size. The
island, it will be seen, is very sparsely inhabited; the most densely
peopled province is that of Imèrina with (1905) 388,000 inhabitants. The
natives, collectively known as Malagasy, are divided into a considerable
number of tribes, each having its distinct customs. Although
geographically an African island, the majority of its inhabitants are
derived, the lighter portion of them from the Malayo-Polynesian stock,
and the darker races from the Melanesian. This is inferred from their
similarity to the peoples of the Indian and Pacific archipelagoes in
their physical appearance, mental habits, customs, and, above all, in
their language. Their traditions also point in the same direction. There
is, however, an undoubted African mixture in the western and some other
tribes. There is also an Arab element both on the north-west and
south-east coasts; and it appears that most of the families of the
ruling classes in all parts of the island are descended from Arabs, who
married native women. It is believed that there are traces of an
aboriginal people (the Vazimba), who occupied portions of the interior
before the advent of the present inhabitants, and these appear to have
been a somewhat dwarfish race, and lighter-coloured than the Malagasy
generally. The Hòva became the dominant tribe from the beginning of the
19th century; they appear to be the latest immigrants, and are the
lightest in colour; and they are also the most intelligent and civilized
of all the peoples inhabiting the island.

The most striking proof of the virtual unity of the inhabitants of
Madagascar is that substantially but one language is spoken over the
whole country. The Malay affinities of Malagasy were noted in the 16th
century; indeed, the second and fifth books published upon the country
(in 1603 and 1613) were comparative vocabularies of these two languages.
Later investigations have confirmed the conclusions thus early arrived
at; and Van der Tuuk, Marre de Marin and W. E. Cousins have shown
conclusively the close relationships between the language of the
Malagasy and those of the Malayo-Polynesian regions; similar connexions
exist, especially in grammatical construction, between the Malagasy and
Melanesian languages. The Malagasy had never invented for themselves a
written character, and had consequently no manuscripts, inscriptions or
books, until their language was reduced to writing, and its orthography
settled by English missionaries. Their speech nevertheless is very full
in many of its verbal and other forms, while it also exhibits some
curious deficiencies. It is very soft and musical, full of vowels and
liquids, and free from all harsh gutturals. Native oratory abounds in
figures, metaphors and parables; and a large number of folk-tales, songs
and legends, together with the very numerous proverbs, give ample
evidence of the mental ability and imaginative powers of the Malagasy.

  Native society in Imèrina among the Hòva was formerly divided into
  three great classes: the Andrìana, or nobles; the Hòva, freemen or
  commoners; and the Andèvo, or slaves; but these last became free by a
  proclamation issued in 1896. The Andrìana are, strictly speaking,
  royal clans, being descendants of petty kings who were conquered or
  otherwise lost their authority through the increasing power of the
  ancestors of the reigning family. Their descendants retained certain
  honours in virtue of their royal origin, such as special terms of
  salutation, the use of the smaller scarlet umbrella (the larger one
  was the mark of royal rank), the right to build a particular kind of
  tomb, &c.; they also enjoyed exemption from certain government
  service, and from some punishments for crime. The Hòva[7] or commoners
  form the mass of the population of Imèrina. They are composed of a
  large number of tribes, who usually intermarry strictly among
  themselves, as indeed do families, so that property and land may be
  kept together. The third great division was the slave population,
  which since 1896 has become merged in the mass of the people. The
  Mozambiques or African slaves, who had been brought from the African
  coast by Arab dhows, were in 1877 formally set free by an agreement
  with the British government.

  Royalty and chieftainship in Madagascar had many peculiar customs. It
  had a semi-sacred character; the chief was, in heathen tribes, while
  living, the high priest for his people, and after death, was
  worshipped as a god; in its modern development among the Hòva
  sovereigns it gathered round it much state and ceremony. There were
  many curious examples of the taboo with regard to actions connected
  with royalty, and also in the words used which relate to Malagasy
  sovereigns and their surroundings. These were particularly seen in
  everything having to do with the burial of a monarch. While the
  foregoing description of native society applied chiefly to the people
  of the central province of Imèrina, it is applicable, with local
  modifications, to most of the Malagasy tribes. But on the island
  becoming a French colony, in 1896, royalty was formally abolished; and
  little regard is paid to native rank by French officials.

  The chief employment of the Malagasy is agriculture. In the
  cultivation of rice they show very great ingenuity, the _kètsa_
  grounds, where the rice is sown before transplanting, being formed
  either on the margins of the streams or in the hollows of the hills in
  a series of terraces, to which water is often conducted from a
  considerable distance. In this agricultural engineering no people
  surpass the Bétsiléo. No plough is used, all work being done by a
  long-handled spade; and oxen are only employed to tread out the soft
  mud preparatory to transplanting. The rice is threshed by being beaten
  in bundles on stones set upright on the threshing-floor; and when
  beaten out the grain is stored by the Hòva in rice-pits dug in the
  hard red soil, but by the coast tribes in small timber houses raised
  on posts. In preparing the rice for use it is pounded in a wooden
  mortar to remove the husk, this work being almost always done by the
  women. The manioc root is also largely consumed, together with several
  other roots and vegetables; but little animal foods (save fish and
  freshwater _Crustacea_) is taken by the mass of the people except at
  festival times. Rice is used less by the western tribes than by those
  of the central and eastern provinces, and the former people are more
  nomadic in their habits than are the others. Large herds of fine
  humped cattle are found almost all over the island.

  The central and eastern peoples have considerable manual dexterity.
  The women spin and weave, and with the rudest appliances manufacture a
  variety of strong and durable cloths of silk, cotton and hemp, and of
  ròfia palm, aloe and banana fibre, of elegant patterns, and often with
  much taste in colour. They also make from straw and papyrus peel
  strong and beautiful mats and baskets in great variety, some of much
  fineness and delicacy, and also hats resembling those of Panama. The
  people of the south and south-east make large use of soft rush matting
  for covering, and they also prepare a rough cloth of bark. Their
  non-employment of skins for clothing is a marked distinction between
  the Malagasy and the South African races, and their use of vegetable
  fibres an equally strong link between them and the Polynesian peoples.
  The men wear a loincloth or _salàka_, the women a _kitàmby_ or apron
  folded round the body from waist to heel, to which a jacket or dress
  is usually added; both sexes use over these the _làmba_, a large
  square of cloth folded round the body something like the Roman toga,
  and which is the characteristic native dress. The Malagasy are skilful
  in metal-working; with a few rude-looking tools they manufacture
  silver chains of great fineness, and filagree ornaments both of gold
  and silver. Their iron-work is of excellent quality, and in copper and
  brass they can produce copies of anything made by Europeans. They
  display considerable inventive power, and they are exceedingly quick
  to adopt new ideas from Europeans.

  There is a considerable variety in the houses of the different
  Malagasy tribes. The majority of Hòva houses were formerly built of
  layers of the hard red soil of the country, with high-pitched roofs
  thatched with grass or rush; while the chiefs and wealthy people had
  houses of framed timber, with massive upright planking, and lofty
  roofs covered with shingles or tiles. But the introduction of
  sun-dried and burnt bricks, and of roofing tiles in the central
  provinces has led to the general use of these materials in the
  building of houses, large numbers of which are made in two storeys and
  in European fashion. The forest and coast tribes make their dwellings
  chiefly of wood framing filled in with the leaf-stalks of the
  traveller's tree, with the leaves themselves forming the roof
  covering. The houses of the Bétsiléo and Sàkalàva are very small and
  dirty, but those of the coast peoples are more cleanly and roomy.
  Among the Hòva and Bétsiléo the old villages were always built for
  security on the summits of lofty hills, around which were dug several
  deep fosses, one within the other. In other districts the villages and
  homesteads are enclosed within formidable defences of prickly-pear or
  thorny mimosa.

  Apart from the modern influence of religious teaching, the people are
  very immoral and untruthful, disregardful of human life and suffering,
  and cruel in war. Until lately polygamy has been common among all the
  Malagasy tribes, and divorce effected in an absurdly easy fashion. At
  the same time the position of woman is much higher in Madagascar than
  in most heathen countries; and, the fact that for nearly seventy years
  there were (with a few months' exception) only female sovereigns,
  helped to give women considerable influence in native society. The
  southern and western peoples still practise infanticide as regards
  children born on several unlucky days in each month. This was formerly
  the general practice all over the island. The old laws among the Hòva
  were very barbarous in their punishments, and death in various cruel
  forms was inflicted for very trifling offences. Drunkenness is very
  prevalent in many parts of the island; and it can hardly be said of
  many of the Malagasy that they are very industrious. But they are
  courageous and loyal to their chiefs and tribe, and for short periods
  are capable of much strenuous exertion. They are affectionate and firm
  in their friendships, kind to their children and their aged and infirm
  relatives, very respectful to old age, most courteous and polite and
  very hospitable to strangers. Slavery had a patriarchal and family
  character, and was seldom exercised in a cruel or oppressive way.

  The Malagasy have never had any organized religious system or forms of
  worship; there are no temples, images or stated seasons of devotion,
  nor is there a priesthood, properly so-called. Yet they have never
  been without some distinct recognition of a supreme being, whom they
  call _Andriamànitra_, "The Fragrant One," and _Zànahàry_, "The
  Creator"--words which are recognized all over the island. They have
  also retained many ancient sayings, proverbial in their style, which
  enforce many of the truths of natural religion as to the attributes of
  God. With all this, however, there has long existed a kind of
  idolatry, which in its origin is simply fetishism--the belief in
  charms--as having power to procure various benefits and protect from
  certain evils. Among the Hòva in modern times four or five of these
  charms had acquired special sanctity and were each honoured as a kind
  of national deity, being called "god," and brought out on all public
  occasions. Together with this idolatry there is also a firm belief in
  the power of witchcraft and sorcery, in divination, in lucky and
  unlucky days and times, in ancestor worship, especially that of the
  sovereign's predecessors, and in several curious ordeals for the
  detection of crime. The chief of these was the celebrated tangèna
  poison ordeal, in which there was implicit belief, and by which, until
  its prohibition by an article in the Anglo-Malagasy treaty of 1865,
  thousands of persons perished every year. Sacrifices of fowls and
  sheep are made at many places at sacred stones and altars, both in
  thanksgiving at times of harvest, &c., and as propitiatory offerings.
  Blood and fat are used to anoint many of these stones, as well as the
  tombs of ancestors, and especially those of the Vazimba. In some of
  the southern districts it is said that human sacrifices were
  occasionally offered. The chief festival among the Hòva, and almost
  confined to them, was that of the New Year, at which time a kind of
  sacrificial killing of oxen took place, and a ceremonial bathing, from
  which the festival took its name of Fàndròana (the Bath). This
  festival is now merged in the French national fête of the 14th of
  July. Another great festival was at circumcision times. This rite was
  observed by royal command at intervals of a few years; these were
  occasions of great rejoicing, but also of much drunkenness and
  licentiousness. Since 1868 circumcision has been observed by each
  family at any time convenient to itself. It is practised by all the
  Malagasy tribes. Funerals were also times of much feasting, and at the
  death of people of rank and wealth numbers of bullocks were and are
  still killed. Although there was no proper priesthood, the
  idol-keepers, the diviners, the day-declarers and some others formed a
  class of people closely connected with heathen customs and interested
  in their continued observance.

_Industries and Commerce._--The rearing of cattle and the dressing of
hides, the collection of rubber and bee culture are important
industries. The chief food crops grown have been indicated (see
_Flora_), and the gold-mining is separately noticed below. Other
industries undertaken or developed by Europeans are silk and cotton
weaving and raphia-fibre preparation, and ostrich farming. Sugar, rice,
soap and other factories have been established. In 1904 the exportation
of straw and other fibre hats began; these resemble those of Panama and
promise to become an important item. Tanning bark, coffee and guano are
also recent exports.

Since 1862, when the country was thrown open to foreign trade, the
growth of over-sea commerce has been comparatively slow. In the early
days cattle were the chief export. About 1870 india-rubber began to be
exported in considerable quantities, and cattle, rubber and hides
continue staple products. Other important exports are raphia fibre and
beeswax. Since 1900 gold has become a leading export, the value of the
gold sent out of the country in the five years 1901-1906 being
£1,384,493. The imports consist chiefly of tissues (mostly cotton
goods), breadstuffs and rice, liquors, metal-ware and coal. Better means
of internal transport and increased production in the island have
greatly reduced the import of rice, which came mostly from Saigon.

Before the occupation of Madagascar by France the duty on imports and
exports was 10% _ad valorem_, and the foreign trade was very largely in
the hands of British and American merchants. In July 1897 the French
tariff was applied and increased rates levied on foreign goods, notably
cottons. This practically killed the American trade and reduced the
British trade to a very small proportion. In 1897 the British imports
were valued at £179,000; the next year, with the new tariff in force,
they had dropped to £42,000. The only export duties are: cattle 2s. per
head and rubber 2d. per lb.

In 1880-1885 the entire foreign trade of Madagascar, imports and
exports, was estimated to be about £1,000,000; in 1900-1906 the volume
of trade had increased to a little over £2,500,000 a year. But while
from 1900 onwards imports had a tendency to decrease (they were
£1,841,310 in 1901 and £1,247,936 in 1905), exports steadily increased,
owing to the working of gold-mines. The total value of the exports rose
from £359,019 in 1901 to £822,470 in 1906.[1] About 90% of the trade is
with France or other French colonies. The remaining trade is nearly all
British and German.

Banking business is in the hands of French companies. The legal currency
is the French 5-franc piece and the smaller French coins. There was no
native coinage, the French 5-franc piece or dollar being the standard,
and all sums under that amount were obtained by cutting up those coins
into all shapes and sizes, which were weighed with small weights and
scales into halves, quarters, eighths, twelfths and twenty-fourths of a
dollar, and even reckoned down to the seven hundred and twentieth
fraction of the same amount.

  _Gold-mining._--Gold-mining has been carried on regularly since 1897,
  and by 1900 the value of the ore extracted exceeded £100,000. Reports
  of rich discoveries attracted considerable attention in South Africa
  and Europe during 1904-1906, but experts, sent from the Transvaal,
  came to the conclusion that Madagascar would not become one of the
  rich goldfields of the world. The chief mining districts have been
  already indicated (see under _Geology_). Rich finds were reported from
  the north of the island during 1907, in which year the export of gold
  was £320,000. The mines afford a lucrative occupation for some
  thousands of persons, and many of the claim-holders are British.
  Decrees of 1902 and 1905 regulate the conditions under which mining is
  carried on. By decree of the 23rd of May 1907, the radius of the
  circle within which claims may be pegged is 2 kilometres (1¼ m.), and
  a tax of 5% is levied on the value of the gold extracted.

  _Communications._--There is regular steamship communication between
  the chief ports and Marseilles, Zanzibar and India (via Mauritius and
  Ceylon); and a submarine cable to Mozambique places the island in
  telegraphic connexion with the rest of the world. The French have
  built carriage roads from the interior to the principal ports as well
  as to connect the principal towns. On these roads large use is made of
  bullock wagons, as well as carts drawn by men, and women also.
  Tamatàve and Antanànarìvo are joined by coast canals and lakes and by
  a railway service. Where other means are not available, goods are
  carried by canoes, or on the shoulders of bearers along the native
  footpaths.

  There is a well-organized postal service, and all the towns of note
  are linked by a telegraph system, which has a length of over 4000
  miles.

_Government, Revenue, &c._--The colony is not represented in the French
Chambers, nor has it self-government. At the head of the administration
is a governor-general, who is assisted by a nominated council of
administration which includes unofficial members. This council must be
consulted on matters affecting the budget. In several towns there are
_chambres consultatives_, composed of local merchants and planters. The
island is divided into _circles_, placed under military officers, and
_provinces_, presided over by a civilian. As far as possible in local
affairs, each of the native races is granted autonomy, the dominion of
the Hòva over the other tribes being abolished. Each province has its
native governor and minor officials, the governor being generally
selected by popular vote. Each village has an organization (the _Fòkon'
òlona_) resembling that of a commune; at its head is a chief or
_mpiadidy_, who serves for three years.

    +-----------------+---------+----------+----------+
    |     Exports:    |   1901  |   1906   | Increase.|
    +-----------------+---------+----------+----------+
    | Rubber          | £26,679 | £301,518 | £274,839 |
    | Hides and skins |  31,548 |  250,339 |  218,791 |
    | Gold            | 131,987 |  270,613 |  138,626 |
    +-----------------+---------+----------+----------+

  For Europeans and in suits between Europeans and natives the French
  judicial code is applicable; suits between natives are tried by native
  tribunals (established 1898) presided over by a European assisted by
  two native assessors. These tribunals judge according to native law
  and usages, except when such customs (e.g. polygamy and slavery) have
  been expressly abolished. Arbitration councils are available
  everywhere for the settlement of disputes between native workmen and
  their employers. The native laws respecting land tenure have been
  improved by the adoption of a method of registration based on the
  Torrens system.

  Revenue is derived from land, house and capitation taxes, from
  customs, posts and telegraphs, ferries, licences and other indirect
  imposts. The excess of expenditure over revenue is made good by
  subventions from France. A considerable portion of the revenue is
  expended on public works. Revenue and expenditure in 1905 were each
  just beneath £1,000,000. This is exclusive of the sums spent by France
  in the island on the army, and for the naval base at Diégo-Suarez.
  There is a public debt amounting (1907) to £4,055,600. As stated in
  the French senate (February 1909), everything is taxed in the island;
  and no sooner has any enterprise become fairly successful than it is
  so heavily taxed as to be no longer worth carrying on, and certain
  crops have therefore been destroyed by the colonists who had planted
  them. This has been the case with tobacco, sugar, rum, and also in
  butter-making, cattle-breeding and other things. Notwithstanding this
  taxation, from 1895 to 1908 £12,000,000 was required for Madagascar
  from the home government, and the demand is constantly increasing.

_History._--From the earliest accounts given of the people of Madagascar
by European travellers, as well as from what may be inferred from their
present condition, they seem for many centuries to have been divided
into a number of tribes, often separated from one another by a wide
extent of uninhabited country. Each of these was under its own chief,
and was often at war with its neighbours. No one tribe seems to have
gained any great ascendancy over the rest until about the middle of the
17th century, when a small but warlike people called Sàkalàva, in the
south-west of Madagascar, advanced northward, conquered all the
inhabitants of the western half of the island, as well as some northern
and central tribes, and eventually founded two kingdoms which retained
their supremacy until the close of the 18th century. About that time,
the Hòva in the central province of Imèrina began to assert their own
position under two warlike and energetic chieftains, Andrianimpòina and
his son Radàma; they threw off the Sàkalàva authority, and after several
wars obtained a nominal allegiance from them; they also conquered the
surrounding tribes, and so made themselves virtual kings of Madagascar.
From that time until 1895 Hòva authority was retained over a large part
of the central and eastern provinces, but it was only nominal over much
of the western side of the island, while in the south-west the people
were quite independent and governed by their own chiefs.


  Arab Intercourse and Influence.

While European intercourse with Madagascar is comparatively recent, the
connexion of the Arabs with the island dates from a very remote epoch;
and in very early times settlements were formed both on the north-west
and south-east coasts. In the latter locality there are still traces of
their influence in the knowledge of Arabic possessed by a few of the
people. But in these provinces they have become merged in the general
mass of the people. It is different, however, in the north-west and west
of the island. Here are several large Arab colonies, occupying the ports
of Anòrontsànga, Mòjangà, Màrovoày and Mòrondàva, and retaining their
distinct nationality. There is also in these districts a Hindu element
in the population, for intercourse has also been maintained for some
centuries between India and northern Madagascar, and in some towns the
Banyan Indian element is as prominent as the Arab element. In the early
times of their intercourse with Madagascar, the Arabs had a very
powerful influence upon the Malagasy. This is seen in the number of
words derived from the Arabic in the native language. Among these are
the names of the months and the days of the week, those used in
astrology and divination, some forms of salutation, words for dress and
bedding, money, musical instruments, books and writings, together with a
number of miscellaneous terms.


  European Intercourse.

The island is mentioned by several of the early Arabic writers and
geographers, but medieval maps show curious ignorance of its size and
position. Marco Polo has a chapter upon it, and terms it "Madeigascar,"
but his accounts are confused with those of the mainland of Africa. The
first European voyager who saw Madagascar was a Portuguese named Diogo
Diaz, captain of one of the ships of a fleet commanded by Pedro Cabral
and bound for India. Separated from his companions by a storm near the
Cape, he sighted the eastern coast of the island on the 10th of August
1500. That day being the feast of St Lawrence, Madagascar was named the
"Isle of St Lawrence," and retained that name on all maps and charts for
a hundred years. The Portuguese gave names to most of the capes, but
made no persistent attempts at colonization. After them the Dutch
endeavoured, but with little success, to form colonies; and in the time
of Charles I. proposals were made to form an English "plantation," but
these were never carried into effect, although for a short time there
was a settlement formed on the south-west coast. In the latter part of
the 17th and during most of the 18th century the French attempted to
establish military positions on the east coast. For some time they held
the extreme south-east point of the island at Fort Dauphin; but several
of their commandants were so incapable and tyrannical that they were
frequently involved in war with the people, and more than once their
stations were destroyed and the French were massacred. Early in the 19th
century all their positions on the mainland were relinquished, and they
retained nothing but the island of Ste Marie on the east coast. In 1811
Tamatàve had been occupied by British troops, and the Treaty of Paris of
1814 recognized as British the "French settlements in Madagascar," but
as a matter of fact France had then no settlements on the mainland. The
then governor of Mauritius, Sir Robert Farquhar, endeavoured to
prosecute British claims and obtained a cession of Diégo-Suarez Bay.
These claims were not backed up by the home government, and a little
later the policy was adopted by Great Britain of supporting the Hòva
authority.


  Radàma I.

  Introduction of Christianity.

The political history of Madagascar as a whole may be said to date from
the reign of Radàma I. (1810-1828). He was a man much in advance of his
age--shrewd, enterprising, and undeterred by difficulty--a kind of Peter
the Great of his time. He saw that it was necessary for his people to be
educated and civilized if the country was to progress; and making a
treaty with the governor of Mauritius to abolish the export of slaves,
he received every year in compensation a subsidy of arms, ammunition,
and uniforms, as well as English training for his troops. He was thus
enabled to establish his authority over a large portion of the island.
For some years a British agent, Mr Hastie, resided at Radàma's court,
and exercised a powerful influence over the king, doing much for the
material advance of the country. At the same period (1820) Christian
teaching was commenced in the capital by the London Missionary Society,
and by its missionaries the language was reduced to a systematic written
form, and the art of printing introduced; books were prepared, the
Scriptures were translated, numerous schools were formed, and several
Christian congregations were gathered together. The knowledge of many of
the useful arts was also imparted, and many valuable natural productions
were discovered. The power of superstition was greatly broken, a result
partly due to the keen good sense of the king, but chiefly to the spread
of knowledge and religious teaching.


  Rànavàlona I.

The bright prospects thus opening up were clouded by the death of Radàma
at the age of thirty-six, and the seizure of the royal authority by one
of his wives, the Princess Rànavàlona. She looked with much suspicion
upon the ideas then gaining power among many of her people, and
determined to strike a decisive blow at the new teaching. In 1835 the
profession of the Christian religion was declared illegal; all worship
was to cease, and all religious books were ordered to be given up. By
the middle of 1836 all the English missionaries were obliged to leave
the island, and for twenty-five years the most strenuous efforts were
made by the queen and her government to suppress all opposition to her
commands. This, however, only served to show in a very remarkable manner
the courage and faith of the Christian Malagasy, of whom about two
hundred suffered death in various cruel forms, while many hundreds were
punished more or less severely by fine, degradation, imprisonment and
slavery. During the queen's reign the political condition of the country
was deplorable; there were frequent rebellions, many of the distant
provinces were desolated by barbarous wars; and for some years all
Europeans were excluded, and foreign commerce almost ceased. This last
circumstance was partly owing to an ill-managed attack upon Tamatàve in
1846 by a combined British and French force, made to redress the wrongs
inflicted upon the foreign traders of that port. But for the leaven of
Christianity and education which had been introduced into the country it
would have reverted to a state of barbarism.


  Radàma II.

This reign of terror was brought to a close in 1861 by the death of the
queen and the accession of her son Radàma II. The island was reopened to
European trade, and missionary efforts were recommenced. A determined
attempt was made by some Frenchmen to gain for their country an
overwhelming influence by means of a treaty which they induced the king
to sign. But this act, as well as the vices and insane follies into
which he was led by worthless foreign and native favourites, soon
brought his reign and his life to an end. He was put to death in his
palace (1863) and his wife was placed on the throne. The new sovereign
and her government refused to ratify the agreement which had been
illegally obtained, choosing rather to pay a million francs as
compensation to the French company. During the five years' reign of
Queen Rasohérina, quiet and steady advances were made in civilization
and education, and treaties were concluded with the British, French and
American governments.


  Rànavàlona II.

At the death of Rasohérina in 1868, she was succeeded by her cousin,
Rànavàlona II. One of the first acts of the new queen was the public
recognition of Christianity; and very soon afterwards she and her
husband, the prime minister, were baptized, and the erection of a chapel
royal was commenced in the palace yard. These acts were followed in the
succeeding year by the burning of the royal idols, and immediately
afterwards by the destruction of the idols throughout the central
provinces, the people generally putting themselves under Christian
instruction. From that time education and enlightenment made great
progress, chiefly through the labours of missionaries of various
societies.


  Native Government.

The native Malagasy government, though theoretically despotic, was
limited in various ways. Radàma I. and Rànavàlona I. were much more
absolute sovereigns than those before or after them, but even they were
largely restrained by public opinion. New laws were announced at large
assemblies of the people, whose consent was asked, and always given
through the headmen of the different divisions of native society; this
custom was no doubt a survival from a time when the popular assent was
not a merely formal act. The large disciplined army formed by Radàma I.
aided much in changing what was formerly a somewhat limited monarchy
into an absolute one. The Hòva queen's authority was maintained over the
central and eastern portions of Madagascar, and at almost all the ports,
by governors appointed by the queen, and supported by small garrisons of
Hòva troops. At the same time the chiefs of the various tribes were left
in possession of a good deal of their former honours and influence.
Rànavàlona II., her predecessor and her successor were successively
married to the prime minister, Ràinilaiàrivòny, a man of great ability
and sagacity, who, by his position as husband and chief adviser of the
sovereign, became virtual ruler of the country. Chiefly owing to his
influence, many measures tending to improve the administration were
introduced. The Hòva army was estimated at from 30,000 to 40,000 men,
several English non-commissioned officers and, latterly, others of
higher rank being engaged to train them in European methods. Revenue was
derived from customs duties, firstfruits, fines and confiscation of
offenders' property, and a money offering called _hàsina_, presented on
a great variety of occasions both to the sovereign in person and to her
representatives; and these were supplemented by "benevolences" (in the
medieval sense of the word) levied upon the people for occasional state
necessities. The government also claimed the unpaid service of all
classes of the community for every kind of public work.


  Foreign Relations.

The Hòva government aspired to have Madagascar recognized as an
independent civilized state, and consuls appointed by the British,
French and American governments were accredited to the Malagasy
sovereign, the queen having a consul in England, and a consular agent at
Mauritius. The treaty with Great Britain, concluded in 1865, gave the
consuls of that nation jurisdiction over the British subjects in the
island. At this period, on the initiative of the 4th earl of Clarendon,
then foreign secretary, an understanding was come to between the British
and French governments by which it was agreed that each power should
respect the independence of Madagascar; and the future of the country
appeared to be bound up in the gradual consolidation of the central Hòva
authority over the whole island. While this prospect would have
satisfied the British interests in the island, it was otherwise with the
French. The tradition of their former settlements in and influence over
the island was strong; in 1840 they had taken under their protection the
Sàkalàva ruler of the small island of Nossi-bé, off the north-west
coast, and in virtue of that act claimed a vague protectorate over the
adjacent shores of the mainland. A treaty, concluded in 1868, while
establishing French consular jurisdiction in Madagascar, recognized
Rànavàlona II. as queen of Madagascar, and under the Second Empire
attempts to establish French political influence were discouraged, and
even as late as 1872 the subsidy enjoyed by the Jesuit missionaries was
withdrawn. In 1878 the French consul, Laborde, died, and a dispute arose
as to the disposal of his property. This dispute was the occasion of
further intervention on the part of the French, for the Paris government
supported the claims of Laborde's heirs, and revived their claim to a
protectorate over the Sàkalàva of the north-west coast, as based on
their agreement with them in 1840, ceding Nossi-bé to France. A policy
of colonial expansion generally, and in Africa in particular at this
time, was manifest in France, as in other European countries, and the
French claims on the Hòva were pressed with vigour.


  Franco-Malagasy War of 1883-85.

  French Protectorate, 1885-1894.

  French Invasion and Conquest, 1895.

Towards the middle of 1882 the relations between the native government
and that of France became much strained, and to settle, if possible,
these causes of dispute, two Hòva officers of high rank were sent to
France as ambassadors, but as they were not authorized to concede any
territory, their visit accomplished very little. Treaties had been
concluded with Great Britain, Germany and America, giving improved
facilities for trade with Madagascar, but before the return of the
envoys matters had come to a crisis in the island. In May 1883 an
ultimatum was sent to the Malagasy queen, requiring immediate compliance
with the demands of France; and as these were refused by the Hòva
government, Tamatàve was bombarded by a French squadron and then
occupied by the marines. The war continued in a desultory fashion for
many months; but no serious attempt was made to invade the interior; and
in 1885 terms of peace were agreed to. By a treaty signed on the 17th of
December it was agreed that the foreign relations of Madagascar should
be directed by France; that a resident should live at the capital, with
a small guard of French soldiers; and that the Bay of Diégo-Suarez,
together with surrounding territory, should be ceded to France. The word
"protectorate" was carefully excluded from the treaty, although
doubtless the French envoys intended that this should be its practical
issue. It was at the same time agreed that there should be no foreign
interference with the internal government of the country, and that the
queen should retain her former position, with all its honours and
dignity. It should be here noticed that the queen, Rànavàlona II., died
just at the beginning of the war, on the 13th of July 1883, and was
succeeded by her niece, Princess Razàfindrahèty, under the title of
Rànavàlona III., who maintained the same policy as her predecessor, and
was much beloved by her people and respected by all. Several French
residents successively represented France at Antanànarìvo; but these
found themselves unable to obtain that influence which the home
authorities thought they had a right to demand. Although the British
government, in return for concessions in Zanzibar, had consented, in
1890, to recognize a French protectorate over Madagascar, the Malagasy
prime minister, Ràinilaiàrivòny, was not disposed to give any advantage
to France and continued to arm and train, by the help of British
officers, a large body of native soldiers. This state of tension and
irritation could not last, and at length, towards the close of 1894, the
French government sent an ultimatum to the Malagasy sovereign, demanding
such powers as would have made French authority supreme in the island.
These demands were refused by the native government, and other
conditions were offered; but the French envoy, together with the
resident's escort, left the capital, as also did the French traders and
others, including the large Jesuit mission. As soon as these had left
the island, the chief ports were occupied by French troops, and an
expeditionary force under General Duchesne was afterwards landed on the
north-west coast at Mòjangà--commonly, but incorrectly, written
Majunga--with the object of breaking the Hòva authority. Owing to the
necessity of making a road for the passage of artillery and military
stores, many months were spent on the march into the interior, and there
was considerable loss of life by fever and other disease among the
invading troops. But no effectual resistance was made by the Malagasy,
and at length, on the 30th of September 1895, the French forces appeared
on the heights north and east of Antanànarìvo, bombarded the city, which
surrendered in the afternoon, and on the evening of the same day the
French entered the capital.


  Rebellion of 1896, and Gradual Subjection of the Malagasy.

The result was that the protectorate of France was re-established in the
central provinces, but the queen was allowed to retain her position.
Early in 1896, however, a serious rebellion broke out in several parts
of Imèrina. This movement was not only anti-French and anti-foreign, but
also distinctly anti-Christian. The French troops gradually broke up the
power of the rebellion in the central provinces, but as there appeared
to be considerable unrest in many other parts of the island, General
Gallieni, an officer with a reputation for vigour and ability in the
Sudan and Tongking campaigns, was sent out to relieve the then
resident-general.


  Administration of General Gallieni.

General Gallieni had a difficult task in establishing the authority of
France throughout the island among numbers of tribes who had never
submitted to any control from others. Among the first steps he took were
to put the country under martial law, to abolish royalty and all
semblance of Hòva government, and to declare Madagascar to be henceforth
a colony of France. Queen Rànavàlona III. was exiled to Réunion, and
subsequently to Algeria. Meanwhile carriage roads were commenced to
connect all the chief centres, and the military posts were gradually
extended so as to consolidate French rule over all the outlying tribes.
French residents and numerous other officials were placed at every
important town, and various projects were started for the civilization
of the Malagasy in accordance with French ideas. At the close of 1899,
General Gallieni was able to report that only portions of the west and
south-west remained to be brought into submission. Not long afterwards
the authority of France was recognized throughout the island. General
Gallieni, whose firm and vigorous administration, and desire to treat
the Malagasy justly and kindly, made him liked by the people, retired in
1905, and was succeeded in that office by M. Victor Augagneur, late
mayor of Lyons. Since the French occupation the Malagasy have conformed
pretty readily to the new order of things, although many of the most
intelligent Hòva deeply regret that their country did not retain its
independence. Justice is administered, on the whole, with fairness and
impartiality; but the taxation seems too heavy for the means of the
people, indeed it is affirmed by trustworthy natives that the well-to-do
classes are being gradually drained of their property. To an outsider it
also appears that the staff of officials is very largely in excess of
any real needs of administration; several monopolies, which interfere
with the habits of the people, tend to produce discontent; and the
taking of their land and houses for public works, roads, &c., while but
a mere fraction of their real value is allowed as compensation, does not
help to increase their acquiescence in foreign control. But the most
serious cause for dislike to government action was the interference by
the governor-general, in 1907, with their religious customs, by the
suppression of hundreds of their congregational schools, and the closing
of numbers of their churches. In July 1910 M. Augagneur was replaced as
governor-general by N. Picquié, a prominent official of the Colonial
Department, who had previously served with acceptance as deputy
governor-general of French Indo-China, and who had a reputation for tact
and impartiality.

  _Christian Missions and Education._--As already noticed, the Malagasy
  owe to missionaries of the London Missionary Society their first
  school system and their first literature, in 1820 and subsequent
  years;[8] and for fifteen years all educational work was carried on by
  them, some 10,000 to 12,000 children having been instructed in their
  schools. On the reopening of the country to Europeans in 1862, the
  L.M.S. mission was resumed and was carried on with vigour for several
  years, stations being formed in several parts of Imèrina, in the
  Bétsiléo and Antsihànaka provinces, and at the ports of Tamatàve,
  Majunga and Fàrafangàna (south-east coast). In 1890 the number of
  their churches was 1220; adherents, 248,000; and scholars, 68,000; so
  that for long the greater part of the educational work was in their
  hands, carried on not only in primary schools, but also in high
  schools and colleges. In 1863 the Church of England began work in the
  island through the Society for the Propagation of the Gospel and the
  Church Missionary Society. After some time, however, the latter
  society withdrew, leaving the field to the S.P.G. A bishop is
  stationed in the capital, with a theological college in its
  neighbourhood, but the chief work of the Anglican mission is on the
  east coast. In 1866 the Norwegian Lutheran Society began work in
  Madagascar, and was joined in 1888 by an American Lutheran Society.
  With a representative church at the capital, the chief work of these
  missions is in the Vàkinankàratra district (south-west of Imèrina), in
  the Bétsiléo province, and on the south-east and south-west coasts; in
  these places they have a large number of converts and (until lately)
  schools. In 1867 a mission was begun by the Society of Friends, who
  gave great attention to education and literary work, and afterwards
  took up as their field of labour the western and south-western parts
  of Imèrina, where they have a large and well-organized mission.
  Immediately after the island became a French possession the French
  Protestant Churches began (in 1896) to take part in the evangelizing
  of their new colony, and about half the area for long occupied by the
  London Missionary Society was transferred to the Paris Society. The
  bulk of the Malagasy Christians are Protestants, probably
  three-fourths or four-fifths of those professing Christianity. A Roman
  Catholic (Jesuit) mission was begun in 1861, and a large force of
  priests with a bishop and lay brethren and sisters engaged in
  education, have been at work in the island since then, except during
  the two Franco-Malagasy wars.[9] Since the French conquest, the north
  of the island has been occupied by a mission of priests of the Saint
  Esprit, and the southern portion by the Lazarist mission, each with a
  bishop at its head. The following table gives the statistics of the
  various Protestant missions at the close of 1906:--

    +-------------------+------------+--------+---------+--------+--------+
    |      Mission      |Missionaries|Churches|Adherents| Members|Scholars|
    +-------------------+------------+--------+---------+--------+--------+
    | Lond. Miss. Soc.  |     25     |   630  | 120,000 | 32,000 | 27,000 |
    | Soc. Prop. Gospel.|     15     |   121  |  13,000 |  4,094 |  7,655 |
    | Norweg. Luth.     |     60     |   892  |  84,000 | 71,500 | 38,000 |
    | Am. Luth.         |     14     |    ?   |    ?    |    ?   |    ?   |
    | Soc. of Friends.  |     27     |   178  |  15,000 |  2,540 |  7,122 |
    | French Prot. Miss.|     29     |   491  | 110,660 | 10,500 | 18,200 |
    +-------------------+------------+--------+---------+--------+--------+

  Since 1897 high schools, and medical and technical schools, and a few
  primary schools, have been formed by the French government; and all
  other schools have been placed under regulations issued by an
  educational department, the scholars being required to learn the
  French language; but until the end of 1906 the bulk of the educational
  work was carried on by the various missions. At that date the
  anti-clerical movement in France began to affect Madagascar. In all
  the missions the churches had, in the vast majority of cases, been
  used as school-houses, but in November 1906 it was strictly forbidden
  to use churches for educational purposes after two months from that
  date; and the effect of the decree, with other provisions, was to
  close hundreds of schools, probably three-fourths of the whole number.

  For many years (1862-1896), all medical aid to the sick, the formation
  of hospitals and dispensaries, the training of native doctors,
  midwives and nurses, and the production of medical literature was
  entirely due to the Protestant missionaries, viz. the London
  Missionary Society, the Friends and the Norwegians. Numbers of young
  men received a full course of medical and surgical training, and were
  awarded diplomas after passing strict examinations. This work is now
  mostly in charge of a government department, and mission medical work
  is much restricted; but for thirty-five years the Malagasy owed all
  such help to the benevolence of European Christians. Besides care for
  the sick in ordinary diseases, asylums for lepers were for many years
  carried on; two by the London Missionary Society, one, a large one,
  with 800 or 900 inmates, by the Norwegian Society, and another by the
  Roman Catholic mission. This last, with one of those of the L.M.S., is
  now taken over by the government.

  AUTHORITIES.--As regards the scientific aspects of the country, almost
  everything of value in previous books and papers is included in the
  magnificent work (1882 et seq.), in 28 4to vols., by Alfred
  Grandidier, entitled _Histoire naturelle, physique, et politique de
  Madagascar_. Many of the volumes consist of coloured lithograph plates
  illustrating the natural history of the country, as well as atlases of
  maps from the earliest period.

  _General_: Étienne de Flacourt, _Histoire de la grande isle
  Madagascar_ (Paris, 1658); _Madagascar, or Robert Drury's Journal
  during Fifteen Years' Captivity on that Island_ (London, 1729; new
  ed., 1890); _Voyages et mémoires de Maurice Auguste, comte de
  Benyowski_ (Paris, 1791); Froberville, _Histoire de Madagascar_ (Isle
  de France, 1809); Ellis, _History of Madagascar_ (London, 1838);
  Guillain, _Documents sur ... la partie occidentale de Madagascar_
  (Paris, 1845); Macé Descartes, _Histoire et géographie de Madagascar_
  (Paris, 1846); Ellis, _Three Visits to Madagascar_ (London, 1859); J.
  Sibree, _Madagascar and its People_ (London, 1870); _Tantara ny
  Andrìana eto Madagascar: Histoire des rois d'Imérina d'après les
  manuscrits malgaches_ (Antanànarìvo, 1875); Mullens, _Twelve Months in
  Madagascar_ (London, 1875); Blanchard, _L'Île de Madagascar_ (Paris,
  1875); Dahle, _Madagaskar og dets Beboere_ (Christiania, 1876-1878);
  Sibree and Baron (eds.), _The Antanànarìvo Annual_, Nos. i-xxiv.
  (1875-1900, pp. 3115); _Notes, reconnaissances, et explorations, revue
  mensuelle_ (Antanànarìvo, 5 vols., 1897-1899, pp. 3041); Sibree, _A
  Madagascar Bibliography_ (Antanànarìvo, 1885); Vaissière, _Histoire de
  Madagascar_ (Paris, 1884), _Vingt ans à Madagascar_ (Paris, 1885);
  Oliver, _Madagascar: an Historical and Descriptive Account_ (2 vols.,
  London, 1886); Cousins, _Madagascar of To-day_ (London, 1895);
  _Bulletin du comité de Madagascar_ (monthly) (Paris, 1895, et seq.);
  Sibree, _Madagascar before the Conquest_ (London, 1896); Catat,
  _Voyage à Madagascar_ (Paris, 1895); _Annuaire de Madagascar_
  (Antanànarìvo, 1898, et seq.); J. S. Gallieni; _Rapport d'ensemble sur
  la situation générale de Madagascar_ (2 vols., Paris, 1899); _Revue de
  Madagascar, mensuelle, illustrée_ (1895, et seq.); _Guide de
  l'immigrant à Madagascar_ (3 vols., with atlas, Paris, 1899);
  _Collection des anciens ouvrages relatifs à Madagascar, par les soins
  du comité de Madagascar_ (a collection and translation of all works
  relating to the island from 1500 to 1800, in 10 vols.), (Paris, 1899
  et seq.); _Bulletin trimestriel de l'académie de Malgache_ (quarterly)
  (Antanànarìvo, 1902 et seq.); G, Grandidier et autres, _Madagascar au
  début du xx^e siècle_ (Paris, 1902); G. Grandidier, _Bibliographie de
  Madagascar_ (2 vols., Paris, 1905 and 1907).

  _Political_: Sibree, "What are 'French Claims' on Madagascar?"
  _Madagascar Tracts_ (1882); Oliver, _True Story of the French Dispute
  in Madagascar_ (London, 1885); Shaw, _Madagascar and France_ (London,
  1885); Saillens, _Nos droits sur Madagascar_ (Paris, 1885); K. Blind
  "The Fictitious French Claim to Madagascar," _Contemp. Rev._ (1894);
  Martineau, _Étude de politique contemporaine. Madagascar_ (Paris,
  1894); Rentier, _Les droits de la France sur Madagascar_ (1895);
  Corlay, _Notre campagne à Madagascar_ (Paris, 1896); Knight,
  _Madagascar in War-time_ (London, 1896); Carol, _Chez les Hovas_
  (Paris, 1898); Gallieni, _Neuf ans à Madagascar_ (Paris, 1908).

  _Philology_: Houtman, _Spraak ende woord boek in de Maleische ende
  Madagaskarsche talen_ (Amsterdam, 1603); _Voyage de C. van Heemskerk;
  vocabulaire de la langue parlée dans l'Île Saint-Laurent_ (Amsterdam,
  1603) Megiser, _Beschreibung der Mechtigen und Weitberhümbten Insul
  Madagascar_, with dictionary and dialogues (Altenburg, 1609); Arthus,
  _Colloquia latino-maleyica et madagascarica_ (Frankfort, 1613);
  Challand, _Vocabulaire français-malgache et malgache-français_ (Île de
  France, 1773); Froberville, _Dictionnaire français-madécasse_ (3
  vols., Île de France, 1809); Freeman and Johns, _Dictionary of the
  Malagasy Language (Eng.-Mal. and Mal.-Eng.)_, (Antanànarìvo, 1835);
  Dalmond, _Vocabulaire et grammaire pour les langues malgaches,
  Sàkalàva et Bétsimisàra_ (Bourbon, 1842); R. C. Missionaries'
  _Dictionnaire français-malgache_ (Réunion, 1853); and _Dictionnaire
  malgache-français_ (Réunion, 1855); Van der Tunk, "Outlines of a
  Grammar of the Malagasy Language," _Jour. Roy. Asiat. Soc._ (1860);
  Ailloud, _Grammaire malgache-hòva_ (Antanànarìvo, 1872); W. E.
  Cousins, _Concise Introduction to the Study of the Malagasy Language
  as spoken in Imèrina_ (Antanànarìvo, 1873); Marre de Marin, _Grammaire
  malgache_ (Paris, 1876); id., _Essai sur le malgache, ou Étude
  comparée des langues javanaise, malgache, et malayse_ (Paris, 1876);
  id., _Le Jardin des racines océaniennes_ (Paris, 1876); Dahle,
  _Specimens of Malagasy Folk-lore_ (Antanànarìvo, 1877); and W. E.
  Cousins, "The Malagasy Language," in _Trans. Phil. Soc._ (1878).
  Besides these there are several valuable papers by Dahle in the yearly
  numbers of The _Antanànarìvo Annual_ (_ante_) (1876-1877); Richardson,
  _A New Malagasy-English Dictionary_ (Antanànarìvo, 1885); Cousins and
  Barrett, _Malagasy Proverbs_ (Antanànarìvo, 1885); Caussèque,
  _Grammaire malgache_ (Antanànarìvo, 1886); Abinal et Malzac,
  _Dictionnaire malgache-français_ (Antanànarìvo, 1889); Brandstetter,
  "Die Beziehungen des Malagasy zum Malaiischen," _Malaio-polynesische
  Forschungen_, pt. 2 (Lucerne, 1893).

  _Missions and Religious History:_ Freeman and Johns, _Narrative of the
  Persecutions of the Christians in Madagascar_ (London, 1840); Prout,
  _Madagascar, its Missions and its Martyrs_ (London, 1863); Ellis,
  _Madagascar Revisited_ (London, 1867); id., _The Martyr Church_
  (London, 1869); "Religion in Madagascar," _Ch. Quar. Rev._ (1878);
  Briggs, _The Madagascar Mission_ (L.M.S. 1879); id., _Ten Years'
  Review of Mission Work in Madagascar_ (L.M.S. 1870-1880, 1881);
  Johnson, _Review of Work of the Friends' Foreign Mission Association
  in Madagascar_, 1867-1880 (Antanànarìvo, 1880); Vaissière, _Histoire
  de Madagascar, ses habitants et ses missionaires_ (Paris, 1884); _The
  Church in Madagascar_ (_S.P.G._, _15 years' progress_, 1874-1889,
  1889); _La Liberté religieuse à Madagascar_ (Paris, 1897); Matthews,
  _Thirty Years in Madagascar_ (London, 1904); Sibree, _The L.M.S.
  Mission in Madagascar_ (L.M.S. Mission Hand Books, London, 1907); id.,
  "Christian Missions in Madagascar and French Colonial Policy," _The
  East and the West_ (Jan. 1909); and General Gallieni's "Neuf ans à
  Madagascar", _Journal of the African Society_ (April 1909).
       (J. Si.*)


FOOTNOTES:

  [1] In the apparent absence of any Cambrian formation above them,
    there is little doubt that these rocks are Archean, although this
    cannot be absolutely proved.

  [2] For most of the information here given on the geology the writer
    is indebted to Captain Mouneyres, chef de services des mines, and the
    Rev. R. Baron, F.G.S., F.L.S.

  [3] See "On a Collection of Fossils from Madagascar," by R. B.
    Newton, _Quart. Journ. Geol. Soc._ (Feb. 1895).

  [4] The following are figures of mean temperature, kindly supplied by
    the Rev. E. Colin, S. J., director of the observatory: Diégo-Suarez,
    N., 79°; Fàrafangàna, S.E. coast, 75°; Màrovoày, W. intr., 81°;
    Mòrondàva, W. coast, 77°; Tullear, S.W. coast, 78°.

  [5] The words in parentheses are the native Malagasy names.

  [6] The census taken in 1905 gives 2,664,000 as the total population,
    but it is probably a little over that amount, as some localities are
    still imperfectly known.

  [7] This is a special and restricted use of the word, Hòva in its
    widest sense being a tribal name, including all ranks of people in
    Imèrina.

  [8] It is true that 200 years earlier than this, persistent efforts
    were made for nineteen years (1600-1619) by Portuguese Roman Catholic
    missionaries to propagate their faith among the south-east coast
    tribes. But although much zeal and self-denial were shown by these
    men, their efforts were abortive, and the mission was at length
    abandoned, leaving no fruit of their labours in a single church or
    convert. Half a dozen small books of devotion are all that remain to
    show their presence in Madagascar.

  [9] The work of the "Frères chrétiens" was, however, almost broken up
    by the anti-clerical policy of the French government.




MADAN, MARTIN (1726-1790), English writer, was educated at Westminster
School, and at Christ Church, Oxford, where he graduated in 1746. In
1748 he was called to the bar, and for some time lived a very gay life,
until he was persuaded to change his ways on hearing a sermon by John
Wesley. He took holy orders, and was appointed chaplain to the Lock
Hospital, London. He was closely connected with the Calvinistic
Methodist movement supported by the countess of Huntingdon, and from
time to time acted as an itinerant preacher. He was a first cousin of
William Cowper, with whom he had some correspondence on religious
matters. In 1767 much adverse comment was aroused by his support of his
friend Thomas Haweis in a controversy arising out of the latter's
possession of the living of Aldwinkle, Northamptonshire (see _Monthly
Review_, xxxvii. 382, 390, 465). In 1780 Madan raised more serious storm
of opposition by the publication of his _Thelyphthora, or A Treatise on
Female Ruin_, in which he advocated polygamy as the remedy for the evils
he deplored. The author was no doubt sincere in his arguments, which he
based chiefly on scriptural authority; but his book called forth many
angry replies. Nineteen attacks on it are catalogued by Falconer Madan
in _Dict. Nat. Biog._ Madan resigned his chaplainship and retired to
Epsom, where he produced, among other works, _A New and Literal
Translation of Juvenal and Persius_ (1789). He died on the 2nd of May
1790.




MADDALONI, a town of Campania, Italy, in the province of Caserta, about
3½ m. S.E. of Caserta, with stations on the railways from Caserta to
Benevento and from Caserta to Avellino, 200 ft. above sea-level. Pop.
(1901), 19,778 (town); 21,270 (commune). It is prettily situated at the
base of one of the Tifata hills, the towers of its medieval castle and
the church of San Michele crowning the heights above. The fine old
palace of the Caraffa family, once dukes of Maddaloni, the old college
now named after Giordano Bruno, and the institute for the sons of
soldiers are the chief points of interest. About 2½ m. east of Valle di
Maddaloni, the Ponte della Valle, an aqueduct built by the orders of
Charles III. of Naples and his son to convey the water of the Tiburno to
Caserta (19 m.), is carried across the valley between Monte Longano and
Monte Gargano by a threefold series of noble arches rising to a height
of 210 ft. The work was designed by Lodovico Vanvitelli, and
constructed between 1753 and 1759.




MADDEN, SIR FREDERIC (1801-1873), English palaeographer, the son of an
officer of Irish extraction, was born at Portsmouth on the 16th of
February 1801. From his earliest years he displayed a strong bent to
linguistic and antiquarian studies. In 1826 he was engaged by the
British Museum to assist in the preparation of the classified catalogue
of printed books then contemplated, and in 1828 he became assistant
keeper of manuscripts. In 1833 he was knighted, and in 1837 succeeded
Josiah Forshall as keeper of manuscripts. He was not entirely successful
in this office, partly owing to want of harmony with his colleagues; he
retired in 1866. He edited for the Roxburghe Club _Havelok the Dane_
(1828), discovered by himself among the Laudian MSS. in the Bodleian,
_William and the Werwolf_ (1832) and the old English versions of the
_Gesta Romanorum_ (1838). In 1839 he edited the ancient metrical
romances of _Syr Gawayne_ for the Bannatyne Club, and in 1847 Layamon's
_Brut_, with a prose translation, for the Society of Antiquaries. In
1850 the magnificent edition, in parallel columns, of what are known as
the "Wycliffite" versions of the Bible, from the original MSS., upon
which he and his coadjutor, Forshall, had been engaged for twenty years,
was published by the university of Oxford. In 1866-1869 he edited the
_Historia Minor_ of Matthew Paris for the Rolls Series. In 1833 he wrote
the text of Henry Shaw's _Illuminated Ornaments of the Middle Ages_; and
in 1850 edited the English translation of Silvestre's _Paléographie
universelle_. He died on the 8th of March 1873, bequeathing his journals
and other private papers to the Bodleian Library, where they were to
remain unopened until 1920.

  Madden was perhaps the first palaeographer of his day. He was an acute
  as well as a laborious antiquary, but his ignorance of German
  prevented his ranking high as a philologist, although he paid much
  attention to the early dialectical forms of French and English. His
  minor contributions to antiquarian research were exceedingly numerous:
  the best known, perhaps, was his dissertation on the orthography of
  Shakespeare's name, which, mainly on the strength of the Florio
  autograph, he contended should be "Shakspere."




MADDER, or DYERS' MADDER, the root of _Rubia tinctorum_ and perhaps also
of _R. peregrina_, both European, _R. cordifolia_, a native of the hilly
districts of India and of north-east Asia and Java, supplying the Indian
madder or _manjit_. _Rubia_ is a genus of about thirty-five species of
the tribe _Galieae_ of the order Rubiaceae, and much resembles the
familiar _Galiums_, e.g. lady's bedstraw (_G. verum_) and the cleavers
(_G. aparine_) of English hedges, having similarly whorled leaves, but
the parts of the flowers are in fives and not fours, while the fruit is
somewhat fleshy. The only British species is _R. peregrina_, which is
found in Wales, the south and west of England, and in east and south
Ireland. The use of madder appears to have been known from the earliest
times, as cloth dyed with it has been found on the Egyptian mummies. It
was the [Greek: ereuthedanon] used for dyeing the cloaks of the Libyan
women in the days of Herodotus (Herod. iv. 189). It is the [Greek:
eruthrodanon] of Dioscorides, who speaks of its cultivation in Caria
(iii. 160), and of Hippocrates (_De morb. mul._ i.), and the _Rubia_ of
Pliny (xix. 17). _R. tinctorum_, a native of western Europe, &c., has
been extensively cultivated in south Europe, France, where it is called
_garance_, and Holland, and to a small extent in the United States.
Large quantities have been imported into England from Smyrna, Trieste,
Leghorn, &c. The cultivation, however, decreased after alizarin, the red
colouring principle of madder, was made artificially. Madder was
employed medicinally by the ancients and in the middle ages. Gerard, in
1597, speaks of it as having been cultivated in many gardens in his day,
and describes its supposed many virtues (_Herball_, p. 960); but any
pharmacological or therapeutic action which madder may possess is
unrecognizable. Its most remarkable physiological effect is that of
colouring red the bones of animals fed upon it, as also the claws and
beaks of birds. This appears to be due to the chemical affinity of
phosphate of lime for the colouring matter (Pereira, _Mat. med._, vol.
ii. pt. 2, p. 52). This property has been of much use in enabling
physiologists to ascertain the manner in which bones develop, and the
functions of the various types of cells found in growing bone. _R.
chilensis_ has been used for dyeing red from time immemorial. The
chay-root, which furnishes a red dye in Coromandel and other parts of
India, is the root-bark of _Oldenlandia umbellata_, a low-growing plant
of the same family as madder.




MADEC, RENÉ-MARIE (1736-1784)--called Medoc in Anglo-Indian
writings--French adventurer in India, was born at Quimper in Brittany on
the 7th of February 1736, of poor parents. He went out to India and
served under Dupleix and Lally, but being taken prisoner by the British
he enlisted in the Bengal army. Deserting with some of his companions
shortly before the battle of Buxar (1764), he became military instructor
to various native princes, organizing successively the forces of
Shuja-ud-Dowlah, nawab of Oudh, and of the Jats and Rohillas. He took
service under the emperor Shah Alam in 1772, and when that prince was
defeated at Delhi by the Mahrattas, Madec rejoined his own countrymen in
Pondicherry, where he took an active part in the defence of the town
(1778). After the capitulation of Pondicherry he returned to France with
a considerable fortune, and died there in 1784. At one time he formed a
scheme for a French alliance with the Mogul emperor against the British,
but the project came to nothing.

  See Émile Barbé, _Le Nabab René Madec_ (1894).




MADEIRA, or THE MADEIRAS, a group of islands in the North Atlantic
Ocean, which belong to Portugal, and consist of two inhabited islands
named Madeira and Porto Santo and two groups of uninhabited rocks named
the Desertas and Selvagens. Pop. (1900), 150,574; area, 314 sq. m.
Funchal, the capital of the archipelago, is on the south coast of
Madeira Island, in 32° 37´ 45´´ N. and 16° 54´ W. It is about 360 m.
from the coast of Africa, 535 from Lisbon, 1215 from Plymouth, 240 from
Teneriffe, and 480 from Santa Maria, the nearest of the Azores.

_Madeira_ (pop. 1900, 148,263), the largest island of the group, has a
length of 30 m., an extreme breadth of 12 m., and a coast-line of 80 or
90 m. Its longer axis lies east and west, in which direction it is
traversed by a mountain chain, the backbone of the island, having a mean
altitude of 4000 ft., up to which many deep ravines penetrate from both
coasts and render travel by land very difficult. Pico Ruivo, the highest
summit, stands in the centre of the island, and has a height of 6056
ft., while some of the adjacent summits are very little lower. The depth
and narrowness of the ravines, the loftiness of the rugged peaks, often
covered with snow, that tower above them, the bold precipices of the
coast, and the proximity of the sea, afford many scenes of picturesque
beauty or striking grandeur. The greater part of the interior is
uninhabited, though cultivated, for the towns, villages and scattered
huts are usually built either at the mouths of ravines or upon the lower
slopes that extend from the mountains to the coast. The ridges between
the ravines usually terminate in lofty headlands, one of which, called
Cabo Girão, has the height of 1920 ft., and much of the seaboard is
bound by precipices of dark basalt. The north coast, having been more
exposed to the erosion of the sea, is more precipitous than the south,
and presents everywhere a wilder aspect. On the south there is left very
little of the indigenous forest which once clothed the whole island and
gave it the name it bears (from the Portuguese _madeira_, Lat.
_materia_, wood), but on the north some of the valleys still contain
native trees of fine growth. A long, narrow and comparatively low rocky
promontory forms the eastern extremity of the island; and here is a
tract of calcareous sand, known as the Fossil Bed, containing land
shells and numerous bodies resembling the roots of trees, probably
produced by infiltration.

_Porto Santo_ is about 25 m. N.E. of Madeira. Pop. (1900), 2311. It has
a length of 6(1/3) m. and a width of 3 m. The capital is Porto Santo,
called locally the _villa_ or town. The island is very unproductive,
water being scarce and wood wholly absent. Around the little town there
is a considerable tract of pretty level ground covered by calcareous
sand containing fossil land-shells. At each end of the island are hills,
of which Pico do Facho, the highest, reaches the altitude of 1663 ft.
Barley, but little else, is grown here, the limited requirements of the
inhabitants being supplied from Funchal.

_The Desertas_ lie about 11 m. S.E. of Madeira, and consist of three
islands, Ilheo Chão, Bugio and Deserta Grande, together with Sail Rock
off the north end of Ilheo Chão. They present lofty precipices to the
sea on all sides. Rabbits and goats abound on them. The archil weed
grows on the rocks, and is gathered for exportation. The largest islet
(Deserta Grande) is 6½ m. long, and attains the height of 1610 ft. These
rocks are conspicuous objects in the sea-views from Funchal.

[Illustration: Map of Madeira Islands.]

The _Selvagens_ or _Salvages_ are a group of three islands, 156 m. from
Madeira, and between Madeira and the Canary Islands. The largest island
is the Great Piton, 3 m. long, and 1 m. broad. The inclusion of the
Selvagens in the Madeira Archipelago is due to political rather than to
geographical reasons.

  _Geology._--All the islands of the group are of volcanic origin. They
  are the summits of very lofty mountains which have their bases in an
  abyssal ocean. The greater part of what is now visible in Madeira is
  of subaerial formation, consisting of basaltic and trachytic lavas,
  beds of tuff and other ejectamenta, the result of a long and
  complicated series of eruptions from innumerable vents. Besides this
  building up by the emission of matter from craters and clefts, a
  certain amount of upheaval in mass has taken place, for at a spot
  about 1200 ft. above the sea in the northern valley of São Vicente,
  and again at about the same height in Porto Santo, there have been
  found fragments of limestone accompanied by tuffs containing marine
  shells and echinoderms of the Miocene Tertiary epoch. We have here
  proof that during or since that epoch portions at least of these
  islands have been bodily uplifted more than 1000 ft. The fossils are
  sufficiently well preserved to admit of their genera, and in many
  instances even their species, being made out.

  There were pauses of considerable duration whilst the island of
  Madeira was being increased in height. The leaf bed and the
  accompanying carbonaceous matter, frequently termed lignite, although
  it displays no trace of structure, which lie under 1200 ft. of lavas
  in the valley of São Jorge, afford proof that there had been
  sufficient time for the growth of a vegetation of high order, many of
  the leaf impressions belonging to species of trees and shrubs which
  still exist on the island. Moreover, great alterations and
  dislocations had taken place in the rocks of various localities before
  other lavas and tuffs had been thrown upon them.

  There are no data for determining when volcanic action began in this
  locality, but looking at the enormous depth of the surrounding sea it
  is clear that a vast period of time must have elapsed to allow of a
  great mountain reaching the surface and then rising several thousand
  feet. Again, considering the comparatively feeble agents for effecting
  the work of denudation (neither glaciers nor thick accumulations of
  alpine snow being found here), and then the enormous erosion that has
  actually taken place, the inference is inevitable that a very great
  lapse of time was required to excavate the deep and wide ravines that
  everywhere intersect the island. Nor is anything known as to the
  period of the cessation of volcanic action. At the present day there
  are no live craters or smoking crevices, as at the Canaries and Cape
  Verdes, nor any hot springs, as at the Azores.

  In one of the northern ravines of Madeira by Porto da Cruz some masses
  of a coarsely crystalline Essexite are exposed to view; this rock is
  evidently the deep-seated representative of the Trachydoleritic and
  Nepheline basalt lavas. Fragments of a sodalite-syenite have also been
  found at Soca in the same neighbourhood.

  In the eastern part of the island several small crater rings are to be
  seen; their rims are formed of spheroidal basalt, while within the
  craters themselves masses of bauxite are found accompanied by
  evidences of fumerolic action.

  In the sections afforded by the ravines, which strike north and south
  from the central ridge of Madeira to the sea, the nucleus of the
  island is seen to consist of a confused mass of more or less
  stratified rock, upon which rest beds of tuff, scoriae and lava, in
  the shape of basalt, trap and trachyte, the whole traversed by dykes.
  These beds are thinnest near the central axis; as they approach the
  coast they become thicker and less intersected by dykes.

  In various parts are elevated tracts of comparatively level ground.
  These are supposed to have been formed by the meeting of numerous
  streams of lava flowing from cones and points of eruption in close
  proximity, various ejectamenta assisting at the same time to fill up
  inequalities. Deep down in some of the lateral ravines may be seen
  ancient cones of eruption which have been overwhelmed by streams of
  melted matter issuing from the central region, and afterwards exposed
  to view by the same causes that excavated the ravines. These ravines
  may be regarded as having been formed at first by subterranean
  movements, both gradual and violent, which dislocated the rocks and
  cut clefts through which streams flowed to the sea. In course of time
  the waters, periodically swollen by melted snows and the copious rains
  of winter, would cut deeper and deeper into the heart of the
  mountains, and would undermine the lateral cliffs, until the valleys
  became as large as we now find them. Even the Curral, which from its
  rounded shape and its position in the centre of the island has been
  usually deemed the ruins of a crater, is thought to be nothing more
  than a valley scooped out in the way described. The rarity of
  crateriform cavities in Madeira is very remarkable. There exists,
  however, to the east of Funchal, on a tract 2000 ft. high, the Lagoa,
  a small but perfect crater, 500 ft. in diameter, and with a depth of
  150 ft.; and there is another, which is a double one, in the district
  known as Fanal, in the north-west of Madeira, nearly 5000 ft. above
  the sea. The basalt, of which much of the outer part of the island is
  composed, is of a dark colour and a tough texture, with small
  disseminated crystals of olivine and augite. It is sometimes full of
  vesicular cavities, formed by the expansion of imprisoned gases. A
  rudely columnar structure is very often seen in the basalt, but there
  is nothing so perfect as the columns of Staffa or the Giant's
  Causeway. The trachytic rocks are small in quantity compared with
  those of the basaltic class. The tufa is soft and friable, and
  generally of a yellow colour; but where it has been overflowed by a
  hot stream of lava it has assumed a red colour. Black ashes and
  fragments of pumice are sometimes found in the tufaceous strata.

  There are no metallic ores, nor has any sulphur been found; but a
  little iron pyrites and specular iron are occasionally met with. The
  basalt yields an excellent building-stone, various qualities of which
  are quarried near Camara de Lobos, five or six miles west of Funchal.

  In Porto Santo the trachytic rocks bear a much greater proportion to
  the basaltic than in Madeira. An adjacent islet is formed of tuffs and
  calcareous rock, indicating a submarine origin, upon which supramarine
  lavas have been poured. The older series contains corals and shells
  (also of the Miocene Tertiary epoch), with water-worn pebbles,
  cemented together by carbonate of lime, the whole appearing to have
  been a coral reef near an ancient beach. The calcareous rock is taken
  in large quantities to Funchal, to be burnt into lime for building
  purposes.

  _Climate._--Observations taken at Funchal Observatory (80 ft. above
  sea-level) in the last twenty years of the 19th century showed that
  the mean annual temperature is about 65° F. The mean minimum for the
  coldest part of the year (October to May inclusive) does not fall
  below 55°, and the average daily variation of temperature in the same
  period does not exceed 10°. Madeira thus has a remarkably mild
  climate, though it lies only 10° north of the Tropic of Cancer. This
  mildness is due to the surrounding ocean, from which the atmosphere
  obtains a large supply of watery vapour. The mean humidity of the air
  is about 75 (saturation = 100). The prevalent winds are from the north
  or from a few points east or west of north, but these winds are much
  mitigated on the south coast by the central range of mountains. The
  west wind usually brings rain. That from the east is a dry wind. A hot
  and dry wind, the leste of the natives, occasionally blows from the
  east-south-east, the direction of the Sahara, and causes the hill
  region to be hotter than below; but even on the coast the thermometer
  under its influence sometimes indicates 93°. The _leste_ is often
  accompanied by sandstorms. As the thermometer has never been known to
  fall as low as 46° at Funchal, frost and snow are there wholly
  unknown; but snow falls on the mountains once or twice during the
  winter, very seldom, however, below the altitude of 2000 ft.
  Thunderstorms are rare, and scarcely ever violent.

  Madeira has long had a high reputation as a sanatory resort for
  persons suffering from diseases of the chest. Notwithstanding the
  ever-increasing competition of other winter resorts, a considerable
  number of invalids, especially English and German, winter at Funchal.

  _Fauna._--No species of land mammal is indigenous to the Madeiras.
  Some of the early voyagers indeed speak of wild goats and swine, but
  these animals must have escaped from confinement. The rabbit, black
  rat, brown rat and mouse have been introduced. The first comers
  encountered seals, and this amphibious mammal (_Monachus albiventer_)
  still lingers at the Desertas. Amongst the thirty species of birds
  which breed in these islands are the kestrel, buzzard and barn owl,
  the blackbird, robin, wagtail, goldfinch, ring sparrow, linnet, two
  swifts, three pigeons, the quail, red-legged partridge, woodcock,
  tern, herring gull, two petrels and three puffins. Only one species is
  endemic, and that is a wren (_Regulus madeirensis_), but five other
  species are known elsewhere only at the Canaries. These are the green
  canary (_Fringilla butyracea_, the parent of the domesticated yellow
  variety), a chaffinch (_Fringilla tintillon_), a swift (_Cypselus
  unicolor_), a wood pigeon (_Columba trocaz_) and a petrel
  (_Thalassidroma Bulwerii_). There is also a local variety of the
  blackcap, distinguishable from the common kind by the extension in the
  male of the cap to the shoulder. About seventy other species have been
  seen from time to time in Madeira, chiefly stragglers from the African
  coast, many of them coming with the _leste_ wind.

  The only land reptile is a small lizard (_Lacerta dugesii_), which is
  abundant and is very destructive to the grape crop. The loggerhead
  turtle (_Caouana caretta_, Gray) is frequently captured, and is cooked
  for the table, but the soup is much inferior to that made from the
  green turtle of the West Indies. A single variety of frog (_Rana
  esculenta_) has been introduced; there are no other batrachians.

  About 250 species of marine fishes taken at Madeira have been
  scientifically determined, the largest families being _Scombridae_
  with 35 species, the sharks with 24, the _Sparidae_ with 15, the rays
  with 14, the _Labridae_ with 13, the _Gadidae_ with 12, the eels with
  12, the _Percidae_ with 11, and the _Carangidae_ with 10. Many kinds,
  such as the mackerel, horse mackerel, groper, mullet, braise, &c..,
  are caught in abundance, and afford a cheap article of diet to the
  people. Several species of tunny are taken plentifully in spring and
  summer, one of them sometimes attaining the weight of 300 lb. The only
  freshwater fish is the common eel, which is found in one or two of the
  streams.

  According to T. V. Wollaston (_Testacea atlantica_, 1878), there have
  been found 158 species of mollusca on the land, 6 inhabiting fresh
  water, and 7 littoral species, making a total of 171. A large majority
  of the land shells are considered to be peculiar. Many of the species
  are variable in form or colour, and some have an extraordinary number
  of varieties. Of the land mollusca 91 species are assigned to the
  genus _Helix_, 31 to the genus _Pupa_, and 15 to the genus _Achatina_
  (or _Lovea_). About 43 species are found both living and fossil in
  superficial deposits of calcareous sand in Madeira or Porto Santo.
  These deposits were assigned by Lyell to the Newer Pliocene period.
  Some 12 or 13 species have not been hitherto discovered alive. More
  than 100 species of _Polyzoa_ (_Bryozoa_) have been collected, among
  them are some highly interesting forms.

  The only order of insects which has been thoroughly examined is that
  of the _Coleoptera_. By the persevering researches of T. V. Wollaston
  the astonishing number of 695 species of beetles has been brought to
  light at the Madeiras. The proportion of endemic kinds is very large,
  and it is remarkable that 200 of them are either wingless or their
  wings are so poorly developed that they cannot fly, while 23 of the
  endemic genera have all their species in this condition. With regard
  to the _Lepidoptera_, 11 or 12 species of butterflies have been seen,
  all of which belong to European genera. Some of the species are
  geographical varieties of well-known types. Upward of 100 moths have
  been collected, the majority of them being of a European stamp, but
  probably a fourth of the total number are peculiar to the Madeiran
  group. Thirty-seven species of _Neuroptera_ have been observed in
  Madeira, 12 of them being so far as is known peculiar.

  The bristle-footed worms of the coast have been studied by Professor
  P. Langerhans, who has met with about 200 species, of which a large
  number were new to science. There are no modern coral reefs, but
  several species of stony and flexible corals have been collected,
  though none are of commercial value. There is, however, a white stony
  coral allied to the red coral of the Mediterranean which would be
  valuable as an article of trade if it could be obtained in sufficient
  quantity. Specimens of a rare and handsome red Paragorgia are in the
  British Museum and Liverpool Museum.

  _Flora._--The vegetation is strongly impressed with a south-European
  character. Many of the plants in the lower region undoubtedly were
  introduced and naturalized after the Portuguese colonization. A large
  number of the remainder are found at the Canaries and the Azores, or
  in one of these groups, but nowhere else. Lastly, there are about a
  hundred plants which are peculiarly Madeiran, either as distinct
  species or as strongly marked varieties. The flowering plants found
  truly wild belong to about 363 genera and 717 species,--the
  monocotyledons numbering 70 genera and 128 species, the dicotyledons
  293 genera and 589 species. The three largest orders are the
  _Compositae_, _Leguminosae_ and _Graminaceae_. Forty-one species of
  ferns grow in Madeira, three of which are endemic species and six
  others belong to the peculiar flora of the North Atlantic islands.
  About 100 species of moss have been collected, and 47 species of
  _Hepaticae_. A connexion between the flora of Madeira and that of the
  West Indies and tropical America has been inferred from the presence
  in the former of six ferns found nowhere in Europe or North Africa,
  but existing on the islands of the east coast of America or on the
  Isthmus of Panama. A further relationship to that continent is to be
  traced by the presence in Madeira of the beautiful ericaceous tree
  _Clethra arborea_, belonging to a genus which is otherwise wholly
  American, and of a _Persea_, a tree laurel, also an American genus.
  The dragon tree (_Dracaena Draco_) is almost extinct. Amongst the
  trees most worthy of note are four of the laurel order belonging to
  separate genera, an _Ardisia_, _Pittosporum_, _Sideroxylon_,
  _Notelaea_, _Rhamnus_ and _Myrica_,--a strange mixture of genera to be
  found on a small Atlantic island. Two heaths of arborescent growth and
  a whortleberry cover large tracts on the mountains. In some parts
  there is a belt of the Spanish chestnut about the height of 1500 ft.
  There is no indigenous pine tree as at the Canaries; but large tracts
  on the hills have been planted with _Pinus pinaster_, from which the
  fuel of the inhabitants is mainly derived. A European juniper (_J.
  Oxycedrus_), growing to the height of 40 or 50 ft., was formerly
  abundant, but has been almost exterminated, as its scented wood is
  prized by the cabinet-maker. Several of the native trees and shrubs
  now grow only in situations which are nearly inaccessible, and some of
  the indigenous plants are of the greatest rarity. But some plants of
  foreign origin have spread in a remarkable manner. Among these is the
  common cactus or prickly pear (_Opuntia Tuna_), which in many spots on
  the coast is sufficiently abundant to give a character to the
  landscape. As to _Algae_, the coast is too rocky and the sea too
  unquiet for a luxuriant marine vegetation, consequently the species
  are few and poor.

_Inhabitants._--The inhabitants are of Portuguese descent, with probably
some intermixture of Moorish and negro blood amongst the lower classes.
The dress of the peasantry, without being picturesque, is peculiar. Both
men and women in the outlying country districts wear the _carapuça_, a
small cap made of blue cloth in shape something like a funnel, with the
pipe standing upwards. The men have trousers of linen, drawn tight, and
terminating at the knees; a coarse shirt enveloping the upper part of
their person, covered by a short jacket, completes their attire, with
the exception of a pair of rough yellow boots. The women's outer
garments consist of a gaudily coloured gown, made from island material,
with a small cape of coarse scarlet or blue woollen cloth. The
population tends to increase rapidly. In 1900 it amounted to 150,574,
including 890 foreigners, of whom the majority were British. The number
of females exceeds that of males by about 6000, partly because many of
the able-bodied males emigrate to Brazil or the United States. The
density of population (479.5 per sq. m.) is very great for a district
containing no large town and chiefly dependent on agriculture and
viticulture.

_Agriculture._--A large portion of the land was formerly entailed in the
families of the landlords (_morgados_), but entails have been abolished
by the legislature, and the land is now absolutely free. The deficiency
of water is a great obstacle to the proper cultivation of the land, and
the rocky nature or steep inclination of the upper parts of the islands
is an effectual bar to all tillage. An incredible amount of labour has
been expended upon the soil, partly in the erection of walls intended to
prevent its being washed away by the rains, and to build up the plots of
ground in the form of terraces. Watercourses have been constructed for
purposes of irrigation, without which at regular intervals the island
would not produce a hundredth part of its present yield. These
watercourses originate high up in the ravines, are built of masonry or
driven through the rock, and wind about for miles until they reach the
cultivated land. Some of them are brought by tunnels from the north side
of the island through the central crest of hill. Each occupier takes his
turn at the running stream for so many hours in the day or night at a
time notified to him beforehand. In this climate flowing water has a
saleable value as well as land, which is useless without irrigation.

  The agricultural implements employed are of the rudest kind, and the
  system of cultivation is extremely primitive. Very few of the
  occupiers own the land they cultivate; but they almost invariably own
  the walls, cottages and trees standing thereon, the land alone
  belonging to the landlord. The tenant can sell his share of the
  property without the consent of the landlord, and if he does not so
  dispose of it that share passes to his heirs. In this way the tenant
  practically enjoys fixity of tenure, for the landlord is seldom in a
  position to pay the price at which the tenant's share is valued. Money
  rents are rare, the métayer system regulating almost universally the
  relations between landlord and tenant; that is, the tenant pays to the
  owner a certain portion of the produce, usually one half or one third.
  The holdings are as a rule rarely larger than one man can cultivate
  with a little occasional assistance. There are few meadows and
  pastures, the cattle being stall-fed when not feeding on the
  mountains. Horses are never employed for draught, all labour of that
  kind being done by oxen.


    Wine.

  The two staple productions of the soil are wine and sugar. The vine
  was introduced from Cyprus or Crete soon after the discovery of the
  island by the Portuguese (1420), but it was not actively cultivated
  until the early part of the 16th century. The vines, after having been
  totally destroyed by the oidium disease, which made its first
  appearance in the island in 1852, were replanted, and in a few years
  wine was again made. The phylloxera also made its way to the island,
  and every vineyard in Madeira was more or less affected by it. The
  wine usually termed Madeira is made from a mixture of black and white
  grapes, which are also made separately into wines called Tinta and
  Verdelho, after the names of the grapes. Other high-class wines, known
  as Bual, Sercial and Malmsey, are made from varieties of grapes
  bearing the same names. (See also WINE.)


    Sugar.

  The sugar cane is said to have been brought from Sicily about 1452,
  and in course of time its produce became the sole staple of the
  island. The cultivation languished, however, as the more abundant
  produce of tropical countries came into the European market, and sugar
  had long ceased to be made when the destruction of the vines compelled
  the peasants to turn their attention to other things. Its cultivation
  was resumed and sugar machinery imported. A considerable quantity of
  spirit is made by the distillation of the juice or of the molasses
  left after extracting the sugar, and this is consumed on the island.
  The cane does not flourish here as luxuriantly as within the tropics;
  but in localities below 1000 ft., where there is a good supply of
  water, it pays the cultivator well.

  The grain produced on the island (principally wheat, barley and Indian
  corn) is not sufficient for the consumption of the people. The common
  potato, sweet potato and gourds of various kinds are extensively
  grown, as well as the _Colocasia esculenta_, the _kalo_ of the Pacific
  islanders, the root of which yields an insipid food. Most of the
  common table vegetables of Europe are plentiful. Besides apples, pears
  and peaches, all of poor quality, oranges, lemons, guavas, mangoes,
  loquats, custard-apples, figs, bananas and pineapples are produced,
  the last two forming articles of export. The date palm is occasionally
  grown, but its fruit is scarcely edible. On the hills large quantities
  of the Spanish chestnut afford an item in the food of the common
  people. A little tobacco is grown, and is made into cigars of inferior
  quality.

  The total foreign trade of Madeira was valued at £628,000 in 1900. The
  principal exports are wine, sugar, embroidery, vegetables, fruits and
  wicker goods. Coal is imported for the ships calling at Funchal, which
  is the headquarters of Madeiran commerce and industry. Spirits, beer,
  olive oil, soap, butter, linen and woollen goods, straw hats and
  leather, are manufactured for home consumption, and there are
  important fisheries.

_Chief Towns and Communications._--Funchal (pop. 20,850) is described in
a separate article. The other chief towns are Camara de Lobos (7150),
Machico (6128), Santa Cruz (5876), Ponta do Sol (5665), São Vicente
(4896), Calheta (3475), Sant' Anna (3011) and Porto Santo (2311). Each
of these is the capital of a commune (_concelho_), to which it gives its
name. Madeira is connected by regular lines of steamships with Great
Britain, Germany, Portugal, Cape Colony, Brazil and the United States.
There is no railway in the archipelago, and partly owing to the
irregularities of the surface of the roads, of which there are some 580
m., are bad, except in the neighbourhood of Funchal. Wheel carriages are
rare, and all heavy goods are transported either on the backs of mules
or upon rude wooden sledges drawn by bullocks. When horses are not
employed, locomotion is effected either by means of hammocks or by
bullock cars. The hammock (_rêde_) is a piece of stout canvas gathered
up and secured at each end to a long pole carried by a couple of
bearers. In place of cabs, curtained cars on sledges, made to hold four
persons, and drawn by a pair of bullocks, are employed. They are
convenient, but the rate of progress is very slow.

_Administration._--The archipelago is officially styled the district of
Funchal; it returns members to the Portuguese Cortes, and is regarded as
an integral part of the kingdom. The district is subdivided into the
eight communes already enumerated, and is administered in accordance
with the same laws that regulate local government on the mainland (see
PORTUGAL). Funchal is a Roman Catholic bishopric in the archiepiscopal
province of Lisbon. Education is compulsory in name only, for less than
2% of the population could read when the census of 1900 was taken. An
infantry regiment and a battery of garrison artillery are permanently
stationed in Madeira.

_History._--It has been conjectured, but on insufficient evidence, that
the Phoenicians discovered Madeira at a very early period. Pliny
mentions certain Purple or Mauretanian Islands, the position of which
with reference to the Fortunate Islands or Canaries might seem to
indicate the Madeiras. There is a romantic story, to the effect that two
lovers, Robert Machim, à Machin, or Macham, and Anna d'Arfet, fleeing
from England to France (c. 1370) were driven out of their course by a
violent storm and cast on the coast of Madeira at the place subsequently
named Machico, in memory of one of them. Both perished here, but some of
their crew escaped to the Barbary coast, and were made slaves. Among
them was the pilot Pedro Morales of Seville, who is said to have been
ransomed and to have communicated his knowledge of Madeira to João
Gonçalvez Zarco (or Zargo). How far this story is true cannot now be
ascertained. It is, however, certain that Zarco first sighted Porto
Santo in 1418, having been driven thither by a storm while he was
exploring the coast of West Africa. Madeira itself was discovered in
1420. It is probable that the whole archipelago had been explored at an
earlier date by Genoese adventurers, and had been forgotten; for an
Italian map dated 1351 (the Laurentian portolano) shows the Madeiras
quite clearly, and there is some reason to believe that they were known
to the Genoese before 1339. When Zarco visited Madeira in 1420 the
islands were uninhabited, but Prince Henry the Navigator at once began
their colonization, aided by the knights of the Order of Christ.
Sanctioned by the pope and by two charters which the king of Portugal
granted in 1430 and 1433, the work proceeded apace; much land was
deforested and brought into cultivation, and the Madeiran sugar trade
soon became important. For the sixty years 1580-1640 Madeira, with
Portugal itself, was united with Spain. Slavery was abolished in Madeira
in 1775, by order of Pombal. In 1801 British troops, commanded by
General Beresford, occupied the island for a few months, and it was
again under the British flag from 1807 to 1814. It shared in the civil
disturbances brought about by the accession of Dom Miguel (see PORTUGAL:
_History_), but after 1833 its history is a record of peaceful
commercial development.

  See A. S. Brown, _Madeira, the Canary Islands and the Azores_ (1903),
  a comprehensive study of the three archipelagoes. _The Land of the
  Wine_, by A. J. D. Biddle (Philadelphia, 1901) is generally valuable,
  but its history cannot be trusted. See also P. Langerhaus, _Handbuch
  für Madeira_ (1884) and Vahl, _Madeira's Vegetation_ (Copenhagen,
  1904).




MADELENIAN, a term derived from La Madeleine, a cave in the Vézère,
about midway between Moustier and Les Eyzies, France, and given by the
French anthropologist Gabriel de Mortillet to the third stage of his
system of cave-chronology, synchronous with the fourth or most recent
division of the Quaternary Age. The Madelenian epoch was a long one,
represented by numerous stations, whose contents show progress in the
arts and general culture. It was characterized by a cold and dry
climate, the existence of man in association with the reindeer, and the
extinction of the mammoth. The use of bone and ivory for various
implements, already begun in the preceding Solutrian epoch, was much
increased, and the period is essentially a Bone age. The bone
instruments are very varied: spear-points, harpoon-heads, borers, hooks
and needles. Most remarkable is the evidence La Madeleine affords of
prehistoric art. Numbers of bones, reindeer antlers and animals' teeth
were found, with rude pictures, carved or etched on them, of seals,
fishes, reindeer, mammoths and other creatures. The best of these are a
mammoth engraved on a fragment of its own ivory; a dagger of reindeer
antler, with handle in form of a reindeer; a cave-bear cut on a flat
piece of schist; a seal on a bear's tooth; a fish well drawn on a
reindeer antler; and a complete picture, also on reindeer antler,
showing horses, an aurochs, trees, and a snake biting a man's leg. The
man is naked, and this and the snake suggest a warm climate, in spite
of the presence of the reindeer. The fauna of the Madelenian epoch
seems, indeed, to have included tigers and other tropical species side
by side with reindeer, blue foxes, Arctic hares and other polar
creatures. Madelenian man appears to have been of low stature,
dolichocephalic, with low retreating forehead and prominent brow ridges.
Besides La Madeleine the chief stations of the epoch are Les Eyzies,
Laugerie Basse, and Gorge d'Enfer in Dordogne; Grotte du Placard in
Charente and others in south-west France.

  See G. de Mortillet, _Le Préhistorique_ (1900); Edouard Lartet and
  Henry Christy, _Reliquiae Aquitanicae_ (1865-1875); Edouard Dupont,
  _Le Temps préhistorique en Belgique_ (1872); Lord Avebury,
  _Prehistoric Times_ (1900).




MADELEY, a market town in the municipal borough of Wenlock, and the
Wellington (Mid) parliamentary division of Shropshire, England, 159 m.
N.W. from London, with stations on the London & North Western (Madeley
Market) and Great Western railways (Madeley Court). Pop. of civil parish
(1901), 8442. There are large ironworks, ironstone and coal are mined,
and potter's clay is raised. The church of St Michael (1796) replaced a
Norman building. The living was held from 1760 to 1783 by John William
Fletcher or de la Flechêre, a close friend of the Wesleys. The parish
includes a portion of Coalbrookdale (q.v.), and the towns of Ironbridge
and Coalport. IRONBRIDGE, a town picturesquely situated on the steep
left bank of the Severn, adjoins Madeley on the south-west. It takes its
name from the iron bridge of one span crossing the river, erected in
1779. This bridge is a remarkable work considering its date; it was
probably the first erected, at any rate on so large a scale, and
attracted great attention. It is the work of Abraham Darby, the third of
the name, one of the famous family of iron-workers in Coalbrookdale.
Here are brick and tile works and lime-kilns. There is a station
(Ironbridge and Broseley) on the Great Western railway, across the
river. COALPORT lies also on the Severn, S. of Madeley and 2 m. S.E. of
Ironbridge, with a station on the Great Western railway. It has large
china works, founded at the close of the 18th century, which
subsequently incorporated those of Caughley, across the Severn, and of
Nantgarw in Glamorganshire.




MADHAVA ACHARYA (_fl._ c. 1380), Hindu statesman and philosopher, lived
at the court of Vijayanagar (the modern Humpi in the district of
Bellary), the vigorous Southern Hindu kingdom that so long withstood
Mahommedan influence and aggression. His younger brother Sayana (d.
1387) was associated with him in the administration and was a famous
commentator on the _Rigveda_. Sayana's commentaries were influenced by
and dedicated to Madhava, who is best known as the author of the
_Sarvadarsana Samgraha_ (_Compendium of Speculations_). With remarkable
mental detachment he places himself in the position of an adherent of
sixteen distinct systems. Madhava also wrote a commentary on the Mimamsa
Sutras. He died as abbot of the monastery of Sringeri.




MADI (A-MADI), a negro race of the Nile valley, occupying both banks of
the Bahr-el-Jebel immediately north of Albert Nyanza. Tradition makes
them immigrants from the north-west. They are remarkable for the
consideration shown to their women, who choose their own husbands, are
never ill-treated or hard-worked, and take part in tribal deliberations.
The Madi build sepulchral monuments of an elaborate type, two huge
narrow stones sloping towards each other with two smaller slabs covering
the opening between them. They have been much harried by the Azandeh and
Abarambo. They were visited by W. Junker in 1882-1883, and described by
him in _Petermann's Mittheilungen_ for May 1883.




MADISON, JAMES (1751-1836), fourth president of the United States, was
born at Port Conway, in King George county, Virginia, on the 16th of
March 1751. His first ancestor in America may possibly have been Captain
Isaac Maddyson, a colonist of 1623 mentioned by John Smith as an
excellent Indian fighter. His father, also named James Madison, was the
owner of large estates in Orange county, Virginia. In 1769 the son
entered the college of New Jersey (now Princeton University), where, in
the same year, he founded the well-known literary club, "The American
Whig Society." He graduated in 1771, but remained for another year at
Princeton studying, apparently for the ministry, under the direction of
John Witherspoon (1722-1794). In 1772 he returned to Virginia, where he
pursued his reading and studies, especially theology and Hebrew, and
acted as a tutor to the younger children of the family. In 1775 he
became chairman of the committee of public safety for Orange county, and
wrote its response to Patrick Henry's call for the arming of a colonial
militia, and in the spring of 1776 he was chosen a delegate to the new
Virginia convention, where he was on the committee which drafted the
constitution for the state, and proposed an amendment (not adopted)
which declared that "all men are equally entitled to the full and free
exercise" of religion, and was more radical than the similar one offered
by George Mason. In 1777, largely, it seems, because he refused to treat
the electors with rum and punch, after the custom of the time, he was
not re-elected, but in November of the same year he was chosen a member
of the privy council or council of state, in which he acted as
interpreter for a few months, as secretary prepared papers for the
governor, and in general took a prominent part from the 14th of January
1778 until the end of 1779, when he was elected a delegate to the
Continental Congress.

He was in Congress during the final stages of the War of Independence,
and in 1780 drafted instructions to Jay, then representing the United
States at Madrid, that in negotiations with Spain he should insist upon
the free navigation of the Mississippi and upon the principle that the
United States succeeded to British rights affirmed by the treaty of
Paris of 1763. When the confederation was almost in a state of collapse
because of the failure of the states to respond to requisitions of
Congress for supplies for the federal treasury, Madison was among the
first to advocate the granting of additional powers to Congress, and
urged that congress should forbid the states to issue more paper money.
In 1781 he favoured an amendment of the Articles of Confederation giving
Congress power to enforce its requisitions, and in 1783, in spite of the
open opposition of the Virginia legislature, which considered the
Virginian delegates wholly subject to its instructions, he advocated
that the states should grant to Congress for twenty-five years authority
to levy an import duty, and suggested a scheme to provide for the
interest on the debt not raised by the import duty--apportioning it
among the states on the basis of population, counting three-fifths of
the slaves, a ratio suggested by Madison himself. Accompanying this plan
was an address to the states drawn up by Madison, and one of the ablest
of his state papers. In the same year, with Oliver Ellsworth of
Connecticut, Nathaniel Gorham of Massachusetts. Gunning Bedford of
Delaware, and John Rutledge of South Carolina, he was a member of the
committee which reported on the Virginia proposal as to the terms of
cession to the Confederation of the "back lands," or unoccupied Western
territory, held by several of the states; the report was a skilful
compromise made by Madison, which secured the approval of the rather
exigent Virginia legislature.

In November 1783 Madison's term in Congress expired, and he returned to
Virginia and took up the study of the law. In the following year he was
elected to the House of Delegates. As a member of its committee on
religion, he opposed the giving of special privileges to the Episcopal
(or any other) church, and contended against a general assessment for
the support of the churches of the state. His petition of remonstrance
against the proposed assessment, drawn up at the suggestion of George
Nicholas (c. 1755-1799), was widely circulated and procured its defeat.
On the 26th of December 1785 Jefferson's Bill for establishing religious
freedom in Virginia, which had been introduced by Madison, was passed.
In the Virginia House of Delegates, as in the Continental Congress, he
opposed the further issue of paper money; and he tried to induce the
legislature to repeal the law confiscating British debts, but he did not
lose sight of the interests of the Confederacy. The boundary between
Virginia and Maryland, according to the Baltimore grant, was the south
shore of the Potomac, a line to which Virginia had agreed on condition
of free navigation of the river and the Chesapeake Bay. Virginia now
feared that too much had been given up, and desired joint regulation of
the navigation and commerce of the river by Maryland and Virginia. On
Madison's proposal commissioners from the two states met at Alexandria
(q.v.) and at Mount Vernon in March 1785. The Maryland legislature
approved the Mount Vernon agreement and proposed to invite Pennsylvania
and Delaware to join in the arrangement. Madison, seeing an opportunity
for more general concert in regard to commerce and trade (and possibly
for the increase of the power of Congress), proposed that all the states
should be invited to send commissioners to consider commercial
questions, and a resolution to that effect was adopted (on Jan. 21,
1786) by the Virginia legislature. This led to the Annapolis convention
of 1786, and that in turn led to the Philadelphia convention of 1787. In
April 1787 Madison had written a paper, _The Vices of the Political
System of the United States_, and from his study of confederacies,
ancient and modern, later summed up in numbers 17, 18, and 19 of _The
Federalist_, he had concluded that no confederacy could long endure if
it acted upon states only and not directly upon individuals. As the time
for the convention of 1787 approached he drew up an outline of a new
system of government, the basis of the "Virginia plan" presented in the
convention by Edmund Jennings Randolph. Madison's scheme, as expressed
in a letter to Washington dated the 16th of April 1787, was that
individual sovereignty of states was irreconcilable with aggregate
sovereignty, but that the "consolidation of the whole into one simple
republic would be as inexpedient as it is unattainable." He considered
as a practical middle ground changing the basis of representation in
Congress from states to population; giving the national government
"positive and complete authority in all cases which require uniformity";
giving it a negative on all state laws, a power which might best be
vested in the Senate, a comparatively permanent body; electing the lower
house, and the more numerous, for a short term; providing for a national
executive, for extending the national supremacy over the judiciary and
the militia, for a council to revise all laws, and for an express
statement of the right of coercion; and finally, obtaining the
ratification of a new constitutional instrument from the people, and not
merely from the legislatures. The "Virginia plan" was the basis of the
convention's deliberations which resulted in the constitution favourably
voted on by the convention on the 17th of September 1787. Among the
features of the plan which were not embodied in the constitution were
the following: proportionate representation in the Senate and the
election of its members by the lower house "out of a proper number of
persons nominated by the individual legislatures"; the vesting in the
national Congress of power to negative state acts; and the establishment
of a council of revision (the executive and a convenient number of
national judges) with veto power over all laws passed by the national
Congress. Madison, always an opponent of slavery, disapproved of the
compromise (in Art. I. § 9 and Art. V.) postponing to 1808 (or later)
the prohibition of the importation of slaves. He took a leading part in
the debates of the convention, of which he kept full and careful notes,
afterwards published by order of Congress (3 vols., Washington, 1843).
Many minute and wise provisions are due to him, and he spoke before the
convention more frequently than any delegate except James Wilson and
Gouverneur Morris. In spite of the opposition to the constitution of the
Virginia leaders George Mason and E. J. Randolph, Madison induced the
state's delegation to stand by the constitution in the convention. His
influence largely shaped the form of the final draft of the
constitution, but the labour was not finished with this draft; that the
constitution was accepted by the people was due in an eminent degree to
the efforts of Madison, who, to place the new constitution before the
public in its true light, and to meet the objections brought against it,
joined Alexander Hamilton (q.v.) and John Jay in writing _The
Federalist_, a series of eighty-five papers, out of which twenty
certainly, and nine others probably, were written by him. In the
Virginia convention for ratifying the constitution (June 1788), when
eight states had ratified and it seemed that Virginia's vote would be
needed to make the necessary nine (New Hampshire's favourable vote was
cast only shortly before that of Virginia), and it appeared that New
York would vote against the constitution if Virginia did not ratify it,
Madison was called upon to defend that instrument again, and he appeared
at his best against its opponents, Patrick Henry, George Mason, James
Monroe, Benjamin Harrison, William Grayson and John Tyler. He answered
their objections in detail, calmly and with an intellectual power and
earnestness that carried the convention. The result was a victory
against an originally adverse public opinion and against the eloquence
of the opponents of the constitution, for Madison and for his
lieutenants, Edmund Pendleton, John Marshall, George Nicholas, Harry
Innes and Henry Lee. At the same time Madison's labours in behalf of the
constitution alienated from him valuable political support in Virginia.
He was defeated by Richard Henry Lee and William Grayson in his
candidacy for the United States Senate, but in his own district he was
chosen a representative to Congress, defeating James Monroe, who seems
to have had the powerful support of Patrick Henry.

Madison took his seat in the House of Representatives in April 1789, and
assumed a leading part in the legislation necessary to the organization
of the new government. He drafted a Tariff Bill giving certain notable
advantages to nations with which the United States had commercial
treaties, hoping to force Great Britain into a similar treaty; but his
policy of discrimination against England was rejected by Congress. It
was his belief that such a system of retaliation would remove the
possibility of war arising from commercial quarrels. He introduced
resolutions calling for the establishment of three executive
departments, foreign affairs, treasury and war, the head of each
removable by the president. Most important of all, he proposed nine
amendments to the constitution, embodying suggestions made by a number
of the ratifying states, especially those made by Virginia at the
instance of George Mason; and the essential principles of Madison's
proposed amendments were included in a Bill of Rights, adopted by the
states in the form of ten amendments. The absence of a Bill of Rights
from the constitution as first adopted had been the point on which the
opposition had made common cause, and the adoption of this now greatly
weakened the same opposition. Although a staunch friend of the
constitution, Madison believed, however, that the instrument should be
interpreted conservatively and not be made the means of introducing
radical innovations. The tide of strict construction was setting in
strongly in his state, and he was borne along with the flood. It is very
probable that Jefferson's influence over Madison, which was greater than
Hamilton's, contributed to this result. Madison now opposed Hamilton's
measures for the funding of the debt, the assumption of state debts, and
the establishment of a National Bank, and on other questions he sided
more and more with the opposition, gradually assuming its leadership in
the House of Representatives and labouring to confine the powers of the
national government within the narrowest possible limits; his most
important argument against Hamilton's Bank was that the constitution did
not provide for it explicitly, and could not properly be construed into
permitting its creation. Madison, Jefferson and Randolph were consulted
by Washington, and they advised him not to sign the bill providing for
the Bank, but Hamilton's counter-argument was successful. On the same
constitutional grounds Madison objected to the carrying out of the
recommendations in Hamilton's famous report on manufactures (Dec. 5,
1791), which favoured a protective tariff. In the presidential campaign
of 1792 Madison seems to have lent his influence to the determined
efforts of the Jeffersonians to defeat John Adams by electing George
Clinton vice-president. In 1793-1796 he strongly criticized the
administration for maintaining a neutral position between Great Britain
and France, writing for the public press five papers (signed
"Helvidius"), attacking the "monarchical prerogative of the executive"
as exercised in the proclamation of neutrality in 1793 and denying the
president's right to recognize foreign states. He found in Washington's
attitude--as in Hamilton's failure to pay an instalment of the moneys
due France--an "Anglified complexion," in direct opposition to the
popular sympathy with France and French Republicanism. In 1794 he tried
again his commercial weapons, introducing in the House of
Representatives resolutions based on Jefferson's report on commerce,
advising retaliation against Great Britain and discrimination in
commercial and navigation laws in favour of France; and he declared that
the friends of Jay's treaty were "a British party systematically aiming
at an exclusive connexion with the British government," and in 1796
strenuously but unsuccessfully opposed the appropriation of money to
carry this treaty into effect. Still thinking that foreign nations could
be coerced through their commercial interests, he scouted as visionary
the idea that Great Britain would go to war on a refusal to carry Jay's
treaty into effect, thinking it inconceivable that Great Britain "would
wantonly make war" upon a country which was the best market she had in
the world for her manufactures, and one with which her export trade was
so much larger than her import.

In 1797 Madison retired from Congress, but not to a life of inactivity.
In 1798 he joined Jefferson in opposing the Alien and Sedition Laws, and
Madison himself wrote the resolutions of the Virginia legislature
declaring that it viewed "the powers of the Federal government as
resulting from the compact to which the states are parties, as limited
by the plain sense and intention of the instrument constituting that
compact; as no further valid than they are authorized by the grants
enumerated in that compact; and that, in case of a deliberate, palpable
and dangerous exercise of other powers, not granted by the said compact,
the states, who are parties thereto, have the right and are in duty
bound to interpose for arresting the progress of the evil, and for
maintaining within their respective limits, the authorities, rights and
liberties appertaining to them." The Virginia resolutions and the
Kentucky resolutions (the latter having been drafted by Jefferson) were
met by dissenting resolutions from the New England states, from New
York, and from Delaware. In answer to these, Madison, who had become a
member of the Virginia legislature in the autumn of 1799, wrote for the
committee to which they were referred a report elaborating and
sustaining in every point the phraseology of the Virginia
resolutions.[1]

Upon the accession of the Republican party to power in 1801, Madison
became secretary of state in Jefferson's cabinet, a position for which
he was well fitted both because he possessed to a remarkable degree the
gifts of careful thinking and discreet and able speaking, and of large
constructive ability; and because he was well versed in constitutional
and international law and practised a fairness in discussion essential
to a diplomat. During the eight years that he held the portfolio of
state, he had continually to defend the neutral rights of the United
States against the encroachments of European belligerents; in 1806 he
published _An Examination of the British Doctrine which subjects to
Capture a Neutral Trade not open in Time of Peace_, a careful
argument--with a minute examination of authorities on international
law--against the rule of war of 1756 extended by Great Britain in 1793
and 1803.

During Jefferson's presidency and whilst Madison was secretary of state,
by the purchase of Louisiana, Madison's campaign begun in 1780 for the
free navigation of the Mississippi was brought to a successful close.
The candidate in 1808 of the Republican party, although bitterly opposed
in the party by John Randolph and George Clinton, Madison was elected
president, defeating C. C. Pinckney, the Federalist candidate, by 122
votes to 47. Madison had no false hopes of placating the Federalist
opposition, but as the preceding administration was one with which he
was in harmony, his position was different from that of Jefferson in
1801, and he had less occasion for removing Federalists from office.
Jefferson's peace policy--or, more correctly, Madison's peace policy--of
commercial restrictions to coerce Great Britain and France he continued
to follow until 1812, when he was forced to change these futile
commercial weapons for a policy of war, which was very popular with the
extreme French wing of his party. There is a charge, which has never
been proved or disproved, that Madison's real desire was for peace, but
that in order to secure the renomination he yielded to that wing of his
party which was resolved on war with Great Britain. The only certain
fact is that Madison, whatever were his personal feelings in this
matter, acted according to the wishes of a majority of the Republicans;
but whether in doing so he was influenced by the desire of another
nomination is largely a matter of conjecture. Madison was renominated on
the 18th of May 1812, issued his war message on the 1st of June, and in
the November elections he was re-elected, defeating De Witt Clinton by
128 votes to 89. His administration during the war was pitiably weak.
His cabinet in great part had been dictated to him in 1809 by a
senatorial clique, and it was hopelessly discordant; for two years he
was to all intents and purposes his own secretary of state, Robert Smith
being a mere figure-head of whom he gladly got rid in 1811, giving
Monroe the vacant place. Madison himself had attempted alternately to
prevent war by his "commercial weapons" and to prepare the country for
war, but he had met with no success, because of the tricky diplomacy of
Great Britain and of France, and because of the general distrust of him
coupled with the particular opposition to the war of the prosperous New
England Federalists, who suggested with the utmost seriousness that his
resignation should be demanded. In brief, Madison was too much the mere
scholar to prove a strong leader in such a crisis. The supreme disgrace
of the administration was the capture and partial destruction in August
1814 of the city of Washington--this was due, however, to incompetence
of the military and not to any lack of prudence on the cabinet's part.
In general, Congress was more blamable than either the president or his
official family, or the army officers. With the declaration of peace the
president again gained a momentary popularity much like that he had won
in 1809 by his apparent willingness at that time to fight France.

Retiring from the presidency in 1817, Madison returned to his home,
Montpelier (in Orange county, Virginia), which he left in no official
capacity save in 1829, when he was a delegate to the state
constitutional convention and served on several of its committees.
Montpelier, like Jefferson's Monticello and Monroe's Oak-Hill, was an
expensive bit of "gentleman farming," which with his generous Virginia
hospitality nearly ruined its owner financially. Madison's home was
peculiarly a centre for literary travellers in his last years; when he
was eighty-three he was visited by Harriet Martineau, who reported her
conversations with him in her _Retrospect of Western Travel_ (1838). He
took a great interest in education--his library was left to the
university of Virginia, where it was burned in 1895--in emancipation,
and in agricultural questions, to the very last. He died at Montpelier
on the 28th of June 1836. Madison married, in 1794, Dorothy Payne Todd
(1772-1849), widow of John Todd, a Philadelphia lawyer. She had great
social charm, and upon Madison's entering Jefferson's cabinet became
"first lady" in Washington society. Her plump beauty was often
remarked--notably by Washington Irving--in contrast to her husband's
delicate and feeble figure and wizened face--for even in his prime
Madison was, as Henry Adams says, "a small man, quiet, somewhat precise
in manner, pleasant, fond of conversation, with a certain mixture of
ease and dignity in his address." Her son, spoiled by his mother and his
step-father, became a wild young fellow, and added his debts to the
heavy burden of Montpelier upon Madison.

  Madison's portrait was painted by Gilbert Stuart and by Charles
  Willson Peale; Giuseppe Ceracchi made a marble bust of him in 1792 and
  John H. J. Browere another in 1827, now in possession of the Virginia
  Historical Society at Richmond. Though commonly dignified and a little
  stiff he seems to have had a strong sense of humour and he was fond of
  telling a good story. Henry Clay, contrasting him with Jefferson, said
  that Jefferson had more genius, Madison more judgment and common
  sense; that Jefferson was a visionary and a theorist; Madison cool,
  dispassionate, practical, and safe.[2] The broadest and most accurate
  scholar among the "founders and fathers," he was particularly an
  expert in constitutional history and theory. In the great causes for
  which Madison fought in his earlier years--religious freedom and
  separation of church and state, the free navigation of the
  Mississippi, and the adoption of the constitution--he met with
  success. His greatest and truest fame is as the "father of the
  constitution." The "commercial weapons" with which he wished to
  prevent armed conflict proved less useful in his day than they have
  since been in international disputes.

  AUTHORITIES.--Madison's personality is perplexingly vague; the
  biographies of him are little more than histories of the period, and
  the best history of the later period in which he was before the
  public, Henry Adams's _History of the United States from 1801 to 1817_
  (1889-1890), gives the clearest sketch and best criticism of him. The
  lives of Madison are: J. Q. Adams's (Boston, 1850); W. C. Rives's
  (Boston, 1859-1869, 3 vols.), covering the period previous to 1797; S.
  H. Gay's (Boston, 1884) in the "American Statesmen Series"; and
  Gaillard Hunt's (New York, 1902). Madison's _Writings_ (7 vols., New
  York, 1900-1906) were edited by Hunt, who also edited _The Journal of
  the Debates in the Convention which framed the Constitution of the
  United States, as Recorded by James Madison_ (2 vols., New York,
  1908). See also Mrs Madison's _Memoirs and Letters_ (Boston, 1887) and
  Maud Wilder Goodwin, _Dolly Madison_ (New York, 1897).


FOOTNOTES:

  [1] Thirty years later Madison's arguments for the Virginia
    resolutions and the resolutions themselves were freely used by
    Calhoun and his followers in support of his doctrine of
    nullification. But Madison insisted that the Resolutions of 1798 did
    not involve the principles of nullification. Nearly all his
    arguments, especially where he attempts to interpret Jefferson's
    writings on the point, notably the Kentucky resolutions, are rather
    strained and specious, but it does seem that the Virginia resolutions
    were based on a different idea from Calhoun's doctrine of
    nullification. Madison's theory was that the legislature of Virginia,
    being one of the bodies which had chosen delegates to the
    constitutional convention, was legally capable of considering the
    question of the constitutionality of laws passed by the Federal
    government, and that the state of Virginia might invite other states
    to join her, but could not singly, as Calhoun argued, declare any law
    of the Federal legislature null and void. (It is to be noted the
    words "null and void" were in Madison's first draft of the Virginia
    resolutions, but that they were omitted by the Virginia legislature.)
    It is notable, besides, that Madison had always feared that the
    national congress would assume too great power, that he had approved
    of Supreme Court checks on the national legislature, and of veto
    power by a council of revision.

  [2] Clay's opinion is given in a report written by Mrs Samuel H.
    Smith of a conversation in 1829 between Clay and her husband, a
    prominent politician.




MADISON, a city and the county-seat of Jefferson county, Indiana,
U.S.A., on the N. bank of the Ohio river, about 90 m. below Cincinnati,
and 44 m. above Louisville, Kentucky. Pop. (1870), 10,709; (1890), 8936;
(1900), 7835 (554 foreign-born and 570 negroes); (1910), 6934. Madison
is served by the Pittsburg, Cincinnati, Chicago & St Louis railroad and
by river steamboats. The city is picturesquely situated on bluffs above
the river and has two public parks. In Madison are a King's Daughters'
Hospital, a children's home, and the Drusilla home for old ladies, and
immediately north of the city are the buildings of the Indiana
South-eastern Insane Hospital. Madison is a trading centre of the
surrounding farming region, whose principal products are burley tobacco,
grain and fruits (peaches, apples, pears, plums and small fruits). The
municipality owns and operates the waterworks. Madison was settled about
the beginning of the 19th century; was incorporated as a town in 1824,
and was first chartered as a city in 1836.




MADISON, a borough of Morris county, New Jersey, U.S.A., 27 m. (by rail)
W. of New York City and 4 m. S.E. of Morristown. Pop. (1890), 2469;
(1900), 3754, of whom 975 were foreign-born and 300 were negroes;
(1905), 4115; (1910), 4658. It is served by the Morris & Essex division
of the Delaware, Lackawanna & Western railroad. The borough is
attractively situated among the hills of Northern New Jersey, is
primarily a residential suburb of New York and Newark, and contains many
fine residences. There are a public library and a beautiful public park,
both given to the borough by Daniel Willis James (1832-1907), a
prominent metal manufacturer; the library is closely allied with the
public schools. Madison is the seat of the well-known Drew theological
seminary (Methodist Episcopal; founded in 1866 and opened in 1867),
named in honour of Daniel Drew (1788-1879), who, having acquired great
wealth from steamboat and railway enterprises, especially from trading
in railway stocks, presented the large and beautiful grounds and most of
the buildings. The seminary's course covers three years; no fee is
charged. In connexion with the seminary the Drew settlement in New York
City--officially the department of applied Christianity--has for its
object the "practical study of present-day problems in city evangelism,
church organization, and work among the poor." In 1907-1908 the seminary
had 9 instructors, 175 students, and a library of more than 100,000
volumes, especially rich in works dealing with the history of Methodism
and in Greek New Testament manuscripts. About 2 m. N.W. of Madison is
Convent Station, the seat of a convent of the Sisters of Charity, who
here conduct the college of St Elizabeth, for girls, founded in 1859;
also conducted by the Sisters of Charity is St Joseph's preparatory
school for boys, founded in 1862. The cultivation of roses and
chrysanthemums is practically the only industry of Madison. Madison owns
and operates its waterworks and electric-lighting plant. Before 1844
when it took its present name (in honour of President Madison), Madison
was called Bottle Hill; it is one of the older places of the state, and
its first church (Presbyterian) was built about 1748. The borough was
incorporated in 1889.




MADISON, the capital of Wisconsin, U.S.A., and the county-seat of Dane
County, situated between Lakes Mendota and Monona in the south central
part of the state, about 82 m. W. of Milwaukee and about 131 m. N.W. of
Chicago. Pop. (1890), 13,426; (1900) 19,164, of whom 3362 were
foreign-born and 69 were negroes; (1910 census) 25,531. Madison is
served by the Chicago & North-Western, the Chicago, Milwaukee & St Paul,
and the Illinois Central railways (being the northern terminus of the
last), and by interurban electric lines, connecting with Janesville,
Beloit and Chicago. It has a picturesque situation in what is known as
"the Four-Lakes region"; this region takes its name from a chain of
lakes, Kegonsa, Waubesa, Monona and Mendota, which, lying in the order
named and connected with one another by the Yahara or Catfish River,
form the head-waters of Rock river flowing southward through Illinois
into the Mississippi. The city occupies a hilly isthmus about a mile
wide between Lakes Mendota and Monona, bodies of water of great
clearness and beauty, with bottoms of white sand and granite.

The state capitol is in a wooded park at the summit of a hill 85 ft.
high in the centre of the city. From this park the streets and avenues
radiate in all directions. The capitol, built in 1860-1867 (with an
addition in 1883) on the site of the original capitol building
(1837-1838), was partially destroyed by fire in 1904, and in 1909-1910
was replaced by a larger edifice. The principal business portion of the
city is built about the capitol park and the university. Among the
public buildings on or near the park are the federal building, housing
the post office and the United States courts, the city hall, the Dane
county court-house, the public library, the Fuller opera-house, the
county gaol, and the high school. Running directly west from the capitol
is State Street, at the western end of which lie the grounds of the
university of Wisconsin (q.v.), occupying a hilly wooded tract of 300
acres, and extending for a mile along the south shore of Lake Mendota.
University Hill, on which the main building of the university stands, is
125 ft. above the lake; at its foot stands the magnificent library
building of the State Historical Society. In it, in addition to the
interesting and valuable historical museum and art gallery, are the
Society's library of more than 350,000 books and pamphlets, the
university library of 150,000 volumes, and the library of the Wisconsin
academy of arts and sciences, 5000 volumes. Other libraries in the city
include the state law library (45,000 volumes) in the capitol, the
Madison public library (22,500 volumes), and the Woodman astronomical
library (7500 volumes). The Madison public library houses also the state
library school maintained by the Wisconsin library commission. Connected
with the university is the Washburn observatory. On the margin of the
city lies the extensive experimental farm of the state college of
agriculture. In addition to the state university, Madison is the seat of
several Roman Catholic and Lutheran parochial schools, two business
schools, and the Wisconsin academy, a non-sectarian preparatory school
of high grade. On the banks of Lake Monona are the beautiful grounds of
the Monona Lake assembly, a summer assembly on the Chautauqua model.
Near the city is one of the five fish-hatcheries maintained by the
state; it is largely devoted to the propagation of trout and other small
fish. North of the city, occupying a tract of 500 acres, on Lake
Mendota, are the buildings and grounds of the state hospital for the
insane, opened in 1860.

The city's streets are broad and heavily shaded with a profusion of elm,
oak and maple trees. There are many fine stone residences dating from
the middle of the 19th century. There are several parks of great beauty,
and along the shores of Lake Mendota there is a broad boulevarded drive
of 12 m. The municipality owns its waterworks, the water being obtained
from eleven artesian wells, and being chemically similar to that of
Waukesha Springs. The city and surrounding region are a summer resort,
the lakes affording opportunities for fishing and for yachting and
boating.

Madison is an important jobbing centre for central and south-western
Wisconsin; it has an extensive trade in farm, garden and dairy products,
poultry and tobacco; and there are various manufactures. In 1905 the
value of the total factory product was $3,291,143, an increase of 22.4%
over that in 1900.

At the time of the settlement by the whites the aboriginal inhabitants
of the Four-Lakes region were the Winnebago. Prehistoric earthworks are
to be seen in the neighbourhood, several animal-shaped mounds upon the
shores of Lakes Mendota, Monona and Waubesa being among the best
examples. A regular trading post is known to have been established on
Lake Mendota as early as 1820. The title to the Indian lands was
acquired by the United States by treaty in 1825. Colonel Ebenezer
Brigham established himself at Blue Mounds, in the western part of Dane
county, in 1827. In 1832 the "Four-Lakes" country was in the theatre of
hostilities during the Black Hawk War; Colonel Henry Dodge held a
conference with Winnebago chiefs on Lake Mendota, and there were several
skirmishes in the neighbourhood between his troops and the followers of
Black Hawk, one of which took place on the site of Madison. After Black
Hawk's defeat on the Bad Axe he fled to the Wisconsin river Dalles, near
the present Kilbourn, where he was betrayed by the Winnebago. In 1836
Stevens T. Mason, governor of Michigan, and James Duane Doty, then U.S.
district judge, who had visited the region as early as 1829, recorded a
tract of land, including most of the present site of Madison. Here they
surveyed a "paper" city which they named in honour of James Madison. On
the 3rd of December 1836 the territorial legislature in session at
Belmont, after a protracted and acrimonious debate, determined, largely
through Doty's influence, to make Madison the permanent capital. The
construction of houses began in the early spring of 1837. The first
constitutional convention met here in 1846, the second in 1847. Madison
was chartered as a city in 1856. In 1862 a large number of Confederate
prisoners were confined in Camp Randall, at Madison, and many of them
died in hospital.

  See D. S. Durrie, _History of Madison, Wisconsin_ (Madison, 1874);
  Lyman C. Draper, _Madison the Capital of Wisconsin_ (Madison, 1857);
  J. D. Butler, "The Four Lakes Country" in _Wisconsin Historical
  Society Collections_, vol. 10 (1888), and R. G. Thwaites, "Madison" in
  _Historic Towns of the Western States_ (New York, 1900), and his
  "Story of Madison" in _The University of Wisconsin_ (Madison, 1900).




MADOU, JEAN BAPTISTE (1796-1877), Belgian painter and lithographer, was
born at Brussels on the 3rd of February 1796. He studied at the Brussels
Academy of Fine Arts and was a pupil of François. While draughtsman to
the topographical military division at Courtrai, he received a
commission for lithographic work from a Brussels publisher. It was about
1820 that he began his artistic career. Between 1825 and 1827 he
contributed to _Les Vues pittoresques de la Belgique, to a Life of
Napoleon_, and to works on the costumes of the Netherlands, and later
made a great reputation by his work in _La Physionomie de la société en
Europe depuis 1400 jusqu' à nos jours_ (1836) and _Les Scènes de la vie
des peintres_. It was not until about 1840 that he began to paint in
oils, and the success of his early efforts in this medium resulted in a
long series of pictures representing scenes of village and city life,
including "The Fiddler," "The Jewel Merchant," "The Police Court," "The
Drunkard," "The Ill-regulated Household," and "The Village Politicians."
Among his numerous works mention may also be made of "The Feast at the
Château" (1851), "The Unwelcome Guests" (1852, Brussels Gallery),
generally regarded as his masterpiece, "The Rat Hunt" (acquired by
Leopold II., king of the Belgians), "The Arquebusier" (1860), and "The
Stirrup Cup." At the age of sixty-eight he decorated a hall in his house
with a series of large paintings representing scenes from La Fontaine's
fables, and ten years later made for King Leopold a series of decorative
paintings for the château of Ciergnon. Madou died at Brussels on the
31st of March 1877.

  For a list of his paintings see the annual report of the Academy of
  Belgium for 1879.     (F. K.*)




MADOZ, PASCUAL (1806-1870), Spanish statistician, was born at Pampeluna
on the 7th of May 1806. In early life he was settled in Barcelona, as a
writer and journalist. He joined the Progresista party formed during the
first Carlist war, 1833-40. He saw some service against the Carlists;
was elected deputy to the Cortes of 1836; took part for Espartero, and
then against him; was imprisoned in 1843; went into exile and returned;
was governor of Barcelona in 1854, and minister of finance in 1855; had
a large share in secularizing the Church lands; and after the revolution
of 1868 was governor of Madrid. He had, however, no great influence as a
leader and soon went abroad, dying at Genoa in 1870. Madoz was
distinguished from most of the politicians of his generation by the fact
that in middle life he compiled what is still a book of value--a
geographical, statistical and historical dictionary of Spain and its
possessions oversea, _Diccionario geográfico, estadístico y historico de
España, y sus posesiones de Ultramar_ (Madrid, 1848-1850).




MADRAS, a presidency of British India--officially styled Fort St
George--occupying, with its dependencies, the entire south of the Indian
peninsula. The north boundary is extremely irregular. On the extreme
N.E. is the Bengal province of Orissa; then the wild highlands of the
Central Provinces; next the dominions of the nizam of Hyderabad; and
lastly, on the N.W., the Bombay districts of Dharwar and North Kanara.
Geographically Mysore and Coorg lie within the bounds of Madras, and
politically it includes the Laccadive Islands, off the Malabar coast, in
the Indian Ocean. Its total area, including native states, is 151,695
sq. m., and its population in 1901 was 42,397,522, showing an increase
of 7.7% in the decade. The seat of government is at Madras city (q.v.).

  _Physical Aspect._--The Madras presidency may be roughly divided into
  three tracts: (1) the long and broad east coast, (2) the shorter and
  narrower west coast, and (3) the high interior table-land. These
  divisions are determined by the great mountain ranges of the Eastern
  and Western Ghats (q.v.). Between these two ranges lies the central
  table-land, with an elevation of 1000 to 3000 ft., which includes the
  whole of Mysore, and extends over about half a dozen districts of
  Madras. The Anaimudi mountain (8837 ft.) in Travancore is the highest
  in southern India. The Nilgiri hills, which join the Ghats, culminate
  in Dodabetta (8760 ft.). There are besides many outlying spurs and
  tangled masses of hills, of which the Shevaroys, Anamalais and Palnis
  are the most important. The Godavari, Kistna and Cauvery rivers, each
  having a large tributary system, all rise in the Western Ghats, and
  run across the peninsula in a south-east direction into the Bay of
  Bengal. In the upper parts of their course they drain rather than
  water the country through which they flow, and are comparatively
  valueless either for navigation or irrigation; but before reaching the
  sea they spread over alluvial deltas. Smaller rivers of the same
  character are the Pennar and South Pennar or Ponniar, Palar, Vaigai,
  Vellar and Tambraparni. The principal lake is that of Pulicat on the
  east coast, which is 37 m. long from north to south, and forms an
  important means of communication between Madras city and the northern
  districts. On the west coast are a remarkable series of backwaters or
  lagoons, fringing the seaboard of Kanara, Malabar and Travancore. The
  largest is the backwater of Cochin, which extends 120 m. from north to
  south.

  _Geology._--By far the greater part of Madras is occupied by granitic
  and gneissic rocks of very ancient date. Among them are the
  "charnockites," a series of associated eruptive rocks characterized by
  the presence of rhombic pyroxenes. In Bellary and Anantapur districts,
  as well as in Mysore and Hyderabad, several long narrow strips of a
  later formation, known as the Dharwar system, are folded or faulted
  into the gneissic floor. They run from N.N.W. to S.S.E., and consist
  of conglomerates, lavas and schists. All the quartz reefs which
  contain gold in paying quantities are found within these Dharwar
  bands, those of the Kolar goldfield in Mysore being the most
  important. The gneissic and Dharwar rocks are overlaid unconformably
  by the sandstones, limestones, shales, &c., of the Cuddapah and
  Kurnool series. It is in the sandstones and shales of the Kurnool
  group that most of the diamonds of southern India are found; but as
  these rocks are of sedimentary origin, it is probable that the
  diamonds were originally derived from some still unknown source. A
  strip of Gondwana beds follows approximately the course of the
  Godavari. In Hyderabad it includes the important Singareni coalfield,
  but in the Presidency no good coal seams have yet been found. Upper
  Gondwana beds also occur in small patches at several other places near
  the east coast. Marine cretaceous deposits are found in three detached
  areas, near Trichinopoly, Viruddhachalam and Pondicherry. Some of the
  coastal sandstones may be of late Tertiary age, but Tertiary fossils
  have not been found except in a few small patches on the west coast,
  the most southerly being near Quilon in Travancore.

  _Climate._--The climate varies in accordance with the height of the
  mountain chain on the western coast. Where this chain is lofty, as
  between Malabar and Coimbatore, the rainclouds are intercepted and
  give a rainfall of 150 in. on the side of the sea, and only 20 in. on
  the landward side. Where the range is lower, the rainclouds pass over
  the hills and carry their moisture to the interior districts. The
  Nilgiri hills enjoy the climate of the temperate zone, with a moderate
  rainfall. The Malabar coast has a rainfall of 150 in., and the clouds
  on the Western Ghats sometimes obscure the sun for months at a time.
  Along the eastern coasts and central table-lands the rainfall is low
  and the heat excessive. At Madras city the average rainfall is 50 in.,
  but this is considerably above the mean of the east coast.

  _Minerals._--The mineral wealth of the province is undeveloped. Iron
  of excellent quality has been smelted by native smiths in many
  localities from time immemorial; but attempts to work the beds after
  European methods have proved unsuccessful. Carboniferous sandstone
  extends across the Godavari valley as far as Ellore, but the coal has
  been found to be of inferior quality. Among other minerals may be
  mentioned manganese in Vizagapatam, and mica in Nellore. Garnets are
  abundant in the sandstone of the Northern Circars, and diamonds of
  moderate value are found in the same region. Stone and gravel quarries
  are very numerous.

  _Forests._--The forest department of Madras was first organized in
  1856, and it is estimated that forests cover a total area of more than
  19,600 sq. m., the whole of which is under conservancy rules. An area
  of about 1500 sq. m. is strictly conserved. In the remaining forests,
  after supplying local wants, timber is either sold direct by the
  department or licences are granted to wood-cutters. The more valuable
  timber trees comprise teak, ebony, rosewood, sandal-wood and redwood.
  The trees artificially reared are teak, sandal-wood, _Casuarina_ and
  eucalyptus. The finest teak plantation is near Beypur in Malabar. At
  Mudumalli there are plantations of both teak and sandal-wood; and the
  eucalyptus or Australian gum-tree grows on the Nilgiris in magnificent
  clumps.

  _Fauna._--The wild animals include the elephant, bison, sambur and
  ibex of the Western Ghats and the Nilgiris. Bison are found also in
  the hill tracts of the Northern Circars. In Travancore state the black
  leopard is not uncommon. The elephant is protected by law from
  indiscriminate destruction. The cattle are small, but in Nellore and
  along the Mysore frontier a superior breed is carefully kept up by the
  wealthier farmers. The best buffaloes are imported from the Bombay
  district of Dharwar.

_Population._--The population in 1901 was divided into Hindus
(37,026,471), Mahommedans (2,732,931), and Christians (1,934,480). The
Hindus may be subdivided into Sivaites, Vishnuvites and Lingayats. The
Sivaites are most numerous in the extreme south and on the west coast,
while the Vishnuvites are chiefly found in the northern districts. The
Lingayats, a sect of Sivaite puritans, derive their name from their
practice of carrying about on their persons the _linga_ or emblem of
Siva. The Brahmans follow various pursuits, and some of them are recent
immigrants, who came south in the train of the Mahratta armies. A
peculiar caste of Brahmans, called Nambudri, is found in Malabar. The
most numerous of the hill tribes are the Kondhs and Savaras, two cognate
races who inhabit the mountainous tracts of the Eastern Ghats, attached
to several of the large estates of Ganjam and Vizagapatam. On the
Nilgiris the best known aboriginal tribe is the Todas (q.v.). The
Mahommedans are subdivided into Labbai, Moplah, Arab, Sheikh, Sayad,
Pathan and Mogul. The Labbais are the descendants of Hindu converts, and
are traders by hereditary occupation, although many now employ
themselves as sailors and fishermen. The Moplahs are the descendants of
Malayalam converts to Islam--the head of the tribe, the raja of
Cannanore, being descended from a fisher family in Malabar. They are a
hard-working, frugal people, but quite uneducated and fanatical, and
under the influence of religious excitement have often disturbed the
public peace. Christians are more numerous in Madras than in any other
part of India. In Travancore and Cochin states the native Christians
constitute as much as one-fourth of the population. The Roman Catholics,
whose number throughout southern India is estimated at upwards of
650,000, owe their establishment to St Francis Xavier and the famous
Jesuit mission of Madura; they are partly under the authority of the
archbishop of Goa, and partly under twelve Jesuit vicariates. Protestant
missions date from the beginning of the 18th century. The Danes were the
pioneers; but their work was taken up by the Society for Promoting
Christian Knowledge, under whom laboured the great Lutherans of the 18th
century--Schultz, Sartorius, Fabricius and Schwartz. The Church
Missionary Society entered the field in 1814; and subsequently an
American mission joined in the work.

_Languages._--Broadly speaking, the entire population of Madras belongs
to the five linguistic offshoots of the great Dravidian stock, dominant
throughout southern India. At an early period, before the dawn of
history, these races appear to have accepted some form of the
Brahmanical or Buddhist faiths. Many storms of conquest have since swept
over the land, and colonies of Mogul and Mahratta origin are to be found
here and there. But the evidence of language proves that the ethnical
character of the population has remained stable under all these
influences, and that the Madras Hindu, Mahommedan, Jain and Christian
are of the same stock. Of the five Dravidian languages in British
territory Telugu is spoken by over 14,000,000 persons; Tamil by over
15,000,000 persons; Kanarese by over 1,500,000 persons; Malayalam by
nearly 3,000,000 persons; and Tulu by about 500,000 persons. Oriya is
the native tongue in the extreme north of Ganjam, bordering on Orissa;
and various sub-dialects of Dravidian origin are used by the hill tribes
of the Eastern Ghats, of whom the Kondhs may be taken as the type.

  _Agriculture._--Over the greater part of the area of Madras artificial
  irrigation is impossible, and cultivation is dependent upon the local
  rainfall, which rarely exceeds 40 in. a year, and is liable to fall
  irregularly. The Malabar coast is the only part where the rainfall
  brought by the south-west monsoon may be trusted both for its amount
  and regularity. Other districts, such as Bellary, are also dependent
  upon this monsoon; but in their case the rainclouds have spent
  themselves in passing over the Western Ghats, and cultivation becomes
  a matter of hazard. Over the greater part of the presidency the rainy
  season is caused by the south-east monsoon, which breaks about the end
  of September. The deltas of the Godavari, Kistna and Cauvery rivers
  are the only spots on the east coast which artificial irrigation is
  able to save from the risk of occasional scarcity. The principal food
  staples are rice, cholam, cambu, ragi and varagu (four kinds of
  millet). The most common oil-seed is gingelly (sesamum). Garden crops
  comprise tobacco, sugar-cane, chillies, betel-leaf and plantains.
  Sugar is chiefly derived from the sap of palms. The fruit trees are
  coco-nut, areca-nut, palmyra palm, jack, tamarind and mango. Special
  crops include cotton, indigo, coffee, tea, cinchona. The best cotton
  is grown in Tinnevelly. The principal coffee tract stretches along the
  slopes of the Western Ghats from the north of Mysore almost down to
  Cape Comorin. The larger portion of this area lies within Mysore,
  Coorg and Travancore states, but the Wynaad and the Nilgiri hills are
  within Madras. The first coffee plantation was opened in the Wynaad in
  1840. Many of the early clearings proved unprofitable, and the
  enterprise made little progress till about 1855. Coffee, which is much
  cultivated on the Nilgiris, covers about 100 sq. m., though the area
  fluctuates. The tea plant was also introduced into the Nilgiri hills
  about 1840, but was not taken up as a commercial speculation till
  1865, and is still unimportant. The cinchona plant was successfully
  introduced into the Nilgiri hills by the government in 1860, and there
  are now a few plantations belonging to private owners.

  The greater part of the soil in Madras is held by the cultivators
  direct from the government under the tenure known as _ryotwari_.
  Besides these lands in the hands of the government, there are also
  proprietary or _zamindari_ estates in all parts of the country. These
  estates are either the remains of ancient principalities, which the
  holder cannot sell or encumber beyond his own life interest, or they
  are creations of British rule and subject to the usual Hindu custom of
  partition. The total area of the _zamindari_ estates is about 26
  million acres, more than one-fourth of the whole presidency. The
  _peshkash_ or tribute payable to government in perpetuity amounts to
  about £330,000 a year. _Ináms_, revenue-free or quit-rent grants of
  lands made for religious endowments or for services rendered to the
  state, occupy an aggregate area of nearly 8 million acres.

  _Manufactures._--Madras possesses few staple manufactures. The chief
  industries of the presidency are cotton-ginning, coffee-curing,
  fish-curing, indigo-pressing, oil-pressing, printing, rice-curing,
  rope-making, sugar-refining, tanning, tile and brick-making, and
  tobacco-curing. Up to the close of the 18th century cotton goods
  constituted the main article of export. Masulipatam, where the first
  English factory on the Coromandel coast was established in 1620,
  enjoyed a special reputation for its chintzes, which were valued for
  the freshness and permanency of their dyes. There is still a small
  demand for these articles in Burma, the Straits and the Persian Gulf;
  but Manchester goods have nearly beaten the Indian exporter out of the
  field. Native looms, however, still hold their own in the local
  market, in face of strenuous opposition. After weaving, working in
  metals appears to be the most widespread native industry. Among local
  specialities which have attracted European curiosity may be mentioned
  the jewelry of Trichinopoly, ornaments of ivory and horn worked at
  Vizagapatam, and sandal-wood carving in Kanara.

  _Commerce and Trade._--The continuous seaboard of the Madras
  presidency, without any natural harbours of the first rank, has tended
  to create a widely diffused trade. Madras city conducts nearly
  one-half of the total sea-borne commerce; next comes Malabar,
  containing the western railway terminus near Calicut; then Godavari,
  with its cluster of ports along the fringe of the delta; Tinnevelly,
  with the harbour at Tuticorin, which has opened large dealings with
  Ceylon and Burma; Tanjore, South Kanara, Ganjam and Vizagapatam. As
  compared with the other provinces, the trade of Madras is broadly
  marked by the larger proportion assigned to coasting trade with other
  Indian ports and with Ceylon. The chief staples of the export trade
  are hides and skins, coffee and raw cotton.

  _Railways and Irrigation._--The presidency is well supplied with
  railways, which naturally have their centre in Madras city, the chief
  seaport. The broad-gauge line of the Madras & Southern Mahratta
  railway connects with Bombay and Bangalore, and also crosses the
  peninsula to Calicut on the western coast. The South Indian
  (narrow-gauge) serves the extreme south, with its terminus at
  Tuticorin, and branches to Tinnevelly, Negapatam, Erade, Pondicherry
  and Nellore. The narrow-gauge line of the Madras & Southern Mahratta
  railway traverses the Deccan districts; and the East Coast line
  (broad-gauge), through the Northern Circars, has brought Madras into
  direct communication with Calcutta. The Madras system of irrigation
  has been most successful in the case of the three great eastern
  rivers, the Godavari, Kistna and Cauvery. Each of these is intercepted
  by an _anicut_ or dam at the head of its delta, from which canals
  diverge on each side for navigation as well as irrigation. The scheme
  for diverting the waters of the Tungabhadra (a tributary of the
  Kistna) over the thirsty uplands of Kurnool proved a failure. The bold
  project of leading the Periyar river through a tunnel across the
  watershed of the Travancore hills on to the plain of Madura has been
  more successful.

_Administration._--The Madras presidency is administered by a governor
and a council, consisting of two members of the civil service, which
number may be increased to four. There is also a board of revenue of
three members. The number of districts is 24, each under the charge of a
collector, with sub-collectors and assistants. The districts are not
grouped into divisions or commissionerships, as in other provinces. For
legislative purposes the council of the governor is augmented by
additional members, numbering 45 in all, of whom not more than 17 may be
nominated officials, while 19 are elected by various representative
constituencies. Members of the legislative council enjoy the right of
interpellation, of proposing resolutions on matters of public interest,
and of discussing the annual financial statement. The principle of local
devolution is carried somewhat further in Madras than in other
provinces. At the bottom are union _panchayats_ or village committees,
whose chief duty is to attend to sanitation. Above them come _taluk_ or
subdivisional boards. At the head of all are district boards, a portion
of whose members are elected by the _taluk_ boards.

_Education._--The chief educational institutions are the Madras
University, the Presidency College, Madras Christian College, and
Pachayyappa's College at Madras; the government arts colleges at
Combaconum and Rajahmundry; the law college, medical college and
engineering college at Madras; the college of agriculture at Coimbatore;
the teachers' college at Saidapet; the school of arts at Madras; and the
military orphanage at Ootacamund, in memory of Sir Henry Lawrence. In
1907, the total number of pupils at all institutions was 1,007,118, of
whom 164,706 were females, and 132,857 were learning English.

_History._--Until the British conquest the whole of southern India had
never acknowledged a single ruler. The difficult nature of the hill
passes and the warlike character of the highland tribes forbade the
growth of great empires, such as succeeded one another on the plains of
Hindustan. The Tamil country in the extreme south is traditionally
divided between the three kingdoms of Pandya, Chola and Chera. The west
coast supplied the nucleus of a monarchy which afterwards extended over
the highlands of Mysore, and took its name from the Carnatic. On the
north-east the kings of Kalinga at one time ruled over the entire line
of seaboard from the Kistna to the Ganges. Hindu legend has preserved
marvellous stories of these early dynasties, but our only authentic
evidence consists in their inscriptions on stone and brass, and their
noble architecture (see India). The Mahommedan invader first established
himself in the south in the beginning of the 14th century. Ala-ud-din,
the second monarch of the Khilji dynasty at Delhi, and his general Malik
Kafur conquered the Deccan, and overthrew the kingdoms of Karnataka and
Telingana, which were then the most powerful in southern India. But
after the withdrawal of the Mussulman armies the native monarchy of
Vijayanagar arose out of the ruins. This dynasty gradually extended its
dominions from sea to sea, and reached a pitch of prosperity before
unknown. At last, in 1565, it was overwhelmed by a combination of the
four Mahommedan principalities of the Deccan. At the close of the reign
of Aurangzeb, although that emperor nominally extended his sovereignty
as far as Cape Comorin, in reality South India had again fallen under a
number of rulers who owned no regular allegiance. The nizam of the
Deccan, himself an independent sovereign, represented the distant court
of Delhi. The most powerful of his feudatories was the nawab of the
Carnatic, with his capital at Arcot. In Tanjore, a descendant of Sivaji
ruled; and on the central table-land a Hindu chieftain was gradually
establishing his authority and founding the state of Mysore, destined
soon to pass to a Mahommedan usurper.

Vasco da Gama cast anchor off Calicut on the 20th of May 1498, and for a
century the Portuguese retained in their control the commerce of India.
The Dutch began to establish themselves on the ruin of the Portuguese at
the beginning of the 17th century, and were quickly followed by the
English, who established themselves at Calicut and Cranganore in 1616.
Tellicherry became the principal English emporium on the west coast of
Madras. The Portuguese eventually retired to Goa, and the Dutch to the
Spice Islands. The first English settlement on the east coast was in
1611, at Masulipatam, even then celebrated for its fabrics. Farther
south a fort, the nucleus of Madras city, was erected in 1640.
Pondicherry was purchased by the French in 1762. For many years the
English and French traders lived peacefully side by side, and with no
ambition for territorial aggrandisement. The war of the Austrian
succession in Europe lit the first flame of hostility on the Coromandel
coast. In 1746 Madras was forced to surrender to La Bourdonnais, and
Fort St David remained the only English possession in southern India. By
the peace of Aix-la-Chapelle Madras was restored to the English; but
from this time the rivalry of the two nations was keen, and found its
opportunities in the disputed successions which always fill a large
place in Oriental politics. English influence was generally able to
secure the favour of the rulers of the Carnatic and Tanjore, while the
French succeeded in placing their own nominee on the throne at
Hyderabad. At last Dupleix rose to be the temporary arbiter of the fate
of southern India, but he was overthrown by Clive, whose defence of
Arcot in 1751 forms the turning point in Indian history. In 1760 the
crowning victory of Wandewash was won by Colonel (afterwards Sir Eyre)
Coote, over Lally, and in the following year, despite help from Mysore,
Pondicherry was captured.

Though the English had no longer any European rival, they had yet to
deal with Mahommedan fanaticism and the warlike population of the
highlands of Mysore. The dynasty founded by Hyder Ali, and terminating
in his son Tippoo Sultan, proved itself in four several wars, which
terminated only in 1799, the most formidable antagonist which the
English had ever encountered (see HYDER ALI and INDIA). Since the
beginning of the 19th century Madras has known no regular war, but
occasional disturbances have called for measures of repression. The
_pálegárs_ or local chieftains long clung to their independence after
their country was ceded to the British. On the west coast, the feudal
aristocracy of the Nairs, and the religious fanaticism of the Moplahs,
have more than once led to rebellion and bloodshed. In the extreme
north, the wild tribes occupying the hills of Ganjam and Vizagapatam
have only lately learned the habit of subordination. In 1836 the
_zamíndarí_ of Gumsur in this remote tract was attached by government
for the rebellious conduct of its chief. An inquiry then instituted
revealed the wide prevalence among the tribe of Kondhs of human
sacrifice, under the name of _meriah_. The practice has since been
suppressed by a special agency. In 1879 the country round Rampa on the
northern frontier was the scene of riots sufficiently serious to lead to
the necessity of calling out troops. The same necessity arose three
years later, when the Hindus and Mahommedans of Salem came into
collision over a question of religious ceremonial. A more serious
disturbance was that known as the "Anti-Shanar riots" of 1899. The
Maravans of Tinnevelly and parts of Madura, resenting the pretensions of
the Shanans, a toddy-drawing caste, to a higher social and religious
status, organized attacks on Shanan villages. The town of Sivakasi was
looted and burnt by five thousand Maravans. Quiet was restored by the
military, and a punitive police force was stationed in the disturbed
area.

The different territories comprising the Madras presidency were acquired
by the British at various dates. In 1763 the tract encircling Madras
city, then known as the Jagir now Chingleput district, was ceded by the
nawab of Arcot. In 1765 the Northern Circars, out of which the French
had recently been driven, were granted to the Company by the Mogul
emperor, but at the price of an annual tribute of £90,000 to the nizam
of Hyderabad. Full rights of dominion were not acquired till 1823, when
the tribute was commuted for a lump payment. In 1792 Tippoo was
compelled to cede the Baramahal (now part of Salem district), Malabar
and Dindigul subdivision of Madura. In 1799, on the reconstruction of
Mysore state after Tippoo's death, Coimbatore and Kanara were
appropriated as the British share; and in the same year the Mahratta
raja of Tanjore resigned the administration of his territory, though his
descendant retained titular rank till 1855. In 1800 Bellary and Cuddapah
were made over by the nizam of Hyderabad to defray the expense of an
increased subsidiary force. In the following year the dominions of the
nawab of the Carnatic, extending along the east coast almost
continuously from Nellore to Tinnevelly, were resigned into the hands of
the British by a puppet who had been put upon the throne for the
purpose. The last titular nawab of the Carnatic died in 1855; but his
representative still bears the title of prince of Arcot, and is
recognized as the first native nobleman in Madras. In 1839 the nawab of
Kurnool was deposed for misgovernment and suspicion of treason, and his
territories annexed.

  See _Madras Manual of Administration_, 3 vols. (Madras, 1885 and
  1893); S. Ayyangar, _Forty Years' Progress in Madras_ (Madras, 1893);
  J. P. Rees, _Madras_ (Society of Arts, 1901); _Madras Provincial
  Gazetteer_ (2 vols., Calcutta, 1908).




MADRAS, the capital of Madras presidency, and the chief seaport on the
eastern coast of India, is situated in 13° 4´ N. and 80° 17´ E. The
city, with its suburbs, extends nine miles along the sea and nearly
four miles inland, intersected by the little river Cooum. Area, 27 sq.
m.; pop. (1901), 509,346, showing an increase of 12.6% in the decade.
Madras is the third city in India.

Although at first sight the city presents a disappointing appearance,
and possesses not a single handsome street, it has several buildings of
architectural pretensions, and many spots of historical interest. It is
spread over a very wide area, and many parts of it are almost rural in
character. Seen from the roadstead, the fort, a row of merchants'
offices, a few spires and public buildings are all that strike the eye.
Roughly speaking, the city consists of the following divisions. (1)
George Town (formerly Black Town, but renamed after the visit of the
Prince of Wales in 1906), an ill-built, densely populated block, about a
mile square, is the business part of the town, containing the banks,
custom house, high court, and all the mercantile offices. The last, for
the most part handsome structures, lie along the beach. On the sea-face
of George Town are the pier and the new harbour. Immediately south of
George Town there is (2) an open space which contains Fort St George,
the Marina, or fashionable drive and promenade by the seashore,
Government House, and several handsome public buildings on the sea-face.
(3) West and south of this lung of the city are crowded quarters known
by native names--Chintadrapet, Turuvaleswarampet, Pudupak, Royapet,
Kistnampet and Mylapur, which bend to the sea again at the old town of
Saint Thomé. (4) To the west of George Town are the quarters of Veperi
and Pudupet, chiefly inhabited by Eurasians, and the suburbs of Egmore,
Nangambakam, and Perambur, adorned with handsome European mansions and
their spacious "compounds" or parks, which make Madras a city of
magnificent distances. (5) South-west and south lie the European
quarters of Tanampet and aristocratic Adyar. Among the most notable
buildings are the cathedral, Scottish church, Government House,
Pachayappa's Hall, senate house, Chepauk palace (now the revenue board),
and the Central railway station.

Madras possesses no special industries. There are several cotton mills,
large cement works, iron foundries and cigar factories. Large sums of
money have from time to time been spent upon the harbour works, but
without any great success. The port remains practically an open
roadstead, protected by two breakwaters, and the P. & O. steamers ceased
to call in 1898. Passengers or cargo are landed or embarked in
flat-bottomed _masula_ boats. The sea bottom is unusually flat, reaching
a depth of ten fathoms only at a mile from the shore. The harbour is not
safe during a cyclone, and vessels have to put out to sea. Madras
conducts about 56% of the foreign trade of the presidency, but a much
smaller share of the coasting trade. As the capital of southern India,
Madras is the centre on which all the great military roads converge. It
is also the terminal station of two lines of railway, the Madras &
Southern Mahratta line and the Madras & Tanjore section of the South
Indian railway. The Buckingham canal, which passes through an outlying
part of the city, connects South Arcot district with Nellore and the
Kistna and Godavari system of canal navigation. The municipal government
of the city was framed by an act of the Madras legislature passed in
1884. The governing body consists of 32 commissioners, of whom 24 are
elected by the ratepayers, together with a paid president. The Madras
University was constituted in 1857, as an examining body, on the model
of the university of London. The chief educational institutions in
Madras city are the Presidency College; six missionary colleges and one
native college; the medical college, the law college, the college of
engineering, the teachers' college in the suburb of Saidapet, all
maintained by government; and the government school of arts.

The foundation of Madras dates from 1640, when Francis Day, chief of the
East India Company's settlement at Armagon, obtained a grant of the
present site of the city from a native ruler. A fort--called Fort St
George, presumably from having been finished on St George's Day (April
23)--was at once constructed, and a gradually increasing population
settled around its walls. In 1653 Madras, which had previously been
subordinate to the settlement of Bantam in Java, was raised to the rank
of an independent presidency. In 1702 Daud Khan, Aurangzeb's general,
blockaded the town for a few weeks, and in 1741 the Mahrattas
unsuccessfully attacked the place. In 1746 La Bourdonnais bombarded and
captured Madras. The settlement was restored to the English two years
later by the Treaty of Aix-la-Chapelle, but the government of the
presidency did not return to Madras till 1762. In 1758 the French under
Lally occupied the Black Town and invested the fort. The siege was
conducted on both sides with great skill and vigour. After two months
the arrival of an English fleet relieved the garrison, and the besiegers
retired with some precipitancy. With the exception of the threatening
approach of Hyder Ali's horsemen in 1769, and again in 1780, Madras has
since the French siege been free from external attack. The town of Saint
Thomé, now part of Madras city, was founded and fortified by the
Portuguese in 1504, and was held by the French from 1672 to 1674.

  See Mrs F. Penny, _Fort St George_ (1900); W. Foster, _Founding of
  Fort St George_ (1902).




MADRAZO Y KUNT, DON FEDERICO DE (1815-1894), Spanish painter, was born
in Rome on the 12th of February 1815. He was the son of the painter
Madrazo y Agudo (1781-1859), and received his first instruction from his
father. While still attending the classes at the Academy of San Fernando
he painted his first picture, "The Resurrection of Christ" (1829), which
was purchased by Queen Christina. Not long afterwards he painted
"Achilles in his Tent," and subsequently presented to the Academy "The
Continence of Scipio," which secured him admission as a member "for
merit." While decorating the palace of Vista Alegre he took up
portraiture. In 1852 he went to Paris, where he studied under
Winterhalter, and painted portraits of Baron Taylor and of Ingres. In
1837 he was commissioned to produce a picture for the gallery at
Versailles, and painted "Godfrey de Bouillon proclaimed King of
Jerusalem." The artist then went to Rome, where he worked at various
subjects, sacred and profane. Then he painted "Maria Christina in the
Dress of a Nun by the bedside of Ferdinand III." (1843), "Queen
Isabella," "The Duchess of Medina-Coeli," and "The Countess de Vilchès"
(1845-1847), besides a number of portraits of the Spanish aristocracy,
some of which were sent to the exhibition of 1855. He received the
Legion of Honour in 1846. He was made a corresponding member of the
Paris Academy of Fine Arts on the 10th of December 1853, and in 1873, on
the death of Schnorr, the painter, he was chosen foreign member. After
his father's death he succeeded him as director of the Prado Gallery and
president of the Academy of San Fernando. He originated in Spain the
production of art reviews and journals, such as _El Artista_, _El
Renacimiento_ and _El Semanario pintoresco_. He died at Madrid on the
11th of June 1894. His brother, DON LOUIS DE MADRAZO, was also known as
a painter, chiefly by his "Burial of Saint Cecilia" (1855). Don
Federico's best-known pupil was his son, DON RAIMUNDO DE MADRAZO (b.
1841).




MADRID, a province of central Spain, formed in 1833 of districts
previously included in New Castile, and bounded on the W. and N. by
Ávila and Segovia, E. by Guadalajara, S.E. by Cuenca and S. by Toledo.
Pop. (1900), 775,034, of whom 539,835 inhabit the city of Madrid; area,
3084 sq. m. Madrid belongs to the basin of the Tagus, being separated
from that of the Douro by the Sierra de Guadarrama on the N.W. and N.,
and by the Sierra de Gredos on the S.W. The Tagus is the southern
boundary for some distance, its chief tributary being the Jarama, which
rises in the Somosierra in the north and terminates at Aranjuez. The
Jarama, in turn, is joined by the Henares and Tajuña on the left, and by
the Lozoya and Manzanares on the right. The Guadarrama, another
tributary of the Tagus, has its upper course within the province. Like
the rest of Castile, Madrid is chiefly of Tertiary formation; the soil
is mostly clayey, but there are tracts of sandy soil. Agriculture is
somewhat backward; the rainfall is deficient, and the rivers are not
utilized as they might be for irrigation. The south-eastern districts
are the best watered, and produce in abundance fruit, vegetables, wheat,
olives, esparto grass and excellent wine. Gardening and viticulture are
carried on to some extent near the capital, though the markets of Madrid
receive their most liberal supply of fruits and vegetables from
Valencia. Sheep, goats and horned cattle are reared, and fish are found
in the Jarama and other rivers. Much timber is extracted from the
forests of the northern and north-eastern parts of the province for
building purposes and for firewood and charcoal. The royal domains of
the Escorial, Aranjuez and El Pardo, and the preserves of the nobility,
are all well wooded and contain much game. Efforts have also been made
by the local authorities to cover the large stretches of waste ground
and commons with pines and other trees.

The Sierra de Guadarrama has quarries of granite, lime and gypsum, and
is known to contain iron, copper and argentiferous lead; but these
resources are undeveloped. Other industries are chiefly confined to the
capital; but cloth, leather, paper, earthenware, porcelain, glass,
bricks and tiles, ironware, soap, candles, chocolate and lace are also
manufactured on a small scale beyond its boundaries. There is very
little commerce except for the supply of the capital with necessaries.

Besides the local lines, all the great railways in the kingdom converge
in this province, and it contains in all 221 m. of line. Besides Madrid,
the towns of Aranjuez (12,670) and Alcalá de Henares (11,206) and the
Escorial are described in separate articles. The other towns with more
than 5000 inhabitants are Vallecas (10,128), Colmenar de Oreja (6182),
Colmenar Viejo (5255) and Carabanchel Bajo (5862).




MADRID, the capital of Spain and of the province of Madrid, on the left
bank of the river Manzanares, a right-hand tributary of the Jarama,
which flows south into the Tagus. Pop. (1877), 397,816; (1887), 472,228;
(1897), 512,150; (1900), 539,835. Madrid was the largest city in Spain
in 1900; it is the see of an archbishop, the focus of the principal
Spanish railways, the headquarters of an army corps, the seat of a
university, the meeting-place of parliament, and the chief residence of
the king, the court, and the captain-general of New Castile. It is,
however, surpassed in ecclesiastical importance by Toledo and in
commerce by Barcelona.

  _Situation and Climate._--Madrid is built on an elevated and
  undulating plateau of sand and clay, which is bounded on the north by
  the Sierra Guadarrama and merges on all other sides into the barren
  and treeless table-land of New Castile. Numerous water-courses
  (_arroyos_), dry except at rare intervals, furrow the surface of the
  plateau; these as they pass through the city have in certain cases
  been converted into roads--e.g. the Paseo de Recoletos and Prado,
  which are still so liable to be flooded after prolonged rain that
  special channels have been constructed to carry away the water. The
  highest point in Madrid is 2372 ft. above sea-level. The city is close
  to the geographical centre of the peninsula, nearly equidistant from
  the Bay of Biscay, the Mediterranean and the Atlantic. Owing to its
  high altitude and open situation it is liable to sudden and frequent
  variations of climate, and the daily range of temperature sometimes
  exceeds 50° F. In summer the heat is rendered doubly oppressive by the
  fiery, dust-laden winds which sweep across the Castilian table-land;
  at this season a temperature of 109° has been registered in the shade.
  In winter the northerly gales from the Sierra Guadarrama bring intense
  cold; snow falls frequently, and skating is carried on in the Buen
  Retiro park. A Spanish proverb describes the wind of Madrid as so
  deadly and subtle that "it will kill a man when it will not blow out a
  candle"; but, though pulmonary diseases are not uncommon, the climate
  appears to be exceptionally healthy. In 1901 the death-rate was 22.07
  per 1000, or lower than that of any other town on the Spanish
  mainland. The Sierra Guadarrama renders the atmosphere unusually dry
  and clear by intercepting the moisture of the north-western winds
  which prevail in summer; hence the average dally number of deaths
  decreases from 80 in winter to about 25 in summer. The sanitation of
  the older quarters is defective, and overcrowding is common, partly
  owing to the royal decrees which formerly prohibited the extension of
  the city; but much has been done in modern times to remove or mitigate
  these evils.

_The Inner City._--The form of Madrid proper (exclusive of the modern
suburbs) is almost that of a square with the corners rounded off; from
east to west it measures rather less than from north to south. It was
formerly surrounded by a poor wall, partly of brick, partly of earth,
some 20 ft. in height, and pierced by five principal gates (_puertas_)
and eleven doorways (_portillos_). Of these only three, the Puerta de
Alcalá on the east, the Puerta de Toledo on the south and the Portillo
de San Vicente on the west, actually exist; the first and the third were
erected in the time of Charles III. (1759-1788), and the second in
honour of the restoration of Ferdinand VII. (1827). The Manzanares--or
rather its bed, for the stream is at most seasons of the year quite
insignificant--is spanned by six bridges, the Puente de Toledo and
Puente de Segovia being the chief.

The Puerta del Sol is the centre of Madrid, the largest of its many
plazas, and the place of most traffic. It derived its name from the
former east gate of the city, which stood here until 1570, and had on
its front a representation of the sun. On its south side stands the
Palacio de la Gobernacion, or ministry of the interior, a heavy square
building by a French architect, J. Marquet, dating from 1768. From the
Puerta del Sol diverge, immediately or mediately, ten of the principal
streets of Madrid--eastward by north, the Calle de Alcalá, terminating
beyond the Buen Retiro park; eastward, the Carrera de San Jeronimo,
terminating by the Plaza de las Cortes in the Prado; southward, the
Calle de Carretas; westward, the Calle Mayor, which leads to the council
chamber and to the palace, and the Calle del Arenal, terminating in the
Plaza de Isabel II. and the royal opera house; north-westward, the
Calles de Preciados and Del Carmen; and northward, the Calle de la
Montera, which afterwards divides into the Calle de Fuencarral to the
left and the Calle de Hortaleza to the right. The contract for another
wide street through central Madrid, to be called the Gran Via, was given
to an English firm in 1905.

  The Calle de Alcalá is bordered on both sides with acacias, and
  contains the Real Academia de Bellas Artes, founded in 1752 as an
  academy of art and music; its collection of paintings by Spanish
  masters includes some of the best-known works of Murillo. The handsome
  Bank of Spain (1884-1891) stands where the Calle de Alcalá meets the
  Prado; in the oval Plaza de Madrid, at the same point, is a fine
  18th-century fountain with a marble group representing the goddess
  Cybele drawn in a chariot by two lions. The Calle de Alcalá is
  continued eastward past the Buen Retiro gardens and park, and through
  the Plaza de Independencia, in the middle of which is the Puerta de
  Alcalá. The Plaza de las Cortes is so called from the Congreso de los
  Diputados, or House of Commons, on its north side. The square contains
  a bronze statue of Cervantes, by Antonio Sola, erected in 1835. The
  Calle de Carretas, on the west side of which is the General Post
  Office, ranks with the Carrera de San Jeronimo and Calle de la Montera
  for the excellence of its shops. From the Calle Mayor is entered the
  Plaza Mayor, a rectangle of about 430 ft. by 330 ft., formerly the
  scene of tournaments, bull fights, autos de fé, acts of canonization
  (including that of Ignatius Loyola in 1622) and similar exhibitions,
  which used to be viewed by the royal family from the balcony of one of
  the houses called the Panaderia (belonging to the guild of bakers).
  The square, which was built under Philip III. in 1619, is surrounded
  by an arcade; the houses are uniform in height and decoration. In the
  centre stands a bronze equestrian statue of Philip III., designed by
  Giovanni da Bologna, after a painting by Pantoja de la Cruz, and
  finished by Pietro Tacca. From the south-east angle of the Plaza Mayor
  the Calle de Atocha, one of the principal thoroughfares of Madrid,
  leads to the outskirts of the inner city; it contains two large
  hospitals and part of the university buildings (faculty of medicine).
  The house occupied by Cervantes from 1606 until his death in 1616
  stands at the point where it meets the Calle de Léon; in this street
  is the Real Academia de la Historia, with a valuable library and
  collections of MSS. and plate. From the south-west angle of the Plaza
  Mayor begins the Calle de Toledo, the chief mart for the various
  woollen and silken fabrics from which the picturesque costumes
  peculiar to the peninsula are made. In the Plaza de Isabel II., at the
  western extremity of the Calle del Arenal, stands the royal
  opera-house, the principal front of which faces the Plaza del Oriente
  and the royal palace. In the centre of the plaza is a fine bronze
  equestrian statue of Philip IV. (1621-1665); it was designed by
  Velazquez and cast by Tacca, while Galileo is said to have suggested
  the means by which the balance is preserved. The gift of the grand
  duke of Tuscany in 1640, it stood in the Buen Retiro gardens until
  1844.

_Modern Development of the City._--The north and east of the city--the
new suburbs--have developed past the Retiro Park as far as the
Bull-ring, and have covered all the vast space included between the
Retiro, the Bull-ring, the long Castellana Drive to the race-course and
the exhibition building. On the slopes of the other side of the
Castellana, and along what were the northern limits of Madrid in 1875,
the modern suburbs have extended to the vicinity of the fine cellular
prison that was built at the close of the reign of King Alphonso XII. to
replace the gloomy building known as El Saladero.

The new parts of the capital, with their broad streets and squares, and
their villas sometimes surrounded with gardens, their boulevards lined
by rather stunted trees, and their modern public buildings, all resemble
the similar features of other European capitals, and contrast with the
old Madrid that has preserved so many of its traits in architecture,
popular life and habits. Some of the streets have been slightly widened,
and in many thoroughfares new houses are being built among the ugly,
irregular dwelling-places of the 18th and earlier centuries. This
contrast is to be seen especially in and about the Calle Mayor, the
Plaza Mayor, the Calle de Toledo, the Rastro, and the heart of the city.

  Few capitals have more extensively developed their electric and horse
  tramways, gas and electric light installations and telephones. Much
  was done to improve the sanitary conditions of the city in the last
  twenty years of the 19th century. The streets are deluged three times
  a day with fire-hose, but even that has little effect upon the dust.
  Unfortunately the water supply, which used to be famed for its
  abundance and purity, became wholly insufficient owing to the growth
  of the city. The old reservoir of the Lozoya canal, a cutting 32 m.
  long, and the additional reservoir opened in 1883, are quite
  inadequate for the requirements of modern Madrid, and were formerly
  kept in such an unsatisfactory state that for several months in 1898
  and 1899 the water not only was on the point of giving out, but at
  times was of such inferior quality that the people had recourse to the
  many wells and fountains available. The construction of new waterworks
  was delayed by a terrible accident, which occurred on the 8th of April
  1905; the whole structure collapsed, and nearly 400 persons lost their
  lives in the flooded ruins. A decided improvement has been made in the
  burial customs of Madrid. No bodies are allowed to be interred in the
  churches and convents. Some of the older burial grounds in the
  northern suburbs have been closed altogether, and in those which
  remain open few coffins are placed in the niche vaults in the depth of
  the thick walls, as was once the practice. A large modern necropolis
  has been established a few miles to the north-east.

_Principal Buildings._--As compared with other capitals Madrid has very
few buildings of much architectural interest. The Basilica de Nuestra
Señora de Atocha, on the Paseo de Atocha, a continuation of the Calle de
Atocha, was originally founded in 1523. After being almost destroyed by
the French, it was restored by Ferdinand VII., and rebuilt after 1896.
The modern church is Romanesque in style; it contains a much venerated
statue of the Virgin, attributed to St Luke. The collegiate church of
San Isidro el Real, in the Calle de Toledo, dates from 1651; it has no
architectural merit, but contains one or two valuable pictures and other
works of art. It was originally owned by the Jesuits, but after their
expulsion in 1769 it was reconsecrated, and dedicated to St Isidore the
Labourer (d. 1170), the patron saint of Madrid, whose remains were
entombed here. When the diocese of Madrid was separated from that of
Toledo San Isidro was chosen as the cathedral. The modern Gothic church
of San Jeronimo el Real occupies a conspicuous site eastward of the
town. The church of San Francisco el Grande, which contains many
interesting monuments, is also known as the National Pantheon. An act
was passed in 1837 declaring that the remains of all the most
distinguished Spaniards should be buried here; but no attempt to enforce
the act systematically was made until 1869, and even then the attempt
failed. Towards the close of the 19th century the church was splendidly
restored at the expense of the state. Its interior was decorated with
paintings and statuary by most of the leading Spanish artists of the
time. Of secular buildings unquestionably the most important is the
royal palace (Palacio Real), on the west side of the town, on rising
ground overhanging the Manzanares. It occupies the site of the ancient
Moorish alcázar (citadel), where a hunting seat was built by Henry IV.;
this was enlarged and improved by Charles V. when he first made Madrid
his residence in 1532; was further developed by Phillip II., but
ultimately was destroyed by fire in 1734. The present edifice was begun
under Philip V. in 1737 by Sacchetti of Turin, and was finished in 1764.
It is in the Tuscan style, and is 470 ft. square and 100 ft. in height,
the material being white Colmenar granite, resembling marble. To the
north of the palace are the royal stables and coach-houses, remarkable
for their extent; to the south is the armoury (Museo de la Real
Armería), containing what is possibly the best collection of the kind in
existence. After the Palacio Real may be mentioned the royal picture
gallery (Real Museo de Pinturas), adjoining the Salon del Prado; it was
built about 1785 for Charles III. by Juan de Villanueva as a museum of
natural history and academy of sciences. It contains the collections of
Charles V., Philip II. and Philip IV., and the pictures number upwards
of two thousand. The specimens of Titian, Raphael, Tintoretto,
Velazquez, Vandyck, Rubens and Teniers give it a claim to be considered
the finest picture gallery in the world. The Biblioteca Nacional, in the
Paseo de Recoletos, was founded in 1866, and completed in 1892. Not only
the national library, with its important collections of MSS. and
documents, but the archaeological museum, the museums of modern painting
and sculpture, and the fine arts academy of San Fernando, are within its
walls. The two houses of the Cortes meet in separate buildings. The
deputies have a handsome building with a very valuable library in the
Carrera San Jeronimo; the senators have an old Augustinian convent which
contains some fine pictures. A large and handsome building near the
Retiro Park contains the offices of the ministers of public works,
agriculture and commerce, and of fine arts and education; nearly
opposite stands the new station of the Southern Railway Company. The
Great Northern and the Spain to Portugal Railway Companies have also
replaced their old stations by very spacious, handsome structures, much
resembling those of Paris. In 1896 the Royal Exchange was installed in a
large monumental building with a fine colonnade facing the Dos de Mayo
monument, not far from the museum of paintings.

Of the promenades and open places of public resort the most fashionable
and most frequented is the Prado (Paseo del Prado, Salon del Prado) on
the east side of the town, with its northward continuation--the Paseo de
Recoletos. To the south of the town is the Paseo de las Delicias, and on
the west, below the royal palace, and skirting the Manzanares, is the
Paseo de la Virgen del Puerto, used chiefly by the poorer classes.
Eastward from the Prado are the Buen Retiro Gardens, with ponds and
pavilions, and a menagerie. The gardens were formerly the grounds
surrounding a royal hunting seat, on the site of which a palace was
built for Philip IV. in 1633; it was destroyed during the French
occupation.

_Education, Religion and Charity._--Madrid University developed
gradually out of the college of Doña Maria de Aragon, established in
1590 by Alphonso Orozco. Schools of mathematics and natural science were
added in the 16th and 17th centuries, and in 1786 the medical and
surgical college of San Carlos was opened. In 1836-1837 the university
of Alcalá de Henares (q.v.) was transferred to the capital and the older
foundations incorporated with it. The university of Madrid thenceforth
became the headquarters of education in central Spain. It has an
observatory, and a library containing more than 2,000,000 printed books
and about 5500 MSS. It gives instruction, chiefly in law and medicine,
but also in literature, philosophy, mathematics and physics, to about
5000 students. Associated with the university is the preparatory school
of San Isidro, founded by Philip IV. (1621-1665), and reorganized by
Charles III. in 1770.

  There are upwards of 100 official primary schools and a large number
  of private ones, among which the schools conducted by the Jesuits and
  the Scolapian fathers claim special mention. Madrid also has schools
  of agriculture, architecture, civil and mining engineering, the fine
  arts, veterinary science and music. The school of military engineering
  is at Guadalajara. Besides these special schools there are a
  self-supporting institute for preparing girls for the higher degrees
  and for certificates as primary teachers, and an institute for
  secondary education, conducted chiefly by ecclesiastics. Among the
  educational institutions may be reckoned the botanical garden, dating
  from 1781, the libraries of the palace, the university, and San
  Isidro, and the museum of natural science, exceedingly rich in the
  mineralogical department. The principal learned society is the royal
  Spanish Academy, founded in 1713 for the cultivation and improvement
  of the Spanish tongue. The Academy of History possesses a good
  library, rich in MSS. and incunabula, as well as a fine collection of
  coins and medals. In addition to the academies of fine arts, the exact
  sciences, moral and political science, medicine and surgery, and
  jurisprudence and legislation, all of which possess libraries, there
  are also anthropological, economic and geographical societies, and a
  scientific and literary athenaeum. Madrid has a British cemetery
  opened in 1853, when the older Protestant cemetery in the Paseo de
  Recoletos was closed. The town also contains a British embassy chapel,
  a German chapel, and several Spanish Protestant chapels, attended by
  over 1200 native Protestants, while the Protestant schools, chiefly
  supported by British, German and American contributions, are attended
  by more than 2500 children. The first Protestant bishop of Madrid was
  consecrated in 1895 by Archbishop Plunkett of Dublin. The charitable
  institutions were greatly improved between 1885 and 1905. The Princess
  Hospital was completely restored on modern methods, and can
  accommodate several hundred patients. The old contagious diseases
  hospital of San Juan de Dios was pulled down and a fine new hospital
  built in the suburbs beyond the Retiro Park, to hold 700 patients. The
  military hospital was demolished and a very good one built in the
  suburbs. There are in all twenty hospitals in Madrid, and a lunatic
  asylum on the outskirts of the capital, founded by one of the most
  eminent of Spanish surgeons, and admirably conducted. New buildings
  have been provided for the orphanages, and for the asylums for the
  blind, deaf and dumb, incurables and aged paupers. There are hospitals
  supported by the French, Italian and Belgian colonies; these are old
  and well-endowed foundations. Public charity generally is very active.
  In Madrid, as in the rest of Spain, there has been an unprecedented
  increase in convents, monasteries and religious institutions,
  societies and Roman Catholic workmen's clubs and classes.

  Apart from private institutions for such purposes, the state maintains
  in the capital a savings bank for the poorer classes, and acts as
  pawnbroker for their benefit. The mercantile and industrial classes
  are organized in gilds, which themselves collect the lump sum of
  taxation exacted by the exchequer and the municipality from each
  _gremio_ or class of taxpayers. The working classes also have
  commercial and industrial _circulos_ or clubs that are obeyed by the
  gilds with great _esprit de corps_, a chamber of commerce and
  industries, and "associations of productions" for the defence of
  economic interests.

_Industries._--The industries of the capital have developed
extraordinarily since 1890. In the town, and within the municipal
boundaries in the suburbs, many manufactories have been established,
giving employment to more than 30,000 hands, besides the 4000 women and
girls of the Tobacco Monopoly Company's factory. Among the most
important factories are those which make every article in leather,
especially cigar and card cases, purses and pocket-books. Next come the
manufactures of fans, umbrellas, sunshades, chemicals, varnishes,
buttons, wax candles, beds, cardboard, porcelain, coarse pottery,
matches, baskets, sweets and preserves, gloves, guitars, biscuits,
furniture, carpets, corks, cards, carriages, jewelry, drinks of all
kinds, plate and plated goods. There are also tanneries, saw and flour
mills, glass and porcelain works, soap works, brickfields, paper mills,
zinc, bronze, copper and iron foundries. The working classes are
strongly imbued with socialistic ideas. Strikes and May Day
demonstrations have often been troublesome. Order is kept by a garrison
of 12,500 men in the barracks of the town and cantonments around, and by
a strong force of civil guards or gendarmes quartered in the town
itself. The civil and municipal authorities can employ beside the
gendarmes the police, about 1400 strong, and what is called the
_guardias urbanos_, another police force whose special duty it is to
regulate the street traffic and prevent breaches of the municipal
regulations. There is not, on the average, more crime in Madrid than in
the provinces.

_History._--Spanish archaeologists have frequently claimed for Madrid a
very high antiquity, but the earliest authentic historical mention of
the town (Majrít, Majoritum) occurs in the Arab chronicle, and does not
take us farther back than to the first half of the 10th century. The
place was finally taken from the Moors by Alphonso VI. (1083), and was
made a hunting-seat by Henry IV., but first rose into importance when
Charles V., benefiting by its keen air, made it his occasional
residence. Philip II. created it his capital and "only court" (_única
corte_) in 1560. It is, however, only classed as a town (_villa_),
having never received the title of city (_ciudad_). Fruitless attempts
were made by Philip III. and Charles III. respectively to transfer the
seat of government to Valladolid and to Seville. (See also SPAIN:
_History_).

  See J. Amador de los Rios, _Historia de la villa y corte de Madrid_
  (Madrid, 1861-1864); Valverdey Alvarez, _La Capitol de España_
  (Madrid, 1883); E. Sepúlveda, _La Vida en Madrid en 1886_ (Madrid,
  1887); H. Peñasco, _Las Calles de Madrid_ (Madrid, 1889); C. Perez
  Pastor, _Bibliografia madrileña, siglo XVI._ (Madrid, 1891); F. X. de
  Palacio y Garcia, count of las Almenas, _La Municipalidad de Madrid_
  (Madrid, 1896); E. Sepúlveda, _El Madrid de los recuerdos: colección
  de artículos_ (Madrid, 1897); P. Hauser, _Madrid bajo el punto de
  vista medico-social_ (Madrid, 1902); L. Williams, _Toledo and Madrid,
  their Records and Romances_ (London, 1903).




MADRIGAL (Ital. _madrigale_), the name of a form of verse, the exact
nature of which has never been decided in English, and of a form of
vocal music.

(1) _In Verse._--The definition given in the _New English Dictionary_,
"a short lyrical poem of amatory character," offers no distinctive
formula; some madrigals are long, and many have nothing whatever to do
with love. The most important English collection of madrigals, not set
to music, was published by William Drummond of Hawthornden (1585-1649)
in his _Poems_ of 1616. Perhaps the best way of ascertaining what was
looked upon in the 17th century as a madrigal is to quote one of
Drummond's:--

  The beauty and the life
  Of life's and beauty's fairest paragon,
  O tears! O grief! hung at a feeble thread.
  To which pale Atropos had set her knife;
  The soul with many a groan
  Had left each outward part,
  And now did take his last leave of the heart;
  Nought else did want, save death, even to be dead;
  When the afflicted band about her bed.
  Seeing so fair him come in lips, cheeks, eyes,
  Cried ah! and can death enter Paradise?

This may be taken as a type of Drummond's madrigals, of which he has
left us about eighty. They are serious, brief, irregular lyrics, in
which neither the amatory nor the complimentary tone is by any means
obligatory. Some of these pieces contain as few as six lines, one as
many as fourteen, but they average from nine to eleven. In the majority
of examples the little poem opens with a line of six syllables, and no
line extends beyond ten syllables. The madrigal appears to be a short
canzone of the Tuscan type, but less rigidly constructed. In French the
madrigal has not this Italian character. It is simply a short piece of
verse, ingenious in its turn and of a gallant tendency. The idea of
compliment is essential. J. F. Guichard (1730-1811) writes:--

  Orgon, poète marital,
      À Venus compare sa femme;
  C'est pour la belle un madrigal,
      C'est pour Venus une épigramme.

This quatrain emphasizes the fact that in French a madrigal is a
trifling piece of erotic compliment, neatly turned but not seriously
meant. The credit of inventing the old French verse-form of madrigal
belongs to Clément Marot, and one of his may be quoted in contrast to
that of Drummond:--

  Un doux nenni avec un doux sourire
    Est tant honneste, il le vous faut apprendre;
  Quant est de oui, si veniez à le dire,
    D'avoir trop dit je voudrois vous reprendre;
    Non que je sois ennuyé d'entreprendre
  D'avoir le fruit dont le désir me point;
    Mais je voudrois qu'en ne le laissant prendre,
    Vous me disiez: vous ne l'aurez point.

In English, when the word first occurred--it has not been traced farther
back than 1588 (in the preface to Nicholas Yonge's _Musica
transalpina_)--it was identified with the chief form of secular vocal
music in the 16th century. In 1741 John Immyns (d. 1764) founded the
Madrigal Society, which met in an ale-house in Bride Lane, Fleet Street;
this association still exists, and is the oldest musical society in
Europe.

The word "madrigal" is frequently also used to designate a sentimental
or trifling expression in a half-contemptuous sense.     (E. G.)

(2) _In Music._--As a definite musical art-form, the madrigal was known
in the Netherlands by the middle of the 15th century; like the motet, it
obviously originated in the treatment of counterpoint on a canto fermo,
some early examples even combining an ecclesiastical canto fermo in the
tenor with secular counterpoint in the other parts. Thus Josquin's
_Déploration de Jehan Okenheim_ (see MUSIC) might equally well be called
a madrigal or motet, if the word "madrigal" were used for compositions
to French texts at all. But by the middle of the 16th century the
Italian supremacy in music had developed the madrigal into the greatest
of secular musical forms, and made it independent of the form of the
words; and thus when Lasso sets Marot's madrigals to appropriately witty
and tuneful music he calls the result a "chanson"; while when Palestrina
composes Petrarca's Sonnets to the Virgin in memory of Laura, the result
appears as a volume of _Madrigali spirituali_. Elegiac madrigals,
whether spiritual or secular, were thus as common as any other kind; so
that when the _Musica transalpina_ brought the word "madrigal" to
England it brought a precedent for the poet Drummond's melancholy type
of madrigal poetry.

Italian madrigals, however, are by no means always elegiac; but the term
always means a highly organized and flowing polyphonic piece, often as
developed as the motet, though, in the mature classical period, distinct
in style. Yet masses were often founded on the themes of madrigals, just
as they were on the themes of motets (see MASS; MOTET); and it is
interesting, in such beautiful cases as Palestrina's _Missa gia fu chi
m'ebbe cara_, to detect the slight strain the mildly scandalous origin
of the themes puts upon the ecclesiastical style.

The breaking strain was put on the madrigal style at the end of the 16th
century, in one way by the new discords of Monteverde and (with more
musical invention) Schütz; and in another way by the brilliant musical
character-drawing of Vecchi, whose _Amfiparnasso_ is a veritable comic
opera in the form of a set of fourteen madrigals, all riotously witty in
the purest and most masterly polyphonic style. It was probably meant, or
at least made use of, to laugh down the earliest pioneers of opera
(q.v.); but it is the beginning of the end for the madrigal as a living
art. Long afterwards we occasionally meet with the word again, when a
17th or 18th century composer sets to some kind of accompanied singing a
poem of madrigalesque character. But this does not indicate any
continuation of the true musical history of the madrigal. The strict
meaning of the word in its musical sense is, then, a musical setting of
an Italian or English non-ecclesiastical poem (typically a canzone) for
unaccompanied chorus, in a 16th-century style less ecclesiastical than
the motet, but as like it in organization as the form and sentiment of
the words admit. The greatest classics in the madrigal style are those
of Italy; and but little, if at all, below them come the English. The
form, though not the name, of course, exists in the 16th-century music
of other languages whenever the poetry is not too light for it.

It is important but easy to distinguish the madrigal from the lighter
16th-century forms, such as the Italian _villanella_ and the English
ballet, these being very homophonic and distinguished by the strong lilt
of their rhythm.

The madrigal has been very successfully revived in modern English music
with a more or less strict adherence to the 16th century principles; the
compositions of De Pearsall being of high artistic merit, while the
_Madrigale spirituale_ in Stanford's oratorio _Eden_ is a movement of
rare beauty.     (D. F. T.)




MADURA (Dutch _Madoera_), an island of the Dutch East Indies, separated
by the shallow Strait of Madura from the N.E. coast of Java. Pop.
(1897), 1,652,580, of whom 1,646,071 were natives, 4252 Chinese and 558
Europeans. It extends from about 112° 32´ to 114° 7´ E., and is divided
into two nearly equal portions by the parallel of 7° S.; the area is
estimated at 1725 sq. m. It is a plateau-like prolongation of the
limestone range of northern Java, with hills (1300 to 1600 ft. high) and
dales. The formation of the coast and plains is Tertiary and recent
alluvium. Hot springs are not infrequent; and in the valley between
Gunong Geger and Banjar lies the mud volcano of Banju Ening. The coasts
are clothed with tropical vegetation; but the soil is better fitted for
pastoral than agricultural purposes. Fishing and cattle-rearing are the
chief means of subsistence. Besides rice and maize, Madura yields
coco-nut oil and _jati_. The manufacture of salt for the government,
abolished in other places, continues in Madura. Hence perhaps the name
is derived (Sansk. _mandura_, salt). Petroleum is found in small
quantities.

The principal town is Sumenep; and there are populous Malay, Arab and
Chinese villages between the town and the European settlement of
Maringan. On a hill in the neighbourhood lies Asta, the burial-place of
the Sumenep princes. Pamekasan is the seat of government. Bangkalang is
a large town with the old palace of the sultan of Madura and the
residences of the princes of the blood; the mosque is adorned with the
first three suras of the Koran, thus differing from nearly all the
mosques in Java and Madura, though resembling those of western Islam. In
the vicinity once stood the Erfprins fort. Arisbaya (less correctly
Arosbaya) is the place where the first mosque was built in Madura, and
where the Dutch sailors first made acquaintance with the natives. The
once excellent harbour is now silted up. Sampang is the seat of an
important market. The Kangean and Sapudi islands, belonging to Madura,
yield timber, trepang, turtle, pisang and other products.

Madura formerly consisted of three native states--Madura or Bangkalang,
Pamekasan and Sumenep. The whole island was considered part of the Java
residency of Surabaya. The separate residency of Madura was constituted
in 1857; it now consists of four "departments"--Pamekasan, Madura,
Sumenep and Sampang.

  See P. J. Veth, Java, vol. iii.; Kielstra, "Het Eiland Madoera," in
  _De Gids_ (1890); H. van Lennep, "De Madoereezen," in _De Indische
  Gids_ (1895), with detailed bibliography.




MADURA, a city and district of British India, in the Madras Presidency.
The city is situated on the right bank of the river Vaigai, and has a
station on the South Indian railway 345 m. S.E. of Madras. Pop. (1901),
105,984. The city was the capital of the old Pandyan dynasty, which
ruled over this part of India from the 5th century B.C. to the end of
the 11th century A.D. Its great temple forms a parallelogram about 847
ft. by 729 ft., and is surrounded by nine _gopuras_, of which the
largest is 152 ft. high. These ornamental pyramids begin with doorposts
of single stones 60 ft. in height, and rise course upon course, carved
with rows of gods and goddesses, peacocks, bulls, elephants, horses,
lions, and a bewildering entanglement of symbolical ornament all
coloured and gilded, diminishing with distance until the stone _trisul_
at the top looks like the finest jeweller's work. The temple, which
contains some of the finest carving in southern India, is said to have
been built in the reign of Viswanath, first ruler of the Nayak dynasty.
Its chief feature is the sculptured "Hall of a Thousand Pillars." The
palace of Tirumala Nayak is the most perfect relic of secular
architecture in Madras. This palace, which covers a large area of
ground, has been restored, and is utilized for public offices. The
Vasanta, a hall 333 ft. long, probably dedicated to the god
Sundareswara, and the Tamakam, a pleasure-palace, now the residence of
the collector, are the other principal buildings of this period.

The last of the old Pandyan kings is said to have exterminated the Jains
and conquered the neighbouring kingdom of Chola; but he was in his turn
overthrown by an invader from the north, conjectured to have been a
Mahommedan. In 1324 a Moslem army under Malik Kafur occupied Madura, and
the Hindus were held in subjection for a period of fifty years.
Subsequently Madura became a province of the Hindu Empire of
Vijayanagar. In the middle of the 16th century the governor Viswanath
established the Nayak dynasty, which lasted for a century. The greatest
of the line was Tirumala Nayak (reigned 1623-1659), whose military
exploits are recorded in the contemporary letters of the Jesuit
missionaries. He adorned Madura with many public buildings, and extended
his empire over the adjoining districts of Tinnevelly, Travancore,
Coimbatore, Salem and Trichinopoly. His repudiation of the nominal
allegiance paid to the raja of Vijayanagar brought him into collision
with the sultan of Bijapur, and after a lapse of three centuries
Mahommedans again invaded Madura and compelled him to pay them tribute.
After the death of Tirumala the kingdom of Madura gradually fell to
pieces, being invaded by both Mahommedans and Mahrattas. About 1736 the
district fell into the hands of the nawab of the Carnatic, and the line
of the Nayaks was extinguished. About 1764 British officers took charge
of Madura in trust for Mahommed Ali (Wallah Jah), the last independent
nawab of the Carnatic, whose son finally ceded his rights of sovereignty
to the East India Company in 1801.

The DISTRICT OF MADURA has an area of 8701 sq. m. Pop. (1901),
2,831,280, an increase of 8.5% in the decade. It consists of a section
of the plain stretching from the mountains east to the sea, coinciding
with the basin of the Vaigai river, and gradually sloping to the S.E.
The plain is broken by the outlying spurs of the Ghats, and by a few
isolated hills and masses of rock scattered over the country. The most
important spur of the Ghats is known as the Palni hills, which project
E.N.E. across the district for a distance of about 54 m. Their highest
peaks are more than 8000 ft. above sea-level, and they enclose a plateau
of about 100 sq. m., with an average height of 7000 ft. On this plateau
is situated the sanatorium of Kodaikanal, and coffee-planting is
successfully carried on. The other principal crops of the district are
millets, rice, other food-grains, oil-seeds and cotton. Tobacco is grown
chiefly in the neighbourhood of Dindigul, whence it is exported to
Trichinopoly, to be made into cigars. There are several cigar factories
and a number of saltpetre refineries. The only other large industry is
that of coffee-cleaning. Madura is traversed by the main line of the
South Indian railway. It has four small seaports, whose trade is chiefly
carried on with Ceylon. The most important irrigation work, known as the
Periyar project, consists of a tunnel through the Travancore hills, to
convey the rainfall across the watershed.

  See _Madura District Gazetteer_ (Madras, 1906).




MADVIG, JOHAN NICOLAI (1804-1886), Danish philologist, was born on the
island of Bornholm, on the 7th of August 1804. He was educated at the
classical school of Frederiksborg and the university of Copenhagen. In
1828 he became reader, and in 1829 professor, of Latin language and
literature at Copenhagen, and in 1832 was appointed university
librarian. In 1848 Madvig entered parliament as a member of what was
called the "Eider-Danish" party, because they desired the Eider to be
the boundary of the country. When this party came into power Madvig
became minister of education. In 1852 be became director of public
instruction. Some years later, from 1856 to 1863, Madvig was president
of the Danish parliament and leader of the National Liberal party. With
these brief interruptions the greater part of his life was devoted to
the study and teaching of Latin and the improvement of the classical
schools, of which he was chief inspector. As a critic he was
distinguished for learning and acumen. He devoted much attention to
Cicero, and revolutionized the study of his philosophical writings by an
edition of _De Finibus_ (1839; 3rd ed., 1876). Perhaps his most widely
known works are those on Latin grammar and Greek syntax, especially his
Latin grammar for schools (Eng. trans. by G. Woods). In 1874 his sight
began to fail, and he was forced to give up much of his work. He still,
however, continued to lecture, and in 1879 he was chosen rector for the
sixth time. In 1880 he resigned his professorship, but went on with his
work on the Roman constitution, which was completed and published before
his death. In this book Madvig takes a strongly conservative standpoint
and attacks Mommsen's views on Caesar's programme of reforms. It is a
clear exposition, though rather too dogmatic and without sufficient
regard for the views of other scholars. His last work was his
autobiography, _Livserindringer_ (published 1887). Madvig died at
Copenhagen on the 12th of December 1886.

  See J. E. Sandys, _History of Classical Scholarship_ (1908), iii.,
  319-324.




MAECENAS, GAIUS (CILNIUS), Roman patron of letters, was probably born
between 74 and 64 B.C., perhaps at Arretium. Expressions in Propertius
(ii. 1, 25-30) seem to imply that he had taken some part in the
campaigns of Mutina, Philippi and Perusia. He prided himself on his
ancient Etruscan lineage, and claimed descent from the princely house of
the Cilnii, who excited the jealousy of their townsmen by their
preponderating wealth and influence at Arretium in the 4th century B.C.
(Livy x. 3). The Gaius Maecenas mentioned in Cicero (_Pro Cluentio_, 56)
as an influential member of the equestrian order in 91 B.C. may have
been his grandfather, or even his father. The testimony of Horace
(_Odes_ iii. 8, 5) and Maecenas's own literary tastes imply that he had
profited by the highest education of his time. His great wealth may have
been in part hereditary, but he owed his position and influence to his
close connexion with the emperor Augustus. He first appears in history
in 40 B.C., when he was employed by Octavian in arranging his marriage
with Scribonia, and afterwards in assisting to negotiate the peace of
Brundusium and the reconciliation with Antony. It was in 39 B.C. that
Horace was introduced to Maecenas, who had before this received Varius
and Virgil into his intimacy. In the "Journey to Brundusium," (Horace,
_Satires_, i. 5) in 37, Maecenas and Cocceius Nerva are described as
having been sent on an important mission, and they were successful in
patching up, by the Treaty of Tarentum, a reconciliation between the two
claimants for supreme power. During the Sicilian war against Sextus
Pompeius in 36, Maecenas was sent back to Rome, and was entrusted with
supreme administrative control in the city and in Italy. He was
vice-gerent of Octavian during the campaign of Actium, when, with great
promptness and secrecy, he crushed the conspiracy of the younger
Lepidus; and during the subsequent absences of his chief in the
provinces he again held the same position. During the latter years of
his life he fell somewhat out of favour with his master. Suetonius
(_Augustus_, 66) attributes the loss of the imperial favour to Maecenas
having indiscreetly revealed to Terentia, his wife, the discovery of the
conspiracy in which her brother Murena was implicated. But according to
Dio Cassius (liv. 19) it was due to the emperor's relations with
Terentia. Maecenas died in 8 B.C., leaving, the emperor heir to his
wealth.

Opinions were much divided in ancient times as to the personal character
of Maecenas; but the testimony as to his administrative and diplomatic
ability was unanimous. He enjoyed the credit of sharing largely in the
establishment of the new order of things, of reconciling parties, and of
carrying the new empire safely through many dangers. To his influence
especially was attributed the humaner policy of Octavian after his first
alliance with Antony and Lepidus. The best summary of his character as a
man and a statesman is that of Velleius Paterculus (ii. 88), who
describes him as "of sleepless vigilance in critical emergencies,
far-seeing and knowing how to act, but in his relaxation from business
more luxurious and effeminate than a woman."

Expressions in the _Odes_ of Horace (ii. 17. i) seem to imply that
Maecenas was deficient in the robustness of fibre characteristic of the
average Roman. His character as a munificent patron of literature--which
has made his name a household word--is gratefully acknowledged by the
recipients of it and attested by the regrets of the men of letters of a
later age, expressed by Martial and Juvenal. His patronage was
exercised, not from vanity or a mere dilettante love of letters, but
with a view to the higher interest of the state. He recognized in the
genius of the poets of that time, not only the truest ornament of the
court, but a power of reconciling men's minds to the new order of
things, and of investing the actual state of affairs with an ideal glory
and majesty. The change in seriousness of purpose between the _Eclogues_
and the _Georgics_ of Virgil was in a great measure the result of the
direction given by the statesman to the poet's genius. A similar change
between the earlier odes of Horace, in which he declares his epicurean
indifference to affairs of state, and the great national odes of the
third book is to be ascribed to the same guidance. Maecenas endeavoured
also to divert the less masculine genius of Propertius from harping
continually on his love to themes of public interest. But if the motive
of his patronage had been merely politic it never could have inspired
the affection which it did in its recipients. The great charm of
Maecenas in his relation to the men of genius who formed his circle was
his simplicity, cordiality and sincerity. Although not particular in the
choice of some of the associates of his pleasures, he admitted none but
men of worth to his intimacy, and when once admitted they were treated
like equals. Much of the wisdom of Maecenas probably lives in the
_Satires_ and _Epistles_ of Horace. It has fallen to the lot of no other
patron of literature to have his name associated with works of such
lasting interest as the _Georgics_ of Virgil, the first three books of
Horace's _Odes_, and the first book of his _Epistles_.

Maecenas himself wrote in both prose and verse. The few fragments that
remain show that he was less successful as an author than as a judge and
patron of literature. His prose works on various subjects--_Prometheus_,
_Symposium_ (a banquet at which Virgil, Horace and Messalla were
present), _De cultu suo_ (on his manner of life)--were ridiculed by
Augustus, Seneca and Quintilian for their strange style, the use of rare
words and awkward transpositions. According to Dio Cassius, Maecenas was
the inventor of a system of shorthand.

  There is no good modern biography of Maecenas. The best known is that
  by P. S. Frandsen (1843), See "Horace et Mecène" by J. Girard, in _La
  Révue politique et littéraire_ (Dec. 27, 1873); V. Gardthausen,
  _Augustus und seine Zeit_, i. 762 seq.; ii. 432 seq. The chief ancient
  authorities for his life are Horace (_Odes_ with Scholia), Dio
  Cassius, Tacitus (_Annals_), Suetonius (_Augustus_). The fragments
  have been collected and edited by F. Harder (1889).




MAECIANUS, LUCIUS VOLUSIUS (2nd cent.) Roman jurist, was the tutor in
law of the emperor Marcus Aurelius. When governor of Alexandria he was
slain by the soldiers, as having participated in the rebellion of
Avidius Cassius (175). Maecianus was the author of works on trusts
(_Fideicommissa_), on the _Judicia publica_, and of a collection of the
Rhodian laws relating to maritime affairs. His treatise on numerical
divisions, weights and measures (_Distributio_) is extant, with the
exception of the concluding portion.

  See Capitolinus, _Antoninus_, 3; Vulcacius Gallicanus, _Avidius
  Cassius_, 7; edition of the metrological work by F. Hultsch in
  _Metrologicorum scriptorum reliquiae,_ ii. (1866); Mommsen in
  _Abhandlungen der sächsischen Gesellschaft der Wissenschaften_, iii.
  (1853).




MAELDUIN (or MAELDUNE), VOYAGE OF (_Imram Maeleduin_), an early Irish
romance. The text exists in an 11th-century redaction, by a certain Aed
the Fair, described as the "chief sage of Ireland," but it may be
gathered from internal evidence that the tale itself dates back to the
8th century. It belongs to the group of Irish romance, the _Navigations_
(_Imrama_), the common type of which was probably imitated from the
classical tales of the wanderings of Jason, of Ulysses and of Aeneas.
Maelduin, the foster-son of an Irish queen, learnt on reaching manhood
that he was the son of a nun, and that his father, Ailill of the edge of
battle, had been slain by a marauder from Leix. He set sail to seek his
father's murderer, taking with him, in accordance with the instructions
of a sorcerer, seventeen men. His three foster-brothers swam after him,
and were taken on board. This increase of the fateful number caused
Maelduin's vengeance to be deferred for three years and seven months,
until the last of the intruders had perished. The travellers visited
many strange islands, and met with a long series of adventures, some of
which are familiar from other sources. The _Voyage of St Brendan_ (q.v.)
has very close similarities with the _Maelduin_, of which it is possibly
a clerical imitation, with the important addition of the whale-island
episode, which it has in common with "Sindbad the Sailor."

  _Imram Curaig Mailduin_ is preserved, in each case imperfectly, in the
  _Lebor na h Uidre_, a MS. in the Royal Irish Academy, Dublin; and in
  the _Yellow Book of Lecan_, MS. H. 216 in the Trinity College Library,
  Dublin; fragments are in Harleian MS. 5280 and Egerton MS. 1782 in the
  British Museum. There are translations by Patrick Joyce, _Old Celtic
  Romances_ (1879), by Whitley Stokes (a more critical version, printed
  together with the text) in _Revue celtique_, vols. ix. and x.
  (1888-1889). See H. Zimmer, "Brendan's Meerfahrt" in _Zeitschrift für
  deutsches Altertum_, vol. xxxiii. (1889). Tennyson's _Voyage of
  Maeldune_, suggested by the Irish romance, borrows little more than
  its framework.




MAELIUS, SPURIUS (d. 439 B.C.), a wealthy Roman plebeian, who during a
severe famine bought up a large amount of corn and sold it at a low
price to the people. Lucius (or Gaius) Minucius, the patrician
_praefectus annonae_ (president of the market), thereupon accused him of
courting popularity with a view to making himself king. The cry was
taken up. Maelius, summoned before the aged Cincinnatus (specially
appointed dictator), refused to appear, and was slain by Gaius Servilius
Ahala; his house was razed to the ground, his corn distributed amongst
the people, and his property confiscated. The open space called
Aequimaelium, on which his house had stood, preserved the memory of his
death. Cicero calls Ahala's deed a glorious one, but, whether Maelius
entertained any ambitious projects or not, his summary execution was an
act of murder, since by the Valerio-Horatian laws the dictator was bound
to allow the right of appeal.

  See Niebuhr's _History of Rome_, ii. 418 (Eng. trans., 1851); G.
  Cornewall Lewis, _Credibility of early Roman History_, ii.; Livy, iv.
  13; Cicero, _De senectute_ 16, _De amicitia_ 8, _De republica_, ii.
  27; Floras, i. 26; Dion. Halic. xii. i.




MAELSTROM (whirlpool), a term originally applied to a strong current
running past the south end of the island of Moskenaes, a member of the
group of Lofoten Islands on the west coast of Norway. It is known also
as the Moskenstrom. Though dangerous in certain states of wind and tide,
the tales of ships being swallowed in this whirlpool are fables. The
word is probably of Dutch origin, from _malen_, to grind or whirl, and
_strom_ or _stroom_, a stream or current. It appears on Mercator's
_Atlas_ of 1595.




MAENADS (Gr. [Greek: Mainades], frenzied women), the female attendants
of Dionysus. They are known by other names--Bacchae, Thyiades, Clodones
and Mimallones (the last two probably of Thracian origin)--all more or
less synonymous.

  See the exhaustive articles by A. Legrand in Daremberg and Saglio's
  _Dictionnaire des antiquités_ and A. Rapp in Roscher's _Lexikon der
  Mythologie_; also editions of Euripides, _Bacchae_ (e.g. J. E.
  Sandys).




MAENIUS, GAIUS, Roman statesman and general. Having completed (when
consul in 338 B.C.) the subjugation of Latium, which with Campania had
revolted against Rome, he was honoured by a triumph, and a column was
erected to him in the Forum. When censor in 318, in order that the
spectators might have more room for seeing the games that were
celebrated in the Forum, he provided the buildings in the neighbourhood
with balconies, which were called after him _maeniana_.

  See Festus, s.v. Maeniana; Livy viii. 13, ix. 34; Pliny, _Nat. Hist._
  xxxiv. 11 (5).




MAERLANT, JACOB VAN (c. 1235-c. 1300), Flemish poet, was born in the
Franc de Burges (tradition says at Damme) between 1230 and 1240. He was
sacristan of Maerlant, in the island of Ost-Voorne, and afterwards clerk
to the magistrates at Damme. His early works are translations of French
romances. Maerlant's most serious work in the field of romance was his
_Ystorien van Troyen_ (c. 1264), a poem of some forty thousand lines,
translated and amplified from the _Roman de Troie_ of Benoît de
Sainte-More. From this time Maerlant rejected romance as idle, and
devoted himself to writing scientific and historical works for the
education and enlightenment of the Flemish people. His _Heimelicheit der
Heimelicheden_ (c. 1266) is a translation of the _Secreta secretorum_, a
manual for the education of princes, ascribed throughout the middle ages
to Aristotle. _Van der Naturen Bloeme_ is a free translation of _De
natura rerum_, a natural history in twenty books by a native of Brabant,
Thomas de Cantimpré; and his _Rijmbijbel_ is taken, with many omissions
and additions, from the _Historia scholastica_ of Petrus Comestor. He
supplemented this metrical paraphrase of Scripture history by _Die Wrake
van Jherusalem_ (1271) from Josephus. Although Maerlant was an orthodox
Catholic, he is said to have been called to account by the priests for
translating the Bible into the vulgar tongue. In 1284 he began his
_magnum opus_, the _Spiegel historiael_, a history of the world, derived
chiefly from the third part of the _Speculum majus_ of Vincent de
Beauvais. This work was completed by two other writers, Philipp
Utenbroeke and Lodowijk van Velthem. Maerlant died in the closing years
of the 13th century, his last poem, _Van den lande van oversee_, dating
from 1291. The greater part of his work consists of translations, but he
also produced poems which prove him to have had real original poetic
faculty. Among these are _Die Clausule van der Bible_, _Der Kerken
Clage_, imitated from the _Complaintes_ of Rutebeuf, and the three
dialogues entitled _Martijn_, in which the fundamental questions of
theology and ethics were discussed. In spite of his orthodoxy, Maerlant
was a keen satirist of the corruptions of the clergy. He was one of the
most learned men of his age, and for two centuries was the most
celebrated of Flemish poets.

  See monographs by J. van Beers (Ghent, 1860); C. A. Serrure (Ghent,
  1861); K. Versnaeyen (Ghent, 1861); J. te Winkel (Leiden, 1877, 2nd
  ed., Ghent, 1892); and editions of _Torec_ (Leiden, 1875) by J. te
  Winkel; of _Naturen Bloeme_, by Eelco Verwijs; of _Alexanders Geesten_
  (Groningen, 1882), by J. Franck; _Merlijn_ (Leiden, 1880-1882), by J.
  van Bloten; _Heimelicheit der Heimelicheden_ (Dordrecht, 1838), by
  Clarisse; _Der Naturen Bloeme_ (Groningen, 1878), by Verwijs; of
  _Rijmbijbel_ (Brussels, 1858-1869), by David; _Spiegel historiael_
  (Leiden 1857-1863), by Verwijs and de Vries; selections from the
  _Ystorien van Troyen_ (1873), by J. Verdam.




MAES, NICOLAS (1632-1693), Dutch painter, was born at Dordrecht, and
went about 1650 to Amsterdam, where he entered Rembrandt's studio.
Before his return to Dordrecht in 1654 Maes painted a few Rembrandtesque
genre pictures, with life-size figures and in a deep glowing scheme of
colour, like the "Reverie" at the Ryks Museum in Amsterdam, the "Card
Players" at the National Gallery, and the "Children with a Goat
Carriage," belonging to Baroness N. de Rothschild. So closely did his
early style resemble that of Rembrandt, that the last-named picture, and
other canvases in the Leipzig and Budapest galleries and in the
collection of Lord Radnor, were or are still ascribed to Rembrandt. In
his best period, from 1655 to 1665, Maes devoted himself to domestic
genre on a smaller scale, retaining to a great extent the magic of
colour he had learnt from Rembrandt. Only on rare occasions did he treat
scriptural subjects, as in the earl of Denbigh's "Hagar's Departure,"
which has been ascribed to Rembrandt. His favourite subjects were women
spinning, or reading the Bible, or preparing a meal. In 1665 he went to
Antwerp, where he remained till 1678, in which year he probably returned
to Amsterdam. His Antwerp period coincides with a complete change in
style and subject. He devoted himself almost exclusively to portraiture,
and abandoned the intimacy and glowing colour harmonies of his earlier
work for a careless elegance which suggests the influence of Van Dyck.
So great indeed was the change, that it gave rise to the theory of the
existence of another Maes, of Brussels. Maes is well represented at the
National Gallery by five paintings: "The Cradle," "The Dutch Housewife,"
"The Idle Servant," "The Card Players," and a man's portrait. At
Amsterdam, besides the splendid examples to be found at the Ryks Museum,
is the "Inquisitive Servant" of the Six collection. At Buckingham Palace
is "The Listening Girl" (repetitions exist), and at Apsley House
"Selling Milk" and "The Listener." Other notable examples are at the
Berlin, Brussels, St Petersburg, the Hague, Frankfort, Hanover and
Munich galleries.




MAESTRO, a north-westerly wind observed in the Adriatic and surrounding
regions, chiefly during summer. The maestro is a "fine weather" wind,
and is the counterpart of the sirocco.




MAETERLINCK, MAURICE (1862-   ), Belgian-French dramatist and poet, of
Flemish extraction, was born at Ghent on the 29th of August 1862. He was
educated at the Collège Sainte-Barbe, and then at the university of his
native city, where, at the age of twenty-four, he was enrolled as a
barrister. In 1887 he settled in Paris, where he immediately became
acquainted with Villiers de l'Isle-Adam and the leaders of the symbolist
school of French poetry. At the death of his father, Maeterlinck
returned to Belgium, where he thenceforth mainly resided: in the winter
at Ghent, in the summer on an estate at Oostacker. He had by this time
determined to devote his whole life to poetry, a dedication which his
fortune permitted. His career as an author began in 1889, when he
published a volume of verse, _Serres chaudes_, and a play, _La Princesse
Maleine_, the latter originally composed in metre, but afterwards
carefully rewritten in prose, the vehicle which the author continued to
use for his dramatic work. Maeterlinck was at this time totally unknown,
but he became famous through an article by Octave Mirbeau, prominently
published in the Paris _Figaro_, entitled "A Belgian Shakespeare." The
enthusiasm of this review and the excellence of the passages quoted
combined to make Maeterlinck the talk of the town. Maeterlinck, among
his Belgian roses, continued to work with extreme deliberation. In 1890
he published, in Brussels, two more plays, _L'Intruse_ and _Les
Aveugles_; followed in 1891 by _Les Sept princesses_. His strong leaning
to mysticism was now explained, or defined, by a translation of the
Flemish medieval visionary, the Admirable Ruysbroeck, which Maeterlinck
brought out in 1891. In 1892 appeared what has been perhaps the most
successful of all his plays on the stage, _Pelléas et Mélisande_,
followed in 1894 by those very curious and powerful little dramas
written to be performed by marionettes: _Alladine el Palomides_,
_Intérieur_ and _La Mort de Tintagiles_. In 1895 Maeterlinck brought
out, under the title of _Annabella_, a translation of Ford's _'Tis Pity
She's a Whore_, with a preface. Two philosophical works followed, a
study on Novalis (1895) and _Le Trésor des humbles_ (1896). In 1896 he
returned to drama with _Aglavaine el Sélysette_ and to lyric verse with
_Douze chansons_. A monograph on the ethics of mysticism, entitled _La
Sagesse et la destinée_, was issued, as a kind of commentary on his own
dramas, in 1898; and in 1901 Maeterlinck produced a fascinating volume
of prose, founded upon observations made in his apiaries at Oostacker,
in which philosophy, fancy and natural history were surprisingly
mingled--_La Vie des abeilles_. In 1902 he published _Le Temple
enseveli_ and _Monna Vanna_; in 1903 _Joyzelle_. In 1901 he began to
issue, in Brussels, an edition of his complete dramatic works.

The nature of Maeterlinck's writings, whether in prose or verse, has
been strictly homogeneous. Few poets have kept so rigorously to a
certain defined direction in the practice of their art. Whether in
philosophy, or drama, or lyric, Maeterlinck is exclusively occupied in
revealing, or indicating, the mystery which lies, only just out of
sight, beneath the surface of ordinary life. In order to produce this
effect of the mysterious he aims at an extreme simplicity of diction,
and a symbolism so realistic as to be almost bare. He allows life itself
to astonish us by its strangeness, by its inexplicable elements. Many of
his plays are really highly pathetic records of unseen emotion; they are
occupied with the spiritual adventures of souls, and the ordinary facts
of time and space have no influence upon the movements of the
characters. We know not who these orphan princesses, these blind
persons, these pale Arthurian knights, these aged guardians of desolate
castles, may be; we are not informed whence they come, nor whither they
go; there is nothing concrete or circumstantial about them. Their life
is intense and consistent, but it is wholly of a spiritual character;
they are mysterious with the mystery of the movements of a soul. These
characteristics, which make the dramatic work of Maeterlinck so curious
and unique, are familiar to most readers in _Pelléas et Mélisande_, but
are carried, perhaps, to their farthest intensity in _Aglavaine et
Sélysette_, which seems to be written for a phantom stage and to be
acted by disembodied spirits. In spite of the violence of his early
admirers, and of the fact that the form of his dramas easily lent itself
to the cheap ridicule of parodists, the talent of Maeterlinck has hardly
met with opposition from the criticism of his time. It has been
universally felt that his spirit is one of grave and disinterested
attachment to the highest moral beauty, and his seriousness, his
serenity and his extreme originality have impressed even those who are
bewildered by his diaphanous graces and offended at his nebulous
mysticism. While the crude enthusiasm which compared him with
Shakespeare has been shown to be ridiculous, the best judges combine
with Camille Mauclair when he says: "Maurice Maeterlinck est un homme
de génie authentique, un très grand phénomène de puissance mentale à la
fin du xix^e siècle." In spite of the shadowy action of Maeterlinck's
plays, which indeed require some special conditions and contrivances for
their performance, they are frequently produced with remarkable success
before audiences who cannot be suspected of mysticism, in most of the
countries of Europe. In his philosophical writings Maeterlinck shows
himself a disciple of Novalis, of Emerson, of Hello, of the Flemish
Catholic mystics, and he evolves from the teachings of those thinkers a
system of aesthetics applicable to the theatre as he conceives it.
     (E. G.)




MAFEKING, a town in the British Bechuanaland division of the Cape, 870
m. N.E. of Cape Town and 492 m. S.S.W. of Bulawayo by rail, and 162 m.
in a direct line W. by N. of Johannesburg. (Pop. 1904), 2713. It is
built on the open veld, at an elevation of 4194 ft., by the banks of the
Upper Molopo, is 9 m. W. of the western frontier of the Transvaal and 15
m. S. of the southern boundary of the Bechuanaland protectorate. The
Madibi goldfields are some 10 m. south of the town. Mafeking is thus an
important trading and distributing centre for Bechuanaland and the
western Transvaal. Here are, too, the chief railway workshops between
Kimberley and Bulawayo. The headquarters of the administration for the
Bechuanaland protectorate are in the town. The chief buildings are the
town-hall, Anglican church, Masonic temple, and hospital.

Mafeking was originally the headquarters of the Barolong tribe of
Bechuana and is still their largest station, the native location (pop.
2860) being about a mile distant from the town. It was from Pitsani
Pothlugo (or Potlogo), 24 m. north of Mafeking, that Dr Jameson started,
on the 29th of December 1895, on his raid into the Transvaal. On the
outbreak of the Anglo-Boer war in 1899 Mafeking was invested by a Boer
force. Colonel R. S. S. Baden-Powell was in command of the defence,
which was stubbornly maintained for 217 days (Oct. 12 to May 17), when a
relief column arrived and the Boers dispersed (see TRANSVAAL:
_History_). The fate of the town had excited the liveliest sympathy in
England, and the exuberant rejoicings in London on the news of its
relief led to the coining of the word _mafficking_ to describe the
behaviour of crowds on occasions of extravagant demonstrations of a
national kind. In September 1904 Lord Roberts unveiled at Mafeking an
obelisk bearing the names of those who fell in defence of the town.

  R. S. S. Baden-Powell's _Sketches in Mafeking and East Africa_ (1907)
  and Lady Sarah Wilson's _South African Memories_ (1909) deal largely
  with the siege of Mafeking.




MAFFEI, FRANCESCO SCIPIONE, MARCHESE DI (1675-1755); Italian
archaeologist and man of letters, was born at Verona on the 1st of June
1675. He studied for five years in Parma, at the Jesuit College, and
afterwards from 1698 at Rome; and in 1703-1704 he took part as a
volunteer in the war of succession, fighting on the Bavarian side at
Donauwerth. In 1709 he began at Padua along with Apostolo Zeno and
Valisnieri the _Giornale dei letterati d'Italia_, a literary periodical
which had but a short career; and subsequently an acquaintance with the
actor Riccoboni led him to exert himself for the improvement of dramatic
art in Italy. His _Merope_, a tragedy, appeared in 1713; _Teatro
italiano_, a small collection of works for presentation on the stage, in
1723-1725; and _Le Ceremonie_, an original comedy, in 1728. From 1718 he
became specially interested in the archaeology of his native town, and
his investigations resulted in the valuable _Verona illustrata_
(1731-1732). Maffei afterwards devoted four years to travel in France,
England, Holland and Germany. He died at Verona on the 11th of February
1755.

  A complete edition of his works appeared at Venice (28 vols., 8vo) in
  1790.




MAFIA (MAFFIA), a secret society of Sicily. Its organization and
purposes much resemble those of the Camorra (q.v.).

  Various derivations are found for the name. Some hold it to be a
  Tuscan synonym for _miseria_; others, a corruption of Fr. _mauvais_
  (bad). Others connect it with the name of an alleged Arab tribe,
  Mà-âfir, once settled at Palermo. Giuseppe Pitré asserts that the word
  is peculiar to western Sicily and that, with its derivatives, it
  formerly meant, in Il Borgo, a district of Palermo, beauty or
  excellence. Thus, a handsome woman showily dressed was said "to have
  _mafia_," or to be _mafiusa_. Often in Palermo the street merchants
  call _arance-mafiuse_ (fine oranges). Thus, Pitré argues, _mafia_,
  applied to a man to express manly carriage and bravery, would
  naturally become the title of a society the members of which were all
  "bravos." A less credible explanation of the term is connected with
  Mazzini, who is said to have formed a secret society the members of
  which were called _Mafiusi_, from _Mafia_, a word composed of the
  initial letters of five Italian words, _Mazzini autorizza furti,
  incendi, avvelenamenti_, "Mazzini authorizes theft, arson and
  poisoning." This theory suggests that the word was unknown before 1859
  or 1860.

The Mafia, however named, existed long before Mazzini's day. In its
crudest form it was co-operative brigandage, blended with the Vendetta
(q.v.). The more strictly organized Mafia was the result of the
disorders consequent upon the expulsion of the king of Naples by
Napoleon. When the Bourbon court took refuge in Sicily there were a
large number of armed retainers in the service of the Sicilian feudal
nobility. Ferdinand IV., at the bidding of England, granted a
constitution to the island in 1812, and with the destruction of
feudalism most of the feudal troops became brigands. Powerless to
suppress them, Ferdinand organized the bandits into a rural
_gendarmerie_, and they soon established a reign of terror. The abject
poverty of the poorer classes, unable to eke out existence by work in
the sulphur mines or on the fields, fostered the growth of two classes
of _mafiusi_--the vast majority of the inhabitants who were glad to put
themselves as passive members under the protection of the Mafia, while
the active members shared in the plunder. The Mafia thus became a
loosely organized society under an unwritten code of laws or ethics
known as _Omertà_, i.e., manliness (from Sicil. _omu_, Ital. _uomo_, a
man), which embodied the rules of the Vendetta. Candidates were admitted
after trial by duel, and were sworn to resist law and defeat justice.
Like the Camorra, the Mafia was soon powerful in all classes, and even
the commander of the royal troops acted in collusion with it. The real
home of Mafia was in and around Palermo, where no traveller was safe
from robbery and the knife. In an organized form the Mafia survives only
in isolated districts. Generally speaking, it is to-day not a compact
criminal association but a complex social phenomenon, the consequence of
centuries of misgovernment. The Mafiuso is governed by a sentiment akin
to arrogance which imposes a special line of conduct upon him. He
considers it dishonourable to have recourse to lawful authority to
obtain redress for a wrong or a crime committed against him. He
therefore hides the identity of the offender from the police, reserving
vengeance to himself or to his friends and dependants. This sentiment,
still widely diffused among the lower classes of many districts, and not
entirely unknown to the upper classes, renders difficult legal proof of
culpability for acts of violence, and multiplies sanguinary private
reprisals. In September 1892 about 150 Mafiusi were arrested at Catania,
but all repressive measures proved useless. The only result was to drive
some of the members abroad, with disastrous results to other countries.
In October 1890 David Hennessy, chief of police in New Orleans, was
murdered. Subsequent legal inquiry proved the crime to be the work of
the Mafia, which had been introduced into the United States thirty years
before. In May 1890 a band of Italians living in New Orleans had
ambushed another gang of their fellow-countrymen belonging to a society
called _Stoppaghera_. The severe police measures taken brought the
vengeance of the society upon Hennessy. Eleven Italians were indicted on
suspicion of being implicated in his murder; but the jury was terrorized
and acquitted six. On the 14th of March 1891 a mob led by well-known New
Orleans citizens broke into the gaol where nineteen Italians were
imprisoned and lynched eleven of them.

  See W. Agnew Paton, _Picturesque Sicily_ (1898); C. W. Heckethorn,
  _Secret Societies of all Ages_ (1897); Alongi, _La Maffia_ (Turin,
  1887); Le Faure, _La Maffia_ (Paris, 1892).





MAFRA, a town of Portugal, in the district of Lisbon (formerly in the
province of Estremadura); near the Atlantic coast and the right bank of
the river Lizandro, and 20 m. N.W. of Lisbon. Pop. (1900), 4769. Mafra
is remarkable for its monastery, church, and palace, built by John V. in
1717-1732, in consequence of a vow made during a dangerous illness to
build a convent for the poorest friary of the kingdom--which proved to
be a small Franciscan settlement here. The architects, Johann Friedrich
Ludwig of Regensburg, and his son Johann Peter, took the Escurial for
their model; but the imitation is less successful than the original,
though the cost exceeded £4,000,000. The building is in the form of a
parallelogram measuring upwards of 800 ft. from north to south and 700
ft. from east to west; it is said to contain 866 rooms, and to be
lighted by no fewer than 5200 windows. The centre is occupied by the
church, sumptuously built of marble, and richly adorned with statues and
other objects of art. In each of the twin towers there is a chime of 57
bells. Part of the palace, originally designed as barracks, is used as a
military academy. Adjoining the palace are fine gardens and a royal
model farm.




MAGADHA, an ancient kingdom of India, mentioned in both the _Ramayana_
and the _Mahabharata_. It comprised that portion of Behar lying S. of
the Ganges, with its capital at Pataliputra or Patna. As the scene of
many incidents in the life of Gautama Buddha, it was a holy land. It was
also the seat of the Maurya Empire, founded by Chandragupta, which
extended over all India under Asoka; and, later, of the powerful Gupta
dynasty.




MAGALDÁN, a town in the northern part of the province of Pangasinan,
Luzon, Philippine Islands, about 2 m. from the shore of the Gulf of
Lingayen. Pop. (1903), 15,841. In 1903 the adjacent municipality of
Mapandan (pop. in 1903, 4198) was annexed to Magaldán. Most of its
inhabitants are engaged in rice culture. The principal language is
Pangasinan; Ilocano is also spoken.




MAGALLANES (Spanish form of _Magellan_), a territory of southern Chile
extending from 47° S. to Cape Horn and including the mainland from the
Argentine frontier to the Pacific coast, the islands extending along
that coast, the Fuegian archipelago, and the western half of Tierra del
Fuego. Area, about 71,127 sq. m.; pop. (1895), 5170. It is one of the
most inhospitable regions of the world, being exposed to cold westerly
storms for most of the year. The islands are barren, but the mainland is
covered with forests, practically inaccessible to exploitation because
of the inclement climate and the wet spongy soil. The coast is indented
with bays and fjords and affords remarkable scenery. There is little
animal life on land, but the coast is frequented by the seal and
sea-otter and the sheltered waters by countless sea-fowl. The only
permanent settlements are at Punta Arenas, the capital, on the Straits
of Magellan, Palomares on Otway Water, Mina Marta on Skyring Water, and
Ultima Esperanza (Last Hope) on the east shore of Worsley Sound. All are
east of the Andean ranges and partially sheltered from the westerly
storms. In this sheltered region there are open plains where sheep are
grazed. A few sheep ranges have been established on Tierra del Fuego.
Some nomadic tribes of Indians inhabit Tierra del Fuego and the extreme
southern end of the mainland, but their numbers are small. Coal has been
found in the vicinity of Punta Arenas, and gold occurs.

  See _The Voyage of the Adventure and Beagle_ (1839).




MAGAZINE, primarily a warehouse for goods or merchandise (Arab.
_makhzan_, a storehouse, from _khazana_, to store up). In Morocco
_makhzan_ (or _maghzen_) has come to be used as the name of the
government. The Spaniards adopted the Arabic in the form _magacen_, and
the English form comes through the older French _magazin_, modern
_magasin_. The meaning of a storehouse or large shop, common in French,
is rare in English except in the military use of the term for a building
for the storage of explosives and ammunition. It is applied to the
chamber of a repeating rifle or machine-gun containing the supply of
cartridges. The name as applied to a periodical publication containing
articles on various subjects was first used in the _Gentleman's
Magazine_ (1731), described as "a monthly collection, to treasure up as
in a magazine" articles on the subjects with which it was proposed to
deal.




MAGDALA (more correctly MAKDALA), a natural stronghold in the country of
the Wollo Gallas, Abyssinia, about 250 m. W. of Jibuti on the Gulf of
Aden, in 11° 22´ N., 39° 25´ E. The basaltic plateau of which it
consists rises 9110 ft. above the sea. It is about three-quarters of a
mile in length by less than half a mile in breadth, and lies more than a
thousand feet higher than the neighbouring plain of Arogié. Chosen about
1860 by the emperor Theodore of Abyssinia as his principal stronghold in
the south, Magdala owes its celebrity to the fact that, as the place of
imprisonment of the English captives, it became the goal of the great
English Expedition of 1868. At the time of its capture it contained huts
for a population of about three thousand. The whole rock was burned bare
by order of the commander of the British force, Sir Robert Napier, who,
on being raised to the peerage for his services on this occasion, took
the title of Lord Napier of Magdala. The plateau was subsequently
refortified by the Abyssinians.

  See Clements Markham, _History of the Abyssinian Expedition_ (1869);
  and H. Rassam, _British Mission to Theodore_ (1869).




MAGDEBURG, a city of Germany, capital of the Prussian province of
Saxony, a fortress of the first rank and one of the principal commercial
towns of the German Empire. It lies in a broad and fertile plain, mainly
on the left bank of the Elbe, 88 m. S.W. from Berlin and at the junction
of main lines to Leipzig, Brunswick, Cassel and Hamburg. Pop. (1885),
159,520; (1890), 202,234; (1905), 240,661. It consists of the town
proper, and of the five suburbs of Friedrichstadt, Wilhelmstadt,
Neustadt, Sudenburg and Buckau; the last four are separated from the
town by the ramparts and glacis, but are all included within the new
line of advanced bastions, while Friedrichstadt lies on the right bank
of the river. In the Elbe, between the old town and the Friedrichstadt,
lies an island whereon stands the citadel; this is united with both
banks by bridges. With the exception of the Breite Weg, a handsome
thoroughfare running from north to south, the streets of the town proper
are narrow and crooked. Along the Elbe, however, extend fine promenades,
the Fürstenwall and the Fürsten Üfer. To the south of the inner town is
the Friedrich Wilhelms Garten, a beautiful park laid out on the site of
the celebrated convent of Berge, which was founded in 968 and suppressed
in 1809. By far the most important building in Magdeburg is the
cathedral, dedicated to SS Maurice and Catherine, a handsome and massive
structure of the 14th century, exhibiting an interesting blending of
Romanesque and Gothic architecture. The two fine western towers were
completed about 1520. The interior contains the tombs of the emperor
Otto the Great and his wife Edith, an English princess, and the fine
monument of Archbishop Ernest (d. 1513), executed in 1495 by Peter
Vischer of Nüremberg. The Liebfrauenkirche, the oldest church in
Magdeburg, is an interesting Romanesque edifice of the 12th and 13th
centuries, which was restored in 1890-1891. The chief secular buildings
are the town-hall (Rathaus), built in 1691 and enlarged in 1866, the
government offices, the palace of justice, the central railway station
and the exchange. The Breite Weg and the old market contain numerous
fine gable-ended private houses in the style of the Renaissance. In
front of the town-hall stands an equestrian statue of Otto the Great,
erected about 1290. The modern streets are spacious, and the houses
well-built though monotonous. There are two theatres, an agricultural
college, an art school, several gymnasia, a commercial and other
schools, an observatory, and two fine hospitals. The first place amongst
the industries is taken by the ironworks (one being a branch of the
Krupp firm, the Grusonwerke, employing about 4000 hands), which produce
naval armour and munitions of war. Of almost equal importance are the
sugar refineries and chicory factories. Then come establishments for
making tobacco, gloves, chocolate, artificial manure, cement, varnish,
chemicals and pottery. There are also distilleries and breweries, and
factories for the manufacture of cotton and silk goods. Magdeburg is
the central market in Germany for sugar and chicory, but trades
extensively also in cereals, fruit, vegetables, groceries, cattle,
horses, wool, cloth, yarn, leather, coal and books. A new winter
harbour, made at a cost of £400,000, facilitates the river traffic along
the Elbe. Three million tons of merchandise pass Magdeburg, going
upstream, and nearly 1 million tons, going downstream, annually.
Magdeburg is the headquarters of the IV. corps of the German army and
the seat of the provincial court of appeal and administrative offices,
and of a Lutheran consistory.

_History._--Magdeburg, which was in existence as a small trading
settlement at the beginning of the 9th century, owes its early
prosperity chiefly to the emperor Otto the Great, who established a
convent here about 937. In 968 it became the seat of an archbishop, who
exercised sway over an extensive territory. Although it was burnt down
in 1188, Magdeburg became a flourishing commercial town during the 13th
century, and was soon an important member of the Hanseatic League. Its
bench of jurats (_Schöppenstuhl_) became celebrated, and "Magdeburg law"
(_Magdeburger Recht_), securing the administrative independence of
municipalities, was adopted in many parts of Germany, Poland and
Bohemia. During the middle ages the citizens were almost constantly at
variance with the archbishops, and by the end of the 15th century had
become nearly independent of them. It should, however, be noted that
Magdeburg never became a free city of the Empire. The town embraced the
Reformation in 1524, and was thenceforth governed by Protestant titular
archbishops (see BISHOP). On the refusal of the citizens to accept the
"Interim," issued by the emperor Charles V., Magdeburg was besieged by
Maurice of Saxony in 1550, and capitulated on favourable terms in
November 1551. During the Thirty Years' War it was twice besieged, and
suffered terribly. It successfully resisted Wallenstein for seven months
in 1629, but was stormed and sacked by Tilly in May 1631. The whole
town, with the exception of the cathedral, and about 140 houses, was
burned to the ground, and the greater part of its 36,000 inhabitants
were butchered without regard to age or sex, but it recovered from this
deadly blow with wonderful rapidity. By the peace of Westphalia (1648)
the archbishopric was converted into a secular duchy, to fall to
Brandenburg on the death of the last administrator, which happened in
1680. In 1806 Magdeburg was taken by the French and annexed to the
kingdom of Westphalia, but it was restored to Prussia in 1814, on the
downfall of Napoleon. Otto von Guericke (1602-1686), the inventor of the
air-pump, was burgomaster of Magdeburg. Count Lazare Carnot died here in
exile, and was buried in the cemetery, but his remains were exhumed in
1889 and conveyed to Paris. Luther was at school here, and sang in the
streets for bread with other poor choristers.

  See W. Kawerau, _Aus Magdeburgs Vergangenheit_ (Halle, 1886) O. von
  Guericke, _Geschichte der Belagerung, Eroberung und Zerstörung von
  Magdeburg_ (Magdeburg, 1887); M. Dittmar, _Beiträge zur Geschichte der
  Stadt Magdeburg_ (Halle, 1885); F. W. Hoffmann, _Geschichte der Stadt
  Magdeburg_ (Magdeburg, 1885-1886); F. Hülsse, _Die Einführung der
  Reformation in der Stadt Magdeburg_ (Magdeburg, 1883); R. Volkholz,
  _Die Zerstörung Magdeburgs_ 1631 (Magdeburg, 1892); W. Leinung and R.
  Stumvoll, _Aus Magdeburgs Sage und Geschichte_ (Magdeburg, 1894); and
  the _Urkundenbuch der Stadt Magdeburg_ (1892).

THE ARCHBISHOPRIC OF MAGDEBURG was carved out of the bishopric of
Halberstadt when it was founded in 968, and its history is largely bound
up with that of the city and of the prelates who have ruled the see. The
first archbishop was Adalbert, and he and his successors had six or
seven suffragan bishops. Several of the archbishops took very prominent
parts in German politics. Early in the 15th century their residence was
fixed at Halle, and about the same time it became the custom to select
them from one of the reigning families of Germany, most often from the
house of Brandenburg. The doctrines of the reformers made their
appearance in the diocese early in the 16th century, and soon Archbishop
Sigismund, a son of Joachim II., elector of Brandenburg, openly avowed
his adherence to Lutheranism. After the issue of the edict of
restitution by the emperor Ferdinand II. in 1629, there were three
rival candidates for the see, and their struggles added to the confusion
caused by the Thirty Years' War. By the peace of Prague, however, in
1635, the archbishopric was given to Augustus, prince of
Saxe-Weissenfels, who retained it until his death in 1680. In 1773 the
area of the see was over 2000 sq. m. It included 29 towns and over 400
villages and contained about 250,000 inhabitants.

  See the _Regesta archiepiscopatus magdeburgensis_, edited by G. A. von
  Mülverstedt (Magdeburg, 1876-1899); and K. Uhlirz, _Geschichte des
  Erzbistums Magdeburg unter den Kaisern aus sächsischem Hause_
  (Magdeburg, 1887).

Distinct both from the archbishopric and from the city was the
BURGRAVIATE OF MAGDEBURG. The office of burgrave dates from the time of
Charlemagne, although its holder was not at first called by this name,
and it soon became one of great importance. The burgrave was the king's
representative; he was charged with the administration of the royal
estates in a given district, and in general with watching the royal
interests therein. The burgraviate of Magdeburg was held by several
countly families in turn until 1269, when it was purchased by Archbishop
Conrad II., who, however, soon sold it. In 1294 it was again united with
the archbishopric and the prelates retained it until 1538; then in 1579
Augustus, elector of Saxony, made an arrangement which again gave the
office to the archbishops, who held it until the secularization of the
see.

The MAGDEBURG CENTURIES (_Magdeburger Zenturien_) is the name given to
the first general history of the Christian Church written from a
Protestant point of view. It was compiled in Magdeburg, and the history
is divided into periods of one hundred years each. It was written in
Latin in 1562, its principal author being the reformer Matthias Flacius,
who was assisted by other Lutheran theologians. The cost of the
undertaking was borne by some of the German Protestant princes. As the
_Historia ecclesiae Christi_ it was first published at Basel in seven
volumes (1559-1574). It deals with the history of the Church down to
1400, and considering the time at which it was written it is a
remarkable monument to the scholarship of its authors. The earlier part
of it has been translated into German (Jena, 1560-1565).

  See E. Schaumkell, _Beitrag zur Entstehungsgeschichte der Magdeburger
  Zenturien_ (Ludwigslust, 1898).




MAGEE, WILLIAM (1766-1831), archbishop of Dublin, was born at
Enniskillen, Co. Fermanagh, and educated at Trinity College, Dublin,
where he was elected fellow in 1788. He was ordained in 1790. Two
sermons, preached in the college chapel in 1798 and 1799, form the basis
of his _Discourses on the Scriptural Doctrines of Atonement and
Sacrifice_ (1801), a polemic against Unitarian theology which was
answered by Lant Carpenter. Magee was appointed professor of mathematics
and senior fellow of Trinity in 1800, but in 1812 he resigned, and
undertook the charge of the livings of Cappagh, Co. Tyrone, and
Killeleagh, Co. Down. Next year he became dean of Cork. He was well
known as a preacher and promoter of the Irish reformation, and in 1819
he was consecrated bishop of Raphoe. In 1822 the archbishop of Dublin
was translated to Armagh, and Magee succeeded him at Dublin. Though in
most respects a tolerant man, he steadily opposed the movement for
Catholic Emancipation. He died on the 18th of August 1831.

  A memoir of his life is included with the _Works of the Most Reverend
  William Magee_, D.D. (1842), by A. H. Kenney.




MAGEE, WILLIAM CONNOR (1821-1891), Anglican divine, archbishop of York,
was born at Cork in 1821. His father was curate of the parish attached
to the Protestant cathedral in that city; his grandfather was archbishop
of Dublin. Young Magee entered Trinity College, Dublin, with a
scholarship at thirteen. He was ordained to the curacy of St Thomas's,
Dublin, but, being threatened with consumption, went after two years to
Malaga. On his return he took a curacy at Bath, and was speedily
appointed to the Octagon Chapel, where his fame both as preacher and
platform speaker continued to spread. Some years afterwards he was made
prebendary of Wells Cathedral. In 1860 the delicate state of his health
caused him to accept the living of Enniskillen. In 1864 he was made
dean of Cork and chaplain to the lord lieutenant. Here he manifested
those great gifts which ultimately raised him to high office; a powerful
grasp of mental, moral and political problems, combined with eloquence
of a high order, and illuminated with brilliant flashes of wit. In 1868
the question of the disestablishment of the Irish Church came to the
front, and Magee threw himself into the task of its defence with his
usual energy and vivacity. The success of his orations caused Disraeli
to offer him the bishopric of Peterborough. He justified his appointment
by his magnificent speech when the Disestablishment Bill reached the
House of Lords in 1869, and then plunged into diocesan and general work
in England. He preached three remarkable sermons on Christian Evidence
in Norwich Cathedral in 1871. He took up the temperance question, and
declared in the House of Lords that he would rather see "England free
than England compulsorily sober," an utterance which the extreme
advocates of total abstinence misquoted and attacked. He was also a
supporter of the movement for abolishing the recitation of the
Athanasian Creed in the public services of the Church of England,
believing, as he said, that the "presence" of the damnatory clauses, "as
they stand and where they stand, is a real peril to the Church and to
Christianity itself," and that those clauses "are no essential part" of
the creed. The project was laid aside in consequence of the hostility of
a large body of the clergy, reinforced by the threat of Dr Pusey and
Canon Liddon to abandon their offices if it were carried. Magee took a
prominent part in the Ritual controversy, opposing what he conceived to
be romanizing excess in ritual, as well as the endeavour of the opposite
party to "put down Ritualism," as Disraeli expressed it, by the
operation of the civil law. His incisive way of putting things earned
for him the title of the "Militant Bishop," but, as he himself remarked
in relation to this title, his efforts were ever for peace.
Unfortunately for the Church, he was not elevated to the see of York
until his energies were exhausted. He died on the 5th of May 1891, about
four months after his appointment. Magee's manifold activities, his
capability as an administrator, his sound judgment, and his remarkable
insight into the ecclesiastical problems of his time, rank him among the
most distinguished of English prelates.

  See _Life and Letters_, by Canon MacDonnell (2 vols. 1896).




MAGELLAN, FERDINAND (in Sp. FERNANDO MAGALLANES, in Port. FERNÃO DE
MAGALHÃES) (c. 1480-1521), the first circumnavigator of the globe, was
born at Sabrosa in the Villa Real district of the Traz-os-Montes
province of Portugal. He was a son of Pedro de Magalhães, and belonged
to the fourth order of Portuguese nobility (_fidalgos de cota de
armas_). He was brought up as one of the pages of Queen Leonor, consort
of King John (João) II "the Perfect." In 1495 he entered the service of
Manuel "the Fortunate," John's successor, and in 1504 enlisted as a
volunteer for the Indian voyage of the first Portuguese viceroy in the
East, Francisco d'Almeida. He sailed on the 25th of March 1505; was
wounded at Cannanore on the 16th of March 1506; was then sent with Nuno
Vaz Pereira to Sofala to build a Portuguese fortress at that place;
returned to India early in 1508; and was again wounded at the battle of
Diu on the 3rd of February 1509. At Cochin (Aug. 19, 1509) he joined
Diogo Lopes de Sequeira on his famous voyage intended for the Spice
Islands, when the Portuguese almost fell victims to Malay treachery at
Malacca. In this crisis he fought bravely and skilfully (though it is
not true, as often asserted, that he discovered the Malay plot); and
before the 10th of October 1510 he had been rewarded for his many
services with the rank of captain. He again distinguished himself at the
taking of Malacca by Albuquerque (July-Aug., 1511), and was then sent on
by the viceroy with Antonio d'Abreu to explore the Spice Islands
(Moluccas). Leaving Malacca at the end of December 1511, this squadron
sailed along the north of Java, passed between Java and Madura, left
Celebes on their left, coasted by the Gunong Api volcano, touched at
Bura, and so reached Amboyna and Banda. At the last-named they found
such abundance of spices that they came straight back to Malacca
without visiting Ternate, as had been intended.

Magellan returned to Portugal in 1512. On the 14th of July of that year
he was raised to the rank of _fidalgo escudeiro_; and in 1513 he
accompanied a Portuguese expedition against Azamor in Morocco. The city
was taken on the 28th-29th of August 1513; but Magellan was subsequently
wounded, and lamed for life, in a sortie; he was also accused of trading
with the Moors. The accusation was subsequently dropped, but Magellan
fell into disfavour with King Manuel, who let him understand that he
would have no further employment in his country's service (after the
15th of May 1514). Magellan formally renounced his nationality, and went
to offer his services to the court of Spain. He reached Seville on the
20th of October 1517, and thence went to Valladolid to see Charles V.
With the help of Juan de Aranda, one of the three chief officials of the
India House at Seville, and of other friends, especially Diogo Barbosa,
a Portuguese like himself, naturalized as a Spaniard, who had acquired
great influence in Seville, and whose daughter he now married, he gained
the ear of Charles and of the powerful minister, Juan Rodriguez de
Fonseca, bishop of Burgos, the persistent enemy of Columbus, the steady
supporter of his great successor. Magellan proposed to reach the Spice
Islands of the East Indies by the west; for that purpose he hoped to
discover a strait at the extreme south of South America, and is said to
have declared himself ready to sail southwards to 75° to realize his
project. Ruy Faleiro the astronomer, another Portuguese exile, aided him
in the working out of his plan, and he found an invaluable financial
ally in Christopher de Haro, a member of a great Antwerp firm, who owed
a grudge to the king of Portugal. On the 22nd of March 1518, Magellan
and Faleiro, as joint captains-general, signed an agreement with Charles
V., by which one-twentieth of the clear profits were to fall to them;
further, the government of any lands discovered was vested in them and
their heirs, with the title of _Adelantados_. On the 10th of August
1519, the fleet of five vessels, under Magellan's command, left Seville
and dropped down the Guadalquivir to S. Lucar de Barrameda, at the mouth
of the river, where they remained more than five weeks. On the 20th of
September the armada put to sea. Of the vessels which composed it, the
"Trinidad" was the flagship, and the "Vittoria" the only one which
accomplished the circumnavigation. The crew, officers, volunteers, &c.,
numbered about 270-280, of whom the names of 268 are preserved; 237 of
these received pay; at least 37 were Portuguese, 30 or more Italians
(mostly Genoese), 19 French, 1 English, 1 German. Only 31 returned in
the "Vittoria"; 4 survivors of the crew of the "Trinidad" reappeared
later. Antonio Pigafetta of Vicenza, an Italian gentleman who has left
the best history of the voyage, went as a volunteer in Magellan's suite.
Faleiro stayed behind, having cast his horoscope and found that the
venture would be fatal to him. The fleet was well armed, and the total
cost of equipment was 8,751,000 maravedis, or £5032 (equal to over
£50,000 in present value). Three-quarters were defrayed by the Spanish
Crown, one-quarter by Christopher Haro and his friends. Before starting,
Magellan made his will and addressed a memorandum to Charles V.,
assigning geographical positions connected with the controversy he was
intending to settle: viz., the proper drawing of a demarcation-line
between the spheres of Spain and Portugal in the East Indies, and the
inclusion of the Moluccas within the Spanish sphere.

Steering south-west and calling at Teneriffe (Sept. 26-Oct. 3), Magellan
sighted South America at Cape St Augustine, near Pernambuco on the 29th
of November; thence he followed the east coast of the New World down to
the La Plata estuary, which he examined in the hope of finding a passage
at this point (Jan. 11-Feb. 6, 1520). On the 31st of March following, he
arrived at Port St Julian (in 49° 20´ S.) where he wintered. Here he
crushed a formidable mutiny (April 1-2), and made acquaintance with the
natives, whom he called _Patagonians_ ("Big Feet"), whose great size and
lofty stature are magnified by Pigafetta to gigantic proportions.
Leaving Port St Julian on the 24th of August 1520, he discovered on the
21st of October the cape of the Eleven Thousand Virgins, the eastern
entrance of the long-sought passage. Through this strait, 360 m. long,
often narrow and very tortuous, fringed by snow-clad mountains, he
guided his armada for thirty-eight days, weakened by the desertion of
one vessel (the "S. Antonio"). On the 21st of November a council of
pilots and captains was held to consider the continuation of the voyage,
and on the 28th of November the fleet rounded Cabo Deseado, the
"desired" western terminus of the strait, variously called by the first
discoverers, "Victoria Strait," "Strait of the Patagonians," "of all
Saints," "of the Eleven Thousand Virgins," or "of Magellan," now only
known by the last of these names. To the south of the passage lay the
forbidding land "stark with eternal cold," which from the many fires
here observed Magellan named "Tierra del Fuego." The expedition now
entered the "Great South Sea," first sighted by Vasco Nuñez de Balboa
(q.v.), which, from the steady and gentle winds that drove the fleet
across the immeasurable expanse, was by Magellan called "Pacific." For
ninety-eight days Magellan crossed this sea, almost beyond the grasp of
man's mind for vastness (as Maximilian of Transylvania puts it), from
Cabo Deseado to the Ladrones. On the whole transit he discovered only
two islands, sterile and uninhabited, which he called "St Paul's" (Jan.
24, 1521) and "Shark Island" (Feb. 3). The first of these has been
identified with Puka Puka in the Tuamotu Archipelago, the second with
Flint Island in the Manihiki group; neither identification seems
convincing. For most of these ninety-eight days the explorers had no
fresh provisions, little water (and that bad), and putrid biscuit; the
ravages of scurvy became terrible. The worst anticipations of Magellan
("he would push on, if they had to eat the leather of the rigging") were
realized; ox-hides, sawdust, and rats became coveted food. At last, on
the 6th of March 1521, the Ladrones (so named by Magellan from the
thievish habits of the natives) came in sight, Guam being probably the
first port of call. Here the fleet rested, watered, revictualled and
refitted; on the 9th of March they started again westward; and on the
16th of March sighted the southern point of Samar Island in the
archipelago, since 1542 called the Philippines, but named by Magellan,
its first discoverer, after St Lazarus. On the 7th of April the squadron
arrived at Cebu, south-west of Samar, in the heart of the Philippines;
here Magellan contracted a close friendship and alliance with the
treacherous native sovereign, who professed Christianity the better to
please and utilize his Catholic friends. Undertaking an expedition to
conquer, for the Catholic faith and the king of Cebu, the neighbouring
island of Mactan, Magellan was killed there in a fight with the
islanders (April 27, 1521). The king of Cebu after this got into his
power several of the leading personages of the squadron, including Juan
Serrano, one of the two admirals elected to replace Magellan, and
murdered them. The survivors, burning one of the three remaining
vessels, left the Philippines, and made their way to the Moluccas (Nov.
6), visiting Borneo on the way (July 9-Sept. 27, 1521). At Tidor a heavy
cargo of cloves was taken in; the "Trinidad," becoming leaky, stayed
behind with her crew; and the "Vittoria," under Juan Sebastian del Cano,
proceeded to Europe alone (Dec. 21, 1521). To double the Cape of Good
Hope the "Vittoria" reached between 40° and 41° S. (April 7-16, 1522)
and suffered from contrary winds, heavy seas, scurvy and starvation. In
the Cape Verde Islands (July 9-15, 1522) thirteen of the crew were
detained prisoners by the Portuguese. Only thirty-one men returned with
del Cano to Seville in the first vessel that had ever made the tour of
the earth. Though Magellan had not quite reached the Spice Islands when
he fell at Mactan, his task had then been accomplished. He had already
reached and passed the longitude of the Moluccas, where he had already
been; the way home from the Philippines by the Indian Ocean and the Cape
of Good Hope was perfectly known to the Portuguese, himself included.
Magellan's name has never received its due recognition in general
history. It ranks with those of Columbus, Marco Polo, and Henry the
Navigator. The circumnavigation of the globe is as great an event as the
discovery of America. Magellan achieved what Columbus planned--the
linking of west Europe with east Asia by direct transit over the western
ocean. Had America not intervened, the project of 1492 must have failed;
by 1519 European pioneers had formed a more adequate notion of the task
and its magnitude.

Magellan's Straits, the Magellanic clouds (not first observed by him),
and Magellan's Land--a name long given to Patagonia and that
hypothetical southern continent of which Tierra del Fuego was considered
only a portion, and now again bestowed by Chile on her territory in the
extreme south--preserve the memory of the first circumnavigator. The
largest of the oceans has also kept the flattering name given to it by
the man who first crossed it.

  No record of his exploits was left by Magellan himself; and
  contemporary accounts are less detailed and consistent than could be
  wished. The best is that of Antonio Pigafetta, a volunteer in the
  fleet. It is printed in Ramusio, and exists in four early MS. copies,
  one in Italian and three in French. The latter was perhaps the
  original language of this work, which was addressed by Pigafetta, as a
  knight of Rhodes, to the Frenchman Villiers de l'Isle Adam, grand
  master of the order of the Hospital of St John. But this view is
  rejected by J. A. Robertson (see below), who believes the Ambrosian
  MS. to be the ultimate text. See the _Primo viaggio intorno al mondo_,
  otherwise the _Navigation et descouvrement de la Indie supérieure
  faicte par moi Anthoyne Pigapheta, Vincentin, chevallier de Rhodes_,
  probably published in 1524 (in August of that year Pigafetta obtained
  leave to print his book in Venice). Of the three French MSS., two are
  in the Bibliothèque Nationale, Paris (5650 and 24,224 Fr.), the latter
  is wrongly supposed by Thomassy, followed by Lord Stanley of Alderley,
  to have been the copy presented by Pigafetta to the regent of France,
  Marie Louise of Savoy, mother of Francis I. The third French MS.,
  often called the MS. of Nancy, first noticed by Thomassy in 1841, was
  bought by Sir Thomas Phillipps at Libri's sale, and became MS.
  Phillipps 16,405. The Italian MS. is in the Ambrosian library at
  Milan. From this Carlo Amoretti, prefect of the Ambrosiana, published
  his Italian edition of Pigafetta in 1800; a French translation of
  this, by Amoretti himself, was issued by H. J. Jansen, 1801. An
  English version of Pigafetta was made by Richard Eden in his _Decades
  of the Newe Worlde_ (London, 1555). The earliest printed edition,
  apparently a summary of the Italian MS., was issued in French by Simon
  de Colines of Paris about 1525. The earliest Italian edition is of
  1534 (or 1536).

  Other authorities are: (1) The narrative of an unknown Portuguese in
  Ramusio's _Navigationi et viaggi_; (2) the _Derrotero_ or Log-Book in
  the Seville Archives, supposed to be the work of Francisco Albo,
  _contramaestre_ of Magellan's flagship, the "Trinidad": this consists
  mainly of nautical observations; (3) the narrative of the so-called
  Genoese pilot, written in excellent Portuguese, and printed in vol.
  iv. of the _Collecão de noticias_ of the Lisbon Academy; (4) various
  _informaciones_ and other papers in the Seville Archives, especially
  bearing on the mutiny; (5) the letter of Maximilian of Transylvania,
  under-secretary to Charles V., to the cardinal of Salzburg; (6) the
  references in Correa and Herrera, often based on good information, and
  adding points of interest to other records. Of these (1)-(3), (5), and
  an instance of (6) are translated in the Hakluyt Society's volume.
  Magellan's two wills (i) executed at Belem on the 17th of December
  1504, on the eve of his departure with Almeida, (ii) executed at
  Seville on the 24th of August, 1519, just before starting on his
  voyage round the world, are both of some value for his life.

  See also Lord Stanley of Alderley, _The First Voyage round the World
  by Magellan, translated from ... Pigafetta, &c._, Hakluyt Society
  (London, 1874); Diego de Barros Arana, _Vida e viagems de Fernão de
  Magalhães_, a trans. of the Spanish life by Fernando de Magalhães
  Villas Boas (Lisbon, 1881); F. H. H. Guillemard, _Life of Magellan_
  (London, 1890); _Magellan ... the original text of the Ambrosian MS_.
  (of Pigafetta), with English translation, notes, bibliography, &c., by
  J. A. Robertson (Cleveland, U.S.A., 1906). Before the appearance of
  this indispensable work, the best edition of Pigafetta had been in
  vol. iii. part 5 of the _Raccolta di documenti e studi pubblicati
  nella r. commissione colombiana_, edited by Andrea da Mosto (Rome,
  Ministry of Public Instruction, 1894).     (C. R. B.)




MAGELLANIC CLOUDS (named after Ferdinand Magellan), two cloud-like
condensations of stars in the southern constellation of Mensa about 69°
S. Dec. and between 5° and 5° 40´ of R. A. They are remarkable in the
resemblance of their stars as regards spectra and physical constitution
to the stars of the Milky Way, though entirely detached from that
object.




MAGENTA, a town of Lombardy, Italy, in the province of Milan, 16 m. by
rail W. of Milan city, 364 ft. about sea-level situated in the midst of
rice-fields. Pop. (1901), 8012. It manufactures silks and matches, and
is famous for the battle (1859) in which the allied French and
Piedmontese defeated the Austrians (see ITALIAN WARS). A memorial chapel
and a monument were erected on the battle-field in 1862. A
crimson-purple aniline dye, discovered about the time of the battle, was
given from it the name of "magenta."




MAGGIORE, LAGO (_Lacus Verbanus_ of the Romans; Fr. _Lac Majeur_; Ger.
_Langensee_), the most extensive of the lakes that extend along the foot
of the Alps in Lombardy, N. Italy. Its area is about 83 sq. m., its
length 37 m., its greatest width 5½ m., and its greatest depth 1198 ft.,
while its surface is 646 ft. about sea-level. It is mainly formed by the
Ticino (Tessin) River, flowing in at the north and out at the south end,
on its way to join the Po, but on the west the lake receives a very
important tributary, the Toce or Tosa River, which flows down through
the Val d'Ossola from the mountains around the Simplon Pass. Other
important affluents are the Maggia (N.W.) and the Tresa (E.). The upper
end of the lake (about 16 sq. m.) is in the Swiss canton of Ticino
(Tessin). Locarno, at the northern or Swiss end, is 14 m. by rail S.W.
of Bellinzona on the St Gotthard line. There is a railway along the
south-eastern shore, from Magadino (10½ m. S.W. of Bellinzona) to Sesto
Calende (36½ m.), at the southern end of the lake and 20 m. by rail from
Novara. The east shore of the lake is reached at Luino by a steam
tramway from Ponte Tresa on the lake of Lugano (8 m.), while the direct
Simplon line runs along the west shore of the lake for 15½ m. from near
Pallanza past Baveno and Stresa to Arona, which is 23 m. by rail from
Novara. On the east shore are Luino (Ital. Luvino) and Laveno. On the
west shore are (reckoning from N. to S.) Cannobio, Pallanza, Baveno,
Stresa and Arona. Opposite (S.E.) Baveno are the famous Borromean
Islands, on the largest of which (Isola Bella) are very remarkable
gardens (formed about 1617), wherein many tropical plants flourish
abundantly, while south-west of Baveno rises the glorious view-point of
the Monte Mottarone (4892 ft.) between Lago Maggiore and the northern
end of the Lake of Orta. In the morning the _tramontana_ wind blows from
the north down the lake, while in the afternoon the _inverna_, blowing
from the south, prevails. The first steamer was placed on the lake in
1826.     (W. A. B. C.)




MAGIC[1] (i.e. "art magic"; Lat. _ars magica_), the general term for the
practice and power of wonder-working, as depending on the employment of
supposed supernatural agencies. Etymologically the Gr. [Greek: mageia]
meant the science and religion of the _magi_, or priests of Zoroaster,
as known among the Greeks; in this sense it was opposed to [Greek:
goêteia] (? necromancy) and [Greek: pharmakeia] (the use of drugs); but
this distinction was not universally recognized, and [Greek: goêteia] is
often used as a synonym of [Greek: mageia]. There is no general
agreement as to the proper definition of "magic," which depends on the
view taken of "religion."


I.--NATURE OF MAGIC

_Theories of Magic._--Existing theories of magic may be classified as
_objective_ or _subjective_. The objective school regards magic as a
thing by itself, entirely distinct from religion, recognizable by
certain characteristics, and traceable to a definite psychological
origin. Magic, on this view, is a system of savage science based on
imaginary laws supposed to operate with the regularity ascribed to
natural laws by the science of to-day. If practices prima facie magical
form part of the recognized ritual of religion, it is because the older
ideas have persisted and at most assumed a veneer of religion. For the
subjective school, on the other hand, only those rites are magical which
their practitioners qualify with the name of magic; there is no inherent
quality which makes a rite magical; practices based on a belief in the
law of sympathy may be religious as well as magical; rites may pass from
the category of religion to that of magic when public recognition is
withdrawn from them.

  a. For E. B. Tylor the distinguishing characteristic of magic is its
  unreality; it is a confused mass of beliefs and practices, and their
  unity consists in the absence of the ordinary nexus of natural cause
  and effect. Under the general head of magic he distinguishes (i) a
  spiritual and (ii) a non-spiritual element. (i) The former is made up
  of such rites as involve the intervention of spiritual beings, ghosts
  of the dead, demons or gods; hence, in Tylor's view, this form of
  magic is merely an inferior branch of religion. (ii) The non-spiritual
  part, but for which the category of magic would be unnecessary,
  depends on imagined powers and correspondences in nature; it is merely
  imperfect reasoning, the mistaking of an ideal connexion for a real
  one. When the American Indian medicine man draws the picture of a deer
  on a piece of bark and expects that shooting at it will cause him to
  kill a real deer the next day, he mistakes a connexion which exists
  only in the mind of the sorcerer for a real bond independent of the
  human mind.

  b. In J. G. Frazer's view all magic is based on the law of
  sympathy--i.e. the assumption that things act on one another at a
  distance through a secret link, due either to the fact that there is
  some similarity between them or to the fact that they have at one time
  been in contact, or that one has formed part of the other. These two
  branches of "sympathetic magic" Frazer denominates "homoeopathic
  magic" and "contagious magic." Homoeopathic or imitative (mimetic)
  magic may be practised by itself, but contagious magic generally
  involves the application of the imitative principle. (i) One of the
  most familiar applications of the former is the belief that an enemy
  may be destroyed or injured by destroying or injuring an image of him.
  (ii) Under the head of contagious magic are included such beliefs as
  that which causes the peasant to anoint the weapon with which he has
  been injured, which, according to Frazer, is founded on the
  supposition that the blood on the weapon continues to feel with the
  blood in the body. (iii) Implicitly Frazer seems to distinguish a
  third kind of magic; "the rain-charm," he says, "operates partly or
  wholly through the dead ... in Halmahera there is a practice of
  throwing stones on a grave, in order that the ghost may fall into a
  passion and avenge the disturbance, as he imagines, by sending heavy
  rain." Here there is no assumption of an invariable course of nature
  set in motion by magical rites; save that it is coercive and not
  propitiatory, the practice does not differ from ordinary religious
  rites.

  In his theory of the origin of magic Frazer follows the associationist
  school. But, as R. R. Marett has pointed out in a criticism of the
  associationist position, it is proved beyond question that even in the
  individual mind association by similarity, contiguity or contrast, is
  but the passive condition, the important element being interest and
  attention. Frazer assumes that magic has everywhere preceded religion:
  man tried to control nature by using what he conceived to be immutable
  laws; failing in this he came to believe in the existence of higher
  powers whom he could propitiate but not coerce; with this
  transformation religion appeared on the scene; the priest supplanted
  the magician, at least in part, and the first blows were struck in the
  perennial warfare of magic and religion. Frazer recognizes, however,
  that magical and religious rites are at the present day, and have been
  in historical times, frequently intermingled; it should be noted that
  for him religion means propitiation and that he does not recognize the
  existence of anything beyond magic among the aborigines of Australia.
  His theory is based on a selection of facts, and not on the whole body
  of beliefs and rites recognized as magical, among which are many
  wherein spirits figure. Frazer's position appears to be that such
  rites are relatively late and may be neglected in framing a definition
  of magic. It may be perfectly true that the idea of magic has been
  progressively extended; but belief in transformation is also for Dr
  Frazer magical; this belief is certainly primitive; yet sympathy will
  not explain it, as it should if Frazer's theory is correct.

  c. L. Marillier distinguished three classes of magic: (i) the magic
  of the word or act; (ii) the magic of the human being, independent of
  rite or formula, &c.; (iii) the magic which demands at once a human
  being of special powers (or in a special state) and the use of certain
  forms. (i) Under the first head he included such rites as mimetic
  dances, rain-making, disease-making, and sympathetic magic generally.
  Some of these rites are conceived to affect the course of nature
  directly, as by influencing winds or the sun, others do so through the
  intermediary of a god or spirit, who controls the course of nature,
  and is himself coerced by man with magical acts and incantations. (ii)
  Other rites cannot be performed by all and sundry: ceremonial purity,
  initiation or other conditions may be needed to make the charm
  effective. (iii) Individuals are found who are invested with magical
  power (_mana_), whose will rules the universe, whose simple words
  bring rain or sunshine, and whose presence gives fertility to the
  fields. Sometimes this power is an attribute of the individual,
  sometimes it is bound up with the office which he fills. In many cases
  the magical powers of both men and other objects, animate and
  inanimate, are put down to the fact that a god resides in them.

  d. Hubert and Mauss have made the most complete and systematic study
  of magic which has yet appeared. They hold that, implicitly at any
  rate, magic is everywhere distinguished from other systems of social
  facts; in order to be magical an act or belief must be common to the
  whole of a society; the acts which the whole of a group does not
  regard as efficacious are not, for this school of thought, magical:
  consequently the practices of gamesters, &c., do not come under the
  head of magic. Magic is essentially traditional; a distinguishing
  characteristic of primitive thought is that the individual mind is
  markedly unoriginal; and this feature is as prominent, if not more so,
  in magic as in technology or any other important element in human
  life. The correspondence between magic and technology can be traced
  far; for the gestures of the craftsman are as strictly prescribed as
  the ritual acts of the magician or priest: but in magic the results of
  the gestures are not of the same order as the results of the
  craftsman's movements, and herein lies the distinction between magic
  and technic. The distinction between magic and religion is to be
  sought not in the sympathetic character of the former, nor in any
  supposed necessary sequence of cause and effect, nor yet in its
  maleficent character. Religion is prescribed, official, an organized
  cult. Magic is prohibited, secret; at most it is permitted, without
  being prescribed. Three important laws may be traced in the machinery
  of magical operations--magical power flows along channels determined
  by the contiguity, similarity or contrast of the object of the act and
  the object to be affected; but these laws do not suffice to explain
  magic: equally insufficient are the demonological theory and the
  theory of properties inherent in the objects used in magical
  operations. The underlying idea of magic is dynamical; to this power
  may be given the name of _mana_ (see below), of which sanctity is a
  special development. This _mana_ operates in a _milieu_ different from
  the ordinary material world; distance is no obstacle to contact;
  wishes are immediately realized; but law reigns in the milieu in
  question, necessary relations are conceived as existing. The notion of
  time as it is found in the world of magic is even more alien from
  European ideas; the notion of sanctity enters into it, but time in
  magic and religion is qualitative rather than quantitative. The
  homogeneity of periods of time not depending on their duration,
  conventional numbers are employed; successive periods of time
  apparently equal are not so for the primitive consciousness; and both
  in magic and religion periods are homogeneous by reason of occupying
  the same position in the calendar.

  e. For A. Lehmann magic is the practice of superstitions, and his
  explanation of magic is purely psychological. Relying mainly on modern
  spiritualism for his examples, he traces magic back to illusions,
  prejudices and false precepts due to strained attention. This is
  ultimately also the view of Hubert and Mauss, who hold that "at the
  root of magic are states of consciousness which generate illusions;
  and that these states are not individual but collective and arise from
  the amalgamation of the ideas of a given person with those current in
  the society of which he forms a part." The reunion of a group supplies
  a soil in which illusions flourish readily, and it is important to
  note that in magic and religion attention is above all necessary for
  the success of a rite, witness the frequent rule imposing silence; but
  this concentration of attention is precisely calculated to favour
  illusions; it is indeed the ordinary condition of successful
  hypnotism; even in civilized countries collective hallucinations
  without verbal suggestion are not unknown.

  f. R. R. Marett regards religion and magic as two forms of a social
  phenomenon originally one and indivisible; primitive man had an
  institution which dealt with the supernatural, and in this institution
  were the germs of both magic and religion, which were gradually
  differentiated; magic and religion differ in respectability; religion
  is always the higher, the accepted cult; but between what is
  definitely religious and what is definitely magical lies a mass of
  indeterminate elements, such as "white-magic," which do not attain to
  the public recognition of religion, nor suffer the condemnation meted
  out to the indisputably magical. For primitive man the abnormal was
  the supernormal, and the supernormal was the supernatural, the object
  of fear; this is especially evident when we consider the case of
  taboo; it may be regarded as a public scare for which no particular
  individual is responsible, which becomes traditional along fairly
  constant lines, growing as it goes. _Mana_ was attributed to taboo
  objects, among which were men in any way abnormal, whether as geniuses
  or idiots; and such men were expected to exercise their powers for the
  good of society; hence came into existence the professional medicine
  man; man originally argued from cause to effect and not vice versa.
  Priest and magician were originally one; but the former, learning
  humility in the face of might greater than his own, discarded the
  spell for the prayer and prostrated himself before a higher power.

_Definition of Magic._--To arrive at a definition of magic we may either
follow the a priori road mapped out by Frazer and decline to recognize
the distinction actually drawn by various societies between magical and
religious practices; or we may ask what magic and corresponding terms
actually connote. Frazer's method ignores the fact that magic, like
religion, is an institution, i.e. a product of society, not of any
single individual; there is no more reason to suppose that a child
reared in isolation would develop any kind of magical practices than
that it would invent for itself a religion; but if this is the case,
the associationist account of magic cannot be true. It is therefore by
an analysis of actually existing practices that we must define and limit
the term magic. There is, however, a serious difficulty in the way of
determining the attitude of non-European peoples towards religio-magical
practices; general terms are things of slow growth; it is therefore
prima facie improbable that peoples in the lower stages of culture will
have anything corresponding to our terms "religion" and "magic";
moreover, if we are right in assuming the fundamental unity of the two,
it is by no means certain that they have even the consciousness of any
distinction. Even when this consciousness is present, it by no means
follows that the whole of the field is mapped out according to our
categories; there will be a large indeterminate area which is neither
magical nor religious. This suggests that the consciousness of the
educated Occidental, for which the spheres of magic and religion in
civilized society are sharply defined and contrasted, should be the
ultimate arbiter; but here again we are confronted by a difficulty, for,
to the educated man, the characteristic of magic is its unreality, and
this does not help us to distinguish primitive magic and religion.

We must, it appears, determine the relation of magic to religion by an
analysis of the conceptions of those who believe in both; but in so
doing we must consider that, like all other institutions, magic has a
history. Even if we go back to the 16th century and take the view of
magic then held by the average European, it is still a complex idea.
When we ask what the most primitive races now on the earth regard as
magic, we are applying to their ideas a touchstone made for a very
different age and culture; as well might we ask what their theory of
knowledge is. If, however, we reverse the process and ask what elements
of primitive institutions correspond most nearly to later conceptions of
magic, we can at once say that the forbidden and private arts are the
prototypes of the magic of later times. Magic is therefore the practice
of maleficent arts which involve the use of religio-magical power, with
perhaps a secondary idea of the use of private arts, which are to
benefit, not the community as a whole, but a single individual. Religion
in the lower stages of culture is essentially the tribal creed which all
practise and in which all believe; if therefore an individual has a cult
of his own, even if otherwise indistinguishable from a public cult, it
is for this very reason on a lower plane, and probably corresponds in a
degree to what is later regarded as magic. But our information as to the
attitude of the uncivilized towards magico-religious rites in general is
seldom sufficiently clear; our terminology is influenced by the
prepossession of alien observers whose accounts cannot be assumed to
correspond to the native view of the case.

_Magico-religious Force._--The mere fact that we cannot draw an exact
line between magic and religion suggests that they may have some
fundamental feature in common. Both terms have greatly changed their
connotation in the course of their existence; _religio_ seems to have
meant originally [Greek: katadesmos] (magical spell), and Pliny says
that [Greek: mageia] is a deceptive art compounded of medicine, religion
and astrology. Among the Greeks, on the other hand, [Greek: mageia]
occupied a respectable position. More important is the fact that taboo
(q.v.) is both religious and magical. There is a universal tendency to
regard as magical the religions of alien races, as well as national
religions which have been superseded; Leland tells us that witchcraft in
Italy is known as _la vecchia religione_. An examination of the ideas of
primitive peoples shows that there is a widely found notion of a power
which manifests itself both in religion and magic. Observers have often
been content to describe ceremonies without attempting to penetrate to
the fundamental ideas which underlie them; this is particularly the case
with magic, and only recently have anthropologists realized that in many
primitive societies exists a fairly well-defined idea of
magico-religious power, to which the generic name of _mana_, from the
Melanesian word, has been given.

  a. _Mana_ in Melanesia is a force, a being, an action, a quality, or a
  state; it is transmissible and contagious, and is hence associated
  with taboo; it may be regarded as material and seen in the form of
  flames or heard; it is the power which is inherent in certain spirits,
  among which are included such of the dead as are denominated
  _tindalos_; it may also be a force inherent in some inanimate object,
  such as a stone which causes the yams to grow, but it is a spiritual
  force and does not act mechanically; it is the power of the magician
  and of the rite; the magic formula is itself _mana_. There seem to be
  a variety of _manas_, but probably the underlying idea is essentially
  one, though it does not follow that the Melanesians have arrived at
  the consciousness of this unity. Hubert and Mauss go even further and
  regard all force as _mana_; it is a quality added to objects without
  prejudice to their other qualities, one which supplements without
  destroying their mechanical action.

  b. Similar ideas are found in other areas. (i) The continental Malays
  have a word _Kramât_ (_hrm_), which means sacred or magical; in
  Indo-China the Bahnars use the word _deng_; in Madagascar _hasina_
  seems to embody in part the same notion. (ii) In Africa the idea is
  less apparent; perhaps the _ngai_ of the Tanganika tribes comes
  nearest to the notion of _mana_; on the Congo _nkici_ has a similar
  but more restricted sense. (iii) In Australia there are two, or
  perhaps three, kinds of magical power distinguished by the aborigines;
  all over the continent we find the maleficent power, _boolya_ in West
  Australia, _arungquiltha_ in the central tribes, _koochie_ in New
  South Wales; the central tribes have certain objects termed
  _churinga_, to which magical power (which we may term _churinga_) is
  attributed; the power of magicians is held to reside in certain
  stones, called _atnongara_, and in this we must, provisionally at any
  rate, see a third kind of magical power: _churinga_ is beneficent and
  seems to originate with the mythical ancestors, whereas _arungquiltha_
  is of immediate origin, created by means of incantations or acquired
  by contact with certain objects; the power of the magicians seems to
  proceed from the ancestors in like manner. (iv) In America these ideas
  are widely found; the _orenda_ of the Hurons has been elaborately
  described by J. N. B. Hewitt; everything in nature, and particularly
  all animate objects, have their _orenda_; so have gods and spirits;
  and natural phenomena are the product of the _orenda_ of their
  spirits. _Orenda_ is distinct from the things to which it is attached;
  the cry of birds, the rustle of the trees, the soughing of the wind,
  are expressions of their _orenda_; the voice of the magician is
  _orenda_, so are the prayer and the spell, and in fact all rites;
  _orenda_ is above all the power of the medicine man. Among the
  Algonquins we find the word _manitu_, among the Sioux _wakanda_,
  _mahowa_, &c., among the Shoshones pokunt; all of which seem to carry,
  at least in part, the same signification. In Central America,
  according to Hubert and Mauss, _naual_ or _nagual_ is the
  corresponding term. (v) Traces of similar ideas may be found in more
  advanced nations; the Hindu _brahman_ is identified by Hubert and
  Mauss as the correlative of _mana_; in Greece [Greek: physis] is
  possibly the echo of a similar idea; but we are yet far from having
  adequately fathomed the dynamical theories of pre-scientific days.

_Origin of Magic._--The associationist theory of magic sets out with the
assumption that primitive man began with general conceptions; he started
with certain means at his disposal--the law of sympathy--by which he
could, in his own belief, influence the outer world. But it is more
probable that he argued from concrete instances and arrived little by
little at abstract ideas of magical power.

  a. Death and disease are universally regarded by uncivilized people as
  due to so-called "magic," i.e. to non-natural causes. Primitive man
  was familiar with the wounds and bruises caused by physical means; he
  would naturally attribute any pain not so caused to the operation of
  analogous but invisible weapons, and eventually attempt to discover
  how he himself could apply on his own behalf the forces thus used
  against him. Similarly he may have asked himself to what causes were
  to be attributed the superiority of one man over another; he may have
  decided the problem by referring it to the superior power of the one,
  and then inquired in what way this power could in individual instances
  be increased. In fact we may say generally that man probably explained
  the already existing and happening by reference to the supernormal,
  and then endeavoured to guide the supernormal for his own benefit,
  direct or indirect.

  b. Ritual, however (the primitive magico-religious plasm), is negative
  as well as positive. The corpse is uncanny, and man's dread of the
  corpse may well have been an early development; this dread, become
  traditional, with accretions of various sorts, crystallized into
  _taboo_, the magico-religious prohibition. The notion of the uncanny,
  once arrived at, may have been exploited positively; psychical
  abnormalities are present among savage races in very different
  degrees; but if they were developed at an early stage in human history
  they doubtless suggested the possibility that man might exploit them
  for the collective advantage. But it by no means follows that
  beneficent rites were originally regarded as magical; and it should be
  noted that the initiator of the so-called magician in Australia is
  often the god of the tribe or nation. The limits of magic or its
  correlatives in the lower stages of culture are thus far undecided.

  c. Magic as it represents itself to the Occidental mind of the present
  day, and perhaps to the great part of the inhabitants of the world,
  seems to be a thing of gradual growth. (i) In the earlier stages
  there was probably no animistic feature about magic; it was
  essentially "the prohibited." (ii) Then with the rise of animistic
  beliefs and practices came the association of the magician with
  demons--the spirits of the dead, or of animals, or unattached
  spirits--upon whose co-operation the powers of the magician are often
  now held to depend. These spirits were not in the position of gods;
  such recognition, worship, or cult as they received was often not a
  social institution, but the work of individuals, liable to fall into
  desuetude at the death of the individual, if not earlier. (iii) Again,
  the magical tends to be the less important and eventually the less
  respectable; therefore ancient cults which are conquered, like the
  religion of Rome by Christianity, come to be reckoned as within the
  sphere of magic and witchcraft. (iv) All non-animistic practices tend
  to become _ipso facto_ magical; many ritual prohibitions fall under
  the head of negative magic. Religion is predominantly animistic, and
  with the rise of gods magic and religion become antagonistic. Thus
  rites of a neutral character, such as leechcraft, and perhaps
  agricultural ceremonies which are not absorbed by religion, tend to
  acquire the reputation of being magical, as also do all amulets and
  talismans, and, in fact, everything not directly associated with
  religion. We therefore arrive at a period when magic is distinguished
  as _white_, i.e. the laudable, or at least permitted form, and
  _black_, i.e. the prohibited form.

_Magic and Demonology._--Primitive psychology tends to anthropomorphize
and personify; it is in many of its stages inclined to an animistic
philosophy. To this is due in part the difficulty of distinguishing
magic from religion. In many rites there is no obvious indication that a
spirit or personal being is concerned. A portion of the ceremonies in
which the spirits of the dead are concerned falls under the head of
religion (see ANCESTOR WORSHIP), but in the very name "necromancy"
([Greek: nekros], corpse) lies an implication of magic; and dealings
with the departed are viewed in this light in many parts of the world,
sometimes concurrently with a cult of ancestors. Side by side with the
human souls we find demons (see DEMONOLOGY); but on the whole only a
small proportion of the world of spirits is recognized as powerful in
magic; others, such as disease-spirits, are objects, not sources, of
magical influence. Magic is sometimes made to depend upon the activity
of demons and spirits, and it is true that the magician usually if not
invariably has a spirit helper, often an animal; but there is no
evidence that magical power had ever been confined to those who are thus
aided. It is not easy to define the relation of fetishism (q.v.) to
magic.

_Magic and Science._--It is a commonplace that the sciences have
developed from non-scientific beginnings; the root of astronomy is to be
sought in astrology (q.v.), of chemistry in alchemy (q.v.), of
leechcraft in the practices of the savage magician, who depends for much
of his success on suggestion, conscious or unconscious, but also relies
on a pharmacopeia of no mean extent. The dynamical theory of magic and
religion brings primitive man from one point of view far nearer to the
modern man of science than was previously suspected, we may fairly say
that the Australians have an idea not unlike that of the transformation
and conservation of energy, that this energy they store in accumulators,
transmit by means of conductors, and so on. The discovery of these
complicated ideas only serves to show how far the present-day peoples in
the lower stages of culture have travelled from the primitive man who
knew neither magic nor religion. But it is perhaps less in respect of
abstract ideas than by its concrete investigations into properties,
experiment and otherwise that magic has been the forerunner of science.

_Magic and Divination._--Magic is an attempt to influence the course of
events, divination (q.v.) to foresee them; but divination is frequently
regarded as magical. It is certain that a large part of divination is
religious, and the knowledge is explained as a message from the gods;
but necromancy, the practice of discovering the future by consulting the
dead, is in many respects essentially magical. Perhaps the magical
character of divination may be in part explained, when we regard it as a
group of practices in many varieties of which animism plays no part; for
non-animistic ceremonies tend to be regarded as magical (cf.
rain-making). Thus, heteroscopic divination seems to involve the idea of
what may be termed a return current of magico-religious force; the event
is not influenced, but itself determines the issue of the diviner's
experiment.


II.--LAWS AND RITUAL OF MAGIC

The practice of magic involves the belief in the operation of certain
laws, and demands certain conditions. The number of positive rites is
not unlimited; a certain rite tends to become stable and is finally used
for all sorts of purposes; and each magician tends to specialize in this
respect. Just as there are well-marked schools of magic, and the
rain-maker is not the same as the fetish-man, so within the school there
are various groups, differentiated not by the purposes at which they aim
nor by the powers they claim to possess, but by the ceremonies which
they practise. Chief among the laws lying at the base of magical
practice is that of sympathy.

_Sympathy._--That the law of sympathy is an essential element of magic
is admitted equally by the associationist school and by its critics.
Under the head of sympathy are embraced the laws of contiguity or
contagion, of similarity or homoeopathy, and of contrariety or
antipathy.

  a. In its simplest form the law of contiguity asserts that whatever
  has once formed part of a body continues to form part of it or to
  represent it for magical purposes; thus, by obtaining possession of
  the parings of a person's nails, or the clippings of his hair, and by
  working magic upon them, it is held to be possible to produce on the
  actual human body the effects which are in reality produced on the
  object of the magical rite. As is clear by the well-known case of the
  "life index," the current of magical power may pass in either
  direction; if the life of a man is supposed to be bound up with the
  life of a tree, so that any injury to the tree reacts on the man, it
  is equally believed that the death of the man will not fail to be
  manifest by the state of the tree. In particular this sympathetic
  relation is predicated of wizards or witches and their animal
  familiars; it is then known by the name of "repercussion." It is not
  only upon parts of the body that contagious magic can be worked;
  anything which has been in contact with the body, such as clothes,
  anything which has been in part assimilated by the body, such as the
  remains of food, and even representations of the body or of parts of
  it such as footprints, &c., may be used as objects of magical rites,
  in order to transmit to the human being some influence, maleficent or
  otherwise. The contact demanded may be actual, or mediate, for in
  Australia it suffices to connect the magician and his patient by a
  thread in order that the disease may be removed. (i) The use of
  clothes for magical purposes gives us perhaps the clue to the
  widespread custom of "rag-trees"; in nearly every part of the world it
  is the practice to suspend wool or rags to trees associated with some
  spirit, or, in Christian countries, with some saint, in order to reap
  a benefit; similarly nails are driven into trees or images; pins are
  dropped into wells, stones are cast upon cairns, and missiles aimed at
  various holy objects; but it cannot be assumed that the same
  explanation lies at the root of the whole group of practices. (ii)
  This law may perhaps be taken as the explanation of the "couvade"; in
  many parts of the world relatives, and in particular the father of a
  new-born child, are compelled to practise various abstinences, in
  order that the health of the child may not be affected, membership of
  the same family therefore establishes a sympathetic relation. (iii) In
  this direct transference of qualities is exemplified another magical
  process, which may also be referred to the operation of the law of
  sympathy; it is a world-wide belief that the assimilation of food
  involves the transference to the eater of the qualities, or of some of
  them, inherent in the source of the food; a South African warrior, for
  example, may not eat hedgehog, because the animal is held to be
  cowardly and the eater would himself become a coward; on the other
  hand, the flesh of lions is fit meat for brave men, because they at
  the same time transfer its courage to themselves.

  b. The law of homoeopathy takes two forms. (i) The magician may
  proceed on the assumption that like produces like; he may, for
  example, take an image of wax or wood, and subject it to heat or other
  influences under the belief that it represents the human being against
  whom his malefice is directed, and that without any contact, real or
  pretended; so that any results produced on the image, which may be
  replaced by an animal or a portion of one, are equally produced in the
  human being. There need not even be any resemblance between the
  representation and the person or thing represented; a pot may serve to
  represent a village; hence step by step we pass from the
  representation to the symbol. (ii) The law of homoeopathy also
  manifests itself in the formula _similia similibus curantur_; the
  Brahman in India treated dropsy with ablutions, not in order to add
  to, but to subtract from, the quantity of liquid in the patient's
  body. So, too, the yellow turmeric was held to be a specific for
  jaundice.

  c. Here we approach the third class of sympathetic rites; it is clear
  that a remedy produces the contrary, when it cures the like;
  conversely, like by producing like expels its contrary.

Some statements of the law of sympathy suggest that it is absolute in
its application. It is true that the current of magical power is
sometimes held to be transmitted along lines indicated by the law of
sympathy, without the intervention of any volition, human or otherwise;
thus, the crow which carries stray hairs away to weave them into the
structure of its nest is nowhere supposed to be engaged in a magical
process; but it is commonly held that the person whose hair is thus used
will suffer from headache or other maladies; this seems to indicate that
the law of sympathy operates mechanically in certain directions, though
the belief may also be explained as a secondary growth. In general the
operation of these laws is limited in the extreme. For example, the
medieval doctrine known as the Law of Signatures asserted that the
effects of remedies were correlated to their external qualities; bear's
grease is good for baldness, because the bear is a hairy animal. But the
transference was held to terminate with the acquisition by the man of
this single quality; in some magical books powdered mummy is recommended
as a means of prolonging life, but it is simply the age of the remedy
which is to benefit the patient; the magician who removes a patient's
pains or diseases does not transfer them to himself; the child whose
parents eat forbidden foods is held to be affected by their
transgression, while they themselves come off unharmed. The magical
effects are limited by exclusive attention and abstraction; and this is
true not only of the kind of effect produced but also as to the
direction in which it is held to be produced.

_The Magic of Names._--For primitive peoples the name is as much a part
of the person as a limb; consequently the magical use of names is in
some of its aspects assimilable to the processes dependent on the law of
sympathy. In some cases the name must be withheld from any one who is
likely to make a wrong use of it, and in some parts of the world people
have secret names which are never used. Elsewhere the name must not be
told by the bearer of it, but any other person may communicate it
without giving an opening for the magical use of it. Not only human
beings but also spirits can be coerced by the use of their names; hence
the names of the dead are forbidden, lest the mention of them act as an
evocation, unintentional though it be. Even among more advanced nations
it has been the practice to conceal the real name of supreme gods; we
may probably explain this as due to the fear that an enemy might by the
use of them turn the gods away from those to whom they originally
belonged. For the same reason ancient Rome had a secret name.

  _Magical Rites._--The magic of names leads us up to the magic of the
  spoken word in general. The spell or incantation and the magical act
  together make up the rite. (a) The manual acts are very frequently
  symbolic or sympathetic in their nature; sometimes they are mere
  reversals of a religious rite; such is the marching against the sun
  (known as _widdershins_ or _deisul_); sometimes they are purificatory;
  and magic has its sacrifices just as much as religion. (b) There are
  many types of oral rites; some of the most curious consist in simply
  reciting the effect intended to be produced, describing the manual
  act, or, especially in Europe, telling a mythical narrative in which
  Christ or the apostles figure, and in which they are represented as
  producing a similar effect to the one desired; in other cases the
  "origin" of the disease or maleficent being is recited. Oral rites,
  which are termed spells or incantations, correspond in many cases to
  the oral rites of religion; they, like the manual rites, are a
  heterogeneous mass and hardly lend themselves to classification. Some
  formulae may be termed sympathetic; it suffices to name the result to
  be produced in order to produce it; but often an incantation is
  employed, not to produce a result directly, but to coerce a god or
  other being and compel him to fulfil the magician's will. The language
  of the incantations often differs from that of daily life; it may be a
  survival of archaic forms or may be a special creation for magical
  purposes. In many languages the word used to express the idea of magic
  means an act, a deed; and it may be assumed that few if any magical
  ceremonies consist of formulae only; on the other hand, it is certain
  that no manual act in magic stands absolutely alone without oral rite;
  if there is no spoken formula, there is at least an unspoken thought.
  It is in many cases difficult to discover the relative proportions and
  importance of manual and oral acts. Not only the words but also the
  tone are of importance in magic; in fact, the tone may be the more
  important. Rhythm and repetition are no less necessary in oral than in
  manual acts. (c) As preliminaries, more seldom as necessary sequels to
  the central feature of the rite, manual or oral, we usually find a
  certain number of accessory observances prescribed, which find their
  parallel in the sacrificial ritual. For example, it is laid down at
  what time of year, at what period of the month or week, at what hour
  of the day a rite must be performed; the waxing or waning of the moon
  must be noted; and certain days must be avoided altogether. Similarly,
  certain places may be prescribed for the performance of the ritual;
  often the altar of the god serves magical purposes also; but elsewhere
  it is precisely the impure sites which are devoted to magical
  operations--the cemeteries and the cross roads. The instruments of
  magic are in like manner often the remains of a sacrifice, or
  otherwise consecrated by religion; sometimes, especially when they
  belong to the animal or vegetable world, they must be sought at
  certain seasons, May Day, St George's Day, Midsummer Day, &c. The
  magician and his client must undergo rites of preparation and the exit
  may be marked by similar ceremonies.

  _Magicians._--Most peoples know the professional worker of magic, or
  what is regarded as magic. (a) In most if not all societies magic, or
  certain sorts of it, may be performed by any one, so far as we can
  see, who has mastered the necessary ritual; in other cases the
  magician is a specialist who owes his position to an accident of birth
  (seventh son of a seventh son); to simple inheritance (families of
  magicians in modern India, rain-makers in New Caledonia); to
  revelation from the gods or the spirits of the dead (Malays), showing
  itself in the phenomena of possession; or to initiation by other
  magicians. (b) From a psychical point of view it may probably be said
  that the initiation of a magician corresponds to the "development" of
  the modern spiritualistic medium; that is to say, that it resolves
  itself into exercises and rites which have for their object the
  creation or evolution of a secondary personality. From this point of
  view it is important to notice that certain things are forbidden to
  magicians under pain of loss of their powers; thus, hot tea is taboo
  to the Arunta medicine man; and if this seems unlikely to cause the
  secondary personality to disappear, it must be remembered that to the
  physiological effects, if any, must be added the effects of
  suggestion. Of this duplication of personality various explanations
  are given; in Siberia the soul of the _shaman_ is said to wander into
  the other world, and this is a widely spread theory; where the
  magician is supposed to remain on earth, his soul is again believed to
  wander, but there is an alternative explanation which gives him two or
  more bodies. Here we reach a point at which the familiar makes its
  appearance; this is at times a secondary form of the magician, but
  more often is a sort of life index or animal helper (see LYCANTHROPY);
  in fact, the magician's power is sometimes held to depend on the
  presence--that is, the independence--of his animal auxiliary.
  Concurrent with this theory is the view that the magician must first
  enter into a trance before the animal makes its appearance, and this
  makes it a double of the magician, or, from the psychological point of
  view, a phase of secondary personality. (c) In many parts of the world
  magical powers are associated with the membership of secret societies,
  and elsewhere the magicians form a sort of corporation; in Siberia,
  for example, they are held to be united by a certain tie of kinship;
  where this is not the case, they are believed, as in Africa at the
  present day or in medieval Europe, to hold assemblies, so-called
  witches' Sabbaths; in Europe the meetings of heretics seem to be
  responsible for the prominence of the idea if not for its origin (see
  WITCHCRAFT). The magician is often regarded as possessed (see
  POSSESSION) either by an animal or by a human or super-human spirit.
  The relations of priest and magician are for various reasons complex;
  where the initiation of the magician is regarded as the work of the
  gods, the magician is for obvious reasons likely to develop into a
  priest, but he may at the same time remain a magician; where a
  religion has been superseded, the priests of the old cult are, for
  those who supersede them, one and all magicians; in the medieval
  church, priests were regarded as especially exposed to the assaults of
  demons, and were consequently often charged with working magic. The
  great magicians who are gods rather than men--e.g. kings of Fire and
  Water in Cambodia--enjoy a reverence and receive a cult which
  separates them from the common herd, and assimilates them to priests
  rather than to magicians. The function of the so-called magician is
  often said to be beneficent; in Africa the witch-doctor's business is
  to counteract evil magic; in Australia the magician has to protect his
  own tribe against the assaults of hostile magicians of other tribes;
  and in Europe "white magic" is the correlative of this beneficent
  power; but it may be questioned how far the beneficent virtue is
  regarded as magical outside Europe.

  _Talismans and Amulets._--Inanimate objects as well as living beings
  are credited with stores of magical force; when they are regarded as
  bringing good, i.e. are positive in their action, they may be termed
  "talismans"; "amulets" are protective or negative in their action, and
  their function is to avert evil; a single object may serve both
  purposes. Broadly speaking, the fetish, whose "magical" properties are
  due to association with a spirit, tends to become a talisman or
  amulet. The "medicine" of the Red Indian, originally carried as means
  of union between him and his _manito_, is perhaps the prototype of
  many European charms. In other cases it is some specific quality of
  the object or animal which is desired; the boar's tusk is worn on the
  Papuan Gulf as a means of imparting courage to the wearer; the
  Lukungen Indians of Vancouver Island rub the ashes of wasps on the
  faces of their warriors, in order that they may be pugnacious. Some
  Bechuanas wear a ferret as a charm, in the belief that it will make
  them difficult to kill, the animal being very tenacious of life. Among
  amulets may be mentioned horns and crescents, eyes or their
  representations, and grotesque figures, all of which are supposed to
  be powerful against the Evil Eye (q.v.). Tylor has shown that the
  brass objects so often seen on harness were originally amuletic in
  purpose, and can be traced back to Roman times. Some amulets are
  supposed to protect from the evil eye simply by attracting the glance
  from the wearer to themselves, but, as a rule, magical power is
  ascribed to them.

  _Evil Magic._--The object of "black" magic is to inflict injury,
  disease, or death on an enemy, and the various methods employed
  illustrate the general principles dealt with above and emphasize the
  conclusion that magic is not simply a matter of sympathetic rites, but
  involves a conception of magical force. (a) It has been mentioned that
  contagious magic makes use of portions of a person's body; the
  Cherokee magician follows his victim till he spits on the ground;
  collecting the spittle mingled with dust on the end of a stick, the
  magician puts it into a tube made of a poisonous plant together with
  seven earth worms, beaten into a paste, and splinters of a tree
  blasted by lightning; the whole is buried with seven yellow stones at
  the foot of a tree struck by lightning, and a fire is built over the
  spot; the magician fasts till the ceremony is over. Probably the worms
  are supposed to feed on the victim's soul, which is said to become
  "blue" when the charm works; the yellow stones are the emblem of
  trouble, and lightning-struck trees are reputed powerful in magic. If
  the charm does not work, the victim survives the critical seven days,
  and the magician and his employer are themselves in danger, for a
  charm gone wrong returns upon the head of him who sent it forth. (b)
  In homoeopathic magic the victim is represented by an image or other
  object. In the Malay Peninsula the magician makes an image like a
  corpse, a footstep long. "If you want to cause sickness, you pierce
  the eye and blindness results; or you pierce the waist and the stomach
  gets sick. If you want to cause death, you transfix the head with a
  palm twig; then you enshroud the image as you would a corpse and you
  pray over it as if you were praying over the dead; then you bury it in
  the middle of the path which leads to the place of the person whom you
  wish to charm, so that he may step over it." Sometimes the wizard
  repeats a form of words signifying that not he but the Archangel
  Gabriel is burying the victim; sometimes he exclaims, "It is not wax I
  slay but the liver, heart and spleen of So-and-so." Finally, the image
  is buried in front of the victim's doors. (c) Very widespread is the
  idea that a magician can influence his victim by charming a bone,
  stick or other object, and then projecting the magical influence from
  it. It is perhaps the commonest form of evil magic in Australia; in
  the Arunta tribe a man desirous of using one of these pointing sticks
  or bones goes away by himself into the bush, puts the bone on the
  ground and crouches over it, muttering a charm: "May your heart be
  rent asunder." After a time he brings the irna back to the camp and
  hides it; then one evening after dark he takes it and creeps near
  enough to see the features of his victim; he stoops down with the
  _irna_ in his hand and repeatedly jerks it over his shoulder,
  muttering curses all the time. The evil magic, _arungquiltha_, is said
  to go straight to the victim, who sickens and dies without apparent
  cause, unless some medicine-man can discover what is wrong and save
  him by removing the evil magic. The _irna_ is concealed after the
  ceremony, for the magician would at once be killed if it were known
  that he had used it. (d) Magicians are often said to be able to assume
  animal form or to have an animal familiar. They are said to suck the
  victim's blood or send a messenger to do so; sometimes they are said
  to steal his soul, thus causing sickness and eventually death. These
  beliefs bring the magician into close relation with the werwolf (see
  LYCANTHROPY).

  _Rain-making._--In the lower stages of culture rain-making assumes
  rather the appearance of a religious ceremony, and even in higher
  stages the magical character is by no means invariably felt. It will,
  however, be well to notice some of the methods here. (a) Among the
  Dieri of Central Australia the whole tribe takes part in the ceremony;
  a hole is dug, and over this a hut is built, large enough for the old
  men; the women are called to look at it and then retire some five
  hundred yards. Two wizards have their arms bound at the shoulder, the
  old men huddle in the hut, and the principal wizard bleeds the two men
  selected by cutting them inside the arm below the elbow. The blood is
  made to flow on the old men, and the two men throw handfuls of down
  into the air. The blood symbolizes the rain; the down is the clouds.
  Then two large stones are placed in the middle of the hut; these two
  represent gathering clouds. The women are again summoned, and then the
  stones are placed high in a tree; other men pound gypsum and throw it
  into a water-hole; the ancestral spirits are supposed to see this and
  to send rain. Then the hut is knocked down, the men butting at it with
  their heads; this symbolizes the breaking of the clouds, and the fall
  of the hut is the rain, if no rain comes they say that another tribe
  has stopped their power or that the _Mura-mura_ (ancestors) are angry
  with them. (b) Rain-making ceremonies are far from uncommon in Europe.
  Sometimes water is poured on a stone; a row of stepping-stones runs
  into one of the tarns on Snowdon, and it is said that water thrown
  upon the last one will cause rain to fall before night. Sometimes the
  images of saints are carried to a river or a fountain and ducked or
  sprinkled with water in the belief that rain will follow; sometimes
  rain is said to ensue when the water of certain springs is troubled;
  perhaps the idea is that the rain-god is disturbed in his haunts. But
  perhaps the commonest method is to duck or drench a human figure or
  puppet, who represents in many instances the vegetation demon. The
  gipsies of Transylvania celebrate the festival of "Green George" at
  Easter or on St George's Day; a boy dressed up in leaves and blossoms
  is the principal figure; he throws grass to the cattle of the tribe,
  and after various other ceremonies a pretence is made of throwing him
  into the water; but in fact only a puppet is ducked in the stream.

_Negative Magic._--There is also a negative side to magic, which,
together with ritual prohibitions of a religious nature, is often
embraced under the name of taboo (q.v.); this extension of meaning is
not justified, for taboo is only concerned with sacred things, and the
mark of it is that its violation causes the taboo to be transmitted. All
taboos are ritual prohibitions, but all ritual prohibitions are not
taboos; they include also (a) interdictions of which the sanction is the
wrath of a god; these may be termed religious interdictions; (b)
interdictions, the violation of which will automatically cause some
undesired magico-religious effect; to these the term negative magic
should be restricted, and they might conveniently be called "bans"; they
correspond in the main to positive rites and are largely based on the
same principles.

  (a) Certain prohibitions, such as those imposed on totem kins, seem to
  occupy an intermediate place; they depend on the sanctity of the totem
  animal without being taboos in the strict sense; to them no positive
  magical rites correspond, for the totemic prohibition is clearly
  religious, not magical.

  (b) Among cases of negative magic may be mentioned (i.) the couvade,
  and prohibitions observed by parents and relatives generally; this is
  most common in the case of young children, but a sympathetic relation
  is held to exist in other cases also. In Madagascar a son may not eat
  fallen bananas, for the result would be to cause the death of his own
  father; the sympathy between father and son establishes a sympathy
  between the father and objects touched or eaten by the son, and, in
  addition, the fall of the bananas is equated with the death of a human
  being. Again, the wife of a Malagasy warrior may not be faithless to
  him when he is absent; if she is, he will be killed or wounded.
  Ownership, too, may create a sympathetic relation of this kind, for it
  is believed in parts of Europe that if a man kills a swallow his cows
  will give bloody milk. In some cases it is even harder to see how the
  sympathetic bond is established; some Indians of Brazil always
  hamstring animals before bringing them home, in the belief that by so
  doing they make it easier for themselves and their children to run
  down their enemies, who are then magically deprived of the use of
  their legs. These are all examples of negative magic with regard to
  persons, but things may be equally affected; thus in Borneo men who
  search for camphor abstain from washing their plates for fear the
  camphor, which is found crystallized in the crevices of trees, should
  dissolve and disappear. (ii.) Rules which regulate diet exist not only
  for the benefit of others but also for that of the eater. Some
  animals, such as the hare, are forbidden, just as others, like the
  lion, are prescribed; the one produces cowardice, while the other
  makes a man's heart bold. (iii.) Words may not be used; Scottish
  fishermen will not mention the pig at sea; the real names of certain
  animals, like the bear, may not be used; the names of the dead may not
  be mentioned; a sacred language must be used, e.g. camphor language in
  the Malay peninsula, or only words of good omen (cf. Gr. [Greek:
  euphêmeite]); or absolute silence must be preserved. Personal names
  are concealed; a man may not mention the names of certain relatives,
  &c. There are customs of avoidance not only as to (iv.) the names of
  relatives, but as to the persons themselves; the mother-in-law must
  avoid the son-in-law, and vice versa; sometimes they may converse at a
  distance, or in low tones, sometimes not at all, and sometimes they
  may not even meet. (v.) In addition to these few classes selected at
  random, we have prohibitions relating to numbers (cf. unlucky
  thirteen, which is, however, of recent date), the calendar (Friday as
  an unlucky day, May as an unlucky month for marriage), places,
  persons, orientation, &c.; but it is impossible to enumerate even the
  main classes. The individual origin of such beliefs, which with us
  form the superstitions of daily life but in a savage or semi-civilized
  community play a large part in regulating conduct, is often shrouded
  in darkness; the meaning of the positive rite is easily forgotten; the
  negative rite persists, but it is observed merely to avoid some
  unknown misfortune. Sometimes we can, however, guess at the meaning of
  our civilized notions of ill luck; it is perhaps as a survival of the
  savage belief that stepping over a person is injurious to him that
  many people regard going under a ladder as unlucky; in the one case
  the luck is taken away by the person stepping over, in the other left
  behind by the person passing under.

_History of Magic._--The subject is too vast and our data are too slight
to make a general sketch of magic possible. Our knowledge of Assyrian
magic, for example, hardly extends beyond the rites of exorcism; the
magic of Africa is most inadequately known, and only in recent years
have we well-analysed repertories of magical rituals from any part of
the world. For certain departments of ancient magic, however, like the
Pythagorean philosophy, there is no lack of illustrative material; it
depended on mystical speculations based on numbers or analogous
principles. The importance of numbers is recognized in the magic of
America and other areas, but the science of the Mediterranean area,
combined with the art of writing, was needed to develop such mystical
ideas to their full extent. Among the neo-Platonists there was a strong
tendency to magical speculation, and they sought to impress into their
service the demons with which they peopled the universe. Alexandria was
the home of many systems of theurgic magic, and gnostic gems afford
evidence of the nature of their symbols. In the middle ages the
respectable branches of magic, such as astrology and alchemy, included
much of the real science of the period; the rise of Christianity
introduced a new element, for the Church regarded all the religions of
the heathen as dealings with demons and therefore magical (see
WITCHCRAFT). In our own day the occult sciences still find devotees
among the educated; certain elements have acquired a new interest, in so
far as they are the subject matter of psychical research (q.v.) and
spiritualism (q.v.). But it is only among what are regarded as the lower
classes, and in England especially the rural population, that belief in
its efficacy still prevails to any large extent.

_Psychology of Magic._--The same causes which operated to produce a
belief in witchcraft (q.v.) aided the creed of magic in general.
Fortuitous coincidences attract attention; the failures are disregarded
or explained away. Probably the magician is never wholly an impostor,
and frequently has a whole-hearted belief in himself; in this connexion
may be noted the fact that juggling tricks have in all ages been passed
off as magical; the name of "conjuring" (q.v.) survives in our own day,
though the conjurer no longer claims that his mysterious results are
produced by demons. It is interesting to note that magical leechcraft
depended for its success on the power of suggestion (q.v.), which is
to-day a recognized element in medicine; perhaps other elements may have
been instrumental in producing a cure, for there are cases on record in
which European patients have been cured by the apparently meaningless
performances of medicine-men, but an adequate study of savage medicine
is still a desideratum.

  BIBLIOGRAPHY.--For a general discussion of magic with a list of
  selected works see Hubert and Mauss in _Année sociologique_, vii.
  1-146; also A. Lehmann, _Aberglaube und Zauberei_; the article
  "Religion" in _La Grande encyclopédie_; K. T. Preuss in _Globus_,
  vols. 86, 87; Mauss, _L'Origine des pouvoirs magiques_, and Hubert,
  _La Réprésentation du temps_ (Reports of École pratique des hautes
  études, Paris). For general bibliographies see Hauck,
  _Realencyklopädie_, _s.v._ "Magie"; A. C. Haddon, _Magic and
  Fetishism_. J. G. T. Graesse's _Bibliotheca magica_ is an exhaustive
  list of early works dealing with magic and superstition. For Australia
  see Spencer and Gillen's works, and A. W. Howitt, _Native Tribes_. For
  America see _Reports of Bureau of Ethnology_, vii. xvii. For India see
  W. Caland, _Altindisches Zauber-ritual_; and W. Crooke, _Popular
  Religion_; also V. Henry, _La Magie_. For the Malays see W. W. Skeat,
  _Malay Magic_. For Babylonia and Assyria see L. W. King's works. For
  magic in Greece and Rome see Daremberg and Saglio, _s.v._ "Magia,"
  "Amuletum," &c. For medieval magic see A. Maury, _La Magie_. For
  illustrations of magic see J. G. Frazer, _The Golden Bough_; E. S.
  Hartland, _Legend of Perseus_; E. B. Tylor, _Primitive Culture_; W. G.
  Black, _Folkmedicine_. For negative magic see the works of Frazer and
  Skeat cited above; also _Journ. Anthrop. Inst._ xxxvi. 92-103;
  _Zeitschrift für Ethnologie_ (Verhandlungen) (1905), 153-162;
  _Bulletin trimestriel de l'académie malgache_, iii. 105-159. See also
  bibliography to TABOO and WITCHCRAFT.     (N. W. T.)


FOOTNOTE:

  [1] For what is often called "magic," but is really
    trick-performance, see CONJURING.




MAGIC SQUARE, a square divided into equal squares, like a chess-board,
in each of which is placed one of a series of consecutive numbers from 1
up to the square of the number of cells in a side, in such a manner that
the sum of the numbers in each row or column and in each diagonal is
constant.

From a very early period these squares engaged the attention of
mathematicians, especially such as possessed a love of the marvellous,
or sought to win for themselves a superstitious regard. They were then
supposed to possess magical properties, and were worn, as in India at
the present day, engraven in metal or stone, as amulets or talismans.
According to the old astrologers, relations subsisted between these
squares and the planets. In later times such squares ranked only as
mathematical curiosities; till at last their mode of construction was
systematically investigated. The earliest known writer on the subject
was Emanuel Moscopulus, a Greek (4th or 5th century). Bernard Frenicle
de Bessy constructed magic squares such that if one or more of the
encircling bands of numbers be taken away the remaining central squares
are still magical. Subsequently Poignard constructed squares with
numbers in arithmetical progression, having the magical summations. The
later researches of Phillipe de la Hire, recorded in the _Mémoires de
l'Académie Royale_ in 1705, are interesting as giving general methods of
construction. He has there collected the results of the labours of
earlier pioneers; but the subject has now been fully systematized, and
extended to cubes.

  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |200|217|232|249|  8| 25| 40| 57| 72| 89|104|121|136|153|168|185|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 58| 39| 26|  7|250|231|218|199|186|167|154|135|122|103| 90| 71|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |198|219|230|251|  6| 27| 38| 59| 70| 91|102|123|134|155|166|187|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 60| 37| 28|  5|252|229|220|197|188|165|156|133|124|101| 92| 69|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |201|216|233|248|  9| 24| 41| 56| 73| 88|105|120|137|152|169|184|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 55| 42| 23| 10|247|234|215|202|183|170|151|138|119|106| 87| 74|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |203|214|235|246| 11| 22| 43| 54| 75| 86|107|118|139|150|171|182|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 53| 44| 21| 12|245|236|213|204|181|172|149|140|117|108| 85| 76|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |205|212|237|244| 13| 20| 45| 52| 77| 84|109 116|141|148|173|180|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 51| 46| 19| 14|243|238|211|206|179|174|147 142|115|110| 83| 78|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |207|210|239|242| 15| 18| 47| 50  79| 82|111 114|143|146|175|178|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 49| 48| 17| 16|241|240|209|208 177|176|145 144|113|112| 81| 80|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |196|221|228|253|  4| 29| 36| 61  68| 93|100 125|132|157|164|189|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 62| 35| 30|  3|254|227|222|195 190|163|158 131|126| 99| 94| 67|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  |194|223|226|255|  2|31 | 34| 63  66| 95| 98 127|130|159|162|191|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  | 64| 33| 32|  1|256|225|224 193|192|161 160|129|128| 97| 96| 65|
  +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

  FIG. 1.

[Illustration: FIG. 2.]

  Two interesting magical arrangements are said to have been given by
  Benjamin Franklin; these have been termed the "magic square of
  squares" and the "magic circle of circles." The first (fig. 1) is a
  square divided into 256 squares, i.e. 16 squares along a side, in Fig.
  2. which are placed the numbers from 1 to 256. The chief properties of
  this square are (1) the sum of the 16 numbers in any row or column is
  2056; (2) the sum of the 8 numbers in half of any row or column is
  1028, i.e. one half of 2056; (3) the sum of the numbers in two
  half-diagonals equals 2056; (4) the sum of the four corner numbers of
  the great square and the four central numbers equals 1028; (5) the sum
  of the numbers in any 16 cells of the large square which themselves
  are disposed in a square is 2056. This square has other curious
  properties. The "magic circle of circles" (fig. 2) consists of eight
  annular rings and a central circle, each ring being divided into eight
  cells by radii drawn from the centre; there are therefore 65 cells.
  The number 12 is placed in the centre, and the consecutive numbers 13
  to 75 are placed in the other cells. The properties of this figure
  include the following: (1) the sum of the eight numbers in any ring
  together with the central number 12 is 360, the number of degrees in a
  circle; (2) the sum of the eight numbers in any set of radial cells
  together with the central number is 360; (3) the sum of the numbers in
  any four adjoining cells, either annular, radial, or both radial and
  two annular, together with half the central number, is 180.

  +---+---+---+---+---+-+---+---+---+---+---+
  |   | a |[e]| 5 |   | |   |   |[e]|   |   |
  |   |   |   |   |   | |   |   |   |   |   |
  +---+---+---+---+---+ +---+---+---+---+---+
  |   | 4 | b |   |[d]| |   | 4 |   |   |[d]|
  |   |   |   |   |   | |   |   |   |   |   |
  +---+---+---+---+---+ +---+---+---+---+---+
  |   |[g]|   | c | 3 | |   |[g]|   |   |   |
  |   |   |   |   |   | |   |   |   |   |   |
  +---+---+---+---+---+ +---+---+---+---+---+
  |   |   | 2 |[b]| d | |   |   |   |   |   |
  |   |   |   |   |   | |   |   |   |   |   |
  +---+---+---+---+---+ +---+---+---+---+---+
  |1 e|   |   |   |   | | e |   |   |   |   |
  |[a]|   |   |   |   | |   |   |   |   |   |
  +---+---+---+---+---+-+---+---+---+---+---+

  FIG. 3.

_Construction of Magic Squares._--A square of 5 (fig. 3) has adjoining
it one of the eight equal squares by which any square may be conceived
to be surrounded, each of which has two sides resting on adjoining
squares, while four have sides resting on the surrounded square, and
four meet it only at its four angles. 1, 2, 3 are placed along the path
of a knight in chess; 4, along the same path, would fall in a cell of
the outer square, and is placed instead in the corresponding cell of the
original square; 5 then falls within the square. a, b, c, d are placed
diagonally in the square; but e enters the outer square, and is removed
thence to the same cell of the square it had left. [alpha], [beta],
[gamma], [delta], [epsilon] pursue another regular course; and the
diagram shows how that course is recorded in the square they have twice
left. Whichever of the eight surrounding squares may be entered, the
corresponding cell of the central square is taken instead. The 1, 2, 3,
..., a, b, c, ..., [alpha], [beta], [gamma], ... are said to lie in
"paths."

  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 1 | 4 | 2 | 5 | 3 |    | 2 | 4 | 0 | 3 | 1 |    |11 |24 | 2 |20 | 8 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 4 | 2 | 5 | 3 | 1 |    | 1 | 2 | 4 | 0 | 3 |    | 9 |12 |25 | 3 |16 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 2 | 5 | 3 | 1 | 4 |    | 3 | 1 | 2 | 4 | 0 |    |17 |10 |13 |21 | 4 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 5 | 3 | 1 | 4 | 2 |    | 0 | 3 | 1 | 2 | 4 |    | 5 |18 | 6 |14 |22 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 3 | 1 | 4 | 2 | 5 |    | 4 | 0 | 3 | 1 | 2 |    |23 | 1 |19 | 7 |15 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+

         FIG. 4.                  FIG. 5.                  FIG. 6.

  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 2 | 1 | 5 | 3 | 4 |    |15 | 5 | 0 |20 |10 |    |17 | 6 | 5 |23 |14 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 3 | 4 | 2 | 1 | 5 |    | 0 |20 |10 |15 | 5 |    | 3 |24 |12 |16 |10 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 1 | 5 | 3 | 4 | 2 |    |10 |15 | 5 | 0 |20 |    |11 |20 | 8 | 4 |22 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 4 | 2 | 1 | 5 | 3 |    | 5 | 0 |20 |10 |15 |    | 9 | 2 |21 |15 |18 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+
  | 5 | 3 | 4 | 2 | 1 |    |20 |10 |15 | 5 | 0 |    |25 |13 |19 | 7 | 1 |
  |   |   |   |   |   |    |   |   |   |   |   |    |   |   |   |   |   |
  +---+---+---+---+---+    +---+---+---+---+---+    +---+---+---+---+---+

         FIG. 7.                  FIG. 8.                  FIG. 9.

_Squares whose Roots are Odd._--Figs 4, 5, and 6 exhibit one of the
earliest methods of constructing magic squares. Here the 3's in fig. 4
and 2's in fig. 5 are placed in opposite diagonals to secure the two
diagonal summations; then each number in fig. 5 is multiplied by 5 and
added to that in the corresponding square in fig. 4, which gives the
square of fig. 6. Figs. 7, 8 and 9 give De la Hire's method; the squares
of figs. 7 and 8, being combined, give the magic square of fig. 9. C. G.
Bachet arranged the numbers as in fig. 10, where there are three numbers
in each of four surrounding squares; these being placed in the
corresponding cells of the central square, the square of fig. 11 is
formed. He also constructed squares such that if one or more outer bands
of numbers are removed the remaining central squares are magical. His
method of forming them may be understood from a square of 5. Here each
summation is 5 × 13; if therefore 13 is subtracted from each number, the
summations will be zero, and the twenty-five cells will contain the
series ± i, ± 2, ± 3, ... ± 12, the odd cell having 0. The central
square of 3 is formed with four of the twelve numbers with + and - signs
and zero in the middle; the band is filled up with the rest, as in fig.
12; then, 13 being added in each cell, the magic square of fig. 13 is
obtained.

_Squares whose Roots are Even._--These were constructed in various ways,
similar to that of 4 in figs. 14, 15 and 16. The numbers in fig. 15
being multiplied by 4, and the squares of figs. 14 and 15 being
superimposed, give fig. 16. The application of this method to squares
the half of whose roots are odd requires a complicated adjustment.
Squares whose half root is a multiple of 4, and in which there are
summations along all the diagonal paths, may be formed, by observing, as
when the root is 4, that the series 1 to 16 may be changed into the
series 15, 13, ... 3, 1, -1, -3, ... -13, -15, by multiplying each
number by 2 and subtracting 17; and, vice versa, by adding 17 to each of
the latter, and dividing by 2. The diagonal summations of a square,
filled as in fig. 17, make zero; and, to obtain the same in the rows and
columns, we must assign such values to the p's and q's as satisfy the
equations p1 + p2 + a1 + a2 = 0, p3 + p4 + a3 + a4 = 0, p1 + p3 - a1 -
a3 = 0, and p2 + p4 - a2 - a4 = 0,--a solution of which is readily
obtained by inspection, as in fig. 18; this leads to the square, fig.
19. When the root is 8, the upper four subsidiary rows may at once be
written, as in fig. 20; then, if 65 be added to each, and the sums
halved, the square is completed. In such squares as these, the two
opposite squares about the same diagonal (except that of 4) may be
turned through any number of right angles, in the same direction,
without altering the summations.

               1
            6     2
        +--+--+--+--+--+          +--+--+--+--+--+
        |11|  | 7|  | 3|          |11|24| 7|20| 3|
        +--+--+--+--+--+          +--+--+--+--+--+
     16 |  |12|  | 8|  | 4        | 4|12|25| 8|16|
        +--+--+--+--+--+          +--+--+--+--+--+
  21    |17|  |13|  | 9|   5      |17| 5|13|21| 9|
        +--+--+--+--+--+          +--+--+--+--+--+
     22 |  |18|  |14|  |10        |10|18| 1|14|22|
        +--+--+--+--+--+          +--+--+--+--+--+
        |23|  |19|  |15|          |23| 6|19| 2|15|
        +--+--+--+--+--+          +--+--+--+--+--+
            24    20
              25

            FIG. 10.                   FIG. 11.

  +---+---+---+---+---+      +---+---+---+---+---+
  | -9| 12|  5| -3| -6|      |  4| 25| 18| 11| 7 |
  +---+---+---+---+---+      +---+---+---+---+---+
  |  1|  7|-11|  4| -1|      | 14| 20|  2| 17| 13|
  +---+---+---+---+---+      +---+---+---+---+---+
  | -8| -3|  0|  3|  8|      |  5| 10| 13| 16| 21|
  +---+---+---+---+---+      +---+---+---+---+---+
  | 10| -4| 11| -7|-10|      | 23|  9| 24|  6|  3|
  +---+---+---+---+---+      +---+---+---+---+---+
  |  6|-12| -5|  2|  9|      | 19|  1|  8| 15| 22|
  +---+---+---+---+---+      +---+---+---+---+---+

         FIG. 12.                   FIG. 13.

  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
  | 1| 3| 2| 4|    | 0| 3| 3| 0|    | 1|15|14| 4|
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
  | 4| 2| 3| 1|    | 2| 1| 1| 2|    |12| 6| 7| 9|
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
  | 4| 2| 3| 1|    | 1| 2| 2| 1|    | 8|10|11| 5|
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
  | 1| 3| 2| 4|    | 3| 0| 0| 3|    |13| 3| 2|16|
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+

     FIG. 14.         FIG. 15.         FIG. 16.

  +---+---+---+---+    +---+---+---+---+    +---+---+---+---+
  | p1| p2| a1| a2|    |  1| -3| 11| -9|    |  9|  7| 14|  4|
  +---+---+---+---+    +---+---+---+---+    +---+---+---+---+
  | p3| p4| a3| a4|    | -5|  7|-15| 13|    |  6| 12|  1| 15|
  +---+---+---+---+    +---+---+---+---+    +---+---+---+---+
  |-a1|-a2|-p1|-p2|    |-11|  9| -1|  3|    |  3| 13|  8| 10|
  +---+---+---+---+    +---+---+---+---+    +---+---+---+---+
  |-a3|-a4|-p3|-p4|    | 15|-13|  5| -7|    | 16|  2| 11|  5|
  +---+---+---+---+    +---+---+---+---+    +---+---+---+---+

       FIG. 17.             FIG. 18.             FIG. 19.

  +---+---+---+---+---+---+---+---+
  | -1|  3|  5| -7|-33| 35| 37|-39|
  +---+---+---+---+---+---+---+---+
  |  9|-11|-13| 15| 41|-43|-45| 47|
  +---+---+---+---+---+---+---+---+
  | 17|-19|-21| 23| 49|-51|-53| 55|
  +---+---+---+---+---+---+---+---+
  |-25| 27| 29|-31|-57| 59| 61|-63|
  +---+---+---+---+---+---+---+---+

               FIG. 20.

  _Nasik Squares._--Squares that have many more summations than in rows,
  columns and diagonals were investigated by A. H. Frost (_Cambridge
  Math. Jour._, 1857), and called Nasik squares, from the town in India
  where he resided; and he extended the method to cubes, various
  sections of which have the same singular properties. In order to
  understand their construction it will be necessary to consider
  carefully fig. 21, which shows that, when the root is a prime, and not
  composite, number, as 7, eight letters a, b, ... h may proceed from
  any, the same, cell, suppose that marked 0, each letter being repeated
  in the cells along different paths. These eight paths are called
  "normal paths," their number being one more than the root. Observe
  here that, excepting the cells from which any two letters start, they
  do not occupy again the same cell, and that two letters, starting from
  any two different cells along different paths, will appear together in
  one and only one cell. Hence, if p1 be placed in the cells of one of
  the n + 1 normal paths, each of the remaining n normal paths will
  contain one, and only one, of these p1's. If now we fill each row with
  p2, p3, ... p_n in the same order, commencing from the p1 in that row,
  the p2's, p3's and p_n's will lie each in a path similar to that of
  p1, and each of the n normal paths will contain one, and only one, of
  the letters p1, p2,... p_n, whose sum will be [Sigma]p. Similarly, if
  q1 be placed along any of the normal paths, different from that of the
  p's, and each row filled as above with the letters q2, q3, ... q_n,
  the sum of the q's along any normal path different from that of the q1
  will be [Sigma]q. The n² cells of the square will now be found to
  contain all the combinations of the p's and q's; and if the q's be
  multiplied by n, the p's made equal to 1, 2, ... n, and the q's to 0,
  1, 2, ... (n - 1) in any order, the Nasik square of n will be
  obtained, and the summations along all the normal paths, except those
  traversed by the p's and q's, will be the constant [Sigma]nq +
  [Sigma]p. When the root is an odd composite number, as 9, 15, &c., it
  will be found that in some paths, different from the two along which
  the p1 and q1 were placed, instead of having each of the p's and q's,
  some will be wanting, while some are repeated. Thus, in the case of 9,
  the triplets, p1p4p7, p2p5p8, p3p6p9, and q1q4q7, q2q5q8, q3q6q9
  occur, each triplet thrice, along paths whose summation should
  be--[Sigma]p 45 and [Sigma]r 36. But if we make p1, p2, ... p9, = 1,
  3, 6, 5, 4, 7, 9, 8, 2, and the r1, r2, ... r9 = 0, 2, 5, 4, 3, 6, 8,
  7, 1, thrice each of the above sets of triplets will equal [Sigma]p
  and [Sigma]q respectively. If now the q's are multiplied by 9, and
  added to the p's in their several cells, we shall have a Nasik square,
  with a constant summation along eight of its ten normal paths. In fig.
  22 the numbers are in the nonary scale; that in the centre is the
  middle one of 1 to 9², and the sum of pair of numbers equidistant from
  and opposite to the central 45 is twice 45; and the sum of any number
  and the 8 numbers 3 from it, diagonally, and in its row and column, is
  the constant Nasical summation, e.g. 72 and 32, 22, 76, 77, 26, 37,
  36, 27. The numbers in fig. 22 being kept in the nonary scale, it is
  not necessary to add any nine of them together in order to test the
  Nasical summation; for, taking the first column, the figures in the
  place of units are seen at once to form the series, 1, 2, 3, ... 9,
  and those in the other place three triplets of 6, 1, 5. For the
  squares of 15 the p's and q's may be respectively 1, 2, 10, 8, 6, 14,
  15, 11, 4, 13, 9, 7, 3, 12, 5, and 0, 1, 9, 7, 5, 13, 14, 10, 3, 12,
  8, 6, 2, 11, 4, where five times the sum of every third number and
  three times the sum of every fifth number makes [Sigma]p and [Sigma]q;
  then, if the q's are multiplied by 15, and added to the p's, the Nasik
  square of 15 is obtained. When the root is the multiple of 4, the same
  process gives us, for the square of 4, fig. 23. Here the columns give
  [Sigma]p, but alternately 2q1, 2q3, and 2q2, 2q4; and the rows give
  [Sigma]q, but alternately 2p1, 2p3, and 2p2, 2p4; the diagonals giving
  [Sigma]p and [Sigma]q. If p1, p2, p3, p4 and q1, q2, q3, q4 be 1, 2,
  4, 3, and 0, 1, 3, 2, we have the Nasik square of fig. 24. A square
  like this is engraved in the Sanskrit character on the gate of the
  fort of Gwalior, in India. The squares of higher multiples of 4 are
  readily obtained by a similar adjustment.

    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | g | f | e | d | c | b |     |63|88|74|13| 8|24|53|48|34|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | d | g | c | f | b | e |     |11| 9|25|51|49|35|61|89|75|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | c | e | g | b | d | f |     |52|47|36|62|87|76|12| 7|26|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | f | d | b | g | e | c |     |68|84|73|18| 4|23|58|44|33|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | e | b | f | c | g | d |     |19| 5|21|59|45|31|69|85|71|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | a | b | c | d | e | f | g |     |57|46|32|67|86|72|17| 6|22|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
    | 0 | h | h | h | h | h | h |     |64|83|78|14| 3|28|54|43|38|
    +---+---+---+---+---+---+---+     +--+--+--+--+--+--+--+--+--+
               FIG. 21.               |15| 1|29|55|41|39|65|81|79|
                                      +--+--+--+--+--+--+--+--+--+
                                      |56|42|37|66|82|77|16| 2|27|
                                      +--+--+--+--+--+--+--+--+--+

                                                 FIG. 22.

  +-----+-----+-----+-----+     +--+--+--+--+
  |     |     |     |     |     |15|10| 3| 6|
  |p4q3 |p2q4 |p4q1 |p2q2 |     +--+--+--+--+
  |     |     |     |     |     | 4| 5|16| 9|
  +-----+-----+-----+-----+     +--+--+--+--+
  |     |     |     |     |     |14|11| 2| 7|
  |p3q1 |p1q2 |p3q3 |p1q4 |     +--+--+--+--+
  |     |     |     |     |     | 1| 8|13|12|
  +-----+-----+-----+-----+     +--+--+--+--+
  |     |     |     |     |        FIG. 24.
  |p2q3 |p4q4 |p2q1 |p4q2 |
  |     |     |     |     |
  +-----+-----+-----+-----+
  |     |     |     |     |
  |p1q1 |p3q2 |p1q3 |p3q4 |
  |     |     |     |     |
  +-----+-----+-----+-----+

          FIG. 23.

                  .
                 / \
                .   .
               / \ / \
              .   .   .
             / \ / \ / \
            .   .   . * .
           / \ / \ / \ / \
          .   . * .   .   .
         / \ / \ / \ / \ / \
        . * .   .   .   .   .
       / \ / \ / \ / \ / \ / \
      .   .   .   .   .   .   .
     / \ / \ / \ / \ / \ / \ / \
  C .   .   .   .   .   . * .   . A
    |\ / \ / \ / \ / \ / \ / \ /|
    . .   .   .   . * .   .   . .
    |\|\ / \ / \ / \ / \ / \ /|/|
    . . .   . * .   .   .   . . .
    |\|\|\ / \ / \ / \ / \ /|/|/|
    . . . .   .   .   .   . . . .
    |\|\|\|\ / \ / \ / \ /|/|/|/|
    .*. . . .   .   .   . .*. . .
    |\|\|\|\|\ / \ / \ /|/|/|/|/|
    . . .*. . .   .   . . . .*. .
    |\|\|\|\|\|\ / \ /|/|/|/|/|/|
    . . . . .*. . * . . . . . .*.
    |\|\|\|\|\|\|\ /|/|/|/|/|/|/|
    . . . . . . .*O*. . . . . . .
     \|\|\|\|\|\|\|/|/|/|/|/|/|/
      .*. . . . . . .*. . . . .
       \|\|\|\|\|\|/|/|/|/|/|/
        . .*. . . . . .*. . .
         \|\|\|\|\|/|/|/|/|/
          . . .*. . . . .*.
           \|\|\|\|/|/|/|/
            . . . . . . .
             \|\|\|/|/|/
              . . . . .
               \|\|/|/
                . . .
                 \|/
                  .
                  B

        FIG. 25--Nasik Cube.

  +--+--+--+--+------------+--+--+--+--+
  | 1| 8|29|28|            |11|14|23|18|
  +--+--+--+--+            +--+--+--+--+
  |30|27| 2| 7|            |21|20| 9|16|
  +--+--+--+--+            +--+--+--+--+
  | 4| 5|32|25|            |10|15|22|19|
  +--+--+--+--+            +--+--+--+--+
  |31|26| 3| 6|            |24|17|12|13|
  +--+--+--+--+------------+--+--+--+--+

                  FIG. 26.

  +--+--+--+--+--+     +--+--+--+--+--+--+
  |23|18|11| 6|25|     |30|21| 6|15|28|19|
  +--+--+--+--+--+     +--+--+--+--+--+--+
  |10| 5|24|17|12|     | 7|16|29|20| 5|14|
  +--+--+--+--+--+     +--+--+--+--+--+--+
  |19|22|13| 4| 7|     |22|31| 8|35|18|27|
  +--+--+--+--+--+     +--+--+--+--+--+--+
  |14| 9| 2|21|16|     | 9|26|17|26|13| 4|
  +--+--+--+--+--+     +--+--+--+--+--+--+
  | 1|20|15| 8| 3|     |32|23| 2|11|34|25|
  +--+--+--+--+--+     +--+--+--+--+--+--+
                       | 1|10|33|24| 3|12|
      FIG. 27.         +--+--+--+--+--+--+

                             FIG. 28.

  _Nasik Cubes._--A Nasik cube is composed of n³ small equal cubes, here
  called cubelets, in the centres of which the natural numbers from 1 to
  n³ are so placed that every section of the cube by planes
  perpendicular to an edge has the properties of a Nasik square; also
  sections by planes perpendicular to a face, and passing through the
  cubelet centres of any path of Nasical summation in that face. Fig. 25
  shows by dots the way in which these cubes are constructed. A dot is
  here placed on three faces of a cubelet at the corner, showing that
  this cubelet belongs to each of the faces AOB, BOC, COA, of the cube.
  Dots are placed on the cubelets of some path of AOB (here the knight's
  path), beginning from O, also on the cubelets of a knight's path in
  BOC. Dots are now placed in the cubelets of similar paths to that on
  BOC in the other six sections parallel to BOC, starting from their
  dots in AOB. Forty-nine of the three hundred and forty-three cubelets
  will now contain a dot; and it will be observed that the dots in
  sections perpendicular to BO have arranged themselves in similar
  paths. In this manner, p1, q1, r1 being placed in the corner cubelet
  O, these letters are severally placed in the cubelets of three
  different paths of AOB, and again along any similar paths in the seven
  sections perpendicular to AO, starting from the letters' position in
  AOB. Next, p2q2r2, p3q3r3, ... p7q7r7 are placed in the other cubelets
  of the edge AO, and dispersed in the same manner as p1q1r1. Every
  cubelet will then be found to contain a different combination of the
  p's, q's and r's. If therefore the p's are made equal to 1, 2, ... 7,
  and the q's and r's to 0, 1, 2, ... 6, in any order, and the q's
  multiplied by 7, and the r's by 7², then, as in the case of the
  squares, the 7³ cubelets will contain the numbers from 1 to 7³, and
  the Nasical summations will be [Sigma]7²r + [Sigma]7q + p. If 2, 4, 5
  be values of r, p, q, the number for that cubelet is written 245 in
  the septenary scale, and if all the cubelet numbers are kept thus, the
  paths along which summations are found can be seen without adding, as
  the seven numbers would contain 1, 2, 3, ... 7 in the unit place, and
  0, 1, 2, ... 6 in each of the other places. In all Nasik cubes, if
  such values are given to the letters on the central cubelet that the
  number is the middle one of the series 1 to n³, the sum of all the
  pairs of numbers opposite to and equidistant from the middle number is
  the double of it. Also, if around a Nasik cube the twenty-six
  surrounding equal cubes be placed with their cells filled with the
  same numbers, and their corresponding faces looking the same way,--and
  if the surrounding space be conceived thus filled with similar cubes,
  and a straight line of unlimited length be drawn through any two
  cubelet centres, one in each of any two cubes,--the numbers along that
  line will be found to recur in groups of seven, which (except in the
  three cases where the same p, q or r recur in the group) together make
  the Nasical summation of the cube. Further, if we take n similarly
  filled Nasik cubes of n, n new letters, s1, s2, ... s_n, can be so
  placed, one in each of the n^4 cubelets of this group of n cubes, that
  each shall contain a different combination of the p's, q's, r's and
  s's. This is done by placing s1 on each of the n² cubelets of the
  first cube that contain p1, and on the n² cubelets of the 2d, 3d, ...
  and nth cube that contain p2, p3, ... p_n respectively. This process
  is repeated with s2, beginning with the cube at which we ended, and so
  on with the other s's; the n^4 cubelets, after multiplying the q's,
  r's, and s's by n, n², and n³ respectively, will now be filled with
  the numbers from 1 to n^4, and the constant summation will be
  [Sigma]n³s + [Sigma]n²r + [Sigma]nq + [Sigma]p. This process may be
  carried on without limit; for, if the n cubes are placed in a row with
  their faces resting on each other, and the corresponding faces looking
  the same way, n such parallelepipeds might be put side by side, and
  the n^5 cubelets of this solid square be Nasically filled by the
  introduction of a new letter t; while, by introducing another letter,
  the n^6 cubelets of the compound cube of n³ Nasik cubes might be
  filled by the numbers from 1 to n^6, and so _ad infinitum_. When the
  root is an odd composite number the values of the three groups of
  letters have to be adjusted as in squares, also in cubes of an even
  root. A similar process enables us to place successive numbers in the
  cells of several equal squares in which the Nasical summations are the
  same in each, as in fig. 26.

  Among the many ingenious squares given by various writers, this
  article may justly close with two by L. Euler, in the _Histoire de
  l'académie royale des sciences_ (Berlin, 1759). In fig. 27 the natural
  numbers show the path of a knight that moves within an odd square in
  such a manner that the sum of pairs of numbers opposite to and
  equidistant from the middle figure is its double. In fig. 28 the
  knight returns to its starting cell in a square of 6, and the
  difference between the pairs of numbers opposite to and equidistant
  from the middle point is 18.

  A model consisting of seven Nasik cubes, constructed by A. H. Frost,
  is in the South Kensington Museum. The centres of the cubes are placed
  at equal distances in a straight line, the similar faces looking the
  same way in a plane parallel to that line. Each of the cubes has seven
  parallel glass plates, to which, on one side, the seven numbers in the
  septenary scale are fixed, and behind each, on the other side, its
  value in the common scale. 1201, the middle number from 1 to 7^4
  occupies the central cubelet of the middle cube. Besides each cube
  having separately the same Nasical summation, this is also obtained by
  adding the numbers in any seven similarly situated cubelets, one in
  each cube. Also, the sum of all pairs of numbers, in a straight line,
  through the central cube of the system, equidistant from it, in
  whatever cubes they are, is twice 1201.     (A. H. F.)

_Fennell's Magic Ring._--It has been noticed that the numbers of magic
squares, of which the extension by repeating the rows and columns of n
numbers so as to form a square of 2n - 1 sides yields n² magic squares
of n sides, are arranged as if they were all inscribed round a cylinder
and also all inscribed on another cylinder at right angles to the first.
C. A. M. Fennell explains this apparent anomaly by describing such magic
squares as Mercator's projections, so to say, of "magic rings."

  The surface of these magic rings is symmetrically divided into n²
  quadrangular compartments or cells by n equidistant zonal circles
  parallel to the circular axis of the ring and by n transverse circles
  which divide each of the n zones between any two neighbouring zonal
  circles into n equal quadrangular cells, while the zonal circles
  divide the sections between two neighbouring transverse circles into n
  unequal quadrangular cells. The diagonals of cells which follow each
  other passing once only through each zone and section, form similar
  and equal closed curves passing once quite round the circular axis of
  the ring and once quite round the centre of the ring. The position of
  each number is regarded as the intersection of two diagonals of its
  cell. The numbers are most easily seen if the smallest circle on the
  surface of the ring, which circle is concentric with the axis, be one
  of the zonal circles. In a perfect magic ring the sum of the numbers
  of the cells whose diagonals form any one of the 2n diagonal curves
  aforesaid is ½n(n² + 1) with or without increment, i.e. is the same
  sum as that of the numbers in each zone and each transverse section.
  But if n be 3 or a multiple of 3, only from 2 to n of the diagonal
  curves carry the sum in question, so that the magic rings are
  imperfect; and any set of numbers which can be arranged to make a
  perfect magic ring or magic square can also make an imperfect magic
  ring, e.g. the set 1 to 16 if the numbers 1, 6, 11, 16 lie thus on a
  diagonal curve instead of in the order 1, 6, 16, 11. From a perfect
  magic ring of n² cells containing one number each, n² distinct magic
  squares can be read off; as the four numbers round each intersection
  of a zonal circle and a transverse circle constitute corner numbers of
  a magic square. The shape of a magic ring gives it the function of an
  indefinite extension in all directions of each of the aforesaid n²
  magic squares.     (C. A. M. F.)

  See F. E. A. Lucas, _Récréations mathématiques_ (1891-1894); W. W. R.
  Ball, _Mathematical Recreations_ (1892); W. E. M. G. Ahrens,
  _Mathematische Unterhaltungen und Spiele_ (1901); H. C. H. Schubert,
  _Mathematische Mussestunden_ (1900). A very detailed work is B.
  Violle, _Traité complet des carrés magiques_ (3 vols., 1837-1838). The
  theory of "path nasiks" is dealt with in a pamphlet by C. Planck
  (1906).




MAGINN, WILLIAM (1793-1842), Irish poet and journalist, was born at Cork
on the 10th of July 1793. The son of a schoolmaster, he graduated at
Trinity College, Dublin, in 1811, and after his father's death in 1813
succeeded him in the school. In 1819 he began to contribute to the
_Literary Gazette_ and to _Blackwood's Magazine_, writing as "R. T.
Scott" and "Morgan O'Doherty." He first made his mark as a parodist and
a writer of humorous Latin verse. In 1821 he visited Edinburgh, where he
made acquaintance with the Blackwood circle. He is credited with having
originated the idea of the _Noctes ambrosianae_, of which some of the
most brilliant chapters were his. His connexion with Blackwood lasted,
with a short interval, almost to the end of his life. His best story was
"Bob Burke's Duel with Ensign Brady." In 1823 he removed to London. He
was employed by John Murray on the short-lived _Representative_, and was
for a short time joint-editor of the _Standard_. But his intemperate
habits and his imperfect journalistic morality prevented any permanent
success. In connexion with Hugh Fraser he established _Fraser's
Magazine_ (1830), in which appeared his "Homeric Ballads." Maginn was
the original of Captain Shandon in _Pendennis_. In spite of his
inexhaustible wit and brilliant scholarship, most of his friends were
eventually alienated by his obvious failings, and his persistent
insolvency. He died at Walton-on-Thames on the 21st of August 1842.

  His _Miscellanies_ were edited (5 vols., New York, 1855-1857) by R.
  Shelton Mackenzie and (2 vols., London, 1885) by R. W. Montagu
  [Johnson].




MAGISTRATE (Lat. _magistratus_, from _magister_, master, properly a
public office, hence the person holding such an office), in general, one
vested with authority to administer the law or one possessing large
judicial or executive authority. In this broad sense the word is used in
such phrases as "the first magistrate" of a king in a monarchy or "the
chief magistrate" of the president of the United States. But it is more
generally applied to minor or subordinate judicial officers, whether
unpaid, as justices of the peace, or paid, as stipendiary magistrates. A
stipendiary magistrate is appointed in London under the Metropolitan
Police Courts Act 1839, in municipal boroughs under the Municipal
Corporations Act 1882, and in particular districts under the Stipendiary
Magistrates Act 1863 and special acts. In London and municipal boroughs
a stipendiary magistrate must be a barrister of at least seven years'
standing, while under the Stipendiary Magistrates Act 1863 he may be of
five years' standing. A stipendiary magistrate may do alone all acts
authorized to be done by two justices of the peace.

The term _magistratus_ in ancient Rome originally implied the office of
_magister_ (master) of the Roman people, but was subsequently applied
also to the holder of the office, thus becoming identical in sense with
_magister_, and supplanting it in reference to any kind of public
office. The fundamental conception of Roman magistracy is tenure of the
_imperium_, the sovereignty which resides with the Roman people, but is
by it conferred either upon a single ruler for life, as in the later
monarchy, or upon a college of magistrates for a fixed term, as in the
Republican period. The Roman theory of magistracy underwent little
change when two consuls were substituted for the king; but the
subdivision of magisterial powers which characterized the first
centuries of the Republic, and resulted in the establishment of twenty
annually elected magistrates of the people, implied some modification of
this principle of the investiture of magistrates with supreme authority.
For when the magistracies were multiplied a distinction was drawn
between magistrates with _imperium_, namely consuls, praetors and
occasionally dictators, and the remaining magistrates, who, although
exercising independent magisterial authority and in no sense agents of
the higher magistrates, were invested merely with an authority
(_potestas_) to assist in the administration of the state. At the same
time the actual authority of every magistrate was weakened not only by
his colleagues' power of veto, but by the power possessed by any
magistrate of quashing the act of an inferior, and by the tribune's
right of putting his veto on the act of any magistrate except a
dictator; and the subdivision of authority, which placed a great deal of
business in the hands of young and inexperienced magistrates, further
tended to increase the actual power as well as the influence of the
senate at the expense of the magistracy.

In the developed Republic magistracies were divided into two classes:
(a) magistrates of the whole people (_populi Romani_) and (b)
magistrates of the _plebs_. The former class is again divided into two
sections: ([alpha]) curule and ([beta]) non-curule, a distinction which
rests mainly on dignity rather than on actual power, for it cuts across
the division of magistrates according to their tenure or non-tenure of
_imperium_.

  a. The magistrates of the people--also known as patrician magistrates,
  probably because the older and more important of these magistracies
  could originally be held only by patricians (q.v.)--were: ([alpha])
  Dictator, master of the horse (see DICTATOR), consuls, praetors,
  curule, aediles and censors (curule); and ([beta]) Quaestors, and the
  body of minor magistrates known as _xxvi. viri_ (non-curule). The
  dictatorship and consulship were as old as the Republic. The first
  praetor was appointed in 366 B.C., a second was added in 242 B.C., and
  the number was gradually increased for provincial government until
  Sulla brought it up to eight, and under the early principate it grew
  to eighteen. Censors were first instituted in 443 B.C., and the office
  continued unchanged until its abolition by Sulla, after which, though
  restored, it rapidly fell into abeyance. Curule aediles were
  instituted at the same time as the praetorship, and continued
  throughout the Republic. The quaestorship was at least as old as the
  Republic, but the number rose during the Republic from two to twenty.
  All these offices except the censorship continued for administrative
  purposes during the principate, though shorn of all important powers.

  b. The plebeian magistrates had their origin in the secession of the
  _plebs_ to Mons Sacer in 494 B.C. (see ROME: _History_). In that year
  tribunes of the _plebs_ were instituted, and two aediles were given
  them as subordinate officials, who were afterwards known as plebeian
  aediles, to distinguish them from the curule magistrates of the same
  name. Both these offices were abolished during the decemvirate, but
  were restored in 449 B.C., and survived into the principate.

The powers possessed by all magistrates alike were two:--that of
enforcing their enactments (_coercitio_) by the exercise of any
punishment short of capital, and that of veto (_intercessio_) of any act
of a colleague or minor magistrate. The right of summoning and presiding
over an assembly of that body of citizens with whose powers the
magistrate was invested lay with the higher magistrates only in each
class, with the consuls and praetors, and with the tribunes of the
_plebs_. Civil jurisdiction was always a magisterial prerogative at
Rome, and criminal jurisdiction also, except in capital cases, the
decision of which was vested in the people at least as early as the
first year of the Republic, was wielded by magistrates until the
establishment of the various _quaestiones perpetuae_ during the last
century of the Republic. But in civil cases the magistrate, though
controlling the trial and deciding matters of law, was quite distinct
from the judge or body of judges who decided the question of fact; and
the _quaestiones perpetuae_, which reduced the magistrate in criminal
cases to a mere president of the court, gave him a position inferior to
that of the praetor, who tried civil cases, only in so far as the
praetor controlled the trial in some degree by his _formula_, under
which the judges decided the question of fact.

Tenure of magistracy was always held to depend upon election by the body
whose powers the magistrate wielded. Thus the magistrates of the _plebs_
were elected by the plebeian council, those of the people in the Comitia
(q.v.). In every case the outgoing magistrate, as presiding officer of
the elective assembly, exercised the important right of nominating his
successor for election.

  See A. H. J. Greenidge, _Roman Public Life_, 152 seq., 363 seq.
  (London, 1901); T. Mommsen, _Römisches Staatsrecht_, I. 11. i. (1887).
       (A. M. Cl.)




MAGLIABECHI, ANTONIO DA MARCO (1633-1714), Italian bibliophile, was born
at Florence on the 28th of October 1633. He followed the trade of a
goldsmith until 1673, when he received the appointment of librarian to
the grand-duke of Tuscany, a post for which he had qualified himself by
his vast stores of self-acquired learning. He died on the 4th of July
1714, bequeathing his large private library to the grand-duke, who in
turn handed it over to the city.




MAGLIANI, AGOSTINO (1824-1891), Italian financier, was a native of
Lanzino, near Salerno. He studied at Naples, and a book on the
philosophy of law based on Liberal principles won for him a post in the
Neapolitan treasury. He entered the Italian Senate in 1871, and had
already secured a reputation as a financial expert before his _Questione
monetaria_ appeared in 1874. In December 1877 he became minister of
finance in the reconstructed Depretis ministry, and he subsequently held
the same office in three other Liberal cabinets. In his second tenure he
carried through (1880) the abolition of the grist tax, to take effect in
1884. Having to face an increased expenditure without offending the
Radical electorate by unpopular taxes, he had recourse to unsound
methods of finance, which seriously embarrassed Italian credit for some
years after he finally laid down office in 1888. He died in Rome on the
22nd of February 1891. He was one of the founders of the
anti-socialistic "Adam Smith Society" at Florence.




MAGNA CARTA, or the Great Charter, the name of the famous charter of
liberties granted at Runnimede in June 1215 by King John to the English
people. Although in later ages its importance was enormously magnified,
it differs only in degree, not in kind, from other charters granted by
the Norman and early Plantagenet kings. Its greater length, however,
still more the exceptional circumstances attending its birth, gave to it
a position absolutely unique in the minds of later generations of
Englishmen. This feeling was fostered by its many confirmations, and in
subsequent ages, especially during the time of the struggle between the
Stuart kings and the parliament, it was regarded as something
sacrosanct, embodying the very ideal of English liberties, which to some
extent had been lost, but which must be regained. Its provisions, real
and imaginary, formed the standard towards which Englishmen must strive.

The causes which led to the grant of Magna Carta are described in the
article on _English History_. Briefly, they are to be found in the
conditions of the time; the increasing insularity of the English barons,
now no longer the holders of estates in Normandy; the substitution of an
unpopular for a popular king, an active spur to the rising forces of
discontent; and the unprecedented demands for money--demands followed,
not by honour, but by dishonour, to the arms of England abroad. So much
for the general causes. The actual crisis may be said to begin with the
quarrel between John and Pope Innocent III. regarding the appointment of
a new archbishop to the see of Canterbury. This was settled in May 1213,
and in the new prelate, the papal nominee, Stephen Langton, who landed
in England and absolved the king in the following July, the baronial
party found an able and powerful ally. But before this event John had
instituted a great inquiry, the inquest of service of June 1212, for the
purpose of finding out how much he could exact from each of his vassals,
a measure which naturally excited some alarm; and then, fearing a
baronial rising, he had abandoned his proposed expedition into Wales,
had taken hostages from the most prominent of his foes, and had sought
safety in London.

His absolution followed, and then he took courage. Turning once more his
attention to the recovery of Normandy, he asked the barons for
assistance for this undertaking; in reply they, or a section of them,
refused, and instead of crossing the seas the king marched northwards
with the intention of taking vengeance on his disobedient vassals, who
were chiefly barons of the north of England. Langton followed his
sovereign to Northampton and persuaded him, at least for the present, to
refrain from any serious measures of revenge. Before this interview a
national council had met at St Albans at the beginning of August 1213,
and this was followed by another council, held in St Paul's church,
London, later in the same month; it was doubtless summoned by the
archbishop, and was attended by many of the higher clergy and a certain
number of the barons. Addressing the gathering, Langton referred to the
laws of Edward the Confessor as "good laws," which the king ought to
observe, and then mentioned the charter granted by Henry I. on his
accession as a standard of good government. This event has such an
important bearing on the issue of Magna Carta that it is not
inappropriate to quote the actual words used by Matthew Paris in
describing the incident. The chronicler represents the archbishop as
saying "Inventa est quoque nunc carta quaedam Henrici primi regis
Angliae per quam, si volueritis, libertates diu amissas poteritis ad
statum pristinum revocare." Those present decided to contend to the
death for their "long-lost liberties," and with this the meeting came to
an end. Nothing, however, was done during the remainder of the year, and
John, feeling his position had grown stronger, went abroad early in
1214, and remained for some months in France. With his mercenaries
behind him he met with some small successes in his fight for Normandy,
but on the 27th of July he and his ally, the emperor Otto IV., met with
a crushing defeat at Bouvines at the hands of Philip Augustus, and even
the king himself was compelled to recognise that his hopes of recovering
Normandy were at an end.

Meanwhile in England, which was ruled by Peter des Roches as justiciar,
the discontent had been increasing rather than diminishing, and its
volume became much larger owing to an event of May 1214. Greatly needing
money for his campaign, John ordered another scutage to be taken from
his tenants; this, moreover, was to be at the unprecedented rate of
three marks on the knight's fee, not as on previous occasions of two
marks, although this latter sum had hitherto been regarded as a very
high rate. The northern barons refused to pay, and the gathering forces
of resistance received a powerful stimulus when a little later came the
news of the king's humiliation at Bouvines. Then in October the beaten
monarch returned to England, no course open to him but to bow before the
storm. In November he met some of his nobles at Bury St Edmunds, but as
they still refused to pay the scutage no agreement was reached. At once
they took another step towards the goal. With due solemnity (_super
majus altare_) they swore to withdraw their allegiance from the king and
to make war upon him, unless within a stated time he restored to them
their rightful laws and liberties. While they were collecting troops in
order to enforce their threats, John on his part tried to divide his
enemies by a concession to the clerical section. By a charter, dated the
21st of November 1214, he granted freedom of election to the church.
However, this did not prevent the prelates from continuing to act to
some extent with the barons, and early in January 1215 the malcontents
asked the king to confirm the laws of Edward the Confessor and the other
liberties of the kingdom. He evaded the request and secured a truce
until Easter was passed. Energetically making use of this period of
respite, he again issued the charter to the church, ordered his subjects
to take a fresh oath of allegiance to him, and sent to the pope for aid;
but neither these precautions, nor his expedient of taking the cross,
deterred the barons from returning to the attack. In April they met in
arms at Stamford, and as soon as the truce had expired they marched to
Brackley, where they met the royal ministers and again presented their
demands. These were carried to the king at Oxford, but angrily he
refused to consider them. Then the storm burst. On the 5th of May the
barons formally renounced their allegiance to John, and appointed Robert
Fitzwalter as their leader. They marched towards London, while John made
another attempt to delay the crisis, or to divide his foes, by granting
a charter to the citizens of London (May 9, 1215), and then by offering
to submit the quarrel to a court of arbitrators under the presidency of
the pope. But neither the one nor the other expedient availed him.
Arbitration under such conditions was contemptuously rejected, and after
the king had ordered the sheriffs to seize the lands and goods of the
revolting nobles, London opened its gates and peacefully welcomed the
baronial army. Other towns showed also that their sympathies were with
the insurgents, and John was forced to his knees. Promising to assent to
their demands, he agreed to meet the barons, and the gathering was fixed
for the 15th of June, and was to take place in a meadow between Staines
and Windsor, called Runnimede.

At the famous conference, which lasted from Monday the 15th to Tuesday
the 23rd of June, the hostile barons were present in large numbers; on
the other hand John, who rode over each day from Windsor, was only
attended by a few followers. At once the malcontents presented their
demands in a document known popularly as the _Articles of the Barons_,
more strictly as _Capitula quae barones petunt et dominus rex concedit_.
Doubtless this had been drawn up beforehand, and was brought by the
baronial leaders to Runnimede; possibly it was identical with the
document presented to the royal ministers at Brackley a few weeks
before. John accepted the Articles on the same day and at once the great
seal was affixed to them. They are forty-eight in number, and on them
Magna Carta was based, the work of converting them into a charter, which
was regarded as a much more binding form of engagement, being taken in
hand immediately. This duty occupied three days, negotiations between
the two parties taking place over several disputed points, and it was
completed by Friday the 19th, when several copies of the charter were
sealed. All then took an oath to keep its terms, and orders were sent to
the sheriffs to publish it, and to see that its provisions were
observed, two or three days being taken up with making and sending out
copies for this purpose. It should be mentioned that, although the
charter was evidently not sealed until the 19th, the four existing
copies of it are dated the 15th, the day on which John accepted the
articles.

The days between Friday the 19th and the following Tuesday, when the
conference came to an end, were occupied in providing, as far as
possible, for the due execution of the reforms promised by the king in
Magna Carta. The document itself provided for an elected committee of
twenty-five barons, whose duty was to compel John, by force if
necessary, to keep his promises; but this was evidently regarded as
insufficient, and the matter was dealt with in a supplementary treaty
(_Conventio facta inter regem Angliae et barones ejusdum regni_). As a
guarantee of his good faith the king surrendered the city of London to
his foes, while the Tower was entrusted to the neutral keeping of the
archbishop of Canterbury. John then asked the barons for a charter that
they on their part would keep the peace. This was refused, and although
some of the bishops entered a mild protest, the question was allowed to
drop. Regarding another matter also, the extent of the royal forests,
the prelates made a protest. John and his friends feared lest the
inquiry promised into the extent of the hated forest areas would be
carried out too rigorously, and that these would be seriously curtailed,
if not abolished altogether. Consequently, the two archbishops and their
colleagues declared that the articles in the charter which provided for
this inquiry, and for a remedy against abuses of the forest laws by the
king, must not be interpreted in too harsh a spirit. The customs
necessary for the preservation of the forests must remain in force.

No securities, however, could bind John. Even before Magna Carta was
signed he had set to work to destroy it, and he now turned to this task
with renewed vigour. He appealed to the pope, and hoped to crush his
enemies by the aid of foreign troops, while the barons prepared for war,
and the prelates strove to keep the peace. Help came first from the
spiritual arm. On the 24th of August 1215 Innocent III. published a bull
which declared Magna Carta null and void. It had been extorted from the
king by force (_per vim et metum_), and in the words of the bull the
pope said "compositionem hujusmodi reprobamus penitus et damnamus." He
followed this up by excommunicating the barons who had obtained it, and
in the autumn of 1215 the inevitable war began. Capturing Rochester
castle, John met with some other successes, and the disheartened barons
invited Louis, son of Philip Augustus of France and afterwards king as
Louis VIII., to take the English crown. In spite of the veto of the pope
Louis accepted the invitation, landed in England in May 1216, and
occupied London and Winchester, the fortune of war having in the
meantime turned against John. The "ablest and most ruthless of the
Angevins," as J. R. Green calls this king, had not, however, given up
the struggle, and he was still in the field when he was taken ill, dying
in Newark castle on the 19th of October 1216.

In its original form the text of Magna Carta was not divided into
chapters, but in later times a division of this kind was adopted. This
has since been retained by all commentators, the number of chapters
being 63.

The preamble states that the king has granted the charter on the advice
of various prelates and barons, some of whom, including the archbishop
of Canterbury, the papal legate Pandulf, and William Marshal, earl of
Pembroke, are mentioned by name.

  Chapter I. declares that the English church shall be free and shall
  enjoy freedom of election. This follows the precedent set in the
  accession charter of Henry I. and in other early charters, although it
  had no place in the Articles of the Barons. On the present occasion it
  was evidently regarded as quite a formal and introductory matter, and
  the same remark applies to the general grant of liberties to all
  freemen and their heirs, with which the chapter concludes.

Then follows a series of chapters intended to restrain the king from
raising money by the harsh and arbitrary methods adopted in the past.
These chapters, however, only afforded protection to the
tenants-in-chief of the crown, and it is clear from their prominent
position that the framers of the charter regarded them as of paramount
importance.

  Chapter II. fixes the amount of the relief to be paid to the king by
  the heir of any of his vassals. Previously John, disregarding the
  custom of the past, had taken as much as he could extort. Henceforward
  he who inherits a barony must pay £100, he who inherits a knight's fee
  100 shillings or less, and for smaller holdings less "according to the
  ancient custom of fiefs."

  Chapters III. to VI. deal with the abuses of the king's privilege of
  acting as guardian of minors and their lands. Money must not be
  extorted from a ward when he receives his inheritance. The guardian or
  his servant must not take from the ward's property more than a
  reasonable amount for his expenses and the like; on the contrary he
  must maintain the houses, estates and other belongings in a proper
  state of efficiency. A ward must be allowed a reasonable liberty in
  the matter of marriage. He or she must not, as had been so often the
  case in the past, be forced to marry some royal favourite, or some one
  who had paid a sum of money for the privilege.

  Chapters VII. and VIII. are for the protection of the widows of
  tenants-in-chief. On the death of her husband a widow must receive her
  rightful inheritance, without delay or hindrance. Moreover she must
  not be compelled to marry, a proceeding sometimes adopted to get her
  lands into the possession of a royal minion.

  Chapter IX. is intended to prevent the king from collecting the money
  owing to him in an oppressive manner.

Now for a short time the document leaves the great questions at issue
between the king and the barons, and two chapters are devoted to
protecting the people generally against the exactions of the Jews.

  Chapter X. declares that money borrowed from the Jews shall not bear
  interest during a minority.

  Chapter XI. provides for the repayment of borrowed money to the Jews,
  and also to other creditors. This, however, is only to be done after
  certain liabilities have been met out of the estate, including the
  services due to the lord of the land.

Having thus disposed of this matter, the grievances of the barons are
again considered, the vexed question of scutage being dealt with.

  Chapter XII. says that in future no scutage or aid, beyond the three
  recognized feudal aids, shall be levied except by the consent of the
  general council of the nation (_commune concilium regni nostri_),
  while the three recognized aids shall only be levied at a reasonable
  rate. In dealing with this matter the Articles of the Barons had
  declared that aids and tallages must not be taken from the citizens of
  London and of other places without the consent of the council. This
  provision was omitted from Magna Carta, except so far as it related to
  aids from the citizens of London. This chapter does not give the
  people the right to control taxation. It gives to the men interested a
  certain control over one form of taxation, and protects one class only
  from arbitrary exactions, and that class the most powerful and the
  most wealthy.

  Chapter XIII. gives to the citizens of London all their ancient
  liberties and free customs.

  Chapter XIV. provides for the assembly of the council when its consent
  is necessary for raising an aid or a scutage. Individual summonses
  must be sent to the prelates and greater barons, while the lesser
  barons will be called together through the sheriffs and bailiffs. At
  least forty days' notice of the meeting must be given, and the cause
  thereof specified. No chapter corresponding to this is found in the
  Articles and none was inserted in the reissues of Magna Carta. It is
  very interesting, but it does not constitute any marked advance in the
  history of parliament, as it merely expresses the customary method of
  summoning a council. It does not, as has been sometimes asserted, in
  any way establish a representative system, as this is understood
  to-day.

  Chapter XV. extends the concessions obtained by the greater barons for
  themselves to the lesser landholders, the tenants of the
  tenants-in-chief.

  Chapter XVI. declares that those who owe military service for their
  lands shall not be called upon to perform more than the due amount of
  such service.

We now come to an important series of articles which deal with abuses in
the administration of justice. Henry II. made the royal courts of law a
lucrative source of revenue, but he gave protection to suitors. Under
his sons justice was equally, perhaps more, costly, while adequate
protection was much harder to obtain. Here were many grievances, and the
barons set to work to redress them.

  Chapter XVII. declares that common pleas must henceforward be heard in
  a fixed place. This had already been to some extent the practice when
  this class of cases was heard; it was now made the rule. From this
  time suitors in this court were not put to the expense and
  inconvenience of following the king from place to place.

  Chapters XVIII. and XIX. deal with the three petty assizes, three
  kinds of cases regarding disputes about the possession of land. These
  must be heard in the county courts before two visiting justices and
  four knights of the shire. The hardship of attendance at the county
  courts was to some extent obviated.

  Chapters XX. to XXII. regulate the amount of fines imposed for
  offences against the law. Property necessary for one's livelihood must
  not be taken. The fines must only be imposed by the oath of honest men
  of the neighbourhood. In the same way earls and barons must only be
  fined by their peers, and a similar privilege is extended to the
  clergy, who, moreover, were not to be fined in accordance with the
  value of their benefices, but only of their other property. It should
  be noticed that trial by one's peers, as understood in Magna Carta, is
  not confined to the nobility; in every class of society an accused man
  is punished in accordance with the verdict of his peers, or equals.

  Chapter XXIII. asserts that persons shall not be compelled to make
  bridges, unless they are bound to do so by ancient custom. John had
  oppressed his subjects in this way before he visited a district for
  purposes of sport, and the hardship was a real one.

  Chapter XXIV. declared that the sheriffs and other officers of the
  king must not hold the pleas of the crown. This was intended to remove
  an old and serious evil, as the sheriffs had earned a very bad
  reputation by their methods of administering justice.

  Chapter XXV. also concerns the sheriffs. It prevents the king from
  increasing by their agency the amount of money annually due to him
  from the various counties and hundreds. The custom was for the king to
  get a fixed sum from the sheriff of each county, this being called the
  _firma comitatus_, and for the sheriff to collect this as best he
  could. Henceforward this amount must not be raised.

  Chapters XXVI. and XXVII. were intended to protect the property of
  deceased persons, and also to secure the full payment of debts due
  therefrom to the crown. Other creditors were also protected, and the
  property of an intestate must be distributed to his heirs under the
  supervision of the church.

  Chapter XXVIII. strikes a blow at the custom of purveyance. Royal
  officials must pay for the corn and provisions which they take on
  behalf of the king.

  Chapter XXIX. says knights must not be compelled to give money instead
  of performing castle-guard, if they are willing to perform this
  service. Castle-guard was the liability incumbent on the holders of
  some estates to serve in the garrison of the royal castles. The
  constables of these castles had adopted the custom of compelling these
  landholders to give money and not service, mercenaries being then
  hired to perform this.

  Chapters XXX. and XXXI. forbid the royal officials to seize the horses
  or carts of freemen for transport duty, or to take wood for the king's
  buildings.

  Chapter XXXII. says that the lands of convicted felons shall be handed
  over to the lords of such lands and not kept by the king beyond a year
  and a day. In cases of treason the king had a right to the forfeited
  lands, but he was not allowed to establish a similar right in cases of
  felony.

  Chapter XXXIII. provided for the removal of kydells, or weirs, from
  all English rivers. This was intended to give greater freedom to
  inland navigation, the rivers being the main highways of trade.

  Chapter XXXIV. limits the use of the writ known as _Praecipe_. This
  writ was one transferring cases concerning the ownership of property
  from the courts of the feudal lords to those of the king. This custom,
  which owes its origin to Henry II., meant a loss of revenue to the
  lords, whose victory in this matter, however, was a step backwards. It
  checked temporarily the process of centralizing the administration of
  justice.

  Chapter XXXV. provides for the uniformity of weights and measures
  throughout the kingdom.

  Chapter XXXVI. promises that in future writs of inquisition shall be
  granted freely without payment of any kind. This kind of writ allowed
  a man to refer the question of his guilt or innocence to the verdict
  of his neighbours instead of proving his innocence by the duel.

  Chapter XXXVII. prevents the king from administering certain kinds of
  land when these fall into the possession of minors. In the past John
  had evidently stretched his authority and seized lands over which
  others had really the right of wardship.

  Chapter XXXVIII. prevents a bailiff from compelling an accused man to
  submit to the ordeal without the approval of credible witnesses.

  Chapter XXXIX. is more important and the English rendering of it may
  be given in full. "No freeman shall be arrested, or detained in
  prison, or deprived of his freehold, or outlawed, or banished, or in
  any way molested; and we will not set forth against him, nor send
  against him, unless by the lawful judgment of his peers and by the law
  of the land." The object of this was clearly to restrain John from
  arbitrary proceedings against his free subjects. The principle of
  judgment by one's peers is asserted, and is obviously the privilege of
  every class of freemen, not of the greater lords alone.

  Chapter XL. simply says, "To no one will we sell, to no one will we
  refuse or delay, right or justice."

  Chapters XLI. and XLII. give permission to merchants, both English and
  foreign, to enter and leave the kingdom, except in time of war. They
  are not to pay "evil tolls." The privilege is extended to all
  travellers, except the prisoner and the outlaw, and natives of a
  country with which England is at war.

  Chapter XLIII. is intended to compel the king to refrain from exacting
  greater dues from an escheated barony than were previously due from
  such barony.

  Chapter XLIV. deals with the hated and oppressive forest laws. In
  future attendance at the forest courts is only obligatory on those who
  have business thereat.

  Chapter XLV. says that the royal officials must know something of the
  law and must be desirous of keeping it.

  Chapter XLVI. gives to the founders of religious houses the right of
  acting as guardians of such houses when they are without heads.

  Chapters XLVII. and XLVIII. deal again with the great grievance of the
  royal forests. John undertakes to disforest all forests which have
  been made in his time, and also to give up such river banks as he has
  seized for his own use when engaged in sport. Twelve knights in each
  county are to make a thorough inquiry into all evil customs connected
  with the forests, and these are to be utterly abolished.

  Chapter XLIX. provides for the restoration of hostages. John had been
  in the habit of taking the children of powerful subjects as pledges
  for the good behaviour of their parents.

  Chapter L. says that certain royal minions, who are mentioned by name,
  are to be removed from their offices.

  Chapter LI. says that as soon as peace is made all foreign mercenaries
  are to be banished.

  Chapters LII. and LIII. are those in which the king promises to make
  amends for the injuries he has done to his barons in the past. He will
  restore lands and castles to those who have been deprived of them
  without the judgment of their peers; he will do the same concerning
  property unlawfully seized by Henry II. or Richard I. and now in his
  hands. In the latter case, however, he was allowed a respite until he
  returned from the projected crusade. He promises also to do right
  concerning forests, abbeys and the wardship of lands which belong
  lawfully to others.

  Chapter LIV. prevents any one from being arrested on the appeal of a
  woman, except on a charge of causing the death of her husband. As a
  woman could not prove her case in the judicial combat, it was felt
  that the earlier practice gave her an unfair advantage.

  Chapter LV. provides for the remission of unjust fines. The decision
  on these matters is to rest with the archbishop of Canterbury and the
  twenty-five barons appointed to see that the terms of the charter are
  carried out.

  Chapters LVI. and LVII. deal with the grievances of Welshmen.
  Restoration of property is promised to them practically in the same
  way as to Englishmen. Welsh law is to be used in Wales, and in the
  marches the law of the marches is to be employed.

  Chapter LVIII. promises that his hostages and his charters shall be
  restored to Llewellyn, prince of Wales.

  Chapter LIX. promises a restoration of hostages to Alexander I. king
  of Scotland. Right is also to be done to him concerning the lands
  which he holds in England.

  Chapter LX. is a general statement that the aforesaid customs and
  liberties are to be observed by all classes.

  Chapter LXI. provides for the execution of the royal promises. A
  committee is to be formed of twenty-five barons. Then if the king or
  any of his servants do wrong and complaint is made to four of the
  twenty-five, they are to ask for redress. In the event of this not
  being granted within forty days the matter is to be referred to the
  twenty-five, who are empowered to seize the lands and property of the
  king, or to obtain justice in any other way possible. They must,
  however, spare the persons of the king, the queen and their children.
  Vacancies in the committee are to be filled by the barons themselves.
  The twenty-five barons were duly appointed, their names being given by
  Matthew Paris. This chronicler also reports that another committee of
  thirty-eight members was appointed to assist and control the
  twenty-five. S. R. Gardiner calls the scheme "a permanent organization
  for making war against the king."

  Chapter LXII. is an expression of general forgiveness.

  Chapter LXIII. repeats the promise of freedom to the English church
  and of their rights and liberties to all.

Magna Carta is an elaboration of the accession charter of Henry I., and
is based upon the Articles of the Barons. It is, however, very much
longer than the former charter and somewhat longer than the Articles.
Moreover, it differs in several particulars from the Articles, these
differences being doubtless the outcome of deliberation and of
compromise. For instance, the provisions in Magna Carta concerning the
freedom of the church find no place in the Articles, while a comparison
between the two documents suggests that in other ways also influences
favourable to the church and the clergy were at work while the famous
charter was being framed. When one reflects how active and prominent
Langton and other prelates were at Runnimede the change is not
surprising. Another difference between the two documents concerns the
towns and the trading classes. Certain privileges granted to them in the
Articles are not found in Magna Carta, although, it must be noted, this
document bestows exceptionally favoured treatment on the citizens of
London. The conclusion is that the friends of the towns and the traders
were less in evidence at Runnimede than they were at the earlier
meetings of the barons, but that the neighbouring Londoners were strong
enough to secure a good price for their support.

Magna Carta throws much light on the condition of England in the early
13th century. By denouncing the evil deeds of John and the innovations
practised by him, it shows what these were and how they were hated; how
money had been raised, how forest areas had been extended, how minors
and widows had been cheated and oppressed. By declaring, as it does,
what were the laws and customs of a past age wherein justice prevailed,
it shows what was the ideal of good government formed by John's prelates
and barons. Magna Carta can hardly be said to have introduced any new
ideas. As Pollock and Maitland (_History of English Law_) say "on the
whole the charter contains little that is absolutely new. It is
restorative." But although mature study has established the truth of
this proposition it was not always so. Statesmen and commentators alike
professed to find in Magna Carta a number of political ideas which
belonged to a later age, and which had no place in the minds of its
framers. It was regarded as having conferred upon the nation nothing
less than the English constitution in its perfect and completed form.
Sir Edward Coke finds in Magna Carta a full and proper legal answer to
every exaction of the Stuart kings, and a remedy for every evil suffered
at the time. Sir William Blackstone is almost equally admiring. Edmund
Burke says "Magna Carta, if it did not give us originally the House of
Commons, gave us at least a House of Commons of weight and consequence."
Lord Chatham used words equally superlative. "Magna Carta, the Petition
of Rights and the Bill of Rights form that code, which I call the Bible
of the English Constitution." Modern historians, although less
rhetorical, speak in the highest terms of the importance of Magna Carta,
the view of most of them being summed up in the words of Dr Stubbs: "The
whole of the constitutional history of England is a commentary on this
charter."

Many regard Magna Carta as giving equal rights to all Englishmen. J. R.
Green says "The rights which the barons claimed for themselves they
claimed for the nation at large." As a matter of fact this statement is
only true with large limitations. The villains, who formed the majority
of the population, got very little from it; in fact the only clauses
which protect them do so because they are property--the property of
their lords--and therefore valuable. They get neither political nor
civil rights under Magna Carta. The traders, too, get little, while
preferential treatment is meted out to the clergy and the barons. Its
benefits are confined to freemen, and of the benefits the lion's share
fell to the larger landholders; the smaller landholders getting, it is
true, some crumbs from the table. It did not establish freedom from
arbitrary arrest, or the right of the representatives of the people to
control taxation, or trial by jury, or other conceptions of a later
generation.

The story of Magna Carta after the death of John is soon told. On the
12th of November 1216 the regent William Marshal, earl of Pembroke,
reissued the charter in the name of the young king Henry III. But
important alterations were made. War was being waged against Louis of
France, and the executive must not be hampered in the work of raising
money; moreover the personal equation had disappeared, the barons did
not need to protect themselves against John. Consequently the chapter
limiting the power of the crown to raise scutages and aids without the
consent of the council vanished, and with it the complementary one which
determined the method of calling a council. Other provisions, the object
of which had been to restrain John from demanding more money from
various classes of his subjects, were also deleted, and the same fate
befell such chapters as dealt with mere temporary matters. The most
important of these was Chapter LXI., which provided for the appointment
of 25 executors to compel John to observe the charter. The next year
peace was made at Lambeth (Sept. 11, 1217) between Henry III. and Louis
and another reissue of the charter was promised. This promise was
carried out, but two charters appeared, one being a revised issue of
Magna Carta proper, and the other a separate charter dealing with the
forests, all references to which were omitted from the more important
document. The date of this issue appears to have been the 6th of
November 1217. The issue of a separate forest charter at this time led
subsequently to some confusion. Roger of Wendover asserts that John
issued a separate charter of this kind when Magna Carta appeared. This
statement was believed by subsequent writers until the time of
Blackstone, who was the first to discover the mistake.

As issued in 1217 Magna Carta consists of 47 chapters only. It declares
that henceforward scutages shall be taken according to the precedents of
Henry II.'s reign. New provisions were introduced for the preservation
of the peace--unlawful castles were to be destroyed--while others were
directed towards making the administration of justice by the visiting
justices less burdensome. With regard to the land and the services due
therefrom a beginning was made of the policy which culminated in the
statutes of Mortmain and of Quia Emptores. The sheriffs were ordered to
publish the revised charter on the 22nd of February 1218. Then in
February 1225 Henry III. again issued the two charters with only two
slight alterations, and this is the final form taken by Magna Carta,
this text being the one referred to by Coke and the other early
commentators. Subsequently the charters were confirmed several times by
Henry III. and by Edward I., the most important occasion being their
confirmation by Edward at Ghent in November 1297. On this occasion some
supplementary articles were added to the charter; these were intended to
limit the taxing power of the crown.

  There are at present in existence four copies of Magna Carta, sealed
  with the great seal of King John, and several unsealed copies. Of the
  four two are in the British Museum. Both came into the possession of
  the Museum with the valuable collection of papers which had belonged
  to Sir Robert Cotton, who had obtained possession of both. One was
  found in Dover castle about 1630. This was damaged by fire in 1731;
  the other is undamaged. The two other sealed copies belong to the
  cathedrals of Lincoln and of Salisbury. Both were written evidently in
  a less hurried fashion than those in the British Museum, and the one
  at Lincoln was regarded as the most perfect by the commissioners who
  were responsible for the appearance of the _Statutes of the Realm_
  1810. The British Museum also contains the original parchment of the
  Articles of the Barons. Magna Carta was first printed by Richard
  Pynson in 1499. This, however, was not the original text, which was
  neglected until the time of Blackstone, who printed the various issues
  of the charter in his book _The Great Charter and the Charter of the
  Forest_ (1759). The earliest commentator of note was Sir Edward Coke,
  who published his _Second Institute_, which deals with Magna Carta, by
  order of the Long Parliament in 1642. Modern commentators, who also
  print the various texts of the charter, are Richard Thomson, _An
  Historical Essay on the Magna Carta of King John_ (1829); C. Bémont,
  in his _Chartes des libertés anglaises_ (1892); and W. Stubbs in his
  _Select Charters_ (1895). A more recent book and one embodying the
  results of the latest research is W. S. McKechnie, _Magna Carta_
  (1905). The text of Magna Carta is also printed in the _Statutes of
  the Realm_ (1810-1828), and in T. Rymer's _Foedera_ (1816-1869). In
  addition to Blackstone, Coke and these later writers, the following
  works may also be consulted: John Reeves, _History of English Law_
  (1783-1784); L. O. Pike, _A Constitutional History of the House of
  Lords_ (1894); W. Stubbs, _Constitutional History of England_ (1897);
  Sir F. Pollock and F. W. Maitland, _The History of English Law_
  (1895); W. S. Holdsworth, _A History of English Law_ (1903), and Kate
  Norgate, _John Lackland_ (1902).     (A. W. H.*)




MAGNA GRAECIA ([Greek: he megale Hellas]), the name given (first,
apparently, in the 6th century B.C.) to the group of Greek cities along
the coast of the "toe" of South Italy (or more strictly those only from
Tarentum to Locri, along the east coast), while the people were called
Italiotes ([Greek: Italiôtai]). The interior, which the Greeks never
subdued, continued to be in the hands of the Bruttii, the native
mountaineers, from whom the district was named in Roman times ([Greek:
Brettia] also in Greek writers). The Greek colonies were established
first as trading stations, which grew into independent cities. At an
early time a trade in copper was carried on between Greece and Temesa
(Homer, _Od._ i. 181).[1] The trade for a long time was chiefly in the
hands of the Euboeans; and Cyme (Cumae) in Campania was founded in the
8th century B.C., when the Euboean Cyme was still a great city. After
this the energy of Chalcis went onward to Sicily, and the states of the
Corinthian Gulf carried out the colonization of Italy, Rhegium having
been founded, it is true, by Chalcis, but after Messana (Zancle), and at
the request of the inhabitants of the latter. Sybaris (721) and Crotona
(703) were Achaean settlements; Locri Epizephyrii (about 710) was
settled by Ozolian Locrians, so that, had it not been for the Dorian
colony of Tarentum, the southern coast of Italy would have been entirely
occupied by a group of Achaean cities. Tarentum (whether or no founded
by pre-Dorian Greeks--its founders bore the unexplained name of
Partheniae) became a Laconian colony at some unknown date, whence a
legend grew up connecting the Partheniae with Sparta, and 707 B.C. was
assigned as its traditional date. Tarentum is remarkable as the only
foreign settlement made by the Spartans. It was industrial, depending
largely on the purple and pottery trade. Ionian Greeks fleeing from
foreign invasion founded Siris about 650 B.C., and, much later, Elea
(540).

The Italian colonies were planted among friendly, almost kindred, races,
and grew much more rapidly than the Sicilian Greek states, which had to
contend against the power of Carthage. After the Achaean cities had
combined to destroy the Ionic Siris, and had founded Metapontum as a
counterpoise to the Dorian Tarentum, there seems to have been little
strife among the Italiotes. An amphictyonic league, meeting in common
rites at the temple of Hera on the Lacinian promontory, fostered a
feeling of unity among them. The Pythagorean and Eleatic systems of
philosophy had their chief seat in Magna Graecia. Other departments of
literature do not seem to have been so much cultivated among them. The
poet Ibycus, though a native of Rhegium, led a very wandering life. They
sent competitors to the Olympic games (among them the famous Milo of
Croton); and the physicians of Croton early in the 6th century
(especially in the person of Democedes) were reputed the best in Greece;
but politically they appear to have generally kept themselves separate.
One ship of Croton, however, fought at Salamis, though it is not
recorded that Greece asked the Italiotes for help when it sent
ambassadors to Gelon of Syracuse. Mutual discord first sapped the
prosperity of Magna Graecia. In 510 Croton, having defeated the
Sybarites in a great battle, totally destroyed their city. Croton
maintained alone the leading position which had belonged jointly to the
Achaean cities (Diod. xiv. 103); but from that time Magna Graecia
steadily declined. In the war between Athens and Syracuse Magna Graecia
took comparatively little part; Locri was strongly anti-Athenian, but
Rhegium, though it was the headquarters of the Athenians in 427,
remained neutral in 415. Foreign enemies pressed heavily on it. The
Lucanians and Bruttians on the north captured one town after another.
Dionysius of Syracuse attacked them from the south; and after he
defeated the Crotoniate league and destroyed Caulonia (389 B.C.),
Tarentum remained the only powerful city. Henceforth the history of
Magna Graecia is only a record of the vicissitudes of Tarentum (q.v.).
Repeated expeditions from Sparta and Epirus tried in vain to prop up the
decaying Greek states against the Lucanians and Bruttians; and when in
282 the Romans appeared in the Tarentine Gulf the end was close at hand.
The aid which Pyrrhus brought did little good to the Tarentines, and his
final departure in 274 left them defenceless. During these constant wars
the Greek cities had been steadily decaying; and in the second Punic
war, when most of them seized the opportunity of revolting from Rome,
their very existence was in some cases annihilated. Malaria increased in
strength as the population diminished. We are told by Cicero (_De am._
4), _Magna Graecia nunc quidem deleta est_. Many of the cities
completely disappeared, and hardly any of them were of great importance
under the Roman empire; some, like Tarentum, maintained their existence
into modern times, and in these only (except at Locri) have
archaeological investigations of any importance been carried on; so that
there still remains a considerable field for investigation.     (T. As.)


FOOTNOTE:

  [1] This passage should perhaps be referred to the 8th century B.C.
    It is the first mention of an Italian place in a literary record.




MAGNATE (Late Lat. _magnas_, a great man), a noble, a man in high
position, by birth, wealth or other qualities. The term is specifically
applied to the members of the Upper House in Hungary, the _Förendihaz_
or House of Magnates (see HUNGARY).




MAGNES (_c._ 460 B.C.), Athenian writer of the Old Comedy, a native of
the deme of Icaria in Attica. His death is alluded to by Aristophanes
(_Equites_, 518-523, which was brought out in 424 B.C.), who states that
in his old age Magnes had lost the popularity which he had formerly
enjoyed. The few titles of his plays that remain, such as the _Frogs_,
the _Birds_, the _Gall-flies_, indicate that he anticipated Aristophanes
in introducing grotesque costumes for the chorus.

  See T. Kock, _Comicorum atticorum fragmenta_, i. (1880); G. H. Bode,
  _Geschichte der hellenischen Dichtkunst_, iii. pt. 2 (1840).




MAGNESIA, in ancient geography the name of two cities in Asia Minor and
of a district in eastern Thessaly, lying between the Vale of Tempe and
the Pagasaean Gulf.

(1) MAGNESIA AD MAEANDRUM, a city of Ionia, situated on a small stream
flowing into the Maeander, 15 Roman miles from Miletus and rather less
from Ephesus. According to tradition, reinforced by the similarity of
names, it was founded by colonists from the Thessalian tribe of the
Magnetes, with whom were associated, according to Strabo, some Cretan
settlers (Magnesia retained a connexion with Crete, as inscriptions
found there attest). It was thus not properly an Ionic city, and for
this reason, apparently, was not included in the Ionian league, though
superior in wealth and prosperity to most of the members except Ephesus
and Miletus. It was destroyed by the Cimmerii in their irruption into
Asia Minor, but was soon after rebuilt, and gradually recovered its
former prosperity. It was one of the towns assigned by Artaxerxes to
Themistocles for support in his exile, and there the latter ended his
days. His statue stood in its market-place. Thibron, the Spartan,
persuaded the Magnesians to leave their indefensible and mutinous city
in 399 B.C. and build afresh at Leucophrys, an hour distant, noted for
its temple of Artemis Leucophryne, which, according to Strabo, surpassed
that at Ephesus in the beauty of its architecture, though inferior in
size and wealth. Its ruins were excavated by Dr K. Humann for the
Constantinople Museum in 1891-1893; but most of the frieze of the temple
of Artemis Leucophryne, representing an Amazon battle, had already been
carried off by Texier (1843) to the Louvre. It was an octostyle,
pseudo-dipteral temple of highly ornate Ionic order, built on older
foundations by Hermogenes of Alabanda at the end of the 3rd century B.C.
The platform has been greatly overgrown since the excavation, but many
bases, capitals, and other architectural members are visible. In front
of the west façade stood a great altar. An immense _peribolus_ wall is
still standing (20 ft. high), but its Doric colonnade has vanished. The
railway runs right through the precinct, and much of Magnesia has gone
into its bridges and embankments. South and west of the temple are many
other remains of the Roman city, including a fairly perfect theatre
excavated by Hiller von Gärtringen, and the shell of a large gymnasium.
Part of the Agora was laid open to Humann, but his trenches have fallen
in. The site is so unhealthy that even the Circassians who settled there
twenty years ago have almost all died off or emigrated. Magnesia
continued under the kings of Pergamum to be one of the most flourishing
cities in this part of Asia; it resisted Mithradates in 87 B.C., and was
rewarded with civic freedom by Sulla; but it appears to have greatly
declined under the Roman empire, and its name disappears from history,
though on coins of the time of Gordian it still claimed to be the
seventh city of Asia.

  See K. Haumann, _Magnesia am Maeander_ (1904).

(2) MAGNESIA AD SIPYLUM (mod. _Manisa_, q.v.), a city of Lydia about 40
m. N.E. of Smyrna on the river Hermus at the foot of Mt Sipylus. No
mention of the town is found till 190 B.C., when Antiochus the Great was
defeated under its walls by the Roman consul L. Scipio Asiaticus. It
became a city of importance under the Roman dominion and, though nearly
destroyed by an earthquake in the reign of Tiberius, was restored by
that emperor and flourished through the Roman empire. It was one of the
few towns in this part of Asia Minor which remained prosperous under the
Turkish rule. The most famous relic of antiquity is the "Niobe of
Sipylus" (_Suratlu Tash_) on the lowest slopes of the mountain about 4
m. east of the town. This is a colossal seated image cut in a niche of
the rock, of "Hittite" origin, and perhaps that called by Pausanias the
"very ancient statue of the Mother of the Gods," carved by Broteas, son
of Tantalus, and sung by Homer. Near it lie many remains of a primitive
city, and about half a mile east is the rock-seat conjecturally
identified with Pausanias' "Throne of Pelops." There are also hot
springs and a sacred grotto of Apollo. The whole site seems to be that
of the early "Tantalus" city.     (D. G. H.)




MAGNESITE, a mineral consisting of magnesium carbonate, MgCO3, and
belonging to the calcite group of rhombohedral carbonates. It is rarely
found in crystals or crystalline masses, being usually compact or earthy
and intermixed with more or less hydrous magnesium silicate
(meerschaum). The compact material has the appearance of unglazed
porcelain, and the earthy that of chalk. In colour it is usually dead
white, sometimes yellowish. The hardness of the crystallized mineral is
4; sp. gr. 3.1. The name magnesite as originally applied by J. C.
Delamétherie in 1797 included several minerals containing magnesium, and
at the present day it is used by French writers for meerschaum. The
mineral has also been called baudisserite from the locality Baudissero
near Ivrea in Piedmont. Breunnerite is a ferriferous variety.

  Magnesite is a product of alteration of magnesium silicates, and
  occurs as veins and patches in serpentine, talc-schist or
  dolomite-rock. It is extensively mined in the island of Euboea in the
  Grecian Archipelago, near Salem in Madras, and in California, U.S.A.
  It is principally used for the manufacture of highly refractory
  fire-bricks for lining steel furnaces and electric furnaces; also for
  making plaster, tiles and artificial stone; for the preparation of
  magnesium salts (Epsom salts, &c.); for whitening; paper-pulp and
  wool; and as a paint.




MAGNESIUM [symbol Mg, atomic weight 24.32 (O = 16)], a metallic chemical
element. The sulphate or "Epsom salts" (q.v.) was isolated in 1695 by N.
Grew, while in 1707 M. B. Valentin prepared _magnesia alba_ from the
mother liquors obtained in the manufacture of nitre. Magnesia was
confounded with lime until 1755, when J. Black showed that the two
substances were entirely different; and in 1808 Davy pointed out that it
was the oxide of a metal, which, however, he was not able to isolate.
Magnesium is found widely distributed in nature, chiefly in the forms of
silicate, carbonate and chloride, and occurring in the minerals olivine,
hornblende, talc, asbestos, meerschaum, augite, dolomite, magnesite,
carnallite, kieserite and kainite. The metal was prepared (in a state
approximating to purity) by A. A. B. Bussy (_Jour. de pharm._ 1829, 15,
p. 30; 1830, 16, p. 142), who fused the anhydrous chloride with
potassium; H. Sainte Claire Deville's process, which used to be employed
commercially, was essentially the same, except that sodium was
substituted for potassium (_Comptes rendus_, 1857, 44, p. 394), the
product being further purified by redistillation. It may also be
prepared by heating a mixture of carbon, oxide of iron and magnesite to
bright redness; and by heating a mixture of magnesium ferrocyanide and
sodium carbonate, the double cyanide formed being then decomposed by
heating it with metallic zinc. Electrolytic methods have entirely
superseded the older methods. The problem of magnesium reduction is in
many respects similar to that of aluminium extraction, but the lightness
of the metal as compared, bulk for bulk, with its fused salts, and the
readiness with which it burns when exposed to air at high temperatures,
render the problem somewhat more difficult.

  Moissan found that the oxide resisted reduction by carbon in the
  electric furnace, so that electrolysis of a fusible salt of the metal
  must be resorted to. Bunsen, in 1852, electrolysed fused magnesium
  chloride in a porcelain crucible. In later processes, carnallite (a
  natural double chloride of magnesium and potassium) has commonly,
  after careful dehydration, been substituted for the single chloride.
  Graetzel's process, which was at one time employed, consisted in
  electrolysing the chloride in a metal crucible heated externally, the
  crucible itself forming the cathode, and the magnesium being deposited
  upon its inner surface. W. Borchers also used an externally heated
  metal vessel as the cathode; it is provided with a supporting collar
  or flange a little below the top, so that the upper part of the vessel
  is exposed to the cooling influence of the air, in order that a crust
  of solidified salt may there be formed, and so prevent the creeping of
  the electrolyte over the top. The carbon anode passes through the
  cover of a porcelain cylinder, open at the bottom, and provided with a
  side-tube at the top to remove the chlorine formed during
  electrolysis. The operation is conducted at a dull red heat (about
  760° C. or 1400° F.), the current density being about 0.64 amperes per
  sq. in. of cathode surface, and the pressure about 7 volts. The
  fusing-point of the metal is about 730° C. (1350° F.), and the
  magnesium is therefore reduced in the form of melted globules which
  gradually accumulate. At intervals the current is interrupted, the
  cover removed, and the temperature of the vessel raised considerably
  above the melting-point of magnesium. The metal is then removed from
  the walls with the aid of an iron scraper, and the whole mass poured
  into a sheet-iron tray, where it solidifies. The solidified chloride
  is then broken up, the shots and fused masses of magnesium are picked
  out, run together in a plumbago crucible without flux, and poured into
  a suitable mould. Smaller pieces are thrown into a bath of melted
  carnallite and pressed together with an iron rod, the bath being then
  heated until the globules of metal float to the top, when they may be
  removed in perforated iron ladles, through the holes in which the
  fused chloride can drain away, but through which the melted magnesium
  cannot pass by reason of its high surface tension. The globules are
  then re-melted. F. Oettel (_Zeit. f. Elektrochem._, 1895, 2, p. 394)
  recommends the electrolytic preparation from carnallite; the mineral
  should be freed from water and sulphates.

Magnesium is a silvery white metal possessing a high lustre. It is
malleable and ductile. Sp. gr. 1.75. It preserves its lustre in dry air,
but in moist air it becomes tarnished by the formation of a film of
oxide. It melts at 632.7° C. (C. T. Heycock and F. H. Neville), and
boils at about 1100°C. Magnesium and its salts are diamagnetic. It burns
brilliantly when heated in air or oxygen, or even in carbon dioxide,
emitting a brilliant white light and leaving a residue of magnesia, MgO.
The light is rich in the violet and ultra-violet rays, and consequently
is employed in photography. The metal is also used in pyrotechny. It
also burns when heated in a current of steam, which it decomposes with
the liberation of hydrogen and the formation of magnesia. At high
temperatures it acts as a reducing agent, reducing silica to silicon,
boric acid to boron, &c. (H. Moissan, _Comptes rendus_, 1892, 114, p.
392). It combines directly with nitrogen, when heated in the gas, to
form the nitride Mg3N2 (see ARGON). It is rapidly dissolved by dilute
acids, with the evolution of hydrogen and the formation of magnesium
salts. It precipitates many metals from solutions of their salts.

  _Magnesium Oxide_, magnesia, MgO, occurs native as the mineral
  periclase, and is formed when magnesium burns in air; it may also be
  prepared by the gentle ignition of the hydroxide or carbonate. It is a
  non-volatile and almost infusible white powder, which slowly absorbs
  moisture and carbon dioxide from air, and is readily soluble in dilute
  acids. On account of its refractory nature, it is employed in the
  manufacture of crucibles, furnace linings, &c. It is also used in
  making hydraulic cements. A crystalline form was obtained by M.
  Houdard (_Abst. J. C. S._, 1907, ii. p. 621) by fusing the oxide and
  sulphide in the electric furnace. _Magnesium hydroxide_ Mg(OH)2,
  occurs native as the minerals brucite and némalite, and is prepared by
  precipitating solutions of magnesium salts by means of caustic soda or
  potash. An artificial brucite was prepared by A. de Schulten (_Comptes
  rendus_, 1885, 101, p. 72) by boiling magnesium chloride with caustic
  potash and allowing the solution to cool. Magnesium hydroxide is a
  white amorphous solid which is only slightly soluble in water; the
  solubility is, however, greatly increased by ammonium salts. It
  possesses an alkaline reaction and absorbs carbon dioxide. It is
  employed in the manufacture of cements.

  When magnesium is heated in fluorine or chlorine or in the vapour of
  bromine or iodine there is a violent reaction, and the corresponding
  halide compounds are formed. With the exception of the fluoride, these
  substances are readily soluble in water and are deliquescent. The
  fluoride is found native as sellaïte, and the bromide and iodide occur
  in sea water and in many mineral springs. The most important of the
  halide salts is the _chloride_ which, in the hydrated form, has the
  formula MgCl2·6H2O. It may be prepared by dissolving the metal, its
  oxide, hydroxide, or carbonate in dilute hydrochloric acid, or by
  mixing concentrated solutions of magnesium sulphate and common salt,
  and cooling the mixture rapidly, when the less soluble sodium
  sulphate separates first. It is also formed as a by-product in the
  manufacture of potassium chloride from carnallite. The hydrated salt
  loses water on heating, and partially decomposes into hydrochloric
  acid and magnesium oxychlorides. To obtain the anhydrous salt, the
  double magnesium ammonium chloride, MgCl2·NH4Cl·6H2O, is prepared by
  adding ammonium chloride to a solution of magnesium chloride. The
  solution is evaporated, and the residue strongly heated, when water
  and ammonium chloride are expelled, and anhydrous magnesium chloride
  remains. Magnesium chloride readily forms double salts with the
  alkaline chlorides. A strong solution of the chloride made into a
  thick paste with calcined magnesia sets in a few hours to a hard,
  stone-like mass, which contains an oxychloride of varying composition.
  Magnesium oxychloride when heated to redness in a current of air
  evolves a mixture of hydrochloric acid and chlorine and leaves a
  residue of magnesia, a reaction which is employed in the
  Weldon-Pechiney and Mond processes for the manufacture of chlorine.

  _Magnesium Carbonate,_ MgCO3.--The normal salt is found native as the
  mineral magnesite, and in combination with calcium carbonate as
  dolomite, whilst hydromagnesite is a basic carbonate. It is not
  possible to prepare the normal carbonate by precipitating magnesium
  salts with sodium carbonate. C. Marignac has prepared it by the action
  of calcium carbonate on magnesium chloride. A salt MgCO3·3H2O or
  Mg(CO3H)(OH)·2H2O may be prepared from the carbonate by dissolving it
  in water charged with carbon dioxide, and then reducing the pressure
  (W. A. Davis, _Jour. Soc. Chem. Ind._ 1906, 25, p. 788). The carbonate
  is not easily soluble in dilute acids, but is readily soluble in water
  containing carbon dioxide. _Magnesia alba_, a white bulky precipitate
  obtained by adding sodium carbonate to Epsom salts, is a mixture of
  Mg(CO3H)(OH)·2H2O, Mg(CO3H)(OH) and Mg(OH)2. It is almost insoluble in
  water, but readily dissolves in ammonium salts.

  _Magnesium Phosphates._--By adding sodium phosphate to magnesium
  sulphate and allowing the mixture to stand, hexagonal needles of
  MgHPO4·7H2O are deposited. The _normal phosphate_, Mg3P2O8, is found
  in some guanos, and as the mineral wagnerite. It may be prepared by
  adding normal sodium phosphate to a magnesium salt and boiling the
  precipitate with a solution of magnesium sulphate. It is a white
  amorphous powder, readily soluble in acids. _Magnesium ammonium
  phosphate_, MgNH4PO4·6H2O, is found as the mineral struvite and in
  some guanos; it occurs also in urinary calculi and is formed in the
  putrefaction of urine. It is prepared by adding sodium phosphate to
  magnesium sulphate in the presence of ammonia and ammonium chloride.
  When heated to 100° C., it loses five molecules of water of
  crystallization, and at a higher temperature loses the remainder of
  the water and also ammonia, leaving a residue of magnesium
  pyrophosphate, Mg2P2O7. _Magnesium Nitrate_, Mg(NO3)2·6H2O, is a
  colourless, deliquescent, crystalline solid obtained by dissolving
  magnesium or its carbonate in nitric acid, and concentrating the
  solution. The crystals melt at 90° C. _Magnesium Nitride_, Mg3N2, is
  obtained as a greenish-yellow amorphous mass by passing a current of
  nitrogen or ammonia over heated magnesium (F. Briegleb and A. Geuther,
  _Ann._, 1862, 123, p. 228; see also W. Eidmann and L. Moeser, _Ber._,
  1901, 34, p. 390). When heated in dry oxygen it becomes incandescent,
  forming magnesia. Water decomposes it with liberation of ammonia and
  formation of magnesium hydroxide. The chlorides of nickel, cobalt,
  chromium, iron and mercury are converted into nitrides when heated
  with it, whilst the chlorides of copper and platinum are reduced to
  the metals (A. Smits, _Rec. Pays Bas_, 1896, 15, p. 135). _Magnesium
  sulphide_, MgS, may be obtained, mixed with some unaltered metal and
  some magnesia, as a hard brown mass by heating magnesia, in sulphur
  vapour. It slowly decomposes in moist air. _Magnesium sulphate_,
  MgSO4, occurs (with IH2O) as Kieserite. A hexahydrate is also known.
  The salt may be obtained from Kieserite: formerly it was prepared by
  treating magnesite or dolomite with sulphuric acid.


    Grignard Reagent.

  _Organic Compounds._--By heating magnesium filings with methyl and
  ethyl iodides A. Cahours (_Ann. chim. phys._, 1860, 58, pp. 5, 19)
  obtained magnesium methyl, Mg(CH3)2, and magnesium ethyl, Mg(C2H5)2,
  as colourless, strongly smelling, mobile liquids, which are
  spontaneously inflammable and are readily decomposed by water. The
  compounds formed by the action of magnesium on alkyl iodides in the
  cold have been largely used in synthetic organic chemistry since V.
  Grignard (_Comptes rendus_, 1900 et seq.) observed that magnesium and
  alkyl or aryl halides combined together in presence of anhydrous ether
  at ordinary temperatures (with the appearance of brisk boiling) to
  form compounds of the type RMgX(R = an alkyl or aryl group and X =
  halogen). These compounds are insoluble in ether, are non-inflammable
  and exceedingly reactive. A. V. Baeyer (_Ber._, 1902, 35, p. 1201)
  regards them as oxonium salts containing tetravalent oxygen
  (C2H5)2:O:(MgR) (X), whilst W. Tschelinzeff (_Ber._, 1906, 39, p. 773)
  considers that they contain two molecules of ether. In preparing the
  Grignard reagent the commencement of the reaction is accelerated by a
  trace of iodine. W. Tschelinzeff (_Ber._, 1904, 37, p. 4534) showed
  that the ether may be replaced by benzene containing a small quantity
  of ether or anisole, or a few drops of a tertiary amine. With
  unsaturated alkyl halides the products are only slightly soluble in
  ether, and two molecules of the alkyl compound are brought into the
  reaction. They are very unstable, and do not react in the normal
  manner. (V. Grignard and L. Tissier, _Comptes rendus_, 1901, 132, p.
  558).

  The products formed by the action of the Grignard reagent with the
  various types of organic compounds are usually thrown out of solution
  in the form of crystalline precipitates or as thick oils, and are then
  decomposed by ice-cold dilute sulphuric or acetic acids, the magnesium
  being removed as a basic halide salt.

  _Applications._--For the formation of primary and secondary alcohols
  see ALDEHYDES and KETONES. Formaldehyde behaves abnormally with
  magnesium benzyl bromide (M. Tiffeneau, _Comptes rendus_, 1903, 137,
  p. 573). forming ortho-tolylcarbinol, CH3·C6H4·CH2OH, and not
  benzylcarbinol, C6H5CH2·CH2OH (cf. the reaction of formaldehyde on
  phenols: O. Manasse, _Ber._ 1894, 27, p. 2904). Acid esters yield
  carbinols, many of which are unstable and readily pass over into
  unsaturated compounds, especially when warmed with acetic anhydride:
  R·CO2R´(R´´)2·R·:C·OMgX -> (R´´)2R·:C·OH.

  Formic ester yields a secondary alcohol under similar conditions. Acid
  chlorides behave in an analogous manner to esters (Grignard and
  Tissier, _Comptes rendus_, 1901, 132, p. 683). Nitriles yield ketones
  (the nitrogen being eliminated as ammonia), the best yields being
  given by the aromatic nitriles (E. Blaise, ibid., 1901, 133, p. 1217):
  R·CN -> RR´:C:NMgI -> R·CO·R´. Acid amides also react to form ketones
  (C. Béis, ibid., 1903, 137, 575):

    R·CONH2 -> RR´:C(OMgX)·NHMgX + R´H -> R·CO·R´;

  the yield increases with the complexity of the organic residue of the
  acid amide. On passing a current of dry carbon dioxide over the
  reagent, the gas is absorbed and the resulting compound, when
  decomposed by dilute acids, yields an organic acid, and similarly with
  carbon oxysulphide a thio-acid is obtained:

    RMgX -> R·CO2MgX -> R·CO2H; COS -> CS(OMgX)·R -> R·CSOH.

  A. Klages (_Ber._, 1902, 35, pp. 2633 et seq.) has shown that if one
  uses an excess of magnesium and of an alkyl halide with a ketone, an
  ethylene derivative is formed. The reaction appears to be perfectly
  general unless the ketone contains two ortho-substituent groups.
  Organo-metallic compounds can also be prepared, for example

    SnBr4 + 4MgBrC6H5 = 4MgBr2 + Sn(C6H5)4.

  For a summary see A. McKenzie, _B. A. Rep._ 1907.

  _Detection._--The magnesium salts may be detected by the white
  precipitate formed by adding sodium phosphate (in the presence of
  ammonia and ammonium chloride) to their solutions. The same reaction
  is made use of in the quantitative determination of magnesium, the
  white precipitate of magnesium ammonium phosphate being converted by
  ignition into magnesium pyrophosphate and weighed as such. The atomic
  weight of magnesium has been determined by many observers. J.
  Berzelius (_Ann. chim. phys._, 1820, 14, p. 375), by converting the
  oxide into the sulphate, obtained the value 12.62 for the equivalent.
  R. F. Marchand and T. Scheerer (_Jour. prakt. Chem._, 1850, 50, p.
  358), by ignition of the carbonate, obtained the value 24.00 for the
  atomic weight, whilst C. Marignac, by converting the oxide into the
  sulphate, obtained the value 24.37. T. W. Richards and H. G. Parker
  (_Zeit. anorg. Chem._, 1897, 13, p. 81) have obtained the value 24.365
  (O = 16).

_Medicine._--These salts of magnesium may be regarded as the typical
_saline purgatives_. Their aperient action is dependent upon the minimum
of irritation of the bowel, and is exercised by their abstraction from
the blood of water, which passes into the bowel to act as a diluent of
the salt. The stronger the solution administered, the greater is the
quantity of water that passes into the bowel, a fact to be borne in mind
when the salt is administered for the purpose of draining superfluous
fluid from the system, as in dropsy. The oxide and carbonate of
magnesium are also invaluable as antidotes, since they form insoluble
compounds with oxalic acid and salts of mercury, arsenic, and copper.
The result is to prevent the local corrosive action of the poison and to
prevent absorption of the metals. As alkaloids are insoluble in alkaline
solutions, the oxide and carbonate--especially the former--may be given
in alkaloidal poisoning. The compounds of magnesium are not absorbed
into the blood in any appreciable quantity, and therefore exert no
remote actions upon other functions. This is fortunate, as the result of
injecting a solution of a magnesium salt into a vein is rapid poisoning.
Hence it is of the utmost importance to avoid the use of salts of this
metal whenever it is necessary--as in diabetic coma--to increase the
alkalinity of the blood rapidly. The usual doses of the oxide and
carbonate of magnesium are from half a drachm to a drachm.




MAGNETISM. The present article is a digest, mainly from an experimental
standpoint, of the leading facts and principles of magnetic science. It
is divided into the following sections:

  1. General Phenomena.

  2. Terminology and Elementary Principles.

  3. Magnetic Measurements.

  4. Magnetization in Strong Fields.

  5. Magnetization in Weak Fields.

  6. Changes of Dimensions attending Magnetization.

  7. Effects of Mechanical Stress on Magnetization.

  8. Effects of Temperature on Magnetism.

  9. Magnetic Properties of Alloys and Compounds of Iron.

  10. Miscellaneous Effects of Magnetization:--Electric
  Conductivity--Hall Effect--Electro-Thermal Relations--Thermo-electric
  Quality--Elasticity--Chemical and Voltaic Effects.

  11. Feebly Susceptible Substances.

  12. Molecular Theory of Magnetism.

  13. Historical and Chronological Notes.

Of these thirteen sections, the first contains a simple description of
the more prominent phenomena, without mathematical symbols or numerical
data. The second includes definitions of technical terms in common use,
together with so much of the elementary theory as is necessary for
understanding the experimental work described in subsequent portions of
the article; a number of formulae and results are given for purposes of
reference, but the mathematical reasoning by which they are obtained is
not generally detailed, authorities being cited whenever the
demonstrations are not likely to be found in ordinary textbooks. The
subjects discussed in the remaining sections are sufficiently indicated
by their respective headings. (See also ELECTROMAGNETISM, TERRESTRIAL
MAGNETISM, MAGNETO-OPTICS and UNITS.)


1. GENERAL PHENOMENA

Pieces of a certain highly esteemed iron ore, which consists mainly of
the oxide Fe3O4, are sometimes found to possess the power of attracting
small fragments of iron or steel. Ore endowed with this curious property
was well known to the ancient Greeks and Romans, who, because it
occurred plentifully in the district of Magnesia near the Aegean coast,
gave it the name of _magnes_, or the _Magnesian stone_. In
English-speaking countries the ore is commonly known as _magnetite_, and
pieces which exhibit attraction as _magnets_; the cause to which the
attractive property is attributed is called _magnetism_, a name also
applied to the important branch of science which has been evolved from
the study of phenomena associated with the magnet.

If a magnet is dipped into a mass of iron filings and withdrawn, filings
cling to certain parts of the stone in moss-like tufts, other parts
remaining bare. There are generally two regions where the tufts are
thickest, and the attraction therefore greatest, and between them is a
zone in which no attraction is evidenced. The regions of greatest
attraction have received the name of _poles_, and the line joining them
is called the _axis_ of the magnet; the space around a magnet in which
magnetic effects are exhibited is called the _field of magnetic force_,
or the _magnetic field_.

Up to the end of the 15th century only two magnetic phenomena of
importance, besides that of attraction, had been observed. Upon one of
these is based the principle of the mariner's compass, which is said to
have been known to the Chinese as early as 1100 B.C., though it was not
introduced into Europe until more than 2000 years later; a magnet
supported so that its axis is free to turn in a horizontal plane will
come to rest with its poles pointing approximately north and south. The
other phenomenon is mentioned by Greek and Roman writers of the 1st
century: a piece of iron, when brought into contact with a magnet, or
even held near one, itself becomes "inductively" magnetized, and
acquires the power of lifting iron. If the iron is soft and fairly pure,
it loses its attractive property when removed from the neighbourhood of
the magnet; if it is hard, some of the induced magnetism is permanently
retained, and the piece becomes an artificial magnet. Steel is much more
retentive of magnetism than any ordinary iron, and some form of steel is
now always used for making artificial magnets. Magnetism may be imparted
to a bar of hardened steel by stroking it several times from end to
end, always in the same direction, with one of the poles of a magnet.
Until 1820 all the artificial magnets in practical use derived their
virtue, directly or indirectly, from the natural magnets found in the
earth: it is now recognized that the source of all magnetism, not
excepting that of the magnetic ore itself, is electricity, and it is
usual to have direct recourse to electricity for producing
magnetization, without the intermediary of the magnetic ore. A wire
carrying an electric current is surrounded by a magnetic field, and if
the wire is bent into the form of an elongated coil or spiral, a field
having certain very useful qualities is generated in the interior. A bar
of soft iron introduced into the coil is at once magnetized, the
magnetism, however, disappearing almost completely as soon as the
current ceases to flow. Such a combination constitutes an
_electromagnet_, a valuable device by means of which a magnet can be
instantly made and unmade at will. With suitable arrangements of iron
and coil and a sufficiently strong current, the intensity of the
temporary magnetization may be very high, and electromagnets capable of
lifting weights of several tons are in daily use in engineering works
(see ELECTROMAGNETISM). If the bar inserted into the coil is of hardened
steel instead of iron, the magnetism will be less intense, but a larger
proportion of it will be retained after the current has been cut off.
Steel magnets of great strength and of any convenient form may be
prepared either in this manner or by treatment with an electromagnet;
hence the natural magnet, or _lodestone_ as it is commonly called, is no
longer of any interest except as a scientific curiosity.

Some of the principal phenomena of magnetism may be demonstrated with
very little apparatus; much may be done with a small bar-magnet, a
pocket compass and a few ounces of iron filings. Steel articles, such as
knitting or sewing needles and pieces of flat spring, may be readily
magnetized by stroking them with the bar-magnet; after having produced
magnetism in any number of other bodies, the magnet will have lost
nothing of its own virtue. The compass needle is a little steel magnet
balanced upon a pivot; one end of the needle, which always bears a
distinguishing mark, points approximately, but not in general exactly,
to the north,[1] the vertical plane through the direction of the needle
being termed the _magnetic meridian_. The bar-magnet, if suspended
horizontally in a paper stirrup by a thread of unspun silk, will also
come to rest in the magnetic meridian with its marked end pointing
northwards. The north-seeking end of a magnet is in English-speaking
countries called the _north pole_ and the other end the _south pole_; in
France the names are interchanged. If one pole of the bar-magnet is
brought near the compass, it will attract the opposite pole of the
compass-needle; and the magnetic action will not be sensibly affected by
the interposition between the bar and the compass of any substance
whatever except iron or other magnetizable metal. The poles of a piece
of magnetized steel may be at once distinguished if the two ends are
successively presented to the compass; that end which attracts the south
pole of the compass needle (and is therefore north) may be marked for
easy identification.

Similar magnetic poles are not merely indifferent to each other, but
exhibit actual repulsion. This can be more easily shown if the compass
is replaced by a magnetized knitting needle, supported horizontally by a
thread. The north pole of the bar-magnet will repel the north pole of
the suspended needle, and there will likewise be repulsion between the
two south poles. Such experiments as these demonstrate the fundamental
law that _like poles repel each other_; _unlike poles attract_. It
follows that between two neighbouring magnets, the poles of which are
regarded as centres of force, there must always be four forces in
action. Denoting the two pairs of magnetic poles by N, S and N´, S´,
there is attraction between N and S´, and between S and N´; repulsion
between N and N´, and between S and S´. Hence it is not very easy to
determine experimentally the law of magnetic force between poles. The
difficulty was overcome by C. A. Coulomb, who by using very long and
thin magnets, so arranged that the action of their distant poles was
negligible, succeeded in establishing the law, which has since been
confirmed by more accurate methods, that _the force of attraction or
repulsion exerted between two magnetic poles varies inversely as the
square of the distance between them_. Since the poles of different
magnets differ in strength, it is important to agree upon a definite
unit or standard of reference in terms of which the strength of a pole
may be numerically specified. According to the recognized convention,
the unit pole is that which acts upon an equal pole at unit distance
with unit force: a north pole is reckoned as positive (+) and a south
pole as negative (-). Other conditions remaining unchanged, the force
between two poles is proportional to the product of their strengths; it
is repulsive or attractive according as the signs of the poles are like
or unlike.

[Illustration: FIG. 1.]

If a wire of soft iron is substituted for the suspended magnetic needle,
either pole of the bar-magnet will attract either end of the wire
indifferently. The wire will in fact become temporarily magnetized by
induction, that end of it which is nearest to the pole of the magnet
acquiring opposite polarity, and behaving as if it were the pole of a
permanent magnet. Even a permanent magnet is susceptible of induction,
its polarity becoming thereby strengthened, weakened, or possibly
reversed. If one pole of a strong magnet is presented to the like pole
of a weaker one, there will be repulsion so long as the two are
separated by a certain minimum distance. At shorter distances the
magnetism induced in the weaker magnet will be stronger than its
permanent magnetism, and there will be attraction; two magnets with
their like poles in actual contact will always cling together unless the
like poles are of exactly equal strength. Induction is an effect of the
field of force associated with a magnet. Magnetic force has not merely
the property of acting upon magnetic poles, it has the additional
property of producing a phenomenon known as _magnetic induction_, or
_magnetic flux_, a physical condition which is of the nature of a flow
continuously circulating through the magnet and the space outside it.
Inside the magnet the course of the flow is from the south pole to the
north pole; thence it diverges through the surrounding space, and again
converging, re-enters the magnet at the south pole. When the magnetic
induction flows through a piece of iron or other magnetizable substance
placed near the magnet, a south pole is developed where the flux enters
and a north pole where it leaves the substance. Outside the magnet the
direction of the magnetic induction is generally the same as that of the
magnetic force. A map indicating the direction of the force in different
parts of the field due to a magnet may be constructed in a very simple
manner. A sheet of cardboard is placed above the magnet, and some iron
filings are sifted thinly and evenly over the surface: if the cardboard
is gently tapped, the filings will arrange themselves in a series of
curves, as shown in fig. 1. This experiment suggested to Faraday the
conception of "lines of force," of which the curves formed by the
filings afford a rough indication; Faraday's lines are however not
confined to the plane of the cardboard, but occur in the whole of the
space around the magnet. A _line of force_ may be defined as an
imaginary line so drawn that its direction at every point of its course
coincides with the direction of the magnetic force at that point.
Through any point in the field one such line can be drawn, but not more
than one, for the force obviously cannot have more than one direction;
the lines therefore never intersect. A line of force is regarded as
proceeding from the north pole towards the south pole of the magnet, its
direction being that in which an isolated north pole would be urged
along it. A south pole would be urged oppositely to the conventional
"direction" of the line; hence it follows that a very small magnetic
needle, if placed in the field, would tend to set itself along or
tangentially to the line of force passing through its centre, as may be
approximately verified if the compass be placed among the filings on the
cardboard. In the internal field of a long coil of wire carrying an
electric current, the lines of force are, except near the ends, parallel
to the axis of the coil, and it is chiefly for this reason that the
field due to a coil is particularly well adapted for inductively
magnetizing iron and steel. The older operation of magnetizing a steel
bar by drawing a magnetic pole along it merely consists in exposing
successive portions of the bar to the action of the strong field near
the pole.

Faraday's lines not only show the direction of the magnetic force, but
also serve to indicate its magnitude or strength in different parts of
the field. Where the lines are crowded together, as in the neighbourhood
of the poles, the force is greater (or the field is stronger) than where
they are more widely separated; hence the strength of a field at any
point can be accurately specified by reference to the concentration of
the lines. The lines presented to the eye by the scattered filings are
too vague and ill-defined to give a satisfactory indication of the
field-strength (see Faraday, _Experimental Researches_, § 3237) though
they show its direction clearly enough. It is however easy to
demonstrate by means of the compass that the force is much greater in
some parts of the field than in others. Lay the compass upon the
cardboard, and observe the rate at which its needle vibrates after being
displaced from its position of equilibrium; this will vary greatly in
different regions. When the compass is far from the magnet, the
vibrations will be comparatively slow; when it is near a pole, they will
be exceedingly rapid, the frequency of the vibrations varying as the
square root of the magnetic force at the spot. In a refined form this
method is often employed for measuring the intensity of a magnetic field
at a given place, just as the intensity of gravity at different parts of
the earth is deduced from observations of the rate at which a pendulum
of known length vibrates.

It is to the non-uniformity of the field surrounding a magnet that the
apparent attraction between a magnet and a magnetizable body such as
iron is ultimately due. This was pointed out by W. Thomson (afterwards
Lord Kelvin) in 1847, as the result of a mathematical investigation
undertaken to explain Faraday's experimental observations. If the
inductively magnetized body lies in a part of the field which happens to
be uniform there will be no resulting force tending to move the body,
and it will not be "attracted." If however there is a small variation of
the force in the space occupied by the body, it can be shown that the
body will be urged, not necessarily towards a magnetic pole, but
_towards places of stronger magnetic force_. It will not in general move
along a line of force, as would an isolated pole, but will follow the
direction in which the magnetic force increases most rapidly, and in so
doing it may cross the lines of force obliquely or even at right angles.

If a magnetized needle were supported so that it could move freely about
its centre of gravity it would not generally settle with its axis in a
horizontal position, but would come to rest with its north-seeking pole
either higher or lower than its centre. For the practical observation of
this phenomenon it is usual to employ a needle which can turn freely in
the plane of the magnetic meridian upon a horizontal axis passing
through the centre of gravity of the needle. The angle which the
magnetic axis makes with the plane of the horizon is called the
_inclination_ or _dip._ Along an irregular line encircling the earth in
the neighbourhood of the geographical equator the needle takes up a
horizontal position, and the dip is zero. At places north of this line,
which is called the _magnetic equator_, the north end of the needle
points downwards, the inclination generally becoming greater with
increased distance from the equator. Within a certain small area in the
Arctic Circle (about 97° W. long., 70° N. lat.) the north pole of the
needle points vertically downwards, the dip being 90°. South of the
magnetic equator the south end of the needle is always inclined
downwards, and there is a spot within the Antarctic Circle (148° E.
long., 74° S. lat.) where the needle again stands vertically, but with
its north end directed upwards. All these observations may be accounted
for by the fact first recognized by W. Gilbert in 1600, that the earth
itself is a great magnet, having its poles at the two places where the
dipping needle is vertical. To be consistent with the terminology
adopted in Britain, it is necessary to regard the pole which is
geographically north as being the south pole of the terrestrial magnet,
and that which is geographically south as the north pole; in practice
however the names assigned to the terrestrial magnetic poles correspond
with their geographical situations. Within a limited space, such as that
contained in a room, the field due to the earth's magnetism is sensibly
uniform, the lines of force being parallel straight lines inclined to
the horizon at the angle of dip, which at Greenwich in 1910 was about
67°. It is by the horizontal component of the earth's total force that
the compass-needle is directed.

The magnets hitherto considered have been assumed to have each two
poles, the one north and the other south. It is possible that there may
be more than two. If, for example, a knitting needle is stroked with the
south pole of a magnet, the strokes being directed from the middle of
the needle towards the two extremities alternately, the needle will
acquire a north pole at each end and a south pole in the middle. By
suitably modifying the manipulation a further number of _consequent
poles_, as they are called, may be developed. It is also possible that a
magnet may have no poles at all. Let a magnetic pole be drawn several
times around a uniform steel ring, so that every part of the ring may be
successively subjected to the magnetic force. If the operation has been
skilfully performed the ring will have no poles and will not attract
iron filings. Yet it will be magnetized; for if it is cut through and
the cut ends are drawn apart, each end will be found to exhibit
polarity. Again, a steel wire through which an electric current has been
passed will be magnetized, but so long as it is free from stress it will
give no evidence of magnetization; if, however, the wire is twisted,
poles will be developed at the two ends, for reasons which will be
explained later. A wire or rod in this condition is said to be
_circularly magnetized_; it may be regarded as consisting of an
indefinite number of elementary ring-magnets, having their axes
coincident with the axis of the wire and their planes at right angles to
it. But no magnet can have a single pole; if there is one, there must
also be at least a second, of the opposite sign and of exactly equal
strength. Let a magnetized knitting needle, having north and south poles
at the two ends respectively, be broken in the middle; each half will be
found to possess a north and a south pole, the appropriate supplementary
poles appearing at the broken ends. One of the fragments may again be
broken, and again two bipolar magnets will be produced; and the
operation may be repeated, at least in imagination, till we arrive at
molecular magnitudes and can go no farther. This experiment proves that
the condition of magnetization is not confined to those parts where
polar phenomena are exhibited, but exists throughout the whole body of
the magnet; it also suggests the idea of _molecular magnetism_, upon
which the accepted theory of magnetization is based. According to this
theory the molecules of any magnetizable substance are little permanent
magnets the axes of which are, under ordinary conditions, disposed in
all possible directions indifferently. The process of magnetization
consists in turning round the molecules by the application of magnetic
force, so that their north poles may all point more or less
approximately in the direction of the force; thus the body as a whole
becomes a magnet which is merely the resultant of an immense number of
molecular magnets.

In every magnet the strength of the south pole is exactly equal to that
of the north pole, the action of the same magnetic force upon the two
poles being equal and oppositely directed. This may be shown by means of
the uniform field of force due to the earth's magnetism. A magnet
attached to a cork and floated upon water will set itself with its axis
in the magnetic meridian, but it will be drawn neither northward nor
southward; the forces acting upon the two poles have therefore no
horizontal resultant. And again if a piece of steel is weighed in a
delicate balance before and after magnetization, no change whatever in
its weight can be detected; there is consequently no upward or downward
resultant force due to magnetization; the contrary parallel forces
acting upon the poles of the magnet are equal, constituting a couple,
which may tend to turn the body, but not to propel it.

Iron and its alloys, including the various kinds of steel, though
exhibiting magnetic phenomena in a pre-eminent degree, are not the only
substances capable of magnetization. Nickel and cobalt are also strongly
magnetic, and in 1903 the interesting discovery was made by F. Heusler
that an alloy consisting of copper, aluminium and manganese (Heusler's
alloy), possesses magnetic qualities comparable with those of iron.
Practically the metals iron, nickel and cobalt, and some of their alloys
and compounds constitute a class by themselves and are called
_ferromagnetic_ substances. But it was discovered by Faraday in 1845
that all substances, including even gases, are either attracted or
repelled by a sufficiently powerful magnetic pole. Those substances
which are attracted, or rather which tend, like iron, to move from
weaker to stronger parts of the magnetic field, are termed
_paramagnetic_; those which are repelled, or tend to move from stronger
to weaker parts of the field, are termed diamagnetic. Between the
ferromagnetics and the paramagnetics there is an enormous gap. The
maximum magnetic susceptibility of iron is half a million times greater
than that of liquid oxygen, one of the strongest paramagnetic substances
known. Bismuth, the strongest of the diamagnetics, has a negative
susceptibility which is numerically 20 times less than that of liquid
oxygen.

Many of the physical properties of a metal are affected by
magnetization. The dimensions of a piece of iron, for example, its
elasticity, its thermo-electric power and its electric conductivity are
all changed under the influence of magnetism. On the other hand, the
magnetic properties of a substance are affected by such causes as
mechanical stress and changes of temperature. An account of some of
these effects will be found in another section.[2]


2. TERMINOLOGY AND ELEMENTARY PRINCIPLES

In what follows the C.G.S. electromagnetic system of units will be
generally adopted, and, unless otherwise stated, magnetic substances
will be assumed to be _isotropic_, or to have the same physical
properties in all directions.

  _Vectors._--Physical quantities such as magnetic force, magnetic
  induction and magnetization, which have direction as well as
  magnitude, are termed vectors; they are compounded and resolved in the
  same manner as mechanical force, which is itself a vector. When the
  direction of any vector quantity denoted by a symbol is to be attended
  to, it is usual to employ for the symbol either a block letter, as H,
  I, B, or a German capital, as [H], [F], [B].[3]

  _Magnetic Poles and Magnetic Axis._--A _unit magnetic pole_ is that
  which acts on an equal pole at a distance of one centimetre with a
  force of one dyne. A pole which points north is reckoned positive, one
  which points south negative. The action between any two magnetic poles
  is mutual. If m1 and m2 are the strengths of two poles, d the distance
  between them expressed in centimetres, and f the force in dynes,

    [f] = m1m2/d²  (1).

  The force is one of attraction or repulsion, according as the sign of
  the product m1m2 is negative or positive. The poles at the ends of an
  infinitely thin uniform magnet, or _magnetic filament_, would act as
  definite centres of force. An actual magnet may generally be regarded
  as a bundle of magnetic filaments, and those portions of the surface
  of the magnet where the filaments terminate, and so-called "free
  magnetism" appears, may be conveniently called poles or polar regions.
  A more precise definition is the following: When the magnet is placed
  in a uniform field, the parallel forces acting on the positive poles
  of the constituent filaments, whether the filaments terminate outside
  the magnet or inside, have a resultant, equal to the sum of the forces
  and parallel to their direction, acting at a certain point N. The
  point N, which is the centre of the parallel forces, is called the
  _north_ or _positive pole_ of the magnet. Similarly, the forces acting
  in the opposite direction on the negative poles of the filaments have
  a resultant at another point S, which is called the _south_ or
  _negative pole_. The opposite and parallel forces acting on the poles
  are always equal, a fact which is sometimes expressed by the statement
  that the total magnetism of a magnet is zero. The line joining the two
  poles is called the _axis of the magnet_.

  _Magnetic Field._--Any space at every point of which there is a finite
  magnetic force is called a _field of magnetic force_, or a _magnetic
  field_. The _strength_ or _intensity_ of a magnetic field at any point
  is measured by the force in dynes which a unit pole will experience
  when placed at that point, the _direction_ of the field being the
  direction in which a positive pole is urged. The field-strength at any
  point is also called the _magnetic force_ at that point; it is denoted
  by H, or, when it is desired to draw attention to the fact that it is
  a vector quantity, by the block letter H, or the German character [H].
  Magnetic force is sometimes, and perhaps more suitably, termed
  _magnetic intensity_; it corresponds to the intensity of gravity g in
  the theory of heavy bodies (see Maxwell, _Electricity and Magnetism_,
  § 12 and § 68, footnote). A _line of force_ is a line drawn through a
  magnetic field in the direction of the force at each point through
  which it passes. A _uniform magnetic field_ is one in which H has
  everywhere the same value and the same direction, the lines of force
  being, therefore, straight and parallel. A magnetic field is generally
  due either to a conductor carrying an electric current or to the poles
  of a magnet. The magnetic field due to a long straight wire in which a
  current of electricity is flowing is at every point at right angles to
  the plane passing through it and through the wire; its strength at any
  point distant r centimetres from the wire is

    H = 2i/r,  (2)

  i being the current in C.G.S. units.[4] The lines of force are
  evidently circles concentric with the wire and at right angles to it;
  their direction is related to that of the current in the same manner
  as the rotation of a corkscrew is related to its thrust. The field at
  the centre of a circular conductor of radius r through which current
  is passing is

    H = 2[pi]i/r,  (3)

  the direction of the force being along the axis and related to the
  direction of the current as the thrust of a corkscrew to its rotation.
  The field strength in the interior of a long uniformly wound coil
  containing n turns of wire and having a length of l centimetres is
  (except near the ends)

    H = 4[pi]in/l.  (4)

  In the middle portion of the coil the strength of the field is very
  nearly uniform, but towards the end it diminishes, and at the ends is
  reduced to one-half. The direction of the force is parallel to the
  axis of the coil, and related to the direction of the current as the
  thrust of a corkscrew to its rotation. If the coil has the form of a
  ring of mean radius r, the length will be 2[pi]r, and the field inside
  the coil may be expressed as

    H = 2ni/r.  (5)

  The uniformity of the field is not in this case disturbed by the
  influence of ends, but its strength at any point varies inversely as
  the distance from the axis of the ring. When therefore sensible
  uniformity is desired, the radius of the ring should be large in
  relation to that of the convolutions, or the ring should have the form
  of a short cylinder with thin walls. The strongest magnetic fields
  employed for experimental purposes are obtained by the use of
  electromagnets. For many experiments the field due to the earth's
  magnetism is sufficient; this is practically quite uniform throughout
  considerable spaces, but its total intensity is less than half a unit.

  _Magnetic Moment and Magnetization._--The moment, M, M or [M], of a
  uniformly and longitudinally magnetized bar-magnet is the product of
  its length into the strength of one of its poles; it is the moment of
  the couple acting on the magnet when placed in a field of unit
  intensity with its axis perpendicular to the direction of the field.
  If l is the length of the magnet, M = ml. The action of a magnet at a
  distance which is great compared with the length of the magnet depends
  solely upon its moment; so also does the action which the magnet
  experiences when placed in a uniform field. The moment of a small
  magnet may be resolved like a force. The _intensity of magnetization_,
  or, more shortly, the _magnetization_ of a uniformly magnetized body
  is defined as the magnetic moment per unit of volume, and is denoted
  by I, I, or [I]. Hence

    I = M/v = ml/v = m/a,

  v being the volume and a the sectional area. If the magnet is not
  uniform, the magnetization at any point is the ratio of the moment of
  an element of volume at that point to the volume itself, or I =
  m·ds/dv. where ds is the length of the element. The direction of the
  magnetization is that of the magnetic axis of the element; in
  isotropic substances it coincides with the direction of the magnetic
  force at the point. If the direction of the magnetization at the
  surface of a magnet makes an angle [epsilon] with the normal, the
  normal component of the magnetization, I cos [epsilon], is called the
  _surface density_ of the magnetism, and is generally denoted by
  [sigma].

  _Potential and Magnetic Force._--The _magnetic potential_ at any point
  in a magnetic field is the work which would be done against the
  magnetic forces in bringing a unit pole to that point from the
  boundary of the field. The line through the given point along which
  the potential decreases most rapidly is the direction of the resultant
  magnetic force, and the rate of decrease of the potential in any
  direction is equal to the component of the force in that direction. If
  V denote the potential, F the resultant force, X, Y, Z, its components
  parallel to the co-ordinate axes and n the line along which the force
  is directed, then

       [delta]V        [delta]V        [delta]V/        [delta]V
     - -------- = F, - -------- = X, - --------- = Y, - -------- = Z.  (6)
       [delta]n        [delta]x        [delta]y         [delta]z

  Surfaces for which the potential is constant are called _equipotential
  surfaces_. The resultant magnetic force at every point of such a
  surface is in the direction of the normal (n) to the surface; every
  line of force therefore cuts the equipotential surfaces at right
  angles. The potential due to a single pole of strength m at the
  distance r from the pole is

    V = m/r,  (7)

  the equipotential surfaces being spheres of which the pole is the
  centre and the lines of force radii. The potential due to a thin
  magnet at a point whose distance from the two poles respectively is r
  and r´ is

    V = m(l/r = l/r´).  (8)

  When V is constant, this equation represents an equipotential surface.

  The equipotential surfaces are two series of ovoids surrounding the
  two poles respectively, and separated by a plane at zero potential
  passing perpendicularly through the middle of the axis. If r and r´
  make angles [theta] and [theta]´ with the axis, it is easily shown
  that the equation to a line of force is

    cos [theta] - cos [theta]´ = constant.  (9)

  [Illustration: FIG. 2.]

  [Illustration: FIG. 3.]

  At the point where a line of force intersects the perpendicular
  bisector of the axis r = r´ = r0, say, and cos [theta] - cos [theta]´
  obviously = l/r0, l being the distance between the poles; l/r0 is
  therefore the value of the constant in (9) for the line in question.
  Fig. 2 shows the lines of force and the plane sections of the
  equipotential surfaces for a thin magnet with poles concentrated at
  its ends. The potential due to a small magnet of moment M, at a point
  whose distance from the centre of the magnet is r, is

    V = M cos [theta]/r²,  (10)

  where [theta] is the angle between r and the axis of the magnet.
  Denoting the force at P (see fig. 3) by F, and its components parallel
  to the co-ordinate axes by X and Y, we have

          [delta]V    M
    X = - -------- = --- (3 cos² [theta] - 1),
          [delta]x   r³

          [delta]V    M
    Y = - -------- = --- (3 sin [theta] cos [theta]).  (11)
          [delta]y   r³

  If F_r is the force along r and F_t that along t at right angles to r,

                                           M
    F_r = X cos [theta] + Y sin [theta] = --- 2 cos [theta],  (12)
                                          r³

                                           M
    F_t = -X sin [theta] + Y cos [theta] = --- sin [theta],  (13)
                                           r³
  For the resultant force at P,

                              M
    F = [root](F_r² + F_t²) = --- [root](3 cos² [theta] + 1).  (14)
                              r³

  The direction of F is given by the following construction: Trisect OP
  at C, so that OC = OP/3; draw CD at right angles to OP, to cut the
  axis produced in D; then DP will be the direction of the force at P.
  For a point in the axis OX, [theta] = 0; therefore cos [theta] = 1,
  and the point D coincides with C; the magnitude of the force is, from
  (14),

    F_x = 2M/r³,  (15)

  its direction being along the axis OX. For a point in the line OY
  bisecting the magnet perpendicularly, [theta] = [pi]/2 therefore cos
  [theta] = 0, and the point D is at an infinite distance. The magnitude
  of the force is in this case

    F_y = M/r³,  (16)

  and its direction is parallel to the axis of the magnet. Although the
  above useful formulae, (10) to (15), are true only for an infinitely
  small magnet, they may be practically applied whenever the distance r
  is considerable compared with the length of the magnet.

  [Illustration: FIG. 4.]

  _Couples and Forces between Magnets._--If a small magnet of moment M
  is placed in the sensibly uniform field H due to a distant magnet, the
  couple tending to turn the small magnet upon an axis at right angles
  to the magnet and to the force is

    MH sin [theta],  (17)

  where [theta] is the angle between the axis of the magnet and the
  direction of the force. In fig. 4 S´N´ is a small magnet of moment M´,
  and SN a distant fixed magnet of moment M; the axes of SN and S´N´
  make angles of [theta] and [phi] respectively with the line through
  their middle points. It can be deduced from (17), (12) and (13) that
  the couple on S´N´ due to SN, and tending to increase [phi], is

    MM´(sin [theta] cos [phi] - 2 sin [phi] cos [theta])/r³.  (18)

  This vanishes if sin [theta] cos [phi] = 2 sin [phi] cos [theta],
  i.e. if tan [phi] = ½ tan [theta], S´N´ being then along a line of
  force, a result which explains the construction given above for
  finding the direction of the force F in (14). If the axis of SN
  produced passes through the centre of S´N´, [theta] = 0, and the
  couple becomes

    2MM´ sin [phi]/r³,  (19)

  tending to diminish [phi]; this is called the "end on" position. If
  the centre of S´N´ is on the perpendicular bisector of SN, [theta] =
  ½[pi], and the couple will be

    MM´ cos [phi]/r³,  (20)

  tending to increase [phi]; this is the "broadside on" position. These
  two positions are sometimes called the first and second (or A and B)
  principal positions of Gauss. The components X, Y, parallel and
  perpendicular to r, of the force between the two magnets SN and S´N´
  are

    X = 3MM´(sin [theta] sin [phi] - 2 cos [theta] cos [phi])/r^4,  (21)
    Y = 3MM´(sin [theta] cos [phi] + sin [phi] cos [theta])/r^4.  (22)

  It will be seen that, whereas the couple varies inversely as the cube
  of the distance, the force varies inversely as the fourth power.

  _Distributions of Magnetism._--A magnet may be regarded as consisting
  of an infinite number of elementary magnets, each having a pair of
  poles and a definite magnetic moment. If a series of such elements,
  all equally and longitudinally magnetized, were placed end to end with
  their unlike poles in contact, the external action of the filament
  thus formed would be reduced to that of the two extreme poles. The
  same would be the case if the magnetization of the filament varied
  inversely as the area of its cross-section a in different parts. Such
  a filament is called a _simple magnetic solenoid_, and the product aI
  is called the _strength_ of the solenoid. A magnet which consists
  entirely of such solenoids, having their ends either upon the surface
  or closed upon themselves, is called a _solenoidal magnet_, and the
  magnetism is said to be distributed solenoidally; there is no free
  magnetism in its interior. If the constituent solenoids are parallel
  and of equal strength, the magnet is also uniformly magnetized. A thin
  sheet of magnetic matter magnetized normally to its surface in such a
  manner that the magnetization at any place is inversely proportional
  to the thickness h of the sheet at that place is called a _magnetic
  shell_; the constant product hI is the _strength_ of the shell and is
  generally denoted by [Phi] or [phi]. The potential at any point due to
  a magnetic shell is the product of its strength into the solid angle
  [omega] subtended by its edge at the given point, or V = [Phi][omega].
  For a given strength, therefore, the potential depends solely upon the
  boundary of the shell, and the potential outside a closed shell is
  everywhere zero. A magnet which can be divided into simple magnetic
  shells, either closed or having their edges on the surface of the
  magnet, is called a _lamellar magnet_, and the magnetism is said to be
  distributed lamellarly. A magnet consisting of a series of plane
  shells of equal strength arranged at right angles to the direction of
  magnetization will be uniformly magnetized.

  It can be shown that uniform magnetization is possible only when the
  form of the body is ellipsoidal. (Maxwell, _Electricity and
  Magnetism_, II., § 437). The cases of greatest practical importance
  are those of a sphere (which is an ellipsoid with three equal axes)
  and an ovoid or prolate ellipsoid of revolution. The potential due to
  a uniformly magnetized sphere of radius a for an external point at a
  distance r from the centre is

    V = (4/3)[pi] a³I cos [theta]/r²,  (23)

  [theta] being the inclination of r to the magnetic axis. Since
  (4/3)[pi]a³I is the moment of the sphere (= volume × magnetization),
  it appears from (10) that the magnetized sphere produces the same
  external effect as a very small magnet of equal moment placed at its
  centre and magnetized in the same direction; the resultant force
  therefore is the same as in (14). The force in the interior is
  uniform, opposite to the direction of magnetization, and equal to
  (4/3)[pi]I. When it is desired to have a uniform magnet with
  definitely situated poles, it it usual to employ one having the form
  of an ovoid, or elongated ellipsoid of revolution, instead of a
  rectangular or cylindrical bar. If the magnetization is parallel to
  the major axis, and the lengths of the major and minor axes are 2a and
  2c, the poles are situated at a distance equal to (2/3)a from the
  centre, and the magnet will behave externally like a simple solenoid
  of length (4/3)a. The internal force F is opposite to the direction of
  the magnetization, and equal to NI, where N is a coefficient depending
  only on the ratio of the axes. The moment = (4/3)[pi] ac²I =
  -(4/3)[pi] ac²FN.

  The distribution of magnetism and the position of the poles in magnets
  of other shapes, such as cylindrical or rectangular bars, cannot be
  specified by any general statement, though approximate determinations
  may be obtained experimentally in individual cases.[5] According to F.
  W. G. Kohlrausch[6] the distance between the poles of a cylindrical
  magnet the length of which is from 10 to 30 times the diameter, is
  sensibly equal to five-sixths of the length of the bar. This
  statement, however, is only approximately correct, the distance
  between the poles depending upon the intensity of the
  magnetization.[7] In general, the greater the ratio of length to
  section, the more nearly will the poles approach the end of the bar,
  and the more nearly uniform will be the magnetization. For most
  practical purpose a knowledge of the exact position of the poles is of
  no importance; the magnetic moment, and therefore the mean
  magnetization, can always be determined with accuracy.

  _Magnetic Induction or Magnetic Flux._--When magnetic force acts on
  any medium, whether magnetic, diamagnetic or neutral, it produces
  within it a phenomenon of the nature of a flux or flow called
  _magnetic induction_ (Maxwell, _loc. cit._, § 428). Magnetic
  induction, like other fluxes such as electrical, thermal or fluid
  currents, is defined with reference to an area; it satisfies the same
  conditions of continuity as the electric current does, and in
  isotropic media it depends on the magnetic force just as the electric
  current depends on the electromotive force. The magnitude of the flux
  produced by a given magnetic force differs in different media. In a
  uniform magnetic field of unit intensity formed in empty space the
  induction or magnetic flux across an area of 1 square centimetre
  normal to the direction of the field is arbitrarily taken as the unit
  of induction. Hence if the induction per square centimetre at any
  point is denoted by B, then in empty space B is numerically equal to
  H; moreover in isotropic media both have the same direction, and for
  these reasons it is often said that in empty space (and practically in
  air and other non-magnetic substances) B and H are identical. Inside a
  magnetized body, B is the force that would be exerted on a unit pole
  if placed in a narrow crevasse cut in the body, the walls of the
  crevasse being perpendicular to the direction of the magnetization
  (Maxwell, § § 399, 604); and its numerical value, being partly due to
  the free magnetism on the walls, is generally very different from that
  of H. In the case of a straight uniformly magnetized bar the direction
  of the magnetic force due to the poles of the magnet is from the north
  to the south pole outside the magnet, and from the south to the north
  inside. The magnetic flux per square centimetre at any point (B, B, or
  [B]) is briefly called the _induction_, or, especially by electrical
  engineers, the _flux-density_. The direction of magnetic induction may
  be indicated by _lines of induction_; a line of induction is always a
  closed curve, though it may possibly extend to and return from
  infinity. Lines of induction drawn through every point in the contour
  of a small surface form a re-entrant tube bounded by lines of
  induction; such a tube is called a _tube of induction_. The
  cross-section of a tube of induction may vary in different parts, but
  the total induction across any section is everywhere the same. A
  special meaning has been assigned to the term "lines of induction."
  Suppose the whole space in which induction exists to be divided up
  into _unit tubes_, such that the surface integral of the induction
  over any cross-section of a tube is equal to unity, and along the axis
  of each tube let a line of induction be drawn. These axial lines
  constitute the system of lines of induction which are so often
  referred to in the specification of a field. Where the induction is
  high the lines will be crowded together; where it is weak they will be
  widely separated, the number per square centimetre crossing a normal
  surface at any point being always equal to the numerical value of B.
  The induction may therefore be specified as B lines per square
  centimetre. The direction of the induction is also of course indicated
  by the direction of the lines, which thus serve to map out space in a
  convenient manner. Lines of induction are frequently but inaccurately
  spoken of as lines of force.

  When induction or magnetic flux takes place in a ferromagnetic metal,
  the metal becomes magnetized, but the magnetization at any point is
  proportional not to B, but to B - H. The factor of proportionality
  will be 1-4[pi], so that

    I = (B - H)/4[pi],  (24)

  or

    B = H + 4[pi] I.  (25)

  Unless the path of the induction is entirely inside the metal, free
  magnetic poles are developed at those parts of the metal where
  induction enters and leaves, the polarity being south at the entry and
  north at the exit of the flux. These free poles produce a magnetic
  field which is superposed upon that arising from other sources. The
  _resultant magnetic field_, therefore, is compounded of two fields,
  the one being due to the poles, and the other to the external causes
  which would be operative in the absence of the magnetized metal. The
  intensity (at any point) of the field due to the magnetization may be
  denoted by H_i, that of the external field by H0, and that of the
  resultant field by H. In certain cases, as, for instance, in an iron
  ring wrapped uniformly round with a coil of wire through which a
  current is passing, the induction is entirely within the metal; there
  are, consequently, no free poles, and the ring, though magnetized,
  constitutes a poleless magnet. Magnetization is usually regarded as
  the direct effect of the resultant magnetic force, which is therefore
  often termed the _magnetizing force_.

  _Permeability and Susceptibility._--The ratio B/H is called the
  _permeability_ of the medium in which the induction is taking place,
  and is denoted by µ. The ratio I/H is called the _susceptibility_ of
  the magnetized substance, and is denoted by [kappa]. Hence

    B = µH and I = [kappa]H.  (26)

  Also

         B    H + 4[pi]I
    µ = --- = ---------- = 1 + 4[pi][kappa],  (27)
         H        H

  and

              µ - 1
    [kappa] = -----  (28)
              4[pi]

  Since in empty space B has been assumed to be numerically equal to H,
  it follows that the permeability of a vacuum is equal to 1. The
  permeability of most material substances differs very slightly from
  unity, being a little greater than 1 in paramagnetic and a little less
  in diamagnetic substances. In the case of the ferromagnetic metals and
  some of their alloys and compounds, the permeability has generally a
  much higher value. Moreover, it is not constant, being an apparently
  arbitrary function of H or of B; in the same specimen its value may,
  under different conditions, vary from less than 2 to upwards of 5000.
  The magnetic susceptibility [kappa] expresses the numerical relation
  of the magnetization to the magnetizing force. From the equation
  [kappa] = (µ - 1)/4[pi], it follows that the magnetic susceptibility
  of a vacuum (where µ = l) is 0, that of a diamagnetic substance (where
  µ < l) has a negative value, while the susceptibility of paramagnetic
  and ferromagnetic substances (for which µ > 1) is positive. No
  substance has yet been discovered having a negative susceptibility
  sufficiently great to render the permeability (= 1 + 4[pi][kappa])
  negative.

  _Magnetic Circuit._--The circulation of magnetic induction or flux
  through magnetic and non-magnetic substances, such as iron and air, is
  in many respects analogous to that of an electric current through good
  and bad conductors. Just as the lines of flow of an electric current
  all pass in closed curves through the battery or other generator, so
  do all the lines of induction pass in closed curves through the magnet
  or magnetizing coil. The total magnetic induction or flux corresponds
  to the current of electricity (practically measured in amperes); the
  induction or flux density B to the density of the current (number of
  amperes to the square centimetre of section); the magnetic
  permeability to the specific electric conductivity; and the line
  integral of the magnetic force, sometimes called the magneto-motive
  force, to the electromotive force in the circuit. The principal points
  of difference are that (1) the magnetic permeability, unlike the
  electric conductivity, which is independent of the strength of the
  current, is not in general constant; (2) there is no perfect insulator
  for magnetic induction, which will pass more or less freely through
  all known substances. Nevertheless, many important problems relating
  to the distribution of magnetic induction may be solved by methods
  similar to those employed for the solution of analogous problems in
  electricity. For the elementary theory of the magnetic circuit see
  ELECTRO-MAGNETISM.

  _Hysteresis, Coercive Force, Retentiveness._--It is found that when a
  piece of ferromagnetic metal, such as iron, is subjected to a magnetic
  field of changing intensity, the changes which take place in the
  induced magnetization of the iron exhibit a tendency to lag behind
  those which occur in the intensity of the field--a phenomenon to which
  J. A. Ewing (_Phil. Trans._ clxxvi. 524) has given the name of
  _hysteresis_ (Gr. [Greek: hystereô], to lag behind). Thus it happens
  that there is no definite relation between the magnetization of a
  piece of metal which has been previously magnetized and the strength
  of the field in which it is placed. Much depends upon its antecedent
  magnetic condition, and indeed upon its whole magnetic history. A
  well-known example of hysteresis is presented by the case of permanent
  magnets. If a bar of hard steel is placed in a strong magnetic field,
  a certain intensity of magnetization is induced in the bar; but when
  the strength of the field is afterwards reduced to zero, the
  magnetization does not entirely disappear. That portion which is
  permanently retained, and which may amount to considerably more than
  one-half, is called the _residual magnetization_. The ratio of the
  residual magnetization to its previous maximum value measures the
  _retentiveness_, or _retentivity_, of the metal.[8] Steel, which is
  well suited for the construction of permanent magnets, is said to
  possess great "coercive force." To this term, which had long been used
  in a loose and indefinite manner, J. Hopkinson supplied a precise
  meaning (_Phil. Trans._ clxxvi. 460). The _coercive force_, or
  _coercivity_, of a material is that reversed magnetic force which,
  while it is acting, just suffices to reduce the residual induction to
  nothing after the material has been temporarily submitted to any great
  magnetizing force. A metal which has great retentiveness may at the
  same time have small coercive force, and it is the latter quality
  which is of chief importance in permanent magnets.

  _Demagnetizing Force._--It has already been mentioned that when a
  ferromagnetic body is placed in a magnetic field, the resultant
  magnetic force H, at a point within the body, is compounded of the
  force H0, due to the external field, and of another force, H_i,
  arising from the induced magnetization of the body. Since H_i
  generally tends to oppose the external force, thus making H less than
  H0, it may be called the _demagnetizing force_. Except in the few
  special cases when a uniform external field produces uniform
  magnetization, the value of the demagnetizing force cannot be
  calculated, and an exact determination of the actual magnetic force
  within the body is therefore impossible. An important instance in
  which the calculation can be made is that of an elongated _ellipsoid
  of revolution_ placed in a uniform field H0, with its axis of
  revolution parallel to the lines of force. The magnetization at any
  point inside the ellipsoid will then be

          [kappa]H0
    I = ------------  (29)
        1 + [kappa]N

  where

              / 1     \   / 1      1 + e \
    N = 4[pi]( --- - 1 ) ( --- log -----  ),
              \ e2    /   \ 2e     1 - e /

  e being the eccentricity (see Maxwell's _Treatise_, § 438). Since I =
  [kappa]H, we have

    [kappa]H + [kappa]NI = [kappa]H0,  (30)

  or

    H = H0 - NI,

  NI being the demagnetizing force H_i. N may be called, after H. du
  Bois (_Magnetic Circuit_, p. 33), the _demagnetizing factor_, and the
  ratio of the length of the ellipsoid 2c to its equatorial diameter 2a
  (= c/a), the _dimensional ratio_, denoted by the symbol [m].

  Since  e = [root](1 - a²/c²) = [root](1 - 1/[m]²),

  the above expression for N may be written

          4[pi]   /        [m]             [m] + [root]([m]² - 1)    \
    N = -------- (  ------------------ log ---------------------- - 1 )
        [m]² - 1  \ 2 [root]([m]² - 1)     [m] - [root]([m]² - 1)    /
                _                                                    _
        4[pi]  |        [m]             /                      \      |
    = -------- |  ---------------- log ( [m] + [root]([m]² - 1) ) - 1 |,
      [m]² - 1 |_ [root]([m]² - 1)      \                      /     _|

  from which the value of N for a given dimensional ratio can be
  calculated. When the ellipsoid is so much elongated that 1 is
  negligible in relation to [m]², the expression approximates to the
  simpler form

        4[pi]
    N = ----- (log 2[m] - 1).  (31)
         [m]²

  In the case of a _sphere_, e = O and N = (4/3)[pi]; therefore from
  (29)

                        [kappa]H0             3[kappa]
    I = [kappa]H = -------------------- = ---------------- H0,  (32)
                   1 + (4/3)[pi][kappa]   3 + 4[pi][kappa]

  Whence

                3               3
    H = ---------------- H0 = ----- H0,  (33)
        3 + 4[pi][kappa]      µ + 2

  and

              3µ
    B = µH = ----- H0.  (34)
             µ + 2

  Equations (33) and (34) show that when, as is generally the case with
  ferromagnetic substances, the value of µ is considerable, the
  resultant magnetic force is only a small fraction of the external
  force, while the numerical value of the induction is approximately
  three times that of the external force, and nearly independent of the
  permeability. The demagnetizing force inside a _cylindrical rod_
  placed longitudinally in a uniform field H0 is not uniform, being
  greatest at the ends and least in the middle part. Denoting its mean
  value by [H]_i, and that of the demagnetizing factor by [N], we have

    H = H0 - [H]_i = H0 - [N]I.  (35)

  Du Bois has shown that when the dimensional ratio [m] (=
  length/diameter) exceeds 100, [N][m]² = constant = 45, and hence for
  long thin rods

    [N] = 45/[m]².  (36)

  From an analysis of a number of experiments made with rods of
  different dimensions H. du Bois has deduced the corresponding mean
  demagnetizing factors. These, together with values of [m]²[N] for
  cylindrical rods, and of N and [m]²N for ellipsoids of revolution, are
  given in the following useful table (_loc. cit._ p. 41):--

  _Demagnetizing Factors._

    +------+--------------------+-------------------+
    |      |      Cylinder.     |     Ellipsoid.    |
    | [m]. +----------+---------+----------+--------+
    |      |    [N].  | [m]²[N].|    N.    | [m]²N. |
    +------+----------+---------+----------+--------+
    |    0 | 12.5664  |    0    | 12.5664  |     0  |
    |  0.5 |   --     |   --    |  6.5864  |   --   |
    |    1 |   --     |   --    |  4.1888  |   --   |
    |    5 |   --     |   --    |  0.7015  |   --   |
    |   10 |  0.2160  |  21.6   |  0.2549  |  25.5  |
    |   15 |  0.1206  |  27.1   |  0.1350  |  30.5  |
    |   20 |  0.0775  |  31.0   |  0.0848  |  34.0  |
    |   25 |  0.0533  |  33.4   |  0.0579  |  36.2  |
    |   30 |  0.0393  |  35.4   |  0.0432  |  38.8  |
    |   40 |  0.0238  |  38.7   |  0.0266  |  42.5  |
    |   50 |  0.0162  |  40.5   |  0.0181  |  45.3  |
    |   60 |  0.0118  |  42.4   |  0.0132  |  47.5  |
    |   70 |  0.0089  |  43.7   |  0.0101  |  49.5  |
    |   80 |  0.0069  |  44.4   |  0.0080  |  51.2  |
    |   90 |  0.0055  |  44.8   |  0.0065  |  52.5  |
    |  100 |  0.0045  |  45.0   |  0.0054  |  54.0  |
    |  150 |  0.0020  |  45.0   |  0.0026  |  58.3  |
    |  200 |  0.0011  |  45.0   |  0.0016  |  64.0  |
    |  300 |  0.00050 |  45.0   |  0.00075 |  67.5  |
    |  400 |  0.00028 |  45.0   |  0.00045 |  72.0  |
    |  500 |  0.00018 |  45.0   |  0.00030 |  75.0  |
    | 1000 |  0.00005 |  45.0   |  0.00008 |  80.0  |
    +------+--------------------+-------------------+

  In the middle part of a rod which has a length of 400 or 500 diameters
  the effect of the ends is insensible; but for many experiments the
  condition of endlessness may be best secured by giving the metal the
  shape of a ring of uniform section, the magnetic field being produced
  by an electric current through a coil of wire evenly wound round the
  ring. In such cases H_i = 0 and H = H0.

  The residual magnetization I_r retained by a bar of ferromagnetic
  metal after it has been removed from the influence of an external
  field produces a demagnetizing force [N]I_r, which is greater the
  smaller the dimensional ratio. Hence the difficulty of imparting any
  considerable permanent magnetization to a short thick bar not
  possessed of great coercive force. The magnetization retained by a
  long thin rod, even when its coercive force is small, is sometimes
  little less than that which was produced by the direct action of the
  field.

  _Demagnetization by Reversals._--In the course of an experiment it is
  often desired to eliminate the effects of previous magnetization, and,
  as far as possible, wipe out the magnetic history of a specimen. In
  order to attain this result it was formerly the practice to raise the
  metal to a bright red heat, and allow it to cool while carefully
  guarded from magnetic influence. This operation, besides being very
  troublesome, was open to the objection that it was almost sure to
  produce a material but uncertain change in the physical constitution
  of the metal, so that, in fact, the results of experiments made before
  and after the treatment were not comparable. Ewing introduced the
  method (_Phil. Trans._ clxxvi. 539) of demagnetizing a specimen by
  subjecting it to a succession of magnetic forces which alternated in
  direction and gradually diminished in strength from a high value to
  zero. By means of a simple arrangement, which will be described
  farther on, this process can be carried out in a few seconds, and the
  metal can be brought as often as desired to a definite condition,
  which, if not quite identical with the virgin state, at least closely
  approximates to it.

  _Forces acting on a Small Body in the Magnetic Field._--If a small
  magnet of length ds and pole-strength m is brought into a magnetic
  field such that the values of the magnetic potential at the negative
  and positive poles respectively are V1 and V2, the work done upon the
  magnet, and therefore its potential energy, will be

    W = m(V2 - V1) = m dV,

  which may be written

             dV     dV
    W = m ds -- = M -- = -MH0 = -vIH0,
             ds     ds

  where M is the moment of the magnet, v the volume, I the
  magnetization, and H0 the magnetic force along _ds_. The small magnet
  may be a sphere rigidly magnetized in the direction of H0; if this is
  replaced by an isotropic sphere inductively magnetized by the field,
  then, for a displacement so small that the magnetization of the sphere
  may be regarded as unchanged, we shall have

                            [kappa]
    dW = -vI dH0 = -v -------------------- H0 dH0;
                      1 + (4/3)[pi][kappa]

  whence

           v       [kappa]
    W = - --- -------------------- H^2_0.  (37)
           2  1 + (4/3)[pi][kappa]

  The mechanical force acting on the sphere in the direction of
  displacement x is

          dW           [kappa]        dH^2_0
    F = - -- = v -------------------- ------.  (38)
          dx     1 + (4/3)[pi][kappa]   dx

  If H0 is constant, the force will be zero; if H0 is variable, the
  sphere will tend to move in the direction in which H0 varies most
  rapidly. The coefficient [kappa]/(1 + (4/3)[pi][kappa]) is positive
  for ferromagnetic and paramagnetic substances, which will therefore
  tend to move from weaker to stronger parts of the field; for all known
  diamagnetic substances it is negative, and these will tend to move
  from stronger to weaker parts. For small bodies other than spheres the
  coefficient will be different, but its sign will always be negative
  for diamagnetic substances and positive for others;[9] hence the
  forces acting on any small body will be in the same directions as in
  the case of a sphere.[10]

  _Directing Couple acting on an Elongated Body._--In a non-uniform
  field every volume-element of the body tends to move towards regions
  of greater or less force according as the substance is paramagnetic or
  diamagnetic, and the behaviour of the whole mass will be determined
  chiefly by the tendency of its constituent elements. For this reason a
  thin bar suspended at its centre of gravity between a pair of magnetic
  poles will, if paramagnetic, set itself along the line joining the
  poles, where the field is strongest, and if diamagnetic, transversely
  to the line. These are the "axial" and "equatorial" positions of
  Faraday. It can be shown[11] that in a uniform field an elongated
  piece of any non-crystalline material is in stable equilibrium only
  when its length is parallel to the lines of force; for diamagnetic
  substances, however, the directing couple is exceedingly small, and it
  would hardly be possible to obtain a uniform field of sufficient
  strength to show the effect experimentally.

  _Relative Magnetization._--A substance of which the real
  susceptibility is [kappa] will, when surrounded by a medium having the
  susceptibility [kappa]´, behave towards a magnet as if its
  susceptibility were [kappa]_a = ([kappa] - [kappa]´)/(1 +
  4[pi][kappa]´). Since 1 + 4[pi][kappa]´ can never be negative, the
  apparent susceptibility [kappa]_a will be positive or negative
  according as [kappa] is greater or less than [kappa]´. Thus, for
  example, a tube containing a weak solution of an iron salt will appear
  to be diamagnetic if it is immersed in a stronger solution of iron,
  though in air it is paramagnetic.[12]

  _Circular Magnetization._--An electric current i flowing uniformly
  through a cylindrical wire whose radius is a produces inside the wire
  a magnetic field of which the lines of force are concentric circles
  around the axis of the wire. At a point whose distance from the axis
  of the wire is r the tangential magnetic force is

    H = 2ir/a²  (39)

  it therefore varies directly as the distance from the axis, where it
  is zero.[13] If the wire consists of a ferromagnetic metal, it will
  become "circularly" magnetized by the field, the lines of
  magnetization being, like the lines of force, concentric circles. So
  long as the wire (supposed isotropic) is free from torsional stress,
  there will be no external evidence of magnetism.

  _Magnetic Shielding._--The action of a hollow magnetized shell on a
  point inside it is always opposed to that of the external magnetizing
  force,[14] the resultant interior field being therefore weaker than
  the field outside. Hence any apparatus, such as a galvanometer, may be
  partially shielded from extraneous magnetic action by enclosing it in
  an iron case. If a hollow sphere[15] of which the outer radius is R
  and the inner radius r is placed in a uniform field H0, the field
  inside will also be uniform and in the same direction as H0, and its
  value will be approximately

                       H0
    H_i = ----------------------------  (40)
          1 + (2/9)(µ - 2) (1 - r³/R³)

  For a cylinder placed with its axis at right angles to the lines of
  force,

                     H0
    H_i = ------------------------  (41)
          1 + ¼(µ - 2) (1 - r²/R²)

  These expressions show that the thicker the screen and the greater its
  permeability µ, the more effectual will be the shielding action. Since
  µ can never be infinite, complete shielding is not possible.

  _Magneto-Crystallic Phenomenon._--In anisotropic bodies, such as
  crystals, the direction of the magnetization does not in general
  coincide with that of the magnetic force. There are, however, always
  three _principal axes_ at right angles to one another along which the
  magnetization and the force have the same direction. If each of these
  axes successively is placed parallel to the lines of force in a
  uniform field H, we shall have

    I1 = [kappa]1H, I2 = [kappa]2H, I3 = [kappa]3H,

  the three susceptibilities [kappa] being in general unequal, though in
  some cases two of them may have the same value. For crystalline bodies
  the value of [kappa] (+ or -) is nearly always small and constant, the
  magnetization being therefore independent of the form of the body and
  proportional to the force. Hence, whatever the position of the body,
  if the field be resolved into three components parallel to the
  principal axes of the crystal, the actual magnetization will be the
  resultant of the three magnetizations along the axes. The body (or
  each element of it) will tend to set itself with its axis of greatest
  susceptibility parallel to the lines of force, while, if the field is
  not uniform, each volume-element will also tend to move towards places
  of greater or smaller force (according as the substance is
  paramagnetic or diamagnetic), the tendency being a maximum when the
  axis of greatest susceptibility is parallel to the field, and a
  minimum when it is perpendicular to it. The phenomena may therefore be
  exceedingly complicated.[16]


3. MAGNETIC MEASUREMENTS

_Magnetic Moment._--The moment M of a magnet may be determined in many
ways,[17] the most accurate being that of C. F. Gauss, which gives the
value not only of M, but also that of H, the horizontal component of the
earth's force. The product MH is first determined by suspending the
magnet horizontally, and causing it to vibrate in small arcs. If A is
the moment of inertia of the magnet, and t the time of a complete
vibration, MH = 4[pi]²A/t² (torsion being neglected). The ratio M/H is
then found by one of the magnetometric methods which in their simplest
forms are described below. Equation (44) shows that as a first
approximation.

  M/H = (d² - l²) tan [theta]/2d,

where l is half the length of the magnet, which is placed in the
"broadside-on" position as regards a small suspended magnetic needle, d
the distance between the centre of the magnet and the needle, and
[theta] the angle through which the needle is deflected by the magnet.
We get therefore

  M² = MH × M/H = 2[pi]²A(d² - l²)² tan [theta]/t²d  (42)

  H² = MH × H/M = 8[pi]²Ad/{t²(d² - l²)² tan [theta]}  (43)

When a high degree of accuracy is required, the experiments and
calculations are less simple, and various corrections are applied. The
moment of a magnet may also be deduced from a measurement of the couple
exerted on the magnet by a uniform field H. Thus if the magnet is
suspended horizontally by a fine wire, which, when the magnetic axis
points north and south, is free from torsion, and if [theta] is the
angle through which the upper end of the wire must be twisted to make
the magnet point east and west, then MH = C[theta], or M = C[theta]/H,
where C is the torsional couple for 1°. A bifilar suspension is
sometimes used instead of a single wire. If P is the weight of the
magnet, l the length of each of the two threads, 2a the distance between
their upper points of attachment, and 2b that between the lower points,
then, approximately, MH = P(ab/l) sin [theta]. It is often sufficient to
find the ratio of the moment of one magnet to that of another. If two
magnets having moments M, M´ are arranged at right angles to each other
upon a horizontal support which is free to rotate, their resultant R
will set itself in the magnetic meridian. Let [theta] be the angle which
the standard magnet M makes with the meridian, then M´/R = sin [theta],
and M/R = cos [theta], whence M´ = M tan [theta].

[Illustration: FIG. 5.]

A convenient and rapid method of estimating a magnetic moment has been
devised by H. Armagnat.[18] The magnet is laid on a table with its north
pole pointing northwards, A compass having a very short needle is placed
on the line which bisects the axis of the magnet at right angles, and is
moved until a neutral point is found where the force due to the earth's
field H is balanced by that due to the magnet. If 2l is the distance
between the poles m and -m, d the distance from either pole to a point P
on the line AB (fig. 5), we have for the resultant force at P

  R = -2 cos [theta] × m/d² = -2lm/d³ = -M/d³.

When P is the neutral point, H is equal and opposite to R; therefore M =
Hd³, or the moment is numerically equal to the cube of the distance from
the neutral point to a pole, multiplied by the horizontal intensity of
the earth's force. The distance between the poles may with sufficient
accuracy for a rough determination be assumed to be equal to five-sixths
of the length of the magnet.

_Measurement of Magnetization and Induction._--The magnetic condition
assumed by a piece of ferromagnetic metal in different circumstances is
determinable by various modes of experiment which may be classed as
magnetometric, ballistic, and traction methods. When either the
magnetization I or the induction B corresponding to a given magnetizing
force H is known, the other may be found by means of the formula B =
4[pi]I + H.

_Magnetometric Methods._--Intensity of magnetization is most directly
measured by observing the action which a magnetized body, generally a
long straight rod, exerts upon a small magnetic needle placed near it.
The magnetic needle may be cemented horizontally across the back of a
little plane or concave mirror, about ¼ or 3/8 in. in diameter, which is
suspended by a single fibre of unspun silk; this arrangement, when
enclosed in a case with a glazed front to protect it from currents of
air, constitutes a simple but efficient magnetometer. Deflections of the
suspended needle are indicated by the movement of a narrow beam of light
which the mirror reflects from a lamp and focusses upon a graduated
cardboard scale placed at a distance of a few feet; the angular
deflection of the beam of light is, of course, twice that of the needle.
The suspended needle is, in the absence of disturbing causes, directed
solely by the horizontal component of the earth's field of magnetic
force H_E, and therefore sets itself approximately north and south. The
magnetized body which is to be tested should be placed in such a
position that the force H_P due to its poles may, at the spot occupied
by the suspended needle, act in a direction at right angles to that due
to the earth--that is, east and west. The direction of the resultant
field of force will then make, with that of H_E, an angle [theta], such
that H_p/H_E = tan [theta], and the suspended needle will be deflected
through the same angle. We have therefore

  H_P = H_E tan [theta].

The angle [theta] is indicated by the position of the spot of light upon
the scale, and the horizontal intensity of the earth's field H_E is
known; thus we can at once determine the value of H_P, from which the
magnetization I of the body under test may be calculated.

  In order to fulfil the requirement that the field which a magnetized
  rod produces at the magnetometer shall be at right angles to that of
  the earth, the rod may be conveniently placed in any one of three
  different positions with regard to the suspended needle.


  [Illustration: FIG. 6.]

  (1) The rod is set in a horizontal position level with the suspended
  needle, its axis being in a line which is perpendicular to the
  magnetic meridian, and which passes through the centre of suspension
  of the needle. This is called the "end-on" position, and is indicated
  in fig. 6. AB is the rod and C the middle point of its axis; NS is the
  magnetometer needle; AM bisects the undeflected needle NS at right
  angles. Let 2l = the length of the rod (or, more accurately, the
  distance between its poles), v = its volume, m and -m the strength of
  its poles, and let d = the distance CM. For most ordinary purposes the
  length of the needle may be assumed to be negligible in comparison
  with the distance between the needle and the rod. We then have
  approximately for the field at M due to the rod

             m          m            4dl
    H_P = -------- - -------- = m ----------.
          (d - l)²   (d + l)²     (d² - l²)²

  Therefore

              (d² - l²)²H_P   (d² - l²)² H_E tan [theta]
    2ml = M = ------------- = --------------------------.  (44)
                    2d                    2d

  And

         M    (d² - l²)²H_E
    I = --- = ------------- tan [theta],  (45)
         v         2dv

  whence we can find the values of I which correspond to different
  angles of deflection.

  (2) The rod may be placed horizontally east and west in such a
  position that the direction of the undeflected suspended needle
  bisects it at right angles. This is known as the "broadside-on"
  position, and is represented in fig. 7. Let the distance of each pole
  of the rod AB from the centre of the magnetometer needle = d. Then,
  since H_P, the force at M due to m and -m, is the resultant of m/d²
  and -m/d², we have

    H_P   2l
    --- = ---
     m     d

  or

          2ml
    H_P = ---,
           d³

  the direction being parallel to AB.

  And


         d³ H_P   d³ H_E
    I =  ------ = ------ tan [theta].  (46)
           v         v

  [Illustration: FIG. 7.]

  [Illustration: FIG. 8.]

  (3) In the third position the test rod is placed vertically with one
  of its poles at the level of the magnetometer needle, and in the line
  drawn perpendicularly to the undeflected needle from its centre of
  suspension. The arrangement is shown in fig. 8, where AB is the
  vertical rod and M indicates the position of the magnetometer needle,
  which is supposed to be perpendicular to the plane of the paper.
  Denoting the distance AM by d1, BM by d2, and AB by l, we have for the
  force at M due to the magnetism of the rod

           m                             m
    H_P = --- - horizontal component of ---
          d1²                           d2²

         /  1    d1  \
    = m (  --- - ---  ).
         \ d1²   d2³ /

  Therefore

           H_P          d1² H_E
    m = ---------  =  ------------ tan [theta],
         1    d1           / d1 \³
        --- - ---     1 - ( ---- )
        d1²   d2³          \ d2 /

  and

             ld1²H_E
    I = ------------------ tan [theta].  (47)
          {      / d1 \³ }
        v { 1 - ( ---- ) }
          {      \ d2 /  }

  This last method of arrangement is called by Ewing the "one-pole"
  method, because the magnetometer deflection is mainly caused by the
  upper pole of the rod (_Magnetic Induction_, p. 40). For experiments
  with long thin rods or wires it has an advantage over the other
  arrangements in that the position of the poles need not be known with
  great accuracy, a small upward or downward displacement having little
  effect upon the magnetometer deflection. On the other hand, a
  vertically placed rod is subject to the inconvenience that it is
  influenced by the earth's magnetic field, which is not the case when
  the rod is horizontal and at right angles to the magnetic meridian.
  This extraneous influence may, however, be eliminated by surrounding
  the rod with a coil of wire carrying a current such as will produce in
  the interior a magnetic field equal and opposite to the vertical
  component of the earth's field.

  If the cardboard scale upon which the beam of light is reflected by
  the magnetometer mirror is a flat one, the deflections as indicated by
  the movement of the spot of light are related to the actual
  deflections of the needle in the ratio of tan 2[theta] to [theta].
  Since [theta] is always small, sufficiently accurate results may
  generally be obtained if we assume that tan 2[theta] = 2 tan [theta].
  If the distance of the mirror from the scale is equal to n scale
  divisions, and if a deflection [theta] of the needle causes the
  reflected spot of light to move over s scale divisions, we shall have

    s/n = tan 2[theta] exactly,

    s/2n = tan [theta] approximately.

  We may therefore generally substitute s/2n for tan [theta] in the
  various expressions which have been given for I.

  Of the three methods which have been described, the first two are
  generally the most suitable for determining the moment or the
  magnetization of a permanent magnet, and the last for studying the
  changes which occur in the magnetization of a long rod or wire when
  subjected to various external magnetic forces, or, in other words, for
  determining the relation of I to H. A plan of the apparatus as
  arranged by Ewing for the latter purpose is shown diagrammatically in
  fig. 9. The cardboard scale SS is placed above a wooden screen, having
  in it a narrow vertical slit which permits a beam of light from the
  lamp L to reach the mirror of the magnetometer M, whence it is
  reflected upon the scale. A is the upper end of a glass tube, half a
  metre or so in length, which is clamped in a vertical position behind
  the magnetometer. The tube is wound over its whole length with two
  separate coils of insulated wire, the one being outside the other. The
  inner coil is supplied, through the intervening apparatus, with
  current from the battery of secondary cells B1; this produces the
  desired magnetic field inside the tube. The outer coil derives
  current, through an adjustable resistance R, from a constant cell B2;
  its object is to produce inside the tube a magnetic field equal and
  opposite to that due to the earth's magnetism. C is a "compensating
  coil" consisting of a few turns of wire through which the magnetizing
  current passes; it serves to neutralize the effect produced upon the
  magnetometer by the magnetizing coil, and its distance from the
  magnetometer is so adjusted that when the circuit is closed, no
  ferromagnetic metal being inside the magnetizing coil, the
  magnetometer needle undergoes no deflection. K is a commutator for
  reversing the direction of the magnetizing current, and G a
  galvanometer for measuring it. The strength of the magnetizing current
  is regulated by adjusting the position of the sliding contact E upon
  the resistance DF. The current increases to a maximum as E approaches
  F, and diminishes to almost nothing when E is brought up to D; it can
  be completely interrupted by means of the switch H.

  [Illustration: FIG. 9.]

  The specimen upon which an experiment is to be made generally consists
  of a wire having a "dimensional ratio" of at least 300 or 400; its
  length should be rather less than that of the magnetizing coil, in
  order that the field H0, to which it is subjected, may be
  approximately uniform from end to end. The wire is supported inside
  the glass tube A with its upper pole at the same height as the
  magnetometer needle. Various currents are then passed through the
  magnetizing coil, the galvanometer readings and the simultaneous
  magnetometer deflections being noted. From the former we deduce H0,
  and from the latter the corresponding value of I, using the formulae
  H0 = 4[pi]in/l and

               d1² H_E
    I = ----------------------- × s,  (48)
        2n[pi]r² {1 - (d1/d2)³}

  where s is the deflection in scale-divisions, n the distance in
  scale-divisions between the scale and the mirror, and r the radius of
  the wire.

  [Illustration: FIG. 10.]

  The curve, fig. 10, shows the result of a typical experiment made upon
  a piece of soft iron (Ewing, _Phil. Trans._ vol. clxxvi. Plate 59),
  the magnetizing field H0 being first gradually increased and then
  diminished to zero. When the length of the wire exceeds 400 diameters,
  or thereabouts, H0 may generally be considered as equivalent to H, the
  actual strength of the field as modified by the magnetization of the
  wire; but if greater accuracy is desired, the value of H_i (= NI) may
  be found by the help of du Bois's table and subtracted from H0. For a
  dimensional ratio of 400, N =0.00028, and therefore H = H0 - 0.00028I.
  This correction may be indicated in the diagram by a straight line
  drawn from 0 through the point at which the line of I = 1000
  intersects that of H = 0.28 (Rayleigh, Phil. Mag. xxii. 175), the true
  value of H for any point on the curve being that measured from the
  sloping line instead of from the vertical axis. The effect of the ends
  of the wire is, as Ewing remarks, to shear the diagram in the
  horizontal direction through the angle which the sloping line makes
  with the vertical.

  Since the induction B is equal to H + 4[pi]I, it is easy from the
  results of experiments such as that just described to deduce the
  relation between B and H; a curve indicating such relation is called a
  curve of induction. The general character of curves of magnetization
  and of induction will be discussed later. A notable feature in both
  classes of curves is that, owing to hysteresis, the ascending and
  descending limbs do not coincide, but follow very different courses.
  If it is desired to annihilate the hysteretic effects of previous
  magnetization and restore the metal to its original condition, it may
  be demagnetized by reversals. This is effected by slowly moving the
  sliding contact E (fig. 9) from F to D, while at the same time the
  commutator K is rapidly worked, a series of alternating currents of
  gradually diminishing strength being thus caused to pass through the
  magnetizing coil.

The magnetometric method, except when employed in connexion with
ellipsoids, for which the demagnetizing factors are accurately known,
is generally less satisfactory for the exact determination of induction
or magnetization than the ballistic method. But for much important
experimental work it is better adapted than any other, and is indeed
sometimes the only method possible.[19]

_Ballistic Methods._--The so-called "ballistic" method of measuring
induction is based upon the fact that a change of the induction through
a closed linear conductor sets up in the conductor an electromotive
force which is proportional to the rate of change. If the conductor
consists of a coil of wire the ends of which are connected with a
suitable galvanometer, the integral electromotive force due to a sudden
increase or decrease of the induction through the coil displaces in the
circuit a quantity of electricity Q = [delta]BnsR, where [delta]B is the
increment or decrement of induction per square centimetre, s is the area
of the coil, n the number of turns of wire, and R the resistance of the
circuit. Under the influence of the transient current, the galvanometer
needle undergoes a momentary deflection, or "throw," which is
proportional to Q, and therefore to [delta]B, and thus, if we know the
deflection produced by the discharge through the galvanometer of a given
quantity of electricity, we have the means of determining the value of
[delta]B.

  The galvanometer which is used for ballistic observations should have
  a somewhat heavy needle with a period of vibration of not less than
  five seconds, so that the transient current may have ceased before the
  swing has well begun; an instrument of the d'Arsonval form is
  recommended, not only because it is unaffected by outside magnetic
  influence, but also because the moving part can be instantly brought
  to rest by means of a short-circuit key, thus effecting a great saving
  of time when a series of observations is being made. In practice it is
  usual to standardize or "calibrate" the galvanometer by causing a
  known change of induction to take place within a standard coil
  connected with it, and noting the corresponding deflection on the
  galvanometer scale. Let s be the area of a single turn of the standard
  coil, n the number of its turns, and r the resistance of the circuit
  of which the coil forms part; and let S, N and R be the corresponding
  constants for a coil which is to be used in an experiment. Then if a
  known change of induction [delta]B_a inside the standard coil is found
  to cause a throw of d scale-divisions, any change of induction
  [delta]B through the experimental coil will be numerically equal to
  the corresponding throw D multiplied by snRB_a/SNrd. For a series of
  experiments made with the same coil this fraction is constant, and we
  may write [delta]B = kD. Rowland and others have used an earth coil
  for calibrating the galvanometer, a known change of induction through
  the coil being produced by turning it over in the earth's magnetic
  field, but for several reasons it is preferable to employ an electric
  current as the source of a known induction. A primary coil of length
  l, having n turns, is wound upon a cylinder made of non-conducting and
  non-magnetic material, and upon the middle of the primary a secondary
  or induction coil is closely fitted. When a current of strength i is
  suddenly interrupted in the primary, the increment of induction
  through the secondary is sensibly equal to 4[pi]in/l units. All the
  data required for standardizing the galvanometer can in this way be
  determined with accuracy.

The ballistic method is largely employed for determining the relation of
induction to magnetizing force in samples of the iron and steel used in
the manufacture of electrical machinery, and especially for the
observation of hysteresis effects. The sample may have the form of a
closed ring, upon which are wound the induction coil and another coil
for taking the magnetizing current; or it may consist of a long straight
rod or wire which can be slipped into a magnetizing coil such as is used
in magnetometric experiments, the induction coil being wound upon the
middle of the wire. With these arrangements there is no demagnetizing
force to be considered, for the ring has not any ends to produce one,
and the force due to the ends of a rod 400 or 500 diameters in length is
quite insensible at the middle portion; H therefore is equal to H0.

  E. Grassot has devised a galvanometer, or "fluxmeter," which greatly
  alleviates the tedious operation of taking ballistic readings.[20] The
  instrument is of the d'Arsonval type; its coil turns in a strong
  uniform field, and is suspended in such a manner that torsion is
  practically negligible, the swings of the coil being limited by
  damping influences, chiefly electromagnetic. The index therefore
  remains almost stationary at the limit of its deflection, and the
  deflection is approximately the same whether the change of induction
  occurs suddenly or gradually.

[Illustration: FIG. 11.]

[Illustration: FIG. 12.]

[Illustration: FIG. 13.]

_Induction and Hysteresis Curves._--Some typical induction curves,
copied from a paper by Ewing (_Proc. Inst. C.E._ vol. cxxvi.), are given
in figs. 11, 12 and 13. Fig. 11 shows the relation of B to H in a
specimen which has never before been magnetized. The experiment may be
made in two different ways: (1) the magnetizing current is increased by
a series of sudden steps, each of which produces a ballistic throw, the
value of B after any one throw being proportional to the sum of that and
all the previous throws; (2) the magnetizing current having been brought
to any desired value, is suddenly reversed, and the observed throw taken
as measuring twice the actual induction. Fig. 12 shows the nature of the
course taken by the curve when the magnetizing current, after having
been raised to the value corresponding to the point a, is diminished by
steps until it is nothing, and then gradually increased in the reverse
direction. The downward course of the curve is, owing to hysteresis,
strikingly different from its upward course, and when the magnetizing
force has been reduced to zero, there is still remaining an induction of
7500 units. If the operation is again reversed, the upward course will
be nearly, but not exactly, of the form shown by the line d e a, fig.
13. After a few repetitions of the reversal, the process becomes
strictly cyclic, the upward and downward curves always following with
precision the paths indicated in the figure. In order to establish the
cyclic condition, it is sufficient to apply alternately the greatest
positive and negative forces employed in the test (greatest H = about ±5
C.G.S. units in the case illustrated in the figure), an operation which
is performed by simply reversing the direction of the maximum
magnetizing current a few times.

The closed figure a c d e a is variously called a _hysteresis curve_ or
_diagram_ or _loop_. The area [int] H dB enclosed by it represents the
work done in carrying a cubic centimetre of the iron through the
corresponding magnetic cycle; expressed in ergs this work is (1/4)[pi]
[int] H dB.[21] To quote an example given by J. A. Fleming, it requires
about 18 foot-pounds of work to make a complete magnetic cycle in a
cubic foot of wrought iron, strongly magnetized first one way and then
the other, the work so expended taking the form of heat in the mass.

  [Illustration: FIG. 14.]

  Fig. 14 shows diagrammatically a convenient arrangement described by
  Ewing (see _Proc. Inst. C.E._ vol. cxxvi., and _Phil. Trans._, 1893A,
  p. 987) for carrying out ballistic tests by which either the simple
  B-H curve (fig. 11) or the hysteresis curve (figs. 12 and 13) can be
  determined. The sample under test is prepared in the form of a ring A,
  upon which are wound the induction and the magnetizing coils; the
  latter should be wound evenly over the whole ring, though for the sake
  of clearness only part of the winding is indicated in the diagram. The
  magnetizing current, which is derived from the storage battery B, is
  regulated by the adjustable resistance R and measured by the
  galvanometer G. The current passes through the rocking key K, which,
  when thrown over to the right, places a in contact with c and b with
  d, and when thrown over to the left, places a in contact with e and b
  with f. When the switch S is closed, K acts simply as a commutator or
  current-reverser, but if K is thrown over from right to left while S
  is opened, not only is the current reversed, but its strength is at
  the same time diminished by the interposition of the adjustable
  resistance R2. The induction coil wound upon the ring is connected to
  the ballistic galvanometer G2 in series with a large permanent
  resistance R3. In the same circuit is also included the induction coil
  E, which is used for standardizing the galvanometer; this secondary
  coil is represented in the diagram by three turns of wire wound over a
  much longer primary coil. The short-circuit key F is kept closed
  except when an observation is about to be made; its object is to
  arrest the swing of the d'Arsonval galvanometer G2. By means of the
  three-way switch C the battery current may be sent either into the
  primary of E, for the purpose of calibrating the galvanometer, or into
  the magnetizing coil of the ring under test. When it is desired to
  obtain a simple curve of induction, such as that in fig. 11, S is kept
  permanently closed, and corresponding values of H and B are determined
  by one of the two methods already described, the strength of the
  battery-current being varied by means of the adjustable resistance R.
  When a hysteresis curve is to be obtained, the procedure is as
  follows: The current is first adjusted by means of R to such a
  strength as will fit it to produce the greatest + and - values of the
  magnetizing force which it is intended to apply in the course of the
  cycle; then it is reversed several times, and when the range of the
  galvanometer throws has become constant, half the extent of an
  excursion indicates the induction corresponding to the extreme value
  of H, and gives the point a in the curve fig. 12. The reversing key K
  having been put over to the left side, the short-circuit key S is
  suddenly opened; this inserts the resistance R, which has been
  suitably adjusted beforehand, and thus reduces the current and
  therefore the magnetizing force to a known value. The galvanometer
  throw which results from the change of current measures the amount by
  which the induction is reduced, and thus a second point on the curve
  is found. In a similar manner, by giving different values to the
  resistance R, any desired number of points between a and c in the
  curve can be determined. To continue the process, the key K is turned
  over to the right-hand side, and then, while S is open, is turned
  back, thereby not only reversing the direction of the current, but
  diminishing its strength by an amount depending upon the previous
  adjustment of R2. In this way points can be found lying anywhere
  between c and d of fig. 12, and the determination of the downward limb
  of the curve is therefore completed. As the return curve, shown in
  fig. 13, is merely an inverted copy of the other, no separate
  determination of it is necessary.

[Illustration: FIG. 15.]

In fig. 15 (J. A. Fleming, _Magnets and Electric Currents_, p. 193) are
shown three very different types of hysteresis curves, characteristic of
the special qualities of the metals from which they were respectively
obtained. The distinguishing feature of the first is the steepness of
its outlines; this indicates that the induction increases rapidly in
relation to the magnetic force, and hence the metal is well suited for
the construction of dynamo magnets. The second has a very small area,
showing that the work done in reversing the magnetization is small; the
metal is therefore adapted for use in alternating current transformers.
On the other hand, the form of the third curve, with its large
intercepts on the axes of H and B, denotes that the specimen to which it
relates possesses both retentiveness and coercive force in a high
degree; such a metal would be chosen for making good permanent magnets.

  Several arrangements have been devised for determining hysteresis more
  easily and expeditiously than is possible by the ballistic method. The
  best known is J. A. Ewing's hysteresis-tester,[22] which is specially
  intended for testing the sheet iron used in transformers. The sample,
  arranged as a bundle of rectangular strips, is caused to rotate about
  a central horizontal axis between the poles of an upright C-shaped
  magnet, which is supported near its middle upon knife-edges in such a
  manner that it can oscillate about an axis in a line with that about
  which the specimen rotates; the lower side of the magnet is weighted,
  to give it some stability. When the specimen rotates, the magnet is
  deflected from its upright position by an amount which depends upon
  the work done in a single complete rotation, and therefore upon the
  hysteresis. The deflection is indicated by a pointer upon a graduated
  scale, the readings being interpreted by comparison with two standard
  specimens supplied with the instrument. G. F. Searle and T. G.
  Bedford[23] have introduced the method of measuring hysteresis by
  means of an electro-dynamometer used ballistically. The fixed and
  suspended coils of the dynamometer are respectively connected in
  series with the magnetizing solenoid and with a secondary wound upon
  the specimen. When the magnetizing current is twice reversed, so as to
  complete a cycle, the sum of the two deflections, multiplied by a
  factor depending upon the sectional area of the specimen and upon the
  constants of the apparatus, gives the hysteresis for a complete cycle
  in ergs per cubic centimetre. For specimens of large sectional area it
  is necessary to apply corrections in respect of the energy dissipated
  by eddy currents and in heating the secondary circuit. The method has
  been employed by the authors themselves in studying the effects of
  tension, torsion and circular magnetization, while R. L. Wills[24] has
  made successful use of it in a research on the effects of temperature,
  a matter of great industrial importance.

  C. P. Steinmetz (_Electrician_, 1891, 26, p. 261; 1892, 28, pp. 384,
  408, 425) has called attention to a simple relation which appears to
  exist between the amount of energy dissipated in carrying a piece of
  iron or steel through a magnetic cycle and the limiting value of the
  induction reached in the cycle. Denoting by W the work in ergs done
  upon a cubic centimetre of the metal ( = 1/4[pi] [int] H dB or [int] H
  dI), he finds W = [eta]B^(1.6) approximately, where [eta] is a number,
  called the hysteretic constant, depending upon the metal, and B is the
  maximum induction. The value of the constant [eta] ranges in different
  metals from about 0.001 to 0.04; in soft iron and steel it is said to
  be generally not far from 0.002. Steinmetz's formula may be tested by
  taking a series of hysteresis curves between different limits of B,
  measuring their areas by a planimeter, and plotting the logarithms of
  these divided by 4[pi] as ordinates against logarithms of the
  corresponding maximum values of B as abscissae. The curve thus
  constructed should be a straight line inclined to the horizontal axis
  at an angle [theta], the tangent of which is 1.6. Ewing and H. G.
  Klaassen (_Phil. Trans._, 1893, 184, 1017) have in this manner
  examined how nearly and within what range a formula of the type W =
  [eta]B^[epsilon] may be taken to represent the facts. The results of
  an example which they quote in detail may be briefly summarized as
  follows:--

    +-----------------+------------+-----------------+-----------+
    |                 | Hysteretic |     Index.      |  Degrees. |
    |   Limits of B.  | Constant.  |    [epsilon]    |  [theta]  |
    |                 |   [eta]    | (= tan [theta]) |           |
    +-----------------+------------+-----------------+-----------+
    |   200 to    500 |     ...    |      1.9        |   62.25   |
    |   500 to  1,000 |     ...    |      1.68       |   59.25   |
    | 1,000 to  2,000 |     ...    |      1.55       |   57.25   |
    | 2,000 to  8,000 |   0.01     |      1.475      |   55.75   |
    | 8,000 to 14,000 |   0.00134  |      1.70       |   59.50   |
    +-----------------+------------+-----------------+-----------+

  It is remarked by the experimenters that the value of the index
  [epsilon] is by no means constant, but changes in correspondence with
  the successive well-marked stages in the process of magnetization. But
  though a formula of this type has no physical significance, and cannot
  be accepted as an equation to the actual curve of W and B, it is,
  nevertheless, the case that by making the index [epsilon] = 1.6, and
  assigning a suitable value to [eta], a formula may be obtained giving
  an approximation to the truth which is sufficiently close for the
  ordinary purposes of electrical engineers, especially when the
  limiting value of B is neither very great nor very small. Alexander
  Siemens (_Journ. Inst. Eng._, 1894, 23, 229) states that in the
  hundreds of comparisons of test pieces which have been made at the
  works of his firm, Steinmetz's law has been found to be practically
  correct.[25] An interesting collection of W-B curves embodying the
  results of actual experiments by Ewing and Klaassen on different
  specimens of metal is given in fig. 16. It has been shown by Kennelly
  (_Electrician_, 1892, 28, 666) that Steinmetz's formula gives
  approximately correct results in the case of nickel. Working with two
  different specimens, he found that the hysteresis loss in ergs per
  cubic centimetre (W) was fairly represented by 0.00125B^(1.6) and
  0.00101B^(1.6) respectively, the maximum induction ranging from about
  300 to 3000. The applicability of the law to cobalt has been
  investigated by Fleming (_Phil. Mag._, 1899, 48, 271), who used a ring
  of cast cobalt containing about 96% of the pure metal. The logarithmic
  curves which accompany his paper demonstrate that within wide ranges
  of maximum induction W = 0.01B^(1.6) = 0.527I^(1.62) very nearly.
  Fleming rightly regards it as not a little curious that for materials
  differing so much as this cast cobalt and soft annealed iron the
  hysteretic exponent should in both cases be so near to 1.6. After
  pointing out that, since the magnetization of the metal is the
  quantity really concerned, W is more appropriately expressed in terms
  of I, the magnetic moment per unit of volume, than of B, he suggests
  an experiment to determine whether the mechanical work required to
  effect the complete magnetic reversal of a crowd of small compass
  needles (representative of magnetic molecules) is proportional to the
  1.6th power of the aggregate maximum magnetic moment before or after
  completion of the cycle.

  [Illustration: FIG. 16.

    a, Fine steel wire 0.257 mm. diam.
    b, Fine iron wire 0.34 mm. diam.
    c, Fine iron wire 0.2475 mm. diam.
    d, Thin sheet iron 0.47 mm. thick.
    e, Iron wire 0.602 mm. diam.
    f, Iron wire 0.975 mm. diam.
    g, Sheet iron 1.95 mm. thick.
    h, Thin sheet iron 0.367 mm. thick.
    i. Very soft iron wire.]

  The experiments of K. Honda and S. Shimizu[26] indicate that
  Steinmetz's formula holds for nickel and annealed cobalt up to B =
  3000, for cast cobalt and tungsten steel up to B = 8000, and for
  Swedish iron up to B = 18,000, the range being in all cases extended
  at the temperature of liquid air.

[Illustration: FIG. 17.]

The diagram, fig. 17, contains examples of ascending induction curves
characteristic of wrought iron, cast iron, cobalt and nickel. These are
to be regarded merely as typical specimens, for the details of a curve
depend largely upon the physical condition and purity of the material;
but they show at a glance how far the several metals differ from and
resemble one another as regards their magnetic properties. Curves of
magnetization (which express the relation of I to H) have a close
resemblance to those of induction; and, indeed, since B = H + 4[pi]I,
and 4[pi]I (except in extreme fields) greatly exceeds H in numerical
value, we may generally, without serious error, put I = B/4[pi], and
transform curves of induction into curves of magnetization by merely
altering the scale to which the ordinates are referred. A scale for the
approximate transformation for the curves in fig. 12 is given at the
right-hand side of the diagram, the greatest error introduced by
neglecting H/4[pi] not exceeding 0.6%. A study of such curves as these
reveals the fact that there are three distinct stages in the process of
magnetization. During the first stage, when the magnetizing force is
small, the magnetization (or the induction) increases rather slowly with
increasing force; this is well shown by the nickel curve in the diagram,
but the effect would be no less conspicuous in the iron curve if the
abscissae were plotted to a larger scale. During the second stage small
increments of magnetizing force are attended by relatively large
increments of magnetization, as is indicated by the steep ascent of the
curve. Then the curve bends over, forming what is often called a "knee,"
and a third stage is entered upon, during which a considerable increase
of magnetizing force has little further effect upon the magnetization.
When in this condition the metal is popularly said to be "saturated."
Under increasing magnetizing forces, greatly exceeding those comprised
within the limits of the diagram, the magnetization does practically
reach a limit, the maximum value being attained with a magnetizing force
of less than 2000 for wrought iron and nickel, and less than 4000 for
cast iron and cobalt. The induction, however, continues to increase
indefinitely, though very slowly. These observations have an important
bearing upon the molecular theory of magnetism, which will be referred
to later.

The magnetic quality of a sample of iron depends very largely upon the
purity and physical condition of the metal. The presence of ordinary
impurities usually tends to diminish the permeability, though, as will
appear later, the addition of small quantities of certain other
substances is sometimes advantageous. A very pure form of iron, which
from the method of its manufacture is called "steel," is now extensively
used for the construction of dynamo magnets; this metal sometimes
contains not more than 0.3% of foreign substances, including carbon, and
is magnetically superior to the best commercial wrought iron. The
results of some comparative tests published by Ewing (_Proc. Inst.
C.E._, 1896) are given in the accompanying table. Those in the second
column are quoted from a paper by F. Lydall and A. W. Pocklington
(_Proc. Roy. Soc._, 1892, 52, 228) and relate to an exceptional specimen
containing nearly 99.9% of the pure metal.

  +----------+-----------------------------------------+
  |          |           Magnetic Induction.           |
  | Magnetic +--------+----------+----------+----------+
  |  Force.  |  Pure  | Low Moor |  Steel   |  Steel   |
  |          |  Iron. |   Iron.  | Forging. | Casting. |
  +----------+--------+----------+----------+----------+
  |     5    | 12,700 |  10,900  |  12,300  |   9,600  |
  |    10    | 14,980 |  13,120  |  14,920  |  13,050  |
  |    15    | 15,800 |  14,010  |  15,800  |  14,600  |
  |    20    | 16,300 |  14,580  |  16,280  |  15,310  |
  |    30    | 16,950 |  15,280  |  16,810  |  16,000  |
  |    40    | 17,350 |  15,760  |  17,190  |  16,510  |
  |    50    |   ..   |  16,060  |  17,500  |  16,900  |
  |    60    |   ..   |  16,340  |  17,750  |  17,180  |
  |    70    |   ..   |  16,580  |  17,970  |  17,400  |
  |    80    |   ..   |  16,800  |  18,180  |  17,620  |
  |    90    |   ..   |  17,000  |  18,390  |  17,830  |
  |   100    |   ..   |  17,200  |  18,600  |  18,030  |
  +----------+--------+----------+----------+----------+

To secure the highest possible permeability it is essential that the
iron should be softened by careful annealing. When it is mechanically
hardened by hammering, rolling or wire-drawing its permeability may be
greatly diminished, especially under a moderate magnetizing force. An
experiment by Ewing showed that by the operation of stretching an
annealed iron wire beyond the limits of elasticity the permeability
under a magnetizing force of about 3 units was reduced by as much as
75%. Ewing has also studied the effect of vibration in conferring upon
iron an apparent or spurious permeability of high value; this effort
also is most conspicuous when the magnetizing force is weak. The
permeability of a soft iron wire, which was tapped while subjected to a
very small magnetizing force, rose to the enormous value of about 80,000
(_Magnetic Induction_, § 85). It follows that in testing iron for
magnetic quality the greatest care must be exercised to guard the
specimen against any accidental vibration.

Low hysteresis is the chief requisite for iron which is to be used for
transformer cores, and it does not necessarily accompany high
permeability. In response to the demand, manufacturers have succeeded in
producing transformer plate in which the loss of energy due to
hysteresis is exceedingly small. Tests of a sample supplied by Messrs.
Sankey were found by Ewing to give the following results, which,
however, are regarded as being unusually favourable. In a valuable
collection of magnetic data (_Proc. Inst. C.E._, cxxvi.) H. F. Parshall
quotes tests of six samples of iron, described as of good quality, which
showed an average hysteresis loss of 3070 ergs per c.cm. per cycle at an
induction of 8000, being 1.6 times the loss shown by Ewing's specimen at
the same induction.

  +------------+----------------+-----------------+
  | Limits of  | Ergs per c.cm. |  Watts per lb.  |
  | Induction. |   per cycle.   | Frequency, 100. |
  +------------+----------------+-----------------+
  |    2000    |       220      |      0.129      |
  |    3000    |       410      |      0.242      |
  |    4000    |       640      |      0.376      |
  |    5000    |       910      |      0.535      |
  |    6000    |      1200      |      0.710      |
  |    7000    |      1520      |      0.890      |
  |    8000    |      1900      |      1.120      |
  |    9000    |      2310      |      1.360      |
  +------------+----------------+-----------------+

The standard induction in reference to determinations of hysteresis is
generally taken as 2500, while the loss is expressed in watts per lb. at
a frequency of 100 double reversals, or cycles, per second. In many
experiments, however, different inductions and frequencies are employed,
and the hysteresis-loss is often expressed as ergs per cubic centimetre
per cycle and sometimes as horse-power per ton. In order to save
arithmetical labour it is convenient to be provided with conversion
factors for reducing variously expressed results to the standard form.
The rate at which energy is lost being proportional to the frequency, it
is obvious that the loss at frequency 100 may be deduced from that at
any other frequency n by simply multiplying by 100/n. Taking the density
of iron to be 7.7, the factor for reducing the loss in ergs per c.cm. to
watts per lb. with a frequency of 100 is 0.000589 (Ewing). Since 1
horse-power = 746 watts, and 1 ton = 2240 lb., the factor for reducing
horse-power per ton to watts per lb. is 746/2240, or just 1/3. The loss
for any induction B within the range for which Steinmetz's law holds may
be converted into that for the standard induction 2500 by dividing it by
B^(1.6)/2500^(1.6). The values of this ratio for different values of B,
as given by Fleming (_Phil. Mag._, 1897), are contained in the second
column of the annexed table. The third column shows the relative amount
of hysteresis deduced by Ewing as a general mean from actual tests of
many samples (_Journ. Inst. Elec. Eng._, 1895). Incidentally, these two
columns furnish an undesigned test of the accuracy of Steinmetz's law:
the greatest difference is little more than 1%.

  +-----------+------------+-------------+
  | Induction |  B^(1.6)   |  Observed   |
  |     B.    | ---------- |  relative   |
  |           | 2500^(1.6) | Hysteresis. |
  +-----------+------------+-------------+
  |   2000    |   0.700    |    0.702    |
  |   2500    |   1.000    |    1.000    |
  |   3000    |   1.338    |    1.340    |
  |   4000    |   2.118    |    2.128    |
  |   5000    |   3.031    |    3.000    |
  |   6000    |   4.058    |    4.022    |
  |   7000    |   5.193    |    5.129    |
  |   8000    |   6.430    |    6.384    |
  +-----------+------------+-------------+

_Curves of Permeability and Susceptibility._--The relations of µ (= B/H)
to B, and of [kappa] (= I/H) to I may be instructively exhibited by
means of curves, a method first employed by H. A. Rowland.[27] The
dotted curve for µ and B in fig. 18 is copied from Rowland's paper. The
actual experiment to which it relates was carried only as the point
marked X, corresponding to a magnetizing force of 65, and an induction
of nearly 17,000. Rowland, believing that the curve would continue to
fall in a straight line meeting the horizontal axis, inferred that the
induction corresponding to the point B--about 17,500--was the highest
that could be produced by any magnetizing force, however great. It has,
however, been shown that, if the magnetizing force is carried far
enough, the curve always becomes convex to the axis instead of meeting
it. The full line shows the result of an experiment in which the
magnetizing force was carried up to 585,[28] but though the force was
thus increased ninefold, the induction only reached 19,800, and the
ultimate value of the permeability was still as much as 33.9.

[Illustration: FIG. 18.]

[Illustration: FIG. 19.]

_Ballistic Method with Yoke._--J. Hopkinson (_Phil. Trans._, 1885, 176,
455) introduced a modification of the usual ballistic arrangement which
presents the following advantages; (1) very considerable magnetizing
forces can be applied with ordinary means; (2) the samples to be tested,
having the form of cylindrical bars, are more easily prepared than rings
or wires; (3) the actual induction at any time can be measured, and not
only changes of induction. On the other hand, a very high degree of
accuracy is not claimed for the results. Fig. 19 shows the apparatus by
which the ends of the bar are prevented from exerting any material
demagnetizing force, while the permeance of the magnetic circuit is at
the same time increased. A A, called the "yoke," is a block of annealed
wrought iron about 18 in. long, 6½ in. wide and 2 in. thick, through
which is cut a rectangular opening to receive the two magnetizing coils
B B. The test bar C C, which slides through holes bored in the yoke, is
divided near the middle into two parts, the ends which come into contact
being faced true and square. Between the magnetizing coils is a small
induction coil D, which is connected with a ballistic galvanometer. The
induction coil is carried upon the end of one portion of the test bar,
and when this portion is suddenly drawn back the coil slips off and is
pulled out of the field by an india-rubber spring. This causes a
ballistic throw proportional to the induction through the bar at the
moment when the two portions were separated. With such an arrangement it
is possible to submit the sample to any series of magnetic forces, and
to measure its magnetic state at the end. The uncertainty with which the
results are affected depends chiefly upon the imperfect contact between
the bar and the yoke and also between the ends of the divided bar. It is
probable that Hopkinson did not attach sufficient importance to the
demagnetizing action of the cut (cf. Ewing, _Phil. Mag._, Sept. 1888, p.
274), and that the values which he assigned to H are consequently
somewhat too high. He applied his method with good effect, however, in
testing a large number of commercial specimens of iron and steel, the
magnetic constants of which are given in a table accompanying his paper.
When it is not required to determine the residual magnetization there is
no necessity to divide the sample bar, and ballistic tests may be made
in the ordinary way--by steps or by reversals--the source of error due
to the transverse cut thus being avoided. Ewing (_Magnetic Induction_, §
194) has devised an arrangement in which two similar test bars are
placed side by side; each bar is surrounded by a magnetizing coil, the
two coils being connected to give opposite directions of magnetization,
and each pair of ends is connected by a short massive block of soft iron
having holes bored through it to fit the bars, which are clamped in
position by set-screws. Induction coils are wound on the middle parts of
both bars, and are connected in series. With this arrangement it is
possible to find the actual value of the magnetizing force, corrected
for the effects of joints and other sources of error. Two sets of
observations are taken, one when the blocks are fixed at the ends of the
bars, and another when they are nearer together, the clear length of the
bars between them and of the magnetizing coils being reduced to
one-half. If H1 and H2 be the values of 4[pi]in/l and 4[pi]i´[(n/2) /
(l/2)] for the same induction B, it can be shown that the true
magnetizing force is H = H1 - (H2 - H1). The method, though tedious in
operation, is very accurate, and is largely employed for determining the
magnetic quality of bars intended to serve as standards.

_Traction Methods._--The induction of the magnetization may be measured
by observing the force required to draw apart the two portions of a
divided rod or ring when held together by their mutual attraction. If a
transverse cut is made through a bar whose magnetization is I and the
two ends are placed in contact, it can be shown that this force is
2[pi]I² dynes per unit of area (Mascart and Joubert, _Electricity and
Magnetism_, § 322); and if the magnetization of the bar is due to an
external field H produced by a magnetizing coil or otherwise, there is
an additional force equal to HI. Thus the whole force, when the two
portions of the bar are surrounded by a loosely-fitting magnetizing
coil, is

  F = 2[pi]I² + HI

expressed as dynes per square centimetre. If each portion of the bar has
an independent magnetizing coil wound tightly upon it, we have further
to take into account the force due to the mutual action of the two
magnetizing coils, which assists the forces already considered. This is
equal to H²8[pi] per unit of sectional area. In the case supposed
therefore the total force per square centimetre is

                       H²
  F = 2[pi]I² + HI + -----
                     8[pi]

      (4[pi]I + H)³
    = -------------
          8[pi]

        B²
    = -----.
      8[pi]

The equation F = B²/8[pi] is often said to express "Maxwell's law of
magnetic traction" (Maxwell, _Electricity and Magnetism_, §§ 642-646).
It is, of course, true for permanent magnets, where H = 0, since then F
= 2[pi]I²; but if the magnetization is due to electric currents, the
formula is only applicable in the special case when the mutual action of
the two magnets upon one another is supplemented by the electromagnetic
attraction between separate magnetizing coils rigidly attached to
them.[29]

The traction method was first employed by S. Bidwell (_Proc. Roy. Soc._,
1886, 40, 486), who in 1886 published an account of some experiments in
which the relation of magnetization to magnetic field was deduced from
observations of the force in grammes weight which just sufficed to tear
asunder the two halves of a divided ring electromagnet when known
currents were passing through the coils. He made use of the expression

  F = Wg = 2[pi]I² + HI,

where W is the weight in grammes per square centimetre of sectional
area, and g is the intensity of gravity which was taken as 981. The term
for the attraction between the coils was omitted as negligibly small
(see _Phil. Mag._, 1890, 29, 440). The values assigned to H were
calculated from H = 2ni/r, and ranged from 3.9 to 585, but inasmuch as
no account was taken of any demagnetizing action which might be due to
the two transverse cuts, it is probable that they are somewhat too high.
The results, nevertheless, agree very well with those for annealed
wrought iron obtained by other methods. Below is given a selection from
Bidwell's tables, showing corresponding values of magnetizing force,
weight supported, magnetization, induction, susceptibility and
permeability:--

  +--------+---------+-------+--------+----------+--------+
  |    H.  |    W.   |   I.  |   B.   | [kappa]. |    µ.  |
  +--------+---------+-------+--------+----------+--------+
  |  3.9   |  2,210  |  587  |  7,390 |  151.0   | 1889.1 |
  |  5.7   |  3,460  |  735  |  9,240 |  128.9   | 1621.3 |
  |  10.3  |  5,400  |  918  | 11,550 |   89.1   | 1121.4 |
  |  22.2  |  8,440  | 1147  | 14,450 |   51.7   |  650.9 |
  |  40    |  9,680  | 1226  | 15,460 |   30.7   |  386.4 |
  | 115    | 12,170  | 1370  | 17,330 |   11.9   |  150.7 |
  | 208    | 13,810  | 1452  | 18,470 |    7.0   |   88.8 |
  | 362    | 14,740  | 1489  | 19,080 |    4.1   |   52.7 |
  | 465    | 15,275  | 1508  | 19,420 |    3.2   |   41.8 |
  | 585    | 15,905  | 1530  | 19,820 |    2.6   |   33.9 |
  +--------+---------+-------+--------+----------+--------+

[Illustration: FIG. 20.]

A few months later R. H. M. Bosanquet (_Phil. Mag._, 1886, 22, 535)
experimented on the relation of tractive force to magnetic induction.
Instead of a divided ring he employed a divided straight bar, each half
of which was provided with a magnetizing coil. The joint was surrounded
by an induction coil connected with a ballistic galvanometer, an
arrangement which enabled him to make an independent measurement of the
induction at the moment when the two portions of the bar were separated.
He showed that there was, on the whole, a fair agreement between the
values determined ballistically and those given by the formula B =
[root](8[pi]F). The greatest weight supported in the experiments was
14,600 grammes per square cm., and the corresponding induction 18,500
units. Taylor Jones subsequently found a good agreement between the
theoretical and the observed values of the tractive force in fields
ranging up to very high intensities (_Phil. Mag._, 1895, 39, 254, and
1896, 41, 153).

  _Permeameters._--Several instruments in which the traction method is
  applied have been devised for the rapid measurement of induction or of
  magnetization in commercial samples of iron and steel. The earliest of
  these is S. P. Thompson's _permeameter_ (_Journ. Sci. Arts_, 1890, 38,
  885), which consists of a rectangular block of iron shaped like
  Hopkinson's yoke, and slotted out in the same way to receive a
  magnetizing coil (fig. 20); the block is bored through at the upper
  end only, and its inner face opposite the hole is made quite flat and
  smooth. The sample has the form of a thin rod, one end of which is
  faced true; it is slipped into the magnetizing coil from above, and
  when the current is turned on its smooth end adheres tightly to the
  surface of the yoke. The force required to detach it is measured by a
  registering spring balance, which is clamped to the upper end of the
  rod, and thence the induction or the magnetization is deduced by
  applying the formula

    (B - H)²/8[pi] = 2[pi]I² = Pg/S,

  where P is the pull in grammes weight, S the sectional area of the rod
  in square cm., and g = 981. If the pull is measured in pounds and the
  area in square inches, the formula may be written B = 1317 ×
  [root](P/S) + H. The instrument exhibited by Thompson would, without
  undue heating, take a current of 30 amperes, which was sufficient to
  produce a magnetizing force of 1000 units. A testing apparatus of a
  similar type devised by Gisbert Kapp (_Journ. Inst. Elec. Eng._ xxiii.
  199) differs only in a few details from Thompson's permeameter. Ewing
  has described an arrangement in which the test bar has a soft-iron
  pole piece clamped to each of its ends; the pole pieces are joined by
  a long well-fitting block of iron, which is placed upon them (like the
  "keeper" of a magnet), and the induction is measured by the force
  required to detach the block. In all such measurements a correction
  should be made in respect of the demagnetizing force due to the joint,
  and unless the fit is very accurate the demagnetizing action will be
  variable. In the _magnetic balance_ of du Bois (_Magnetic Circuit_, p.
  346) the uncertainty arising from the presence of a joint is avoided,
  the force measured being that exerted between two pieces of iron
  separated from each other by a narrow air-gap of known width. The
  instrument is represented diagrammatically in fig. 21. The test-piece
  A, surrounded by a magnetizing coil, is clamped between two soft-iron
  blocks B, B´. Y Y´ is a soft iron yoke, which rocks upon knife-edges K
  and constitutes the beam of the balance. The yoke has two projecting
  pieces C, C´ at unequal distances from the knife-edges, and separated
  from the blocks B, B´ by narrow air-gaps. The play of the beam is
  limited by a stop S and a screw R, the latter being so adjusted that
  when the end Y of the beam is held down the two air-gaps are of equal
  width. W is a weight capable of sliding from end to end of the yoke
  along a graduated scale. When there is no magnetization, the yoke is
  in equilibrium; but as soon as the current is turned on the block C is
  drawn downwards as far as the screw R will allow, for, though the
  attractive forces F between B and C and between B´ and C´ are equal,
  the former has a greater moment. The weight W is moved along the scale
  until the yoke just tilts over upon the stop S; the distance of W from
  its zero position is then, as can easily be shown, proportional to F,
  and therefore to B², and approximately to I². The scale is graduated
  in such a manner that by multiplying the reading by a simple factor
  (generally 10 or 2) the absolute value of the magnetization is
  obtained. The actual magnetizing force H is of course less than that
  due to the coil; the corrections required are effected automatically
  by the use of a set of demagnetization lines drawn on a sheet of
  celluloid which is supplied with the instrument. The celluloid sheet
  is laid upon the squared paper, and in plotting a curve horizontal
  distances are reckoned from the proper demagnetization line instead of
  from the vertical axis. An improved but somewhat more complex form of
  the instrument is described in _Ann. d. Phys._, 1900, 2, 317.

  [Illustration: FIG. 21.]

  In Ewing's _magnetic balance_ (_Journ. Inst. Elec. Eng._ 1898, 27,
  526), the value of the magnetic induction corresponding to a single
  stated magnetizing force is directly read off on a divided scale. The
  specimen, which has the form of a turned rod, 4 in. long and ¼ in. in
  diameter, is laid across the poles of a horseshoe electromagnet,
  excited by a current of such strength as to produce in the rod a
  magnetizing force H = 20. One pole has a V-shaped notch for the rod to
  rest in; the surface of the other is slightly rounded, forming a
  portion of a cylinder, the axis of which is perpendicular to the
  direction of the length of the rod. The rod touches this pole at a
  single point, and is pulled away from it by the action of a lever, the
  long arm of which is graduated and carries a sliding weight. The
  position of the weight at the moment when contact is broken indicates
  the induction in the rod. The standard force H = 20 was selected as
  being sufficiently low to distinguish between good and bad specimens,
  and at the same time sufficiently high to make the order of merit the
  same as it would be under stronger forces.

  _Permeability Bridges._--Several pieces of apparatus have been
  invented for comparing the magnetic quality of a sample with that of a
  standard iron rod by a zero method, such as is employed in the
  comparison of electrical resistances by the Wheatstone bridge. An
  excellent instrument of the class is Ewing's _permeability bridge_.
  The standard rod and the test specimen, which must be of the same
  dimensions, are placed side by side within two magnetizing coils, and
  each pair of adjacent ends is joined by a short rectangular block or
  "yoke" of soft iron. An iron bar shaped like an inverted L projects
  upwards from each of the yokes, the horizontal portions of the bars
  being parallel to the rods, and nearly meeting at a height of about 8
  in. above them (thus [symbol]). A compass needle placed in the gap
  serves to detect any flow of induction that may exist between the bent
  bars. For simplicity of calculation, the clear length of each rod
  between the yokes is made 12.56 (= 4[pi]) centimetres, while the coil
  surrounding the standard bar contains 100 turns; hence the magnetizing
  force due to a current of n amperes will be 10n C.G.S. units. The
  effective number of turns in the coil surrounding the test rod can be
  varied by means of three dial switches (for hundreds, tens and units),
  which also introduce compensating resistances as the number of
  effective turns in the coil is reduced, thus keeping the total
  resistance of the circuit constant. The two coils are connected in
  series, the same current passing through both. Suppose the switches to
  be adjusted so that the effective number of turns in the variable coil
  is 100; the magnetizing forces in the two coils will then be equal,
  and if the test rod is of the same quality as the standard, the flow
  of induction will be confined entirely to the iron circuit, the two
  yokes will be at the same magnetic potential, and the compass needle
  will not be affected. If, however, the permeability of the test rod
  differs from that of the standard, the number of lines of induction
  flowing in opposite directions through the two rods will differ, and
  the excess will flow from one yoke to the other, partly through the
  air, and partly along the path provided by the bent bars, deflecting
  the compass needle. But a balance may still be obtained by altering
  the effective number of turns in the test coil, and thus increasing or
  decreasing the magnetizing force acting on the test rod, till the
  induction in the two rods is the same, a condition which is fulfilled
  when reversal of the current has no effect on the compass needle. Let
  m be the number of turns in use, and H1 and H2 the magnetizing forces
  which produce the same induction B in the test and the standard rods
  respectively; then H1 = H2 × m/100. The value of B which corresponds
  to H2m/100 can be found from the (B, H) curve for the standard, which
  is assumed to have been determined; and this same value corresponds to
  the force H in the case of the test bar. Thus any desired number of
  corresponding values of H and B can be easily and quickly found.

_Measurement of Field Strength. Exploring Coil._--Since in air B = H,
the ballistic method of measuring induction described above is also
available for determining the strength of a magnetic field, and is more
often employed than any other. A small coil of fine wire, connected in
series with a ballistic galvanometer, is placed in the field, with its
windings perpendicular to the lines of force, and then suddenly reversed
or withdrawn from the field, the integral electromotive force being
twice as great in the first case as in the second. The strength of the
field is proportional to the swing of the galvanometer-needle, and, when
the galvanometer is calibrated, can be expressed in C.G.S. units.
Convenient arrangements have been introduced whereby the coil is
reversed or withdrawn from the field by the action of a spring.

_Bismuth Resistance._--The fact, which will be referred to later, that
the electrical resistance of bismuth is very greatly affected by a
magnetic field has been applied in the construction of apparatus for
measuring field intensity. A little instrument, supplied by Hartmann and
Braun, contains a short length of fine bismuth wire wound into a flat
double spiral, half an inch or thereabouts in diameter, and attached to
a long ebonite handle. Unfortunately the effects of magnetization upon
the specific resistance of bismuth vary enormously with changes of
temperature; it is therefore necessary to take two readings of the
resistance, one when the spiral is in the magnetic field, the other when
it is outside.

_Electric Circuit._--If a coil of insulated wire is suspended so that it
is in stable equilibrium when its plane is parallel to the direction of
a magnetic field, the transmission of a known electric current through
the coil will cause it to be deflected through an angle which is a
function of the field intensity.

  One of the neatest applications of this principle is that described by
  Edser and Stansfield (_Phil. Mag._, 1893, 34, 186), and used by them
  to test the stray fields of dynamos. An oblong coil about an inch in
  length is suspended from each end by thin strips of rolled German
  silver wire, one of which is connected with a spiral spring for
  regulating the tension, the other being attached to a torsion-head.
  Inside the torsion-head is a commutator for automatically reversing
  the current, so that readings may be taken on each side of zero, and
  the arrangement is such that when the torsion-head is exactly at zero
  the current is interrupted. To take a reading the torsion-head is
  turned until an aluminium pointer attached to the coil is brought to
  the zero position on a small scale; the strength of the field is then
  proportional to the angular torsion. The small current required is
  supplied to the coil from a single dry cell. The advantages of
  portability, very considerable range (from H = 1 upwards), and fair
  accuracy are claimed for the instrument.

_Polarized Light._--The intensity of a field may be measured by the
rotation of the plane of polarization of light passing in the direction
of the magnetic force through a transparent substance. If the field is
uniform, H = [theta]/[omega]d, where [theta] is the rotation, d the
thickness of the substance arranged as a plate at right angles to the
direction of the field, and [omega] Verdet's constant for the substance.

  For the practical measurement of field intensity du Bois has used
  plates of the densest Jena flint glass. These are preferably made
  slightly wedge-shape, to avoid the inconvenience resulting from
  multiple internal reflections, and they must necessarily be rather
  thin, so that double refractions due to internal strain may not exert
  a disturbing influence. Since Verdet's constant is somewhat uncertain
  for different batches of glass even of the same quality, each plate
  should be standardized in a field of known intensity. As the source of
  monochromatic light a bright sodium burner is used, and the rotation,
  which is exactly proportional to H, is measured by an accurate
  polarimeter. Such a plate about 1 mm. in thickness is said to be
  adapted for measuring fields of the order of 1000 units. A part of one
  surface of the plate may be silvered, so that the polarized ray, after
  having once traversed the glass, is reflected back again; the rotation
  is thus doubled, and moreover, the arrangement is, for certain
  experiments, more convenient than the other.


4. MAGNETIZATION IN STRONG FIELDS

_Fields due to Coils._--The most generally convenient arrangement for
producing such magnetic fields as are required for experimental
purposes is undoubtedly a coil of wire through which an electric current
can be caused to flow. The field due to a coil can be made as nearly
uniform as we please throughout a considerable space; its intensity,
when the constants of the coil are known, can be calculated with ease
and certainty and may be varied at will through wide ranges, while the
apparatus required is of the simplest character and can be readily
constructed to suit special purposes. But when exceptionally strong
fields are desired, the use of a coil is limited by the heating effect
of the magnetizing current, the quantity of heat generated per unit of
time in a coil of given dimensions increasing as the square of the
magnetic field produced in its interior. In experiments on magnetic
strains carried out by H. Nagaoka and K. Honda (_Phil. Mag._, 1900, 49,
329) the intensity of the highest field reached in the interior of a
coil was 2200 units; this is probably the strongest field produced by a
coil which has hitherto been employed in experimental work. In 1890 some
experiments in which a coil was used were made by du Bois (_Phil. Mag._,
1890, 29, 253, 293) on the magnetization of iron, nickel, and cobalt
under forces ranging from about 100 to 1250 units. Since the
demagnetizing factor was 0.052, the strongest field due to the coil was
about 1340; but though arrangements were provided for cooling the
apparatus by means of ice, great difficulty was experienced owing to
heating. Du Bois's results, which, as given in his papers, show the
relation of H to the magnetic moment per unit of mass, have been reduced
by Ewing to the usual form, and are indicated in fig. 22, the earlier
portions of the curves being sketched in from other data.

[Illustration: FIG. 22.]

_Fields due to Electromagnets._--The problem of determining the
magnetization of iron and other metals in the strong fields formed
between the poles of an electromagnet was first attacked by J. A. Ewing
and W. Low. An account of their preliminary experiments by what they
call the _isthmus method_ was published in 1887 (_Proc. Roy. Soc._ 42,
200), and in the following year they described a more complete and
perfect series (_Phil. Trans._, 1889, 180, 221).

[Illustration: FIG. 23.]

  The sample to be inserted between the magnet poles was prepared in the
  form of a bobbin resembling an ordinary cotton reel, with a short
  narrow neck (constituting the "isthmus") and conical ends. Upon the
  central neck was wound a coil consisting of one or two layers of very
  fine wire, which was connected with a ballistic galvanometer for
  measuring the induction in the iron; outside this coil, and separated
  from it by a small and accurately determined distance, a second coil
  was wound, serving to measure the induction in the iron, together with
  that in a small space surrounding it. The difference of the ballastic
  throws taken with the two coils measured the intensity of the field in
  the space around the iron, and it also enabled a correction to be made
  for the non-ferrous space between the iron neck and the centre of the
  thickness of the inner coil. The pole pieces of the electromagnet (see
  fig. 23) were furnished with a pair of truncated cones _b b_, of soft
  iron forming an extension of the conical ends of the bobbin c. The
  most suitable form for the pole faces is investigated in the paper,
  and the conclusion arrived at is that to produce the greatest
  concentration of force upon the central neck, the cones should have a
  common vertex in the middle of the neck with a semi-vertical angle of
  54° 44´, while the condition for a uniform field is satisfied when the
  cones have a semi-vertical angle of 39° 14´; in the latter case the
  magnetic force in the air just outside is sensibly equal to that
  within the neck. A pair of cones having a semi-vertical angle of 45°
  were considered to combine high concentrative power with a sufficient
  approximation to uniformity of field. In most of the experiments the
  measurements were made by suddenly withdrawing the bobbin from its
  place between the pole pieces. Two groups of observations were
  recorded, one giving the induction in the inner coil and the other
  that in the outer coil. The value of the residual induction which
  persisted when the bobbin was drawn out was added to that of the
  induction measured, and thus the total induction in the iron was
  determined. The highest induction reached in these experiments was
  45,350 units, more than twice the value of any previously recorded.
  The corresponding intensity of the outside field was 24,500, but,
  owing to the wide angle of the cones used (about 2 × 63°), this was
  probably greater than the value of the magnetic force within the
  metal. The following table shows some results of other experiments in
  which H was believed to have sensibly the same value inside as outside
  the metal. Values of I are derived from (B - H)/4[pi] and of µ from
  B/H.

    +--------------+--------+--------+------+-------+
    |    Metal.    |   H    |   B    |  I   |   µ   |
    +--------------+--------+--------+------+-------+
    |              |  1,490 | 22,650 | 1680 | 15.20 |
    |              |  6,070 | 27,130 | 1680 |  4.47 |
    | Swedish Iron |  8,600 | 30,270 | 1720 |  3.52 |
    |              | 19,450 | 40,820 | 1700 |  2.10 |
    |              | 19,880 | 41,140 | 1700 |  2.07 |
    +--------------+--------+--------+------+-------+
    |              |  4,560 | 20,070 | 1230 |  4.40 |
    | Cast Iron    | 13,460 | 28,710 | 1210 |  2.13 |
    |              | 16,200 | 30,920 | 1170 |  1.91 |
    |              | 16,900 | 31,760 | 1180 |  1.88 |
    +--------------+--------+--------+------+-------+
    |              |  6,210 | 25,480 | 1530 |  4.10 |
    |              |  9,970 | 29,650 | 1570 |  2.97 |
    | Tool Steel   | 12,170 | 31,620 | 1550 |  2.60 |
    |              | 14,660 | 34,550 | 1580 |  2.36 |
    |              | 15,530 | 35,820 | 1610 |  2.31 |
    +--------------+--------+--------+------+-------+
    |              |  2,220 |  7,100 |  390 |  3.20 |
    |              |  4,440 |  9,210 |  380 |  2.09 |
    | Hard Nickel  |  7,940 | 12,970 |  400 |  1.63 |
    |              | 14,660 | 19,640 |  400 |  1.34 |
    |              | 16,000 | 21,070 |  400 |  1.32 |
    +--------------+--------+--------+------+-------+
    |              |  1,350 | 16,000 | 1260 | 12.73 |
    | Cobalt       |  4,040 | 18,870 | 1280 |  4.98 |
    |              |  8,930 | 23,890 | 1290 |  2.82 |
    |              | 14,990 | 30,210 | 1310 |  2.10 |
    +--------------+--------+--------+------+-------+

These results are of extreme interest, for they show that under
sufficiently strong magnetizing forces the intensity of magnetization I
reaches a maximum value, as required by W. E. Weber's theory of
molecular magnetism. There appears to be no definite limit to the value
to which the induction B may be raised, but the magnetization I attains
a true saturation value under magnetizing forces which are in most cases
comparatively moderate. Thus the magnetization which the sample of
Swedish iron received in a field of 1490 was not increased (beyond the
limits of experimental error) when the intensity of the field was
multiplied more than thirteen-fold, though the induction was nearly
doubled. When the saturation value of I has been reached, the relation
of magnetic induction to magnetic force may be expressed by

  B = H + constant.

  The annexed table gives the saturation values of I for the particular
  metals examined by Ewing and Low:--

                           Saturation
                           Value of I

    Wrought iron              1,700
    Cast iron                 1,240
    Nickel (0.75% iron)         515
      "    (0.56%   " )         400
    Cobalt (1.66%   " )       1,300

  It is shown in the paper that the greatest possible force which the
  isthmus method can apply at a point in the axis of the bobbin is

    F = 11.137 I_s log 10 b/a,

  I_s being the saturation value of the magnet poles, a the radius of the
  neck on which the cones converge, and b the radius of the bases of the
  cones.

  Some experiments made by H. du Bois (_Phil. Mag._, 1890, 29, 293) with
  an electromagnet specially designed for the production of strong
  fields, confirm Ewing's results for iron, nickel and cobalt. The
  method employed did not admit of the production of such high
  magnetizing forces, but was of special interest in that both B and I
  were measured optically--B by means of the rotation of a polarized ray
  inside a glass plate, as before described, and I by the rotation of a
  polarized ray reflected from the polished surface of the magnetized
  metal (see "Kerr's constant," MAGNETO-OPTICS). H(= B - 4[pi]I) was
  calculated from corresponding values of I and B. Taylor Jones (_Wied.
  Ann._, 1896, 57, 258, and _Phil. Mag._, 1896, 41, 153), working with
  du Bois's electromagnet and using a modification of the isthmus
  method, succeeded in pushing the induction B up to 74,200 with H =
  51,600, the corresponding value of I being 1798, and of µ only 1.44.
  The diameter of the isthmus was 0.241 mm., and the electromagnet was
  excited by a current of 40 amperes.

_Tractive Force of a Magnet._--Closely connected with the results just
discussed is the question what is the greatest tractive force that can
be exerted by a magnet. In the year 1852 J. P. Joule (_Phil. Mag._,
1852, 3, 32) expressed the opinion that no "force of current could give
an attraction equal to 200 lb. per sq. in.," or 14,000 grms. per square
centimetre, and a similar view prevailed among high authorities more
than twenty years later. For the greatest possible "lifting power" of
permanent magnets this estimate is probably not very far from the truth,
but it is now clearly understood that the force which can be exerted by
an electromagnet, or by a pair of electromagnets with opposite poles in
contact, is only limited by the greatest value to which it is
practically possible to raise the magnetizing force H. This is at once
evident when the tractive force due to magnetization is expressed as
2[pi]I²+ HI. For fields of moderate intensity the first term of the
expression is the more important, but when the value of H exceeds 12,000
or thereabouts, the second preponderates, and with the highest values
that have been actually obtained, HI is several times greater than
2[pi]I². If H could be increased without limit, so also could the
tractive force. The following table shows the greatest "lifting powers"
experimentally reached at the dates mentioned:--

  +-----------+-----------+---------+------+
  | Observer. | Kilos per | lb. per | Date.|
  |           |  sq. cm.  | sq. in. |      |
  +-----------+-----------+---------+------+
  | Joule     |    12.3   |    175  | 1852 |
  | Bidwell   |    15.9   |    226  | 1886 |
  | Wilde     |    26.8   |    381  | 1891 |
  | T. Jones  |   114.9   |   1634  | 1896 |
  +-----------+-----------+---------+------+


5. MAGNETIZATION IN VERY WEAK FIELDS

Some interesting observations have been made of the effects produced by
very small magnetic forces. It was first pointed out by C. Baur (_Wied.
Ann._, 1880, 11, 399) that in weak fields the relation of the
magnetization I to the magnetizing force H is approximately expressed by
an equation of the form

  I = aH + bH²,

or

  [kappa] = I/H = a + bH,

whence it appears that within the limits of Baur's experiments the
magnetization curve is a parabola, and the susceptibility curve an
inclined straight line, [kappa] being therefore a known function of H.
If these equations could be assumed to hold when H is indefinitely
small, it would follow that [kappa] has a finite initial value, from
which there would be no appreciable deviation in fields so weak that bH
was negligibly small in comparison with a. Such an assumption could not,
however, without dangerous extrapolation, be founded upon the results of
Baur's experiments, which did not go far enough to justify it. In some
experiments carried out in 1887, Lord Rayleigh (_Phil. Mag._, 1887, 23,
225) approached very much more nearly than Baur to the zero of magnetic
force. Using an unannealed Swedish iron wire, he found that when H was
gradually diminished from 0.04 to 0.00004 C.G.S. unit, the ratio of
magnetization to magnetizing force remained sensibly constant at 6.4,
which may therefore with great probability be assumed to represent the
initial value of [kappa] for the specimen in question. Experiments with
annealed iron gave less satisfactory results, on account of the slowness
with which the metal settled down into a new magnetic state, thus
causing a "drift" of the magnetometer needle, which sometimes persisted
for several seconds. Apart from this complication, it appeared that I
was proportional to H when the value of H was less than 0.02.

  The observations of Baur and Rayleigh have been confirmed and
  discussed by (amongst others) W. Schmidt (_Wied. Ann._, 1895, 54,
  655), who found the limiting values of [kappa] to be 7.5 to 9.5 for
  iron, and 11.2 to 13.5 for steel, remaining constant up to H = .06; by
  P. Culmann (_Elekt. Zeit._, 1893, 14, 345; _Wied. Ann._, 1895, 56,
  602); and by L. Holborn (_Berl. Ber._, 1897, p. 95, and _Wied. Ann._,
  1897, 61, 281). The latter gives values of the constants a and b for
  different samples of iron and steel, some of which are shown in the
  following table:--

    [kappa] = a + bH

              Metal.             a        b

    English tungsten steel     8.90    0.264
    Tungsten steel, hardened   2.23    0.032
    Silver steel               8.66    0.384
    Tool steel                 8.30    0.400
    Refined steel             11.28    1.92
    Cast iron                  3.16    0.236
    Soft iron                 16.6    18.6
    Hard drawn iron            5.88    1.76

  For most samples of steel the straight-line law was found to hold
  approximately up to H = 3; in the case of iron and of soft steel the
  approximation was less close.

The behaviour of nickel in weak fields has been observed by Ewing
(_Phil. Trans._, 1888, 179A, 325), who found that the initial value of
[kappa] was 1.7, and that it remained sensibly constant until H had
reached a value of about five units. While therefore the initial
susceptibility of nickel is less than that of iron and steel, the range
of magnetic force within which it is approximately constant is about one
hundred times greater. Ewing has also made a careful study (_Proc. Roy.
Soc._, 1889, 46, 269) of "magnetic viscosity" under small forces--the
cause of the magnetometer "drift" referred to by Rayleigh. On the
application of a small magnetizing force to a bar of soft annealed iron,
a certain intensity of magnetization is instantly produced; this,
however, does not remain constant, but slowly increases for some seconds
or even minutes, and may ultimately attain a value nearly twice as great
as that observed immediately after the force was applied.[30] When the
magnetizing current is broken, the magnetization at once undergoes
considerable diminution, then gradually falls to zero, and a similar
sudden change followed by a slow one is observed when a feeble current
is reversed. Ewing draws attention to a curious consequence of this
time-lag. By the alternate application and withdrawal of a small
magnetizing force a cyclic condition may be established in an iron rod.
If now the alternations are performed so rapidly that time is not
allowed for more than the first sudden change in the magnetization,
there will be no hysteresis loss, the magnetization exactly following
the magnetizing force. Further, if the alternations take place so slowly
that the full maximum and minimum values of the magnetization are
reached in the intervals between the reversals, there will again be no
dissipation of energy. But at any intermediate frequency the ascending
and descending curves of magnetization will enclose a space, and energy
will be dissipated. It is remarkable that the phenomena of magnetic
viscosity are much more evident in a thick rod than in a thin wire, or
even in a large bundle of thin wires. In hardened iron and steel the
effect can scarcely be detected, and in weak fields these metals exhibit
no magnetic hysteresis of any kind.


6. CHANGES OF DIMENSIONS ATTENDING MAGNETIZATION

It is well known that the form of a piece of ferromagnetic metal is in
general slightly changed by magnetization. The phenomenon was first
noticed by J. P. Joule, who in 1842 and 1847 described some experiments
which he had made upon bars of iron and steel. His observations, were
for the most part confirmed by a number of subsequent workers, notably
by A. M. Mayer; but with the single exception of the discovery by W. F.
Barrett in 1882 that a nickel bar contracts when magnetized, nothing of
importance was added by Joule's results for nearly forty years. Later
researches have however thrown much new light upon a class of phenomena
which cannot fail to have an important bearing upon the complete theory
of molecular magnetism.[31] According to Joule's observations, the
length of a bar of iron or soft steel was increased by magnetization,
the elongation being proportional up to a certain point to the square of
the intensity of magnetization; but when the "saturation point" was
approached the elongation was less than this law would require, and a
stage was finally reached at which further increase of the magnetizing
force produced little or no effect upon the length. From data contained
in Joule's paper it may be calculated that the strongest external field
H0 produced by his coil was about 126 C.G.S. units, but since the
dimensional ratio of his bars was comparatively small, the actual
magnetizing force H must have been materially below that value. In 1885
it was shown by Bidwell, in the first of a series of papers on the
subject, that if the magnetizing force is pushed beyond the point at
which Joule discontinued his experiments, the extension of the bar does
not remain unchanged, but becomes gradually less and less, until the
bar, after first returning to its original length, ultimately becomes
actually shorter than when in the unmagnetized condition. The elongation
is generally found to reach a maximum under a magnetizing force of 50 to
120 units, and to vanish under a force of 200 to 400, retraction
occurring when still higher forces are applied. In order to meet the
objection that the phenomenon might be due to electromagnetic action
between the coil and the rod, Bidwell made some experiments with iron
rings, and found that the length of their diameters varied under
magnetization in precisely the same manner as the length of a straight
rod. Experiments were afterwards made with rods of iron, nickel, and
cobalt, the external field being carried up to the high value of 1500
units. The results are indicated in Fig. 24. It appears that the
contraction which followed the initial extension of the iron reached a
limit in fields of 1000 or 1100. Nickel exhibited retraction from the
very beginning (as observed by Barrett), its greatest change of length
considerably exceeding that undergone by iron; in a field of 800 the
original length was diminished by as much as 1/40,000 part, but stronger
forces failed to produce any further effect. The curve for cobalt is a
very remarkable one. Little or no change of length was observed until
the strength of the field H0 reached about 50; then the rod began to
contract, and after passing a minimum at H0 = 400, recovered its
original length at H0 = 750; beyond this point there was extension, the
amount of which was still increasing fast when the experiment was
stopped at H0 = 1400. Similar results were obtained with three different
samples of the metal. Roughly speaking, therefore, cobalt behaves
oppositely to iron.

[Illustration: FIG. 24]

Joule and others experimented with hardened steel, but failed to find a
key to the results they obtained, which are rather complex, and have
been thought to be inconsistent. The truth appears to be that a hardened
steel rod generally behaves like one of iron or soft steel in first
undergoing extension under increasing magnetizing force, and recovering
its original length when the force has reached a certain critical value,
beyond which there is contraction. But this "critical value" of the
force is found to depend in an unexpected manner upon the hardness of
the steel; the critical value diminishes as the hardness becomes greater
_up to a certain point_, corresponding to a yellow temper, after which
it increases and with the hardest steel becomes very high. For steel
which has been made red-hot, suddenly cooled, and then let down to a
yellow temper, the critical value of the magnetizing force is smaller
than for steel which is either softer or harder; it is indeed so small
that the metal contracts like nickel even under weak magnetizing forces,
without undergoing any preliminary extension that can be detected.

[Illustration: FIG. 25.]

Joule also made experiments upon iron wires under tension, and drew the
erroneous inference (which has been often quoted as if it were a
demonstrated fact) that under a certain critical tension (differing for
different specimens of iron but independent of the magnetizing force)
magnetization would produce no effect whatever upon the dimensions of
the wire. What actually happens when an iron wire is loaded with various
weights is clearly shown in Fig. 25. Increased tension merely has the
effect of diminishing the maximum elongation and hastening the
contraction; with the two greatest loads used in the experiment there
was indeed no preliminary extension at all.[32] The effects of tension
upon the behaviour of a nickel wire are of a less simple character. In
weak fields the magnetic contraction is always diminished by pulling
stress; in strong fields the contraction increases under a small load
and diminishes under a heavy one. Cobalt, curiously enough, was found to
be quite unaffected by tensile stress.

Certain experiments by C. G. Knott on magnetic twist, which will be
referred to later, led him to form the conclusion that in an iron wire
carrying an electric current the magnetic elongation would be increased.
This forecast was shown by Bidwell to be well founded. The effect
produced by a current is exactly opposite to that of tension, raising
the elongation curve instead of depressing it. In the case of a wire
0.75 mm. in diameter the maximum elongation was nearly doubled when a
current of two amperes was passing through the iron, while the "critical
value" of the field was increased from 130 to 200. Yet notwithstanding
this enormous effect in iron, the action of a current upon nickel and
cobalt turned out to be almost inappreciable.

Some experiments were next undertaken with the view of ascertaining how
far magnetic changes of length in iron were dependent upon the hardness
of the metal, and the unexpected result was arrived at that softening
produces the same effect as tensile stress; it depresses the elongation
curve, diminishing the maximum extension, and reducing the "critical
value" of the magnetizing force. A thoroughly well annealed ring of soft
iron indeed showed no extension at all, beginning to contract, like
nickel, under the smallest magnetizing forces. The experiments were not
sufficiently numerous to indicate whether, as is possible, there is a
critical degree of hardness for which the height of the elongation curve
is a maximum.

Finally, experiments were made to ascertain the effect of magnetization
upon the dimensions of iron rings in directions perpendicular to the
magnetization, and upon the volume of the rings.[33] It was found that
the curve showing the relation of transverse changes of dimensions to
magnetizing force was similar in general character to the familiar
elongation curves, but the signs were reversed; the curve was inverted,
indicating at first retraction, which, after passing a maximum and
vanishing in a critical field, was succeeded by elongation. The curve
showing the circumferential (or longitudinal) changes was also plotted,
and from the two curves thus obtained it was easy, on the assumption
that the metal was isotropic in directions at right angles to the
magnetization, to calculate changes of volume; for if circumferential
elongation be denoted by l1, and transverse elongation by l2, then the
cubical dilatation (+ or -) = l1 + 2l2 approximately. If l1 were exactly
equal to -2l2 for all values of the magnetizing force, it is clear that
the volume of the ring would be unaffected by magnetization. In the case
of the ring in question, the circumferential changes were in weak fields
less than twice as great as the transverse ones, while in strong fields
they were more than twice as great; under increasing magnetic force
therefore the volume of the ring was first diminished, then it regained
its original value (for H = 90), and ultimately increased. It was also
shown that annealing, which has such a large effect upon circumferential
(or longitudinal) changes, has almost none upon transverse ones. Hence
the changes of volume undergone by a given sample of wrought iron under
increasing magnetization must depend largely upon the state of the metal
as regards hardness; there may be always contraction, or always
expansion, or first one and then the other.

Most of the experiments described above have been repeated and the
results confirmed by other workers, some of whom have added fresh
observations. The complicated hysteresis effects which attend magnetic
elongation and retraction have been studied by H. Nagaoka, who also, in
conjunction with K. Honda, measured the changes of length of various
metals shaped in the form of ovoids instead of cylindrical rods, and
determined the magnetization curves for the same specimens; a higher
degree of accuracy was thus attained, and satisfactory data were
provided for testing theories. Among other things, it was found that the
behaviour of cast cobalt was entirely changed by annealing; the sinuous
curve shown in Fig. 24 was converted into an almost perfectly straight
line passing through the origin, and lying below the horizontal axis;
while the permeability of the metal was greatly diminished by the
operation. They also tested several varieties of nickel-steel in the
form of both ovoids and wires. With a sample containing 25% of nickel no
appreciable change was detected; others containing larger percentages,
and tested in fields up to 2000, all exhibited elongation, which tended
to an asymptotic value as the field was increased. The influence of
temperature varying between wide limits has formed the subject of a
research by K. Honda and S. Shimizu. For soft iron, tungsten-steel and
nickel little difference appeared to result from lowering the
temperature down to -186° C. (the temperature of liquid air); at
sufficiently high temperatures, 600° to 1000° or more, it was remarked
that the changes of length in iron, steel and cobalt tended in every
case to become proportional to the magnetic force, the curves being
nearly straight lines entirely above the axis. The retraction of nickel
was diminished by rising temperature, and at 400° had almost vanished.
The influence of high temperature on cobalt was very remarkable,
completely altering the character of the change of length: the curves
for annealed cobalt show that at 450° this metal behaves just like iron
at ordinary temperatures, lengthening in fields up to about 300 and
contracting in stronger ones. The same physicists have made some
additional experiments upon the effect of tension on magnetic change of
length. Bidwell's results for iron and nickel were confirmed, and it was
further shown that the elongation of nickel-steel was very greatly
diminished by tension; when magnetized under very heavy loads, the wire
was indeed found to undergo slight contraction. Honda subjected tubes of
iron, steel and nickel to the simultaneous action of circular and
longitudinal fields, and observed the changes of length when one of the
fields was varied while the other remained constant at different
successive values from zero upwards. The experimental results agreed in
sign though not in magnitude with those calculated from the changes
produced by simple longitudinal magnetization, discrepancies being
partly accounted for by the fact that the metals employed were not
actually isotropic. Heusler's alloy has been tested for change of length
by L. Austin, who found continuous elongation with increasing fields,
the curves obtained bearing some resemblance to curves of magnetization.

As regards the effect of magnetization upon volume there are some
discrepancies. Nagaoka and Honda, who employed a fluid dilatometer,
found that the volume of several specimens of iron, steel and nickel was
always slightly increased, no diminution being indicated in low fields;
cobalt, on the other hand, was diminished in volume, and the amount of
the change, though still very small, was greater than that shown by the
other metals. Various nickel-steels all expanded under magnetization,
the increase being generally considerable and proportional to the field;
in the case of an alloy containing 29% of nickel the change was nearly
40 times greater than in soft iron. C. G. Knott, who made an exhaustive
series of experiments upon various metals in the form of tubes,
concluded that in iron there was always a slight increase of volume, and
in nickel and cobalt a slight decrease. It is uncertain how far these
various results are dependent upon the physical condition of the metals.

  Attempts have been made to explain magnetic deformation by various
  theories of magnetic stress,[34] notably that elaborated by G. R.
  Kirchhoff (_Wied. Ann._, 1885, 24, 52, and 1885, 25, 601), but so far
  with imperfect success. E. Taylor Jones showed in 1897 that only a
  small proportion of the contraction exhibited by a nickel wire when
  magnetized could be accounted for on Kirchhoff's theory from the
  observed effects of pulling stress upon magnetization; and in a more
  extended series of observations Nagaoka and Honda found wide
  quantitative divergences between the results of experiment and
  calculation, though in nearly all cases there was agreement as to
  quality. They consider, however, that Kirchhoff's theory, which
  assumes change of magnetization to be simply proportional to strain,
  is still in its infancy, the present stage of its evolution being
  perhaps comparable with that reached by the theory of magnetization at
  the time when the ratio I/H was supposed to be constant. In the light
  of future researches further development may reasonably be expected.

  It has been suggested[35] that an iron rod under magnetization may be
  in the same condition as if under a mechanically applied longitudinal
  stress tending to shorten the iron. If a long magnetized rod is
  divided transversely and the cut ends placed nearly in contact, the
  magnetic force inside the narrow air gap will be B = H + 4[pi]I. The
  force acting on the magnetism of one of the faces, and urging this
  face towards the other, will be less than B by 2[pi]I, the part of the
  total force due to the first face itself; hence the force per unit of
  area with which the faces would press against each other if in contact
  is

    P = (B - 2[pi]I)I = 2[pi]I² + HI = (B² - H²) / 8[pi].

  The width of the gap may be diminished until it is no greater than the
  distance between two neighbouring molecules, when it will cease to be
  distinguishable, but, assuming the molecular theory of magnetism to be
  true, the above statement will still hold good for the intermolecular
  gap. The same pressure P will be exerted across any imaginary section
  of a magnetized rod, the stress being sustained by the intermolecular
  springs, whatever their physical nature may be, to which the
  elasticity of the metal is due. The whole of the rod will therefore be
  subject to a compressive longitudinal stress P, the associated
  contraction R, expressed as a fraction of the original length, being

    R = P/M = (B² - H²) / 8[pi]M,

  where M is Young's modulus. This was found to be insufficient to
  account for the whole of the retraction exhibited by iron in strong
  fields, but it was pointed out by L. T. More[36] that R ought to be
  regarded as a "correction" to be applied to the results of
  experiments on magnetic change of length, the magnetic stress being no
  less an extraneous effect than a stress applied mechanically. Those
  who support this view generally speak of the stress as "Maxwell's
  stress," and assume its value to be B^2/8[pi]. The stress in question
  seems, however, to be quite unconnected with the "stress in the
  medium" contemplated by Maxwell, and its value is not exactly
  B^2/8[pi] except in the particular case of a permanent ring magnet,
  when H = O. Further, Maxwell's stress is a tension along the lines of
  force, and is equal to B^2/8[pi] only when B = H, and there is no
  magnetization.[37] Some writers have indeed contended that the stress
  in magnetized iron is not compressive, but tensile, even when, as in
  the case of a ring-magnet, there are no free ends. The point at issue
  has an important bearing upon the possible correlation of magnetic
  phenomena, but, though it has given rise to much discussion, no
  accepted conclusion has yet been reached.[38]


7. EFFECTS OF MECHANICAL STRESS UPON MAGNETIZATION

The effects of traction, compression and torsion in relation to
magnetism have formed the subject of much patient investigation,
especially at the hands of J. A. Ewing, C. G. Knott and the
indefatigable physicists of Tokyo University. The results of their
experiments embrace a multiplicity of details of which it is impossible
to give an adequate summary. Only a few of the most important can be
mentioned here; the reader who wishes for fuller information should
consult the original papers.[39]

It was first discovered by E. Villari in 1868 that the magnetic
susceptibility of an iron wire was increased by stretching when the
magnetization was below a certain value, but diminished when that value
was exceeded; this phenomenon has been termed by Lord Kelvin, who
discovered it independently, the "Villari reversal," the value of the
magnetization for which stretching by a given load produces no effect
being known as the "Villari critical point" for that load. The Villari
critical point for a given sample of iron is reached with a smaller
magnetizing force when the stretching load is great than when it is
small; the reversal also occurs with smaller loads and with weaker
fields when the iron is soft than when it is hard. The following table
shows the values of I and H corresponding to the Villari critical point
in some of Ewing's experiments:--

  +------------------------------+-----------------------------+
  |          Soft Iron.          |          Hard Iron.         |
  +-----------------+------+-----+-----------------+------+----+
  |Kilos per sq. mm.|  I.  |  H. |Kilos per sq. mm.|  I.  | H. |
  +-----------------+------+-----+-----------------+------+----+
  |       2.15      | 1220 | 7.3 |       27.6      | 1180 | 34 |
  |       4.3       | 1040 | 4.3 |       32.2      | 1150 | 32 |
  |       8.6       |  840 | 3.4 |       37.3      | 1110 | 29 |
  |      12.9       |  690 | 3.05|       42.5      | 1020 | 25 |
  +-----------------+------+-----+-----------------+------+----+

The effects of pulling stress may be observed either when the wire is
stretched by a constant load while the magnetizing force is varied, or
when the magnetizing force is kept constant while the load is varied. In
the latter case the first application of stress is always attended by an
increase--often a very great one--of the magnetization, whether the
field is weak or strong, but after a load has been put on and taken off
several times the changes of magnetization become cyclic. From
experiments of both classes it appears that for a given field there is a
certain value of the load for which the magnetization is a maximum, the
maximum occurring at a smaller load the stronger the field. In very
strong fields the maximum may even disappear altogether, the effect of
the smallest stress being to diminish the magnetization; on the other
hand, with very weak fields the maximum may not have been reached with
the greatest load that the wire can support without permanent
deformation. When the load on a hardened wire is gradually increased,
the maximum value of I is found to correspond with a greater stress than
when the load is gradually diminished, this being an effect of
hysteresis. Analogous changes are observed in the residual magnetization
which remains after the wire has been subjected to fields of different
strength. The effects of longitudinal pressure are opposite to those of
traction; when the cyclic condition has been reached, pressure reduces
the magnetization of iron in weak fields and increases it in strong
fields (Ewing, _Magnetic Induction_, 1900, 223).

The influence of traction in diminishing the susceptibility of nickel
was first noticed by Kelvin (W. Thomson), and was subsequently
investigated by Ewing and Cowan. The latter found the effect to be
enormous, not only upon the induced magnetization, but in a still
greater degree upon the residual. Even under so "moderate" a load as 33
kilogrammes per square mm., the induced magnetization of a hard-drawn
nickel wire in a field of 60 fell from 386 to 72 units, while the
residual was reduced from about 280 to 10. Ewing has also examined the
effects produced by longitudinal compression upon the susceptibility and
retentiveness of nickel, and found, as was to be expected, that both
were greatly increased by pressure. The maximum susceptibility of one of
his bars rose from 5.6 to 29 under a stress of 19.8 kilos per square mm.
There were reasons for believing that no Villari reversal would be found
in nickel. Ewing and Cowan looked carefully for it, especially in weak
fields, but failed to discover anything of the kind.[40] Some
experiments by A. Heydweiller,[41] which appeared to indicate a reversal
in weak fields (corresponding to I = 5, or thereabouts), have been shown
by Honda and Shimizu to be vitiated by the fact that his specimen was
not initially in a magnetically neutral state; they found that when the
applied field had the same direction as that of the permanent
magnetization, Heydweiller's fallacious results were easily obtained;
but if the field were applied in the direction opposite to that of the
permanent magnetization, or if, as should rightly be the case, there
were no permanent magnetization at all, then there was no indication of
any Villari reversal. Thus a very important question, which has given
rise to some controversy, appears to be now definitely settled.

The effects of longitudinal pressure upon the magnetization of cast
cobalt have been examined by C. Chree,[42] and also by J. A. Ewing.[43]
Chree's experiments were undertaken at the suggestion of J. J. Thomson,
who, from the results of Bidwell's observations on the magnetic
deformation of cobalt, was led to expect that that metal would exhibit a
reversal opposite in character to the effect observed in iron. The
anticipated reversal was duly found by Chree, the critical point
corresponding, under the moderate stress employed, to a field of about
120 units. Ewing's independent experiments showed that the magnetization
curve for a cobalt rod under a load of 16.2 kilogrammes per square mm.
crossed the curve for the same rod when not loaded at H = 53. Both
observers noticed analogous effects in the residual magnetization. The
effect of tension was subsequently studied by Nagaoka and Honda, who in
1902 confirmed, _mutatis mutandis_, the results obtained by Chree and
Ewing for cast cobalt, while for annealed cobalt it turned out that
tension always caused diminution of magnetization, the diminution
increasing with increasing fields. They also investigated the magnetic
behaviour of various nickel-steels under tension, and found that there
was always increase of magnetization. Thus it has been proved that in
annealed cobalt and in nickel-steel there is no Villari reversal.

It has been pointed out by J. J. Thomson (_Applications of Dynamics to
Physics and Chemistry_, 47) that on dynamical principles there must be a
reciprocal relation between the changes of dimensions produced by
magnetization and the changes of magnetization attending mechanical
strain. Since, for example, stretching diminishes the magnetization of
nickel, it follows from theory that the length of a nickel rod should be
diminished by magnetization and conversely. So, too, the Villari
reversals in iron and cobalt might have been predicted--as indeed that
in cobalt actually was--from a knowledge of the changes of length which
those metals exhibit when magnetized.

The complete reciprocity of the effects of magnetization upon length and
of stretching upon magnetization is shown by the following parallel
statements:--

      _Iron._

    Magnetization produces increase     Tension produces increase of
    of length in weak fields,           magnetization in weak fields,
    decrease in strong fields.          decrease in strong fields.

      _Cast Cobalt._

    Magnetization produces decrease     Tension produces decrease of
    of length in weak fields,           magnetization in weak fields,
    increase in strong fields.          increase in strong fields.

      _Nickel and Annealed Cobalt._

    Magnetization produces decrease     Tension produces decrease of
    of length in all fields.            magnetization in all fields.

      _Nickel-Steel._

    Magnetization produces increase     Tension produces increase of
    of length in all fields.            magnetization in all fields.

  Nagaoka and Honda (_Phil. Mag._, 1898, 46, 261) have investigated the
  effects of hydrostatic pressure upon magnetization, using the same
  pieces of iron and nickel as were employed in their experiments upon
  magnetic change of volume. In the iron cylinder and ovoid, which
  expanded when magnetized, compression caused a diminution of
  magnetization; in the nickel rod, which contracted when magnetized,
  pressure was attended by an increase of magnetization. The amount of
  the change was in both cases exceedingly small, that in iron being
  less than 0.1 C.G.S. unit with a pressure of 250 atmospheres and H =
  54. It would hardly be safe to generalize from these observations; the
  effects may possibly be dependent upon the physical condition of the
  metals. In the same paper Nagaoka and Honda describe an important
  experiment on the effect of transverse stress. An iron tube, having
  its ends closed by brass caps, was placed inside a compressing vessel
  into which water was forced until the pressure upon the outer surface
  of the tube reached 250 atmospheres. The experiment was the reverse of
  one made by Kelvin with a gun-barrel subjected to internal hydrostatic
  pressure (_Phil. Trans._, 1878, 152, 64), and the results were also
  the reverse. Under increasing magnetizing force the magnetization
  first increased, reached a maximum, and then diminished until its
  value ultimately became less than when the iron was in the unstrained
  condition. Experiments on the effect of external hydrostatic pressure
  upon the magnetization of iron rings have also been made by F.
  Frisbie,[44] who found that for the magnetizing forces used by Nagaoka
  and Honda pressure produced a small _increase_ of magnetization, a
  result which appears to be in accord with theory.

The relations of torsion to magnetization were first carefully studied
by G. Wiedemann, whose researches are described in his _Elektricität_,
iii. 671. The most interesting of his discoveries, now generally known
as the "Wiedemann effect," is the following: If we magnetize
longitudinally a straight wire which is fixed at one end and free at the
other, and then pass an electric current through the wire (or first pass
the current and then magnetize), the free end of the wire will twist in
a certain direction depending upon circumstances: if the wire is of
iron, and is magnetized (with a moderate force) so that its free end has
north polarity, while the current through it passes from the fixed to
the free end, then the free end as seen from the fixed end will twist in
the direction of the hands of a watch; if either the magnetization or
the current is reversed, the direction of the twist will be reversed. To
this mechanical phenomenon there is a magnetic reciprocal. If we twist
the free end of a ferromagnetic wire while a current is passing through
it, the wire becomes longitudinally magnetized, the direction of the
magnetization depending upon circumstances: if the wire is of iron and
is twisted so that its free end as seen from the fixed end turns in the
direction of the hands of a watch, while the current passes from the
fixed to the free end, then the direction of the resulting magnetization
will be such as to make the free end a north pole. The twist effect
exhibited by iron under moderate longitudinal magnetization has been
called by Knott a _positive_ Wiedemann effect; if the twist were
reversed, the other conditions remaining the same, the sign of the
Wiedemann effect would be _negative_. An explanation of the twist has
been given by Maxwell (_Electricity and Magnetism_, § 448). The wire is
subject to two superposed magnetizations, the one longitudinal, the
other circular, due to the current traversing the wire; the resultant
magnetization is consequently in the direction of a screw or spiral
round the wire, which will be right-handed or left-handed according as
the relation between the two magnetizations is right-handed or
left-handed; the magnetic expansion or contraction of the metal along
the spiral lines of magnetization produces the Wiedemann twist. Iron
(moderately magnetized) expands along the lines of magnetization, and
therefore for a right-handed spiral exhibits a right-handed twist. This
explanation was not accepted by Wiedemann,[45] who thought that the
effect was accounted for by molecular friction. Now nickel contracts
instead of lengthening when it is magnetized, and an experiment by Knott
showed, as he expected, that _caeteris paribus_ a nickel wire twists in
a sense opposite to that in which iron twists. The Wiedemann effect
being positive for iron is negative for nickel. Further, although iron
lengthens in fields of moderate strength, it contracts in strong ones;
and if the wire is stretched, contraction occurs with smaller
magnetizing forces than if it is unstretched. Bidwell[46] accordingly
found upon trial that the Wiedemann twist of an iron wire vanished when
the magnetizing force reached a certain high value, and was reversed
when that value was exceeded; he also found that the vanishing point was
reached with lower values of the magnetizing force when the wire was
stretched by a weight. These observations have been verified and
extended by Knott, whose researches have brought to light a large number
of additional facts, all of which are in perfect harmony with Maxwell's
explanation of the twist.

[Illustration: FIG. 26.]

Maxwell has also given an explanation of the converse effect, namely,
the production of longitudinal magnetization by twisting a wire when
circularly magnetized by a current passing through it. When the wire is
free from twist, the magnetization at any point P is in the tangential
direction PB (see fig. 26). Suppose the wire to be fixed at the top and
twisted at the bottom in the direction of the arrow-head T; then the
element of the wire at P will be stretched in the direction Pe and
compressed in the direction Pr. But tension and compression produce
opposite changes in the magnetic susceptibility; if the metal is iron
and its magnetization is below the Villari critical point, its
susceptibility will be greater along Pe than along Pr; the direction of
the magnetization therefore tends to approach Pe and to recede from Pr,
changing, in consequence of the twist, from PB to some such direction as
PB´, which has a vertical component downwards; hence the lower and upper
ends will respectively acquire north and south polarity, which will
disappear when the wire is untwisted. This effect has never been
actually reversed in iron, probably, as suggested by Ewing, because the
strongest practicable circular fields fail to raise the components of
the magnetization along Pe and Pr up to the Villari critical value.
Nagaoka and Honda have approached very closely to a reversal, and
consider that it would occur if a sufficiently strong current could be
applied without undue heating.

One other effect of torsion remains to be noticed. If a longitudinally
magnetized wire is twisted, circular magnetization is developed; this is
evidenced by the transient electromotive force induced in the iron,
generating a current which will deflect a galvanometer connected with
the two ends of the wire. The explanation given of the last described
phenomenon will with the necessary modification apply also to this; it
is a consequence of the aeolotropy produced by the twist. There are
then three remarkable effects of torsion:

  A. A wire magnetized longitudinally and circularly becomes twisted.

  B. Twisting a circularly magnetized wire produces longitudinal
  magnetization.

  C. Twisting a longitudinally magnetized wire produces circular
  magnetization.

And it has been shown earlier that--

  D. Magnetization produces change of length.

  E. Longitudinal stress produces change of magnetization.

Each of these five effects may occur in two opposite senses. Thus in A
the twist may be right-handed or left-handed; in B the polarity of a
given end may become north or south; in C the circular magnetization may
be clockwise or counter-clockwise; in D the length may be increased or
diminished; in E the magnetization may become stronger or weaker. And,
other conditions remaining unchanged, the "sense" of any effect depends
upon the nature of the metal under test, and (sometimes) upon the
intensity of its magnetization. Let each of the effects A, B, C, D and E
be called positive when it is such as is exhibited by moderately
magnetized iron, and negative when its sense is opposite. Then the
results of a large number of investigations may be briefly summarized as
follows:

  (W) = weakly magnetized. (S) = strongly magnetized.

      _Metal._             _Effects._     _Sign._

  Iron (W)               A, B, C, D, E       +
  Unannealed Cobalt (S)  A,       D, E       +
  Nickel-Steel (W)       A,       D, E       +
  Nickel                 A, B, C, D, E       -
  Annealed Cobalt                 D, E       -
  Iron (S)               A,    C, D, E       -
  Unannealed Cobalt      A,       D, E       -

Several gaps remain to be filled, but the results so far recorded can
leave no doubt that the five effects, varied as they may at first sight
appear, are intimately connected with one another. For each of the
metals tabulated in the first column all the effects hitherto observed
have the same sign; there is no single instance in which some are
positive and others negative. Until the mysteries of molecular
constitution have been more fully explored, perhaps D may be most
properly regarded as the fundamental phenomenon from which the others
follow. Nagaoka and Honda have succeeded in showing that the observed
relations between twist and magnetization are in qualitative agreement
with an extension of Kirchhoff's theory of magnetostriction.

  The effects of magnetization upon the torsion of a previously twisted
  wire, which were first noticed by Wiedemann, have been further studied
  by F. J. Smith[47] and by G. Moreau.[48] Nagaoka[49] has described the
  remarkable influence of combined torsion and tension upon the magnetic
  susceptibility of nickel, and has made the extraordinary observation
  that, under certain conditions of stress, the magnetization of a
  nickel wire may have a direction opposite to that of the magnetizing
  force.


8. EFFECTS OF TEMPERATURE UPON MAGNETISM

_High Temperature._--It has long been known that iron, when raised to a
certain "critical temperature" corresponding to dull red heat, loses its
susceptibility and becomes magnetically indifferent, or, more
accurately, is transformed from a ferromagnetic into a paramagnetic
body. Recent researches have shown that other important changes in its
properties occur at the same critical temperature. Abrupt alterations
take place in its density, specific heat, thermo-electric quality,
electrical conductivity, temperature-coefficient of electrical
resistance, and in some at least of its mechanical properties. Ordinary
magnetizable iron is in many respects an essentially different substance
from the non-magnetizable metal into which it is transformed when its
temperature is raised above a certain point (see _Brit. Assoc. Report_,
1890, 145). The first exact experiments demonstrating the changes which
occur in the permeability of iron, steel and nickel when heated up to
high temperatures were those of J. Hopkinson (_Phil. Trans._, 1889, 180,
443; _Proc. Roy. Soc._, 1888, 44, 317). The metal to be tested was
prepared in the form of a ring, upon which were wound primary and
secondary coils of copper wire insulated with asbestos. The primary coil
carried the magnetizing current; the secondary, which was wound inside
the other, could be connected either with a ballistic galvanometer for
determining the induction, or with a Wheatstone's bridge for measuring
the resistance, whence the temperature was calculated. The ring thus
prepared was placed in a cast-iron box and heated in a gas furnace. The
following are the chief results of Hopkinson's experiments: For small
magnetizing forces the magnetization of iron steadily increases with
rise of temperature till the critical temperature is approached, when
the rate of increase becomes very high, the permeability in some cases
attaining a value of about 11,000; the magnetization then with
remarkable suddenness almost entirely disappears, the permeability
falling to about 1.14. For strong magnetizing forces (which in these
experiments did not exceed H = 48.9) the permeability remains almost
constant at its initial value (about 400), until the temperature is
within nearly 100° of the critical point; then the permeability
diminishes more and more rapidly until the critical point is reached and
the magnetization vanishes. Steel behaves in a similar manner, but the
maximum permeability is not so high as in iron, and the fall, when the
critical point is approached, is less abrupt. The critical temperature
for various samples of iron and steel ranges from 690° C. to 870° C.; it
is the temperature at which Barrett's "recalescence" occurs. The
critical temperature for the specimen of nickel examined (which
contained nearly 5% of impurities) was 310° C. F. Lydall and A. W.
Pocklington found that the critical temperature of nearly pure iron was
874° C. (_Proc. Roy. Soc._, 1893, 52, 228).

An exhaustive research into the effects of heating on the magnetic
properties of iron has been carried out by D. K. Morris (_Proc. Phys.
Soc._, 1897, 15, 134; and _Phil. Mag._, 1897, 44, 213), the results
being embodied in a paper containing twelve pages of tables and upwards
of 120 curves. As in Hopkinson's experiments, ring magnets were
employed; these were wound with primary and secondary coils of insulated
platinum wire, which would bear a much higher temperature than copper
without oxidation or fusion. A third platinum coil, wound
non-inductively between the primary and the secondary, served to carry
the current by which the ring was heated; a current of 4.6 amperes, with
16 volts across the terminals, was found sufficient to maintain the ring
at a temperature of 1150° C. In the ring itself was embedded a
platinum-thermometer wire, from the resistance of which the temperature
was determined. The whole was wrapped in several coverings of asbestos
and placed in a glass vessel from which the air was partially exhausted,
additional precautions being taken to guard against oxidation of the
iron.

[Illustration: FIG. 27.]

  Some preliminary experiments showed the striking difference in the
  effects of annealing at a red heat (840° C.) and at a low white heat
  (1150° C). After one of the rings had been annealed at 840°, its
  maximum permeability at ordinary temperatures was 4000 for H = 1.84;
  when it had been subsequently annealed at 1150°, the maximum
  permeability rose to 4680 for H = 1.48, while the hysteresis loss for
  B= ±4000 was under 500 ergs per c.cm. As regards the effects of
  temperature, Morris's results are in general agreement with those of
  Hopkinson, though no doubt they indicate details with greater
  clearness and accuracy. Specimens of curves showing the relation of
  induction to magnetic field at various temperatures, and of
  permeability to temperature with fields of different intensities, are
  given in figs. 27 and 28. The most striking feature presented by these
  is the enormous value, 12,660, which, with H = 0.153, is attained by
  the permeability at 765° C., followed by a drop so precipitous that
  when the temperature is only 15° higher, the value of the permeability
  has become quite insignificant. The critical temperatures for three
  different specimens of iron were 795°, 780°, and 770° respectively.
  Above these temperatures the little permeability that remained was
  found to be independent of the magnetizing force, but it appeared to
  vary a little with the temperature, one specimen showing a
  permeability of 100 at 820°, 2.3 at 950°, and 17 at 1050°. These last
  observations are, however, regarded as uncertain. The effects of
  temperature upon hysteresis were also carefully studied, and many
  hysteresis loops were plotted. The results of a typical experiment are
  given in the annexed table, which shows how greatly the hysteresis
  loss is diminished as the critical temperature is approached. The
  coercive force at 764°.5 is stated to have been little more than 0.1
  C.G.S. unit; above the critical temperature no evidence of hysteresis
  could be obtained.

  [Illustration: FIG. 28.]

    Hysteresis Loss in Ergs per c.cm. Max. H. = ±6.83.

   Temp. C.°   Ergs.    Temp. C.°    Ergs.

     764.5      120   |    457       2025
     748        328   |    352       2565
     730        426   |    249       3130
     695        797   |    137.5     3500
     634       1010   |    24        3660
     554       1345   |

  A paper by H. Nagaoka and S. Kusakabe[50] generally confirms Morris's
  results for iron, and gives some additional observations for steel,
  nickel and cobalt. The magnetometric method was employed, and the
  metals, in the form of ovoids, were heated by a specially designed
  burner, fed with gas and air under pressure, which directed 90 fine
  jets of flame upon the asbestos covering the ovoid. The temperature
  was determined by a platinum-rhodium and platinum thermo-junction in
  contact with the metal. Experiments were made at several constant
  temperatures with varying magnetic fields, and also at constant fields
  with rising and falling temperatures. For ordinary steel the critical
  temperature, at which magnetization practically disappeared, was found
  to be about 830°, and the curious fact was revealed that, on cooling,
  magnetization did not begin to reappear until the temperature had
  fallen 40° below the critical value. This retardation was still more
  pronounced in the case of tungsten-steel, which lost its magnetism at
  910° and remained non-magnetic till it was cooled to 570°, a
  difference of 240°. For nearly pure nickel the corresponding
  temperature-difference was about 100°. This phenomenon is of the same
  nature as that first discovered by J. Hopkinson for nickel-steel. The
  paper contains tables and curves showing details of the magnetic
  changes, sometimes very complex, at different temperatures and with
  different fields. The behaviour of cobalt is particularly noticeable;
  its permeability increased with rising temperature up to a maximum at
  500°, when it was about twice as great as at ordinary temperatures,
  while at 1600°, corresponding to white heat, there was still some
  magnetization remaining.

  Further contributions to the subject have been made by K. Honda and S.
  Shimizu,[51] who experimented at temperatures ranging from -186° to
  1200°. As regards the higher temperatures, the chief point of interest
  is the observation that the curve of magnetization for annealed cobalt
  shows a small depression at about 450°, the temperature at which they
  had found the sign of the length-change to be reversed for all fields.
  In the case of all the metals tested a small but measurable trace of
  magnetization remained after the so-called critical temperature had
  been exceeded; this decreased very slightly up to the highest
  temperature reached (1200°) without undergoing any such variation as
  had been suspected by Morris. When the curve after its steep descent
  has almost reached the axis, it bends aside sharply and becomes a
  nearly horizontal straight line; the authors suggest that the critical
  temperature should be defined as that corresponding to the point of
  maximum curvature. As thus defined the critical temperatures for iron,
  nickel and cobalt were found to be 780°, 360° and 1090° respectively,
  but these values are not quite independent of the magnetizing force.

  Experiments on the effect of high temperatures have also been made by
  M. P. Ledeboer,[52] H. Tomlinson,[53] P. Curie,[54] and W. Kunz,[55]
  R. L. Wills,[56] J. R. Ashworth[57] and E. P. Harrison.[58]

_Low Temperature._--J. A. Fleming and J. Dewar (_Proc. Roy. Soc._, 1896,
60, 81) were the first to experiment on the permeability and hysteresis
of iron at low temperatures down to that of liquid air (-186° C.).
Induction curves of an annealed soft-iron ring were taken first at a
temperature of 15° C., and afterwards when the ring was immersed in
liquid air, the magnetizing force ranging from about 0.8 to 22. After
this operation had been repeated a few times the iron was found to have
acquired a stable condition, and the curves corresponding to the two
temperatures became perfectly definite. They showed that the
permeability of this sample of iron was considerably diminished at the
lower temperature. The maximum permeability (for H = 2) was 3400 at 15°
and only 2700 at -186°, a reduction of more than 20%; but the percentage
reduction became less as the magnetizing force departed from the value
corresponding to maximum permeability. Observations were also made of
the changes of permeability which took place as the temperature of the
sample slowly rose from -186° to 15°, the magnetizing force being kept
constant throughout an experiment. The values of the permeability
corresponding to the highest and lowest temperatures are given in the
following table. Most of the permeability-temperature curves were more
or less convex

  +------------------+--------+------------+-------------+
  |  Sample of Iron. |    H.  |  µ at 15°. | µ at -186°. |
  +------------------+--------+------------+-------------+
  | Annealed Swedish |   1.77 |   2835     |    2332     |
  | Unannealed  "    |   1.78 |    917     |    1272     |
  |     "       "    |   9.79 |   1210     |    1293     |
  | Hardened    "    |   2.66 |     56     |     132     |
  |     "       "    |   4.92 |    106.5   |     502     |
  |     "       "    |  11.16 |    447.5   |     823     |
  |     "       "    | 127.7  |    109     |     124     |
  | Steel wire       |   7.50 |     86     |      64.5   |
  |     "            |  20.39 |    361     |     144     |
  +------------------+--------+------------+-------------+

towards the axis of temperature, and in all the experiments, except
those with annealed iron and steel wire, the permeability was greatest
at the lowest temperature.[59] The hysteresis of the soft annealed iron
turned out to be sensibly the same for equal values of the induction at
-186° as at 15°, the loss in ergs per c.cm. per cycle being
approximately represented by 0.002 B(1.56) when the maximum limits of B
were ±9000. Experiments with the sample of unannealed iron failed to
give satisfactory results, owing to the fact that no constant magnetic
condition could be obtained.

  Honda and Shimizu have made similar experiments at the temperature of
  liquid air, employing a much wider range of magnetizing forces (up to
  about 700 C.G.S.) and testing a greater variety of metals. They found
  that the permeability of Swedish iron, tungsten-steel and nickel, when
  the metals were cooled to -186°, was diminished in weak fields but
  increased in strong ones, the field in which the effect of cooling
  changed its sign being 115 for iron and steel and 580 for nickel. The
  permeability of cobalt, both annealed and unannealed, was always
  diminished at the low temperature. The hysteresis-loss in Swedish iron
  was decreased for inductions below about 9000 and increased for higher
  inductions; in tungsten-steel, nickel and cobalt the hysteresis-loss
  was always increased by cooling. The range of ±B within which
  Steinmetz's formula is applicable becomes notably increased at low
  temperature. It may be remarked that, whereas Fleming and Dewar
  employed the ballistic method, their specimens having the form of
  rings, Honda and Shimizu worked magnetometrically with metals shaped
  as ovoids.

_Permanent Magnets._--Fleming and Dewar (loc. cit. p. 57) also
investigated the changes which occurred in permanently magnetized
metals when cooled to the temperature of liquid air. The metals, which
were prepared in the form of small rods, were magnetized between the
poles of an electromagnet and tested with a magnetometer at temperatures
of -186° and 15°. The first immersion into liquid air generally produced
a permanent decrease of magnetic moment, and there was sometimes a
further decrease when the metal was warmed up again; but after a few
alternations of temperature the changes of moment became definite and
cyclic. When the permanent magnetic condition had been thus established,
it was found that in the case of all the metals, except the two alloys
containing large percentages of nickel, the magnetic moment was
temporarily increased by cooling to -186°. The following table shows the
principal results. It is suggested that a permanent magnet might
conveniently be "aged" (or brought into a constant condition) by dipping
it several times into liquid air.

    +---------------------------------+--------------------------------+
    |                                 |     Percentage Gain or Loss    |
    |             Metal.              |      of Moment at -186° C.     |
    |                                 +----------------+---------------+
    |                                 |  First Effect. | Cyclic Effect.|
    +---------------------------------+----------------+---------------+
    | Carbon steel, hard              |      -6        |      +12      |
    |    "     "    medium            |    Decrease    |      +22      |
    |    "     "    annealed          |      -33       |      +33      |
    | Chromium steels (four samples)  |    Increase    |      +12      |
    | Aluminium steels (three samples)|      -2        |      +10      |
    | Nickel steels, up to  7.65%     |     Small      |      +10      |
    |    "     "       "   19.64%     |      -50       |      -25      |
    |    "     "       "   29%        |      -20       |      -10      |
    | Pure nickel                     |    Decrease    |      +3       |
    | Silicon steel, 2.67%            |       "        |      +4       |
    | Iron, soft                      |      None      |      +2.5     |
    |   "   hard                      |    Decrease    |      +10      |
    | Tungsten steel, 15%             |       "        |      +6       |
    |    "      "     7.5%            |       "        |      +10      |
    |    "      "      1%             |       "        |      +12      |
    +---------------------------------+----------------+---------------+

  Other experiments relating to the effect of temperature upon permanent
  magnets have been carried out by J. R. Ashworth,[60] who showed that
  the temperature coefficient of permanent magnets might be reduced to
  zero (for moderate ranges of temperature) by suitable adjustment of
  temper and dimension ratio; also by R. Pictet,[61] A. Durward[62] and
  J. Trowbridge.[63]

_Alloys of Nickel and Iron._--A most remarkable effect of temperature
was discovered by Hopkinson (_Proc. Roy. Soc._, 1890, 47, 23; 1891, 48,
1) in 1889. An alloy containing about 3 parts of iron and 1 of
nickel--both strongly magnetic metals--is under ordinary conditions
practically non-magnetizable (µ = 1.4 for any value of H). If, however,
this non-magnetic substance is cooled to a temperature a few degrees
below freezing-point, it becomes as strongly magnetic as average
cast-iron (µ = 62 for H = 40), and retains its magnetic properties
indefinitely at ordinary temperatures. But if the alloy is heated up to
580° C. it loses its susceptibility--rather suddenly when H is weak,
more gradually when H is strong--and remains non-magnetizable till it is
once more cooled down below the freezing-point. This material can
therefore exist in either of two perfectly stable conditions, in one of
which it is magnetizable, while in the other it is not. When
magnetizable it is a hard steel, having a specific electrical resistance
of 0.000052; when non-magnetizable it is an extremely soft, mild steel,
and its specific resistance is 0.000072. Alloys containing different
proportions of nickel were found to exhibit the phenomenon, but the two
critical temperatures were less widely separated. The following
approximate figures for small magnetizing forces are deduced from
Hopkinson's curves:--

  Percentage of  Susceptibility lost  Susceptibility gained
     Nickel.          at temp. C.          at temp. C.

       0.97              890                   --
       4.7               820                   660
       4.7               780                   600
      24.5               680                   -10
      30.0               140                   125
      33.0               207                   193
      73.0               202                   202

  Honda and Shimizu (_loc. cit._) have determined the two critical
  temperatures for eleven nickel-steel ovoids, containing from 24.04 to
  70.32% of nickel, under a magnetizing force of 400, and illustrated by
  an interesting series of curves, the gradual transformation of the
  magnetic properties as the percentage of nickel was decreased. They
  found that the hysteresis-loss, which at ordinary temperatures is very
  small, was increased in liquid air, the increase for the alloys
  containing less than 30% of nickel being enormous. Steinmetz's formula
  applies only for very weak inductions when the alloys are at the
  ordinary temperature, but at the temperature of liquid air it becomes
  applicable through a wide range of inductions. According to C. E.
  Guillaume[64] the temperature at which the magnetic susceptibility of
  nickel-steel is recovered is lowered by the presence of chromium; a
  certain alloy containing chromium was not rendered magnetic even by
  immersion in liquid air. Experiments on the subject have also been
  made by E. Dumont[65] and F. Osmond.[66]


9. ALLOYS AND COMPOUNDS OR IRON

In 1885 Hopkinson (_Phil. Trans._, 1885, 176, 455) employed his yoke
method to test the magnetic properties of thirty-five samples of iron
and steel, among which were steels containing substantial proportions of
manganese, silicon, chromium and tungsten. The results, together with
the chemical analysis of each sample, are given in a table contained in
this paper, some of them being also represented graphically. The most
striking phenomenon which they bring into prominence is the effect of
any considerable quantity of manganese in annihilating the magnetic
property of iron. A sample of Hadfield's manufacture, containing 12.36%
of manganese, differed hardly at all from a non-magnetic substance, its
permeability being only 1.27. According to Hopkinson's calculation, this
sample behaved as if 91% of the iron contained in it had completely lost
its magnetic property.[67] Another point to which attention is directed
is the exceptionally great effect which hardening has upon the magnetic
properties of chrome steel; one specimen had a coercive force of 9 when
annealed, and of no less than 38 when oil-hardened. The effect of the
addition of tungsten in increasing the coercive force is very clearly
shown; in two specimens containing respectively 3.44 and 2.35% of
tungsten the coercive force was 64.5 and 70.7. These high values render
hardened tungsten-steel particularly suitable for the manufacture of
permanent magnets. Hopkinson (_Proc. Roy. Soc._, 1890, 48, 1) also
noticed some peculiarities of an unexpected nature in the magnetic
properties of the nickel-steel alloys already referred to. The
permeability of the alloys containing from 1 to 4.7% of nickel, though
less than that of good soft iron for magnetizing forces up to about 20
or 30, was greater for higher forces, the induction reached in a field
of 240 being nearly 21,700. The induction for considerable forces was
found to be greater in a steel containing 73% of nickel than in one with
only 33%, though the permeability of pure nickel is much less than that
of iron.

The magnetic qualities of various alloys of iron have been submitted to
a very complete examination by W. F. Barrett, W. Brown and R. A.
Hadfield (_Trans. Roy. Dub. Soc._, 1900, 7, 67; _Journ. Inst. Elec.
Eng._, 1902, 31, 674).[68] More than fifty different specimens were
tested, most of which contained a known proportion of manganese, nickel,
tungsten, aluminium, chromium, copper or silicon: in some samples two of
the substances named were present. Of the very numerous results
published, a few of the most characteristic are collected in the
following table. The first column contains the symbols of the various
elements which were added to the iron, and the second the percentage
proportion in which each element was present; the sample containing
0.03% of carbon was a specimen of the best commercial iron, the values
obtained for it being given for comparison. All the metals were
annealed.

  A few among several interesting points should be specially noticed.
  The addition of 15.2% of manganese produced an enormous effect upon
  the magnetism of iron, while the presence of only 2.25% was
  comparatively unimportant. When nickel was added to the iron in
  increasing quantities the coercive force increased until the
  proportion of nickel reached 20%; then it diminished, and when the
  proportion of nickel was 32% the coercive force had fallen to the
  exceedingly low value of 0.5. In the case of iron containing 7.5% of
  tungsten (W), the residual induction had a remarkably high value; the
  coercive force, however, was not very great. The addition of silicon
  in small quantities considerably diminished permeability and increased
  coercive force; but when the proportion amounted to 2.5% the maximum
  permeability (µ = 5100 for H = 2) was greater than that of the nearly
  pure iron used for comparison, while the coercive force was only
  0.9.[69] A small percentage of aluminium produced still higher
  permeability (µ = 6000 for H = 2), the induction in fields up to 60
  being greater than in any other known substance, and the
  hysteresis-loss for moderate limits of B far less than in the purest
  commercial iron. Certain non-magnetizable alloys of nickel,
  chromium-nickel and chromium-manganese were rendered magnetizable by
  annealing.

    +--------+---------+-----------+---------+----------+--------+
    |Element.|Per cent.|     B     |    B    |     µ    |Coercive|
    |        |         |for H = 45.|residual.|for H = 8.| Force. |
    +--------+---------+-----------+---------+----------+--------+
    |  C     |   0.03  |   16800   |   9770  |   1625   |   1.66 |
    |  Cu    |   2.5   |   14300   |  10410  |    ..    |   5.4  |
    |  Mn    |   2.25  |   14720   |  10460  |   1080   |   6.0  |
    |  Mn    |  15.2   |       0   |    ..   |    ..    |   ..   |
    |  Ni    |   3.82  |   16190   |   9320  |   1375   |   2.76 |
    |  Ni    |  19.64  |    7770   |   4770  |     90   |  20.0  |
    |  Ni    |  31.4   |    4460   |   1720  |    357   |   0.5  |
    |  W     |   7.5   |   15230   |  13280  |    500   |   9.02 |
    |  Al    |   2.25  |   16900   |  10500  |   1700   |   1.0  |
    |  Cr    |   3.25  |     ..    |    ..   |    ..    |  12.25 |
    |  Si    |   2.5   |   16420   |   4080  |   1680   |   0.9  |
    |  Si    |   5.5   |   15980   |   3430  |   1630   |   0.85 |
    +--------+---------+-----------+---------+----------+--------+

  Later papers[70] give the results of a more minute examination of
  those specimens which were remarkable for very low and very high
  permeabilities, and were therefore likely to be of commercial
  importance. The following table gives the exact composition of some
  alloys which were found to be non-magnetizable, or nearly so, in a
  field of 320.

    +---------------------------------------------------------------+
    |              An. = Annealed.  Un. = Unannealed.               |
    +------+----------------------------------------+---------------+
    |State.|        Percentage Composition.         |I, for H = 320.|
    +------+----------------------------------------+---------------+
    | Un.  | Fe, 85.77; C, 1.23; Mn, 13.            |       0       |
    | An.  | Fe, 84.64; C, 0.15; Mn, 15.2           |       0       |
    | An.  | Fe, 80.16; C, 0.8; Mn, 5.04; Ni, 14.55.|       3       |
    | Un.  | Ditto                                  |       0       |
    | Un.  | Fe, 75.36; C, 0.6; Mn, 5.04; Ni, 19.   |       3       |
    | An.  | Fe, 86.61; C, 1.08; Mn, 10.2; W, 2.11. |       5       |
    +------+----------------------------------------+---------------+

  A very small difference in the constitution often produces a
  remarkable effect upon the magnetic quality, and it unfortunately
  happens that those alloys which are hardest magnetically are generally
  also hardest mechanically and extremely difficult to work; they might
  however be used rolled or as castings. The specimens distinguished by
  unusually high permeability were constituted as follows:--

    Silicon-iron.--Fe, 97.3; C, 0.2; Si, 2.5.

    Aluminium-iron.--Fe, 97.33; C, 0.18; Al, 2.25.

  The silicon-iron had, in fields up to about 10, a greater permeability
  than a sample of the best Swedish charcoal-iron, and its
  hysteresis-loss for max. B = 9000, at a frequency of 100 per second,
  was only 0.254 watt per pound, as compared with 0.382 for the Swedish
  iron. The aluminium-iron attained its greatest permeability in a field
  of 0.5, about that of the earth's force, when its value was 9000, this
  being more than twice the maximum permeability of the Swedish iron.
  Its hysteresis-loss for B = 9000 was 0.236 per pound. It was, however,
  found that the behaviour of this alloy was in part due to a layer of
  pure iron ("ferrite") averaging 0.1 mm. in thickness, which occurred
  on the outside of the specimen, and the exceptional magnetic quality
  which has been claimed for aluminium-iron cannot yet be regarded as
  established.

A number of iron alloys have been examined by Mme. Curie (_Bull. Soc.
d'Encouragement_, 1898, pp. 36-76), chiefly with the object of
determining their suitability for the construction of permanent magnets.
Her tests appear to show that molybdenum is even more effective than
tungsten in augmenting the coercive force, the highest values observed
being 70 to 74 for tungsten-steel, and 80 to 85 for steel containing 3.5
to 4% of molybdenum. For additional information regarding the
composition and qualities of permanent magnet steels reference may be
made to the publications cited below.[71] Useful instructions have been
furnished by Carl Barus (_Terrestrial Magnetism_, 1897, 2, 11) for the
preparation of magnets calculated to withstand the effects of time,
percussion and ordinary temperature variations. The metal, having first
been uniformly tempered glass-hard, should be annealed in steam at 100°
C. for twenty or thirty hours; it should then be magnetized to
saturation, and finally "aged" by a second immersion in steam for about
five hours.

_Magnetic Alloys of Non-Magnetic Metals._--The interesting discovery was
made by F. Heusler[72] in 1903 that certain alloys of the non-magnetic
metal manganese with other non-magnetic substances were strongly
magnetizable, their susceptibility being in some cases equal to that of
cast iron. The metals used in different combinations included tin,
aluminium, arsenic, antimony, bismuth and boron; each of these, when
united in certain proportions with manganese, together with a larger
quantity of copper (which appears to serve merely as a menstruum),
constituted a magnetizable alloy. So far, the best results have been
attained with aluminium, and the permeability was greatest when the
percentages of manganese and aluminium were approximately proportional
to the atomic weights of the two metals. Thus in an alloy containing
26.5% of manganese and 14.6% of aluminium, the rest being copper, the
induction for H = 20 was 4500, and for H = 150, 5550. When the
proportion of aluminium to manganese was made a little greater or
smaller, the permeability was diminished. Next to aluminium, tin was
found to be the most effective of the metals enumerated above. In all
such magnetizable alloys the presence of manganese appears to be
essential, and there can be little doubt that the magnetic quality of
the mixtures is derived solely from this component. Manganese, though
belonging (with chromium) to the iron group of metals, is commonly
classed as a paramagnetic, its susceptibility being very small in
comparison with that of the recognized ferromagnetics; but it is
remarkable that its atomic susceptibility in solutions of its salts is
even greater than that of iron. Now iron, nickel and cobalt all lose
their magnetic quality when heated above certain critical temperatures
which vary greatly for the three metals, and it was suspected by
Faraday[73] as early as 1845 that manganese might really be a
ferromagnetic metal having a critical temperature much below the
ordinary temperature of the air. He therefore cooled a piece of the
metal to -105° C., the lowest temperature then attainable, but failed to
produce any change in its magnetic quality. The critical temperature (if
there is one) was not reached in Faraday's experiment; possibly even the
temperature of -250° C., which by the use of liquid hydrogen has now
become accessible, might still be too high.[74] But it has been shown
that the critical temperatures of iron and nickel may be changed by the
addition of certain other substances. Generally they are lowered,
sometimes, however, they are raised[75]; and C. E. Guillaume[76]
explains the ferromagnetism of Heusler's alloy by supposing that the
naturally low critical temperature of the manganese contained in it is
greatly raised by the admixture of another appropriate metal, such as
aluminium or tin; thus the alloy as a whole becomes magnetizable at the
ordinary temperature. If this view is correct, it may also be possible
to prepare magnetic alloys of chromium, the only other paramagnetic
metals of the iron group.

  J. A. Fleming and R. A. Hadfield[77] have made very careful
  experiments on an alloy containing 22.42% of manganese, 11.65% of
  aluminium and 60.49% of copper. The magnetization curve was found to
  be of the same general form as that of a paramagnetic metal, and gave
  indications that with a sufficient force magnetic saturation would
  probably be attained. There was considerable hysteresis, the
  energy-loss per cycle being fairly represented by W =
  0.0005495B^(2.238). The hysteretic exponent is therefore much higher
  than in the case of iron, nickel and cobalt, for which its value is
  approximately 1.6.


10. MISCELLANEOUS EFFECTS OF MAGNETIZATION

_Electrical Conductivity._--The specific resistance of many electric
conductors is known to be temporarily changed by the action of a
magnetic field, but except in the case of bismuth the effect is very
small.

  A. Gray and E. Taylor Jones (_Proc. Roy. Soc._, 1900, 67, 208) found
  that the resistance of a soft iron wire was increased by about 1/700
  in a field of 320 C.G.S. units. The effect appeared to be closely
  connected with the intensity of magnetization, being approximately
  proportional to I. G. Barlow (_Proc. Roy. Soc._, 1903, 71, 30),
  experimenting with wires of iron, steel and nickel, showed that in
  weak fields the change of resistance was proportional to a function
  aI^2 + bI^4 + cI^6, where a, b and c are constants for each specimen.
  W. E. Williams (_Phil. Mag._, 1902, 4, 430) found that for nickel the
  curves showing changes of resistance in relation to magnetizing force
  were strikingly similar in form to those showing changes of length. H.
  Tomlinson (_Phil. Trans._, 1883, Part I., 153) discovered in 1881 that
  the resistance of a bismuth rod was slightly increased when the rod
  was subjected to longitudinal magnetic force, and a year or two later
  A. Righi (_Atti R. A. Lincei_, 1883-1884, 19, 545) showed that a more
  considerable alteration was produced when the magnetic force was
  applied transversely to the bismuth conductor; he also noticed that
  the effect was largely dependent upon temperature (see also P. Lenard,
  _Wied. Ann._, 1890, 39, 619). Among the most important experiments on
  the influence of magnetic force at different temperatures are those of
  J. B. Henderson and of Dewar and Fleming. Henderson (_Phil. Mag._,
  1894, 38, 488) used a little spiral of the pure electrolytic bismuth
  wire prepared by Hartmann and Braun; this was placed between the
  pole-pieces of an electromagnet and subjected to fields of various
  strengths up to nearly 39,000 units. At constant temperature the
  resistance increased with the field; the changes in the resistance of
  the spiral when the temperature was 18° C. are indicated in the
  annexed table, from which it will be seen that in the strongest

      H.       R.    |     H.       R.
        0    1.000   |   27450    2.540
     6310    1.253   |   32730    2.846
    12500    1.630   |   38900    3.334
    20450    2.160   |

  transverse field reached the resistance was increased more than
  threefold. Other experiments showed the relation of resistance to
  temperature (from 0° to about 90°) in different constant fields. It
  appears that as the temperature rises the resistance decreases to a
  minimum and then increases, the minimum point occurring at a higher
  temperature the stronger the field. For H = 11,500 the temperature of
  minimum resistance was about 50°; for much lower or higher values of H
  the actual minimum did not occur within the range of temperature dealt
  with. Dewar and Fleming (_Proc. Roy. Soc._, 1897, 60, 425) worked with
  a similar specimen of bismuth, and their results for a constant
  temperature of 19° agree well with those of Henderson. They also
  experimented with constant temperatures of -79°, -185° and -203°, and
  found that at these low temperatures the effect of magnetization was
  enormously increased. The following table gives some of their results,
  the specific resistance of the bismuth being expressed in C.G.S.
  units.

    +-----------+-----------------------+------------------------+
    |           |       Temp. 19°C.     |      Temp. -185°C.     |
    |   Field   +-----------+-----------+-----------+------------+
    | Strength. | Spec. Res.| Comp. Res.| Spec. Res.| Comp. Res. |
    +-----------+-----------+-----------+-----------+------------+
    |      0    |  116200   |   1.000   |   41000   |    1.00    |
    |   1375    |  118200   |   1.017   |  103300   |    2.52    |
    |   2750    |  123000   |   1.059   |  191500   |    4.67    |
    |   8800    |  149200   |   1.284   |  738000   |    18.0    |
    |  14150    |  186200   |   1.602   | 1730000   |    42.2    |
    |  21800    |  257000   |   2.212   | 6190000   |   151      |
    +-----------+-----------+-----------+-----------+------------+

  At the temperature of liquid air (-185°) the application of a field of
  21,800 multiplied the resistance of the bismuth no less than 150
  times. Fig. 29 shows the variations of resistance in relation to
  temperature for fields of different constant values. It will be seen
  that for H = 2450 and H = 5500 the minimum resistance occurs at
  temperatures of about -80° and -7° respectively.

_Hall Effect._--If an electric current is passed along a strip of thin
metal, and the two points at opposite ends of an equipotential line are
connected with a galvanometer, its needle will of course not be
deflected. But the application of a magnetic field at right angles to
the plane of the metal causes the equipotential lines to rotate through
a small angle, and the points at which the galvanometer is connected
being no longer at the same potential, a current is indicated by the
galvanometer.[78] The tranverse electromotive force is equal to KCH/D,
where C is the current, H the strength of the field, D the thickness of
the metal, and K a constant which has been termed the _rotatory power_
or _rotational coefficient_. (See Hopkinson, _Phil. Mag._, 1880, 10,
430). The following values of K for different metals are given by E. H.
Hall, the positive sign indicating that the electromotive force is in
the same direction as the mechanical force acting upon the conductor. A.
von Ettinghausen and W. Nernst (_Wien. Ber._, 1886, 94, 560) have found
that the rotational coefficient of tellurium is more than fifty times
greater than that of bismuth, its sign being positive. Several
experimenters have endeavoured to find a Hall effect in liquids, but
such results as have been hitherto obtained are by no means free from
doubt. E. A. Marx (_Ann. d. Phys._, 1900, 2, 798) observed a
well-defined Hall effect in incandescent gases. A large effect,
proportional to the field, has been found by H. A. Wilson (_Cam. Phil.
Soc. Proc._, 1902, 11, pp. 249, 391) in oxygen, hydrogen and air at low
pressures, and by C. D. Child (_Phys. Rev._, 1904, 18, 370) in the
electric arc.

  Metal.     K × 10^15 |  Metal.       K × 10^15
                       |
  Antimony    +114000  |  Copper           -520
  Steel        +12060  |  Gold             -660
  Iron          +7850  |  Nickel         -14740
  Cobalt        +2460  |  Bismuth[79]  -8580000
  Zinc           +820  |

[Illustration: _Fig._ 29.]

_Electro-Thermal Relations._--The Hall electromotive force is only one
of several so-called "galvano-magnetic effects" which are observed when
a magnetic field acts normally upon a thin plate of metal traversed by
an electric current. It is remarkable that if a flow of heat be
substituted for a current of electricity a closely allied group of
"thermo-magnetic effects" is presented. The two classes of phenomena
have been collated by M. G. Lloyd (_Am. Journ. Sci._, 1901, 12, 57), as
follows:--

   _Galvano-Magnetic Effects._              _Thermo-Magnetic Effects._

    1. A transverse difference of         i. A transverse difference of
  electric potential (Hall effect).     electric potential (Nernst effect).

    2. A transverse difference of         ii. A transverse difference of
  temperature(Ettinghausen effect).     temperature (Leduc effect).

    3. Longitudinal change of             iii. Longitudinal change of
  electric conductivity.                thermal conductivity.

    4. Longitudinal difference of         iv. Longitudinal difference of
  temperature.                          electric potential.[80]

    +---------------------+
    |          C          |
    |                     |
    | A                 B |
    |          D          |
    +---------------------+

If in the annexed diagram ABCD represents the metallic plate through
which the current of electricity or heat flows in the direction AB,
then effects (1), (2), (i.) and (ii.) are exhibited at C and D, effects
(4) and (iv.) at A and B, and effects (3) and (iii.) along AB. The
transverse effects are reversed in direction when either the magnetic
field or the primary current (electric or thermal) is reversed, but the
longitudinal effects are independent of the direction of the field. It
has been shown by G. Moreau (_C. R._, 1900, 130, pp. 122, 412, 562) that
if K is the coefficient of the Hall effect (1) and K´ the analogous
coefficient of the Nernst effect (i.) (which is constant for small
values of H), then K´ = K[sigma]/[rho], [sigma] being the coefficient of
the Thomson effect for the metal and [rho] its specific resistance. He
considers that Hall's is the fundamental phenomenon, and that the Nernst
effect is essentially identical with it, the primary electromotive force
in the case of the latter being that of the Thomson effect in the
unequally heated metal, while in the Hall experiment it is derived from
an external source.

Attempts have been made to explain these various effects by the electron
theory.[81]

_Thermo-electric Quality._--The earliest observations of the effect of
magnetization upon thermo-electric power were those of W. Thomson (Lord
Kelvin), who in 1856 announced that magnetization rendered iron and
steel positive to the unmagnetized metals.[82] It has been found by
Chassagny,[83] L. Houllevigue[84] and others that when the magnetizing
force is increased, this effect passes a maximum, while J. A. Ewing[85]
has shown that it is diminished and may even be reversed by tensile
stress. Nickel was believed by Thomson to behave oppositely to iron,
becoming negative when magnetized; but though his conclusion was
accepted for nearly fifty years, it has recently been shown to be an
erroneous one, based, no doubt, upon the result of an experiment with an
impure specimen. Nickel when magnetized is always positive to the
unmagnetized metal. So also is cobalt, as was found by H. Tomlinson.[86]
The curves given by Houllevigue for the relation of thermo-electric
force to magnetic field are of the same general form as those showing
the relation of change of length to field. E. Rhoads[87] obtained a
cyclic curve for iron which indicated thermo-electric hysteresis of the
kind exhibited by Nagaoka's curves for magnetic strain. He also
experimented with nickel and again found a resemblance to the strain
curve. The subject was further investigated by S. Bidwell,[88] who,
adopting special precautions against sources of error by which former
work was probably affected, measured the changes of thermo-electric
force for iron, steel, nickel and cobalt produced by magnetic fields up
to 1500 units. In the case of iron and nickel it was found that, when
correction was made for mechanical stress due to magnetization, magnetic
change of thermo-electric force was, within the limits of experimental
error, proportional to magnetic change of length. Further, it was shown
that the thermo-electric curves were modified both by tensile stress and
by annealing in the same manner as were the change-of-length curves, the
modification being sometimes of a complex nature. Thus a close connexion
between the two sets of phenomena seems to be established. In the case
of cobalt no such relation could be traced; it appeared that the
thermo-electric power of the unmagnetized with respect to the magnetized
cobalt was proportional to the square of the magnetic induction or of
the magnetization. Of nickel six different specimens were tested, all
of which became, like iron, thermo-electrically positive to the
unmagnetized metals.

  As to what effect, if any, is produced upon the thermo-electric
  quality of bismuth by a magnetic field there is still some doubt. E.
  van Aubel[89] believes that in pure bismuth the thermo-electric force
  is increased by the field; impurities may neutralize this effect, and
  in sufficient quantities reverse it.

_Elasticity._--The results of experiments as to the effect of
magnetization were for long discordant and inconclusive, sufficient care
not having been taken to avoid sources of error, while the effects of
hysteresis were altogether disregarded. The subject, which is of
importance in connexion with theories of magnetostriction, has been
investigated by K. Honda and T. Terada in a research remarkable for its
completeness and the ingenuity of the experimental methods employed.[90]
The results are too numerous to discuss in detail; some of those to
which special attention is directed are the following: In Swedish iron
and tungsten-steel the change of elastic constants (Young's modulus and
rigidity) is generally positive, but its amount is less than 0.5%;
changes of Young's modulus and of rigidity are almost identical. In
nickel the maximum change of the elastic constants is remarkably large,
amounting to about 15% for Young's modulus and 7% for rigidity; with
increasing fields the elastic constants first decrease and then
increase. In nickel-steels containing about 50 and 70% of nickel the
maximum increase of the constants is as much as 7 or 8%. In a 29%
nickel-steel, magnetization increases the constants by a small amount.
Changes of elasticity are in all cases dependent, not only upon the
field, but also upon the tension applied; and, owing to hysteresis, the
results are not in general the same when the magnetization follows as
when it precedes the application of stress; the latter is held to be the
right order.

_Chemical and Voltaic Effects._--If two iron plates, one of which is
magnetized, are immersed in an electrolyte, a current will generally be
indicated by a galvanometer connected with the plates.

  As to whether the magnetized plate becomes positive or negative to the
  other, different experimenters are not in agreement. It has, however,
  been shown by Dragomir Hurmuzescu (_Rap. du Congrès Int. de Phys._,
  Paris, 1900, p. 561) that the true effect of magnetization is liable
  to be disguised by secondary or parasitic phenomena, arising chiefly
  from polarization of the electrodes and from local variations in the
  concentration and magnetic condition of the electrolyte; these may be
  avoided by working with weak solutions, exposing only a small surface
  in a non-polar region of the metal, and substituting a capillary
  electrometer for the galvanometer generally used. When such
  precautions are adopted it is found that the "electromotive force of
  magnetization" is, for a given specimen, perfectly definite both in
  direction and in magnitude; it is independent of the nature of the
  corrosive solution, and is a function of the field-strength alone, the
  curves showing the relation of electromotive force to field-intensity
  bearing a rough resemblance to the familiar I-H curves. The value of
  the E.M.F. when H = 2000 is of the order of 1/100 volt for iron,
  1/1000 volt for nickel and 1/10,000 for bismuth. When the two
  electrodes are ferromagnetic, the direction of the current through the
  liquid is from the unmagnetized to the magnetized electrode, the
  latter being least attacked; with diamagnetic electrodes the reverse
  is the case. Hurmuzescu shows that these results are in accord with
  theory. Applying the principle of the conservation of internal energy,
  he demonstrates that for iron in a field of 1000 units and upwards the
  E.M.F. of magnetization is

           l         I²
    E = ------- × --------  approximately,
        [delta]   2[kappa]

  l being the electrochemical equivalent and [delta] the density of the
  metal. Owing to the difficulty of determining the magnetization I and
  the susceptibility [kappa] with accuracy, it has not yet been possible
  to submit this formula to a quantitative test, but it is said to
  afford an indication of the results given by actual experiment. It has
  been discovered by E. L. Nichols and W. S. Franklin (_Am. Journ.
  Sci._, 1887, 34, 419; 1888, 35, 290) that the transition from the
  "passive" to the active state of iron immersed in strong nitric acid
  is facilitated by magnetization, the temperature of transition being
  lowered. This is attributed to the action of local currents set up
  between unequally magnetized portions of the iron. Similar results
  have been obtained by T. Andrews (_Proc. Roy. Soc._, 1890, 48, 116).


11. FEEBLY SUSCEPTIBLE SUBSTANCES

_Water._--The following are recent determinations of the magnetic
susceptibility of water:--

    Observer.          [kappa] × 10^6.                Publication.

  G. Quincke       -0.797 at 18° C.            _Wied. Ann._, 1885, 24, 387.
  H. du Bois       -0.837 (1 - 0.0025t - 15°)  _Wied. Ann._, 1888, 35, 137.
  P. Curie         -0.790 at 4° C.             _C. R._, 1893, 116, 136.
  J. Townsend      -0.77                       _Phil. Trans._, 1896, 187, 544.
  J. A. Fleming    -0.74                       _Proc. Roy. Soc._, 1898, 63,
    and J. Dewar                                  311.
  G. Jäger and     -0.689(1 - 0.0016t)         _Wied. Ann._, 1899, 67,
    S. Meyer 707.
  J. Koenigsberger -0.781 at 22° C.            _Ann. d. Phys._, 1901, 6, 506.
  H. D. Stearns    -0.733 at 22° C.            _Phys. Rev._, 1903, 16, 1.
  A. P. Wills      -0.720 at 18° C.            _Phys. Rev._, 1905, 20, 188.

Wills found that the susceptibility was constant in fields ranging from
4200 to 15,000.

_Oxygen and Air._--The best modern determinations of the value of
[kappa] for gaseous oxygen agree very fairly well with that given by
Faraday in 1853 (_Exp. Res._ III, 502). Assuming that for water [kappa]
= -0.8 × 10^(-6), his value of [kappa] for oxygen at 15° C. reduces to
0.15 × 10^(-6). Important experiments on the susceptibility of oxygen at
different pressures and temperatures were carried out by P. Curie
(_C.R._ 1892, 115, 805; 1893, 116, 136). _Journ. de Phys._, 1895, 4,
204. He found that the susceptibility for unit of mass, K, was
independent of both pressure and magnetizing force, but varied inversely
as the absolute temperature, [theta], so that 10^6K = 33700/[theta].
Since the mass of 1 cub. cm. of oxygen at 0° C. and 760 mm. pressure is
0.00141 grm., the mass at any absolute temperature [theta] is by
Charles's law 0.00141 × 273[theta] = 0.3849/[theta] grm.; hence the
susceptibility per unit of volume at 760 mm. will be

  [kappa] = 10^(-6) × 0.3849 × 33700/[theta]²
          = 10^(-6) × 12970/[theta]².

At 15° C. [theta] = 273 + 15 = 288, and therefore [kappa] = 0.156 ×
10^(-6), nearly the same as the value found by Faraday. At 0° C.,
[kappa] = 0.174 × 10^(-6). For air Curie calculated that the
susceptibility per unit mass was 10^6K = 7830/[theta]; or, taking the
mass of 1 c.c. of air at 0° C. and 760 mm. as 0.001291 grm., [kappa] =
10^(-6) × 2760/[theta]² for air at standard atmospheric pressure. It is
pointed out that this formula may be used as a temperature correction in
magnetic determinations carried out in air.

Fleming and Dewar determined the susceptibility of liquid oxygen (_Proc.
Roy. Soc._, 1896, 60, 283; 1898, 63, 311) by two different methods. In
the first experiments it was calculated from observations of the mutual
induction of two conducting circuits in air and in the liquid; the
results for oxygen at -182° C. were

  µ = 1.00287, [kappa] = 228 × 10^(-6).

In the second series, to which greater importance is attached,
measurements were made of the force exerted in a divergent field upon
small balls of copper, silver and other substances, first when the balls
were in air and afterwards when they were immersed in liquid oxygen. If
V is the volume of a ball, H the strength of the field at its centre,
and [kappa]´ its apparent susceptibility, the force in the direction x
is f = [kappa]´VH × dH/dx; and if [kappa]´_a and [kappa]´^0 are the
apparent susceptibilities of the same ball in air and in liquid oxygen,
[kappa]´_a - [kappa]´0 is equal to the difference between the
susceptibilities of the two media. The susceptibility of air being
known--practically it was negligible in these experiments--that of
liquid oxygen can at once be found. The mean of 36 experiments with 7
balls gave

  µ = 1.00407, [kappa] = 324 × 10^(-6).

A small but decided tendency to a decrease of susceptibility in very
strong fields was observed. It appears, therefore, that liquid oxygen is
by far the most strongly paramagnetic liquid known, its susceptibility
being more than four times greater than that of a saturated solution of
ferric chloride. On the other hand, its susceptibility is about fifty
times less than that of Hadfield's 12% manganese steel, which is
commonly spoken of as non-magnetizable.

_Bismuth._--Bismuth is of special interest, as being the most strongly
diamagnetic substance known, the mean value of the best determinations
of its susceptibility being about -14 × 10^(-6) (see G. Meslin, _C. R._,
1905, 140, 449). The magnetic properties of the metal at different
temperatures and in fields up to 1350 units have been studied by P.
Curie (_loc. cit._), who found that its "specific susceptibility" (K)
was independent of the strength of the field, but decreased with rise of
temperature up to the melting-point, 273°C. His results appear to show
the relation

  -[Kappa] × 10^6 = 1.381 - 0.00155t°.

Assuming the density of Bi to be 9.8, and neglecting corrections for
heat dilatation, his value for the susceptibility at 20°C. is equivalent
to [kappa] = -13.23 × 10^(-6). As the temperature was raised up to 273°,
[kappa] gradually fell to -9.38 × 10^[-6], rising suddenly when fusion
occurred to -0.37 × 10^(-6), at which value it remained constant when
the fluid metal was further heated. Fleming and Dewar give for the
susceptibility the values -13.7 × 10^(-6) at 15°C. and -15.9 × 10^(-6)
at -182°, the latter being approximately equivalent to [Kappa] × 10^6 =
-1.62. Putting t° = -182 in the equation given above for Curie's
results, we get [Kappa] × 10^6 = -1.66, a value sufficiently near that
obtained by Fleming and Dewar to suggest the probability that the
diamagnetic susceptibility varies inversely as the temperature between
-182° and the melting-point.

_Other Diamagnetics._--The following table gives Curie's determinations
(_Journ. de Phys._, 1895, 4, 204) of the specific susceptibility [Kappa]
of other diamagnetic substances at different temperatures. It should be
noted that [Kappa] = [kappa]/density.

  Substance                       Temp. °C.  -[Kappa] × 10^6.

  Water                             15-189        0.790
  Rock salt                         16-455        0.580
  Potassium chloride                18-465        0.550
       "    sulphate                17-460        0.430
       "    nitrate (fusion 350°)   18-420        0.330
  Quartz                            18-430        0.441
  Sulphur, solid or fused           18-225        0.510
  Selenium, solid or fused          20-200        0.320
      "     fused                   240-415        0.307
  Tellurium                         20-305        0.311
  Bromine                           20            0.410
  Iodine, solid or fused            18-164        0.385
  Phosphorus, solid or fused        19-71         0.920
       "      amorphous             20-275        0.730
  Antimony, electrolytic            20            0.680
       "                           540            0.470
  Bismuth, solid                    20            1.350
     "       "                     273            0.957
     "     fused                   273-405        0.038

For all diamagnetic substances, except antimony and bismuth, the value
of [Kappa] was found to be independent of the temperature.

_Paramagnetic Substances._--Experiments by J. S. Townsend (_Phil.
Trans._, 1896, 187, 533) show that the susceptibility of solutions of
salts of iron is independent of the magnetizing force, and depends only
on the quantity of iron contained in unit volume of the liquid. If W is
the weight of iron present per c.c. at about 10°C., then for ferric
salts

  10^6[kappa] = 266W - 0.77

and for ferrous salts

  10^6[kappa] = 206W - 0.77,

the quantity -0.77 arising from the diamagnetism of the water of
solution. Annexed are values of 10^6[kappa] for the different salts
examined, w being the weight of the salt per c.c. of the solution.

   Salt.     10^6[kappa] + 0.77 |  Salt.    10^6[kappa] + 0.77
                                |
  Fe2Cl6           91.6w        |  FeCl2           90.8w
  Fe2(SO4)3        74.5w        |  FeSO4           74.9w
  Fe2(NO3)6        61.5w

Susceptibility was found to diminish greatly with rise of temperature.
According to G. Jäger and S. Meyer (_Wien. Akad. Sitz._, 1897, 106, II.
a, p. 623, and 1898, 107, II. a, p. 5) the atomic susceptibilities k of
the metals nickel, chromium, iron, cobalt and manganese in solutions of
their salts are as follows:--

  Metal.       k × 10^6      |  Metal.      k × 10^6.
                             |
   Ni       4.95 = 2.5 × 2   |   Co       10.0 = 2.5 × 4
   Cr       6.25 = 2.5 × 2.5 |   Fe(2)    12.5 = 2.5 × 5
   Fe(1)    7.5 = 2.5 × 3    |   Mn       15.0 = 2.5 × 6


Fe(1) is iron contained in FeCl2 and Fe(2) iron contained in Fe2(NO3)6.

Curie has shown, for many paramagnetic bodies, that the specific
susceptibility K is inversely proportional to the absolute temperature
[theta]. Du Bois believes this to be an important general law,
applicable to the case of every paramagnetic substance, and suggests
that the product K[theta] should be known as "Curie's constant" for the
substance.

_Elementary Bodies and Atomic Susceptibility._--Among a large number of
substances the susceptibilities of which have been determined by J.
Koenigsberger (_Wied. Ann._, 1898, 66, 698) are the following
elements:--

   Element.   [kappa] × 10^6. |    Element.   [kappa] × 10^6.
                              |
  Copper           -0.82      |   Tellurium       - 2.10
  Silver           -1.51      |   Graphite        + 2
  Gold             -3.07      |   Aluminium       + 1.80
  Zinc             -0.96      |   Platinum        +22
  Tin              +0.46      |   Palladium       +50 to 60
  Lead             -1.10      |   Tungsten        +14
  Thallium         -4.61      |   Magnesium       + 4
  Sulphur          -0.86      |   Sodium          + 2.2
  Selenium (red)   -0.50      |   Potassium       + 3.6

In a table accompanying Koenigsberger's paper the elements are arranged
upon the periodic system and the atomic susceptibility (product of
specific susceptibility into atomic weight) is given for each. It
appears that the elements at about the middle of each row are the most
strongly paramagnetic; towards the ends of a row the susceptibility
decreases, and ultimately becomes negative. Thus a relation between
susceptibility and atomic weight is clearly indicated. Tables similarly
arranged, but much more complete, have been published by S. Meyer
(_Wied. Ann._, 1899, 68, 325 and 1899, 69, 236), whose researches have
filled up many previously existing gaps. The values assigned to the
atomic susceptibilities of most of the known elements are appended.
According to the notation adopted by Meyer the atomic susceptibility k =
[kappa] × atomic-weight/(density × 1000).

  Meyer thinks that the susceptibilities of the metals praseodymium,
  neodymium, ytterbium, samarium, gadolinium, and erbium, when obtained
  in a pure form, will be found to equal or even exceed those of the
  well-known ferromagnetic metals. Many of their compounds are very
  strongly magnetic; erbium, for example, in Er2O3 being four times as
  strong as iron in the familiar magnetite or lodestone, Fe2O3. The
  susceptibilities of some hundreds of inorganic compounds have also
  been determined by the same investigator (loc. cit.). Among other
  researches relating to atomic and molecular magnetism are those of O.
  Liebknecht and A. P. Wills (_Ann. d. Phys._, 1900, 1, 178), H. du Bois
  and O. Liebknecht (ibid. p. 189), and Meyer (ibid. p. 668). An
  excellent summary regarding the magnetic properties of matter, with
  many tables and references, has been compiled by du Bois (_Report to
  the Congrès Int. de Phys._, Paris, 1900, ii. 460).

  +--------------------+--------------------+-------------------+
  | _Element_   10^6k  | _Element_   10^6k  | _Element_   10^6k |
  +--------------------+--------------------+-------------------+
  | Be        +0.72    | Cu        -0.006   | Cs       -0.03*   |
  | B         +0.05    | Zn        -0.010   | Ba       -0.02*   |
  | C         -0.05    | Ga        -        | La       +13.0    |
  | N           ?      | Ge        -        | Ce       +34.0    |
  | O         +        | As           ?     | Pr       +\       |
  | F         -0.01*   | Se        -0.025   | Nd       +| Strong|
  |....................| Br        -0.033   | Sa       +|       |
  | Na        -0.005*  |....................| Gd       +/       |
  | Mg        +0.014   | Rb        -0.02*   |...................|
  | Al        +        | Sr        -0.02*   | Er       +41.8(?) |
  | Si        +0.002   | Y         +3.2(?)  |...................|
  | P         -0.007   | Zr        -0.014   | Yb       + (?)    |
  | S         -0.011   | Nb        +0.49(?) | Ta       +1.02(?) |
  | Cl        -0.02*   | Mo        +0.024   | W        +0.1     |
  |....................| Ru        +        | Os       +0.074   |
  | K         -0.001*  | Rh        +        | Ir       +        |
  | Ca        -0.003*  | Pd        +0.55    | Pt       +0.227   |
  | Sc         ?       | Ag        -0.016   | Au       -0.031   |
  | Ti        +0.09    | Cd        -0.015   | Hg       -0.030   |
  | V         +0.17    | In        +0.01*   | Tl       -0.93    |
  | Cr        +\       | Sn        +0.004*  | Pb       -0.025   |
  | Mn        +|       | Sb        -0.069   | Bi       -0.023   |
  | Fe        +|Strong | Te        -0.039   |...................|
  | Co        +|       | I         -0.040   | Th       +16.0(?) |
  | Ni        +/       |....................| U        +0.21    |
  +--------------------+--------------------+-------------------+
    * Calculated.


12. MOLECULAR THEORY OF MAGNETISM

According to W. E. Weber's theory, the molecules of a ferromagnetic
metal are small permanent magnets, the axes of which under ordinary
conditions are turned indifferently in every direction, so that no
magnetic polarity is exhibited by the metal as a whole; a magnetic force
acting upon the metal tends to turn the axes of the little magnets in
one direction, and thus the entire piece acquires the properties of a
magnet. If, however, the molecules could turn with perfect freedom, it
is clear that the smallest magnetizing force would be sufficient to
develop the highest possible degree of magnetization, which is of course
not the case. Weber therefore supposed each molecule to be acted on by a
force tending to preserve it in its original direction, the position
actually assumed by the axis being in the direction of the resultant of
this hypothetical force and the applied magnetizing force. Maxwell
(_Electricity and Magnetism_, § 444), recognizing that the theory in
this form gave no account of residual magnetization, made the further
assumption that if the deflection of the axis of the molecule exceeded a
certain angle, the axis would not return to its original position when
the deflecting force was removed, but would retain a permanent set.
Although the amended theory as worked out by Maxwell is in rough
agreement with certain leading phenomena of magnetization, it fails to
account for many others, and is in some cases at variance with observed
facts.

J. A. Ewing (_Proc. Roy. Soc._, 1890, 48, 342) has demonstrated that it
is quite unnecessary to assume either the directive force of Weber, the
permanent set of Maxwell, or any kind of frictional resistance, the
forces by which the molecular magnets are constrained being simply those
due to their own mutual attractions and repulsions. The effect of these
is beautifully illustrated by a model consisting of a number of little
compass needles pivoted on sharp points and grouped near to one another
upon a board, which is placed inside a large magnetizing coil. When no
current is passing through the coil and the magnetic field is of zero
strength, the needles arrange themselves in positions of stable
equilibrium under their mutual forces, pointing in many different
directions, so that there is no resultant magnetic moment. This
represents the condition of the molecules in unmagnetized iron. If now a
gradually increasing magnetizing force is applied, the needles at first
undergo a stable deflection, giving to the group a small resultant
moment which increases uniformly with the force; and if the current is
interrupted while the force is still weak, the needles merely return to
their initial positions. This illustrates the first stage in the process
of magnetization, when the moment is proportional to the field and there
is no hysteresis or residual magnetism (see _ante_). A somewhat stronger
field will deflect many of the needles beyond the limits of stability,
causing them to turn round and form new stable combinations, in which
the direction assumed by most of them approximates to that of the field.
The rearrangement is completed within a comparatively small range of
magnetizing force, a rapid increase of the resultant moment being thus
brought about. When the field is removed, many of the newly formed
combinations are but slightly disturbed, and the group may consequently
retain a considerable resultant moment. This corresponds to the second
stage of magnetization, in which the susceptibility is large and
permanent magnetization is set up. A still stronger magnetizing force
has little effect except in causing the direction of the needles to
approach still more nearly to that of the field; if the force were
infinite, every member of the group would have exactly the same
direction and the greatest possible resultant moment would be reached;
this illustrates "magnetic saturation"--the condition approached in the
third stage of magnetization. When the strong magnetizing field is
gradually diminished to zero and then reversed, the needles pass from
one stable position of rest to another through a condition of
instability; and if the field is once more reversed, so that the cycle
is completed, the needles again pass through a condition of instability
before a position of stable equilibrium is regained. Now the unstable
movements of the needles are of a mechanically irreversible character;
the energy expended in dissociating the members of a combination and
placing them in unstable positions assumes the kinetic form when the
needles turn over, and is ultimately frittered down into heat. Hence in
performing a cycle there is a waste of energy corresponding to what has
been termed hysteresis-loss.

Supposing Ewing's hypothesis to be correct, it is clear that if the
magnetization of a piece of iron were reversed by a strong rotating
field instead of by a field alternating through zero, the loss of energy
by hysteresis should be little or nothing, for the molecules would
rotate with the field and no unstable movements would be possible.[91]
Some experiments by F. G. Baily (_Phil. Trans._, 1896, 187, 715) show
that this is actually the case. With small magnetizing forces the
hysteresis was indeed somewhat larger than that obtained in an
alternating field, probably on account of the molecular changes being
forced to take place in one direction only; but at an induction of about
16,000 units in soft iron and 15,000 in hard steel the hysteresis
reached a maximum and afterwards rapidly diminished. In one case the
hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B =
15,900, and only 1200 ergs for B = 20,200, the highest induction
obtained in the experiment; possibly it would have vanished before B had
reached 21,000.[92] These experiments prove that actual friction must be
almost entirely absent, and, as Baily remarks, the agreement of the
results with the previously suggested deduction affords a strong
verification of Ewing's form of the molecular theory. Ewing has himself
also shown how satisfactorily this theory accords with many other
obscure and complicated phenomena, such as those presented by coercive
force, differences of magnetic quality, and the effects of vibration,
temperature and stress; while as regards simplicity and freedom from
arbitrary assumptions it leaves little to be desired.

The fact being established that magnetism is essentially a molecular
phenomenon, the next step is to inquire what is the constitution of a
magnetic molecule, and why it is that some molecules are ferromagnetic,
others paramagnetic, and others again diamagnetic. The best known of the
explanations that have been proposed depend upon the magnetic action of
an electric current. It can be shown that if a current i circulates in a
small plane circuit of area S, the magnetic action of the circuit for
distant points is equivalent to that of a short magnet whose axis is
perpendicular to the plane of the circuit and whose moment is iS, the
direction of the magnetization being related to that of the circulating
current as the thrust of a right-handed screw to its rotation.
Ferromagnetism was explained by Ampère on the hypothesis that the
magnetization of the molecule is due to an electric current constantly
circulating within it. The theory now most in favour is merely a
development of Ampère's hypothesis, and applies not only to
ferromagnetics, but to paramagnetics as well. To account for
diamagnetism, Weber supposed that there exist within the molecules of
diamagnetic substances certain channels around which an electric current
can circulate without any resistance. The creation of an external
magnetic field H will, in accordance with Lenz's law, induce in the
molecule an electric current so directed that the magnetization of the
equivalent magnet is opposed to the direction of the field. The strength
of the induced current is -HScos[theta]/L, where [theta] is the
inclination of the axis of the circuit to the direction of the field,
and L the coefficient of self-induction; the resolved part of the
magnetic moment in the direction of the field is equal to
-HS²cos²[theta]/L, and if there are n molecules in a unit of volume,
their axes being distributed indifferently in all directions, the
magnetization of the substance will be -(1/3)nHS²/L, and its
susceptibility -(1/3)S²/L (Maxwell, _Electricity and Magnetism_, § 838).
The susceptibility is therefore constant and independent of the field,
while its negative sign indicates that the substance is diamagnetic.
There being no resistance, the induced current will continue to
circulate round the molecule until the field is withdrawn, when it will
be stopped by the action of an electromotive force tending to induce an
exactly equal current in the opposite direction. The principle of
Weber's theory, with the modification necessitated by lately acquired
knowledge, is the basis of the best modern explanation of diamagnetic
phenomena.

There are strong reasons for believing that magnetism is a phenomenon
involving rotation, and as early as 1876 Rowland, carrying out an
experiment which had been proposed by Maxwell, showed that a revolving
electric charge produced the same magnetic effects as a current. Since
that date it has more than once been suggested that the molecular
currents producing magnetism might be due to the revolution of one or
more of the charged atoms or "ions" constituting the molecule. None of
the detailed hypotheses which were based on this idea stood the test of
criticism, but towards the end of the 19th century the researches of J.
J. Thomson and others once more brought the conception of moving
electric charges into prominence. Thomson has demonstrated the existence
under many different conditions of particles more minute than anything
previously known to science. The mass of each is about 1/1700th part of
that of a hydrogen atom, and with each is indissolubly associated a
charge of negative electricity equal to about 3.1 × 10^(-10) C.G.S.
electrostatic unit. These particles, which were termed by their
discoverer _corpuscles_, are more commonly spoken of as _electrons_,[93]
the particle thus being identified with the charge which it carries. An
electrically neutral atom is believed to be constituted in part, or
perhaps entirely, of a definite number of electrons in rapid motion
within a "sphere of uniform positive electrification" not yet explained.
One or more of the electrons may be detached from the system by a finite
force, the number so detachable depending on the valency of the atom; if
the atom loses an electron, it becomes positively electrified; if it
receives additional electrons, it is negatively electrified. The process
of electric conduction in metals consists in the movement of detached
electrons, and many other phenomena, both electrical and thermal, can be
more or less completely explained by their agency. It has been supposed
that certain electrons revolve like satellites in orbits around the
atoms with which they are associated, a view which receives strong
support from the phenomena of the Zeeman effect, and on this assumption
a theory has been worked out by P. Langevin,[94] which accounts for many
of the observed facts of magnetism. As a consequence of the structure of
the molecule, which is an aggregation of atoms, the planes of the orbits
around the latter may be oriented in various positions, and the
direction of revolution may be right-handed or left-handed with respect
to the direction of any applied magnetic field. For those orbits whose
projection upon a plane perpendicular to the field is right-handed, the
period of revolution will be accelerated by the field (since the
electron current is negative), and the magnetic moment consequently
increased; for those which are left-handed, the period will be retarded
and the moment diminished. The effect of the field upon the speed of the
revolving electrons, and therefore upon the moments of the equivalent
magnets, is necessarily a very small one. If S is the area of the orbit
described in time [tau] by an electron of charge e, the moment of the
equivalent magnet is M = eS[tau]; and the change in the value of M due
to an external field H is shown to be [Delta]M = -He^2 S/4[pi]m, m being
the mass of the electron. Whence

  [Delta]M   H[tau]e
  -------- = -------.
      M      4[pi]m

According to the best determinations the value of e/m does not exceed
1.8 × 10^7, and [tau] is of the order of 10^(-15) second, the period of
luminous vibrations; hence [Delta]M/M must always be less than 10^(-9)H,
and therefore the strongest fields yet reached experimentally, which
fall considerably short of 10^5, could not change the magnetic moment M
by as much as a ten-thousandth part. If the structure of the molecule is
so perfectly symmetrical that, in the absence of any external field, the
resultant magnetic moment of the circulating electrons is zero, then the
application of a field, by accelerating the right-handed (negative)
revolutions, and retarding those which are left-handed, will induce in
the substance a resultant magnetization opposite in direction to the
field itself; a body composed of such symmetrical molecules is therefore
diamagnetic. If however the structure of the molecule is such that the
electrons revolving around its atoms do not exactly cancel one another's
effects, the molecule constitutes a little magnet, which under the
influence of an external field will tend to set itself with its axis
parallel to the field. Ordinarily a substance composed of asymmetrical
molecules is paramagnetic, but if the elementary magnets are so
conditioned by their strength and concentration that mutual action
between them is possible, then the substance is ferromagnetic. In all
cases however it is the diamagnetic condition that is initially set
up--even iron is diamagnetic--though the diamagnetism may be completely
masked by the superposed paramagnetic or ferromagnetic condition.
Diamagnetism, in short, is an atomic phenomenon; paramagnetism and
ferromagnetism are molecular phenomena. Hence may be deduced an
explanation of the fact that, while the susceptibility of all known
diamagnetics (except bismuth and antimony) is independent of the
temperature, that of paramagnetics varies inversely as the absolute
temperature, in accordance with the law of Curie.


13. HISTORICAL AND CHRONOLOGICAL NOTES

The most conspicuous property of the lodestone, its attraction for iron,
appears to have been familiar to the Greeks at least as early as 800
B.C., and is mentioned by Homer, Plato, Aristotle, Theophrastus and
others. A passage in _De rerum natura_ (vi. 910-915) by the Roman poet,
Lucretius (96-55 B.C.), in which it is stated that the stone can support
a chain of little rings, each adhering to the one above it, indicates
that in his time the phenomenon of magnetization by induction had also
been observed. The property of orientation, in virtue of which a freely
suspended magnet points approximately to the geographical north and
south, is not referred to by any European writer before the 12th
century, though it is said to have been known to the Chinese at a much
earlier period. The application of this property to the construction of
the mariner's compass is obvious, and it is in connexion with navigation
that the first references to it occur (see COMPASS). The needles of the
primitive compasses, being made of iron, would require frequent
re-magnetization, and a "stone" for the purpose of "touching the needle"
was therefore generally included in the navigator's outfit. With the
constant practice of this operation it is hardly possible that the
repulsion acting between like poles should have entirely escaped
recognition; but though it appears to have been noticed that the
lodestone sometimes repelled iron instead of attracting it, no clear
statement of the fundamental law that unlike poles attract while like
poles repel was recorded before the publication in 1581 of the _New
Attractive_ by Robert Norman, a pioneer in accurate magnetic work. The
same book contains an account of Norman's discovery and correct
measurement of the dip (1576). The downward tendency of the north pole
of a magnet pivoted in the usual way had been observed by G. Hartmann of
Nüremberg in 1544, but his observation was not published till much
later.

The foundations of the modern science of magnetism were laid by William
Gilbert (q.v.). His _De magnete magneticisque corporibus et de magno
magnete tellure physiologia nova_ (1600), contains many references to
the expositions of earlier writers from Plato down to those of the
author's own age. These show that the very few facts known with
certainty were freely supplemented by a number of ill-founded
conjectures, and sometimes even by "figments and falsehoods, which in
the earliest times, no less than nowadays, used to be put forth by raw
smatterers and copyists to be swallowed of men."[95] Thus it was taught
that "if a lodestone be anointed with garlic, or if a diamond be near,
it does not attract iron," and that "if pickled in the salt of a sucking
fish, there is power to pick up gold which has fallen into the deepest
wells." There were said to be "various kinds of magnets, some of which
attract gold, others silver, brass, lead; even some which attract flesh,
water, fishes;" and stories were told about "mountains in the north of
such great powers of attraction that ships are built with wooden pegs,
lest the iron nails should be drawn from the timber." Certain occult
powers were also attributed to the stone. It was "of use to thieves by
its fume and sheen, being a stone born, as it were, to aid theft," and
even opening bars and locks; it was effective as a love potion, and
possessed "the power to reconcile husbands to their wives, and to recall
brides to their husbands." And much more of the same kind, which, as
Gilbert says, had come down "even to [his] own day through the writings
of a host of men, who, to fill out their volumes to a proper bulk, write
and copy out pages upon pages on this, that and the other subject, of
which they know almost nothing for certain of their own experience."
Gilbert himself absolutely disregarded authority, and accepted nothing
at second-hand. His title to be honoured as the "Father of Magnetic
Philosophy" is based even more largely upon the scientific method which
he was the first to inculcate and practise than upon the importance of
his actual discoveries. Careful experiment and observation, not the
inner consciousness, are, he insists, the only foundations of true
science. Nothing has been set down in his book "which hath not been
explored and many times performed and repeated" by himself. "It is very
easy for men of acute intellect, apart from experiment and practice, to
slip and err." The greatest of Gilbert's discoveries was that the globe
of the earth was magnetic and a magnet; the evidence by which he
supported this view was derived chiefly from ingenious experiments made
with a spherical lodestone or _terrella_, as he termed it, and from his
original observation that an iron bar could be magnetized by the earth's
force. He also carried out some new experiments on the effects of heat,
and of screening by magnetic substances, and investigated the influence
of shape upon the magnetization of iron. But the bulk of his work
consisted in imparting scientific definiteness to what was already
vaguely known, and in demolishing the errors of his predecessors.

No material advance upon the knowledge recorded in Gilbert's book was
made until the establishment by Coulomb in 1785 of the law of magnetic
action. The difficulties attending the experimental investigation of the
forces acting between magnetic poles have already been referred to, and
indeed a rigorously exact determination of the mutual action could only
be made under conditions which are in practice unattainable.
Coulomb,[96] however, by using long and thin steel rods, symmetrically
magnetized, and so arranged that disturbing influences became negligibly
small, was enabled to deduce from his experiments with reasonable
certainty the law that the force of attraction or repulsion between two
poles varies inversely as the square of the distance between them.
Several previous attempts had been made to discover the law of force,
with various results, some of which correctly indicated the inverse
square; in particular the German astronomer, J. Tobias Mayer (_Gött.
Anzeiger_, 1760), and the Alsatian mathematician, J. Heinrich Lambert
(_Hist. de l'Acad. Roy. Berlin_, 1766, p. 22), may fairly be credited
with having anticipated the law which was afterwards more satisfactorily
established by Coulomb. The accuracy of this law was in 1832 confirmed
by Gauss,[97] who employed an indirect but more perfect method than that
of Coulomb, and also, as Maxwell remarks, by all observers in magnetic
observatories, who are every day making measurements of magnetic
quantities, and who obtain results which would be inconsistent with each
other if the law of force had been erroneously assumed.

Coulomb's researches provided data for the development of a mathematical
theory of magnetism, which was indeed initiated by himself, but was
first treated in a complete form by Poisson in a series of memoirs
published in 1821 and later.[98] Poisson assumed the existence of two
dissimilar magnetic fluids, any element of which acted upon any other
distant element in accordance with Coulomb's law of the inverse square,
like repelling and unlike attracting one another. A magnetizable
substance was supposed to consist of an indefinite number of spherical
particles, each containing equivalent quantities of the two fluids,
which could move freely within a particle, but could never pass from one
particle to another. When the fluids inside a particle were mixed
together, the particle was neutral; when they were more or less
completely separated, the particle became magnetized to an intensity
depending upon the magnetic force applied; the whole body therefore
consisted of a number of little spheres having north and south poles,
each of which exerted an elementary action at a distance. On this
hypothesis Poisson investigated the forces due to bodies magnetized in
any manner, and also originated the mathematical theory of magnetic
induction. The general confirmation by experiment of Poisson's
theoretical results created a tendency to regard his hypothetical
magnetic fluids as having a real existence; but it was pointed out by W.
Thomson (afterwards Lord Kelvin) in 1849 that while no physical evidence
could be adduced in support of the hypothesis, certain discoveries,
especially in electromagnetism, rendered it extremely improbable
(_Reprint_, p. 344). Regarding it as important that all reasoning with
reference to magnetism should be conducted without any uncertain
assumptions, he worked out a mathematical theory upon the sole
foundation of a few well-known facts and principles. The results were
substantially the same as those given by Poisson's theory, so far as the
latter went, the principal additions including a fuller investigation of
magnetic distribution, and the theory of magnetic induction in
aeolotropic or crystalline substances. The mathematical theory which was
constructed by Poisson, and extended and freed from doubtful hypotheses
by Kelvin, has been elaborated by other investigators, notably F. E.
Neumann, G. R. Kirchhoff, and Maxwell. The valuable work of Gauss on
magnetic theory and measurements, especially in relation to terrestrial
magnetism, was published in his _Intensitas vis magneticae terrestris_,
1833, and in memoirs communicated to the _Resultate aus den
Beobachtungen des magnetischen Vereins_, 1838 and 1839, which, with
others, are contained in vol. 5 of the collected _Werke_. Weber's
molecular theory, which has already been referred to, appeared in
1852.[99]

An event of the first importance was the discovery made in 1819 by H. C.
Oersted [100] that a magnet placed near a wire carrying an electric
current tended to set itself at right angles to the wire, a phenomenon
which indicated that the current was surrounded by a magnetic field.
This discovery constituted the foundation of electromagnetism, and its
publication in 1820 was immediately followed by A. M. Ampère's
experimental and theoretical investigation of the mutual action of
electric currents,[101] and of the equivalence of a closed circuit to a
polar magnet, the latter suggesting his celebrated hypothesis that
molecular currents were the cause of magnetism. In the same year D. F.
Arago[102] succeeded in magnetizing a piece of iron by the electric
current, and in 1825 W. Sturgeon[103] publicly exhibited an apparatus
"acting on the principle of powerful magnetism and feeble galvanism"
which is believed to have constituted the first actual electromagnet.
Michael Faraday's researches were begun in 1831 and continued for more
than twenty years. Among the most splendid of his achievements was the
discovery of the phenomena and laws of magneto-electric induction, the
subject of two papers communicated to the Royal Society in 1831 and
1832. Another was the magnetic rotation of the plane of polarization of
light, which was effected in 1845, and for the first time established a
relation between light and magnetism. This was followed at the close of
the same year by the discovery of the magnetic condition of all matter,
a discovery which initiated a prolonged and fruitful study of
paramagnetic and diamagnetic phenomena, including magnecrystallic action
and "magnetic conducting power," now known as permeability. Throughout
his researches Faraday paid special regard to the medium as the true
seat of magnetic action, being to a large extent guided by his pregnant
conception of "lines of force," or of induction, which he considered to
be "closed curves passing in one part of the course through the magnet
to which they belong, and in the other part through space," always
tending to shorten themselves, and repelling one another when they were
side by side (_Exp. Res._ §§ 3266-8, 3271). In 1873 James Clerk Maxwell
published his classical _Treatise on Electricity and Magnetism_, in
which Faraday's ideas were translated into a mathematical form. Maxwell
explained electric and magnetic forces, not by the action at a distance
assumed by the earlier mathematicians, but by stresses in a medium
filling all space, and possessing qualities like those attributed to the
old luminiferous ether. In particular, he found that the calculated
velocity with which it transmitted electromagnetic disturbances was
equal to the observed velocity of light; hence he was led to believe,
not only that his medium and the ether were one and the same, but,
further, that light itself was an electromagnetic phenomenon. Since the
experimental confirmation of Maxwell's views by H. R. Hertz in 1888
(_Weid. Ann._, 1888, 34, 155, 551, 609; and later vols.) they have
commanded universal assent, and his methods are adopted in all modern
work on electricity and magnetism.

The practice of measuring magnetic induction and permeability with
scientific accuracy was introduced in 1873 by H. A. Rowland,[104] whose
careful experiments led to general recognition of the fact previously
ignored by nearly all investigators, that magnetic susceptibility and
permeability are by no means constants (at least in the case of the
ferromagnetic metals) but functions of the magnetizing force. New light
was thrown upon many important details of magnetic science by J. A.
Ewing's _Experimental Researches_ of 1885; throughout the whole of his
work special attention was directed to that curious lagging action to
which the author applied the now familiar term "hysteresis."[105] His
well-known modification[106] of Weber's molecular theory, published in
1890, presented for the first time a simple and sufficient explanation
of hysteresis and many other complexities of magnetic quality. The
amazing discoveries made by J. J. Thomson in 1897 and 1898[107] resulted
in the establishment of the electron theory, which has already effected
developments of an almost revolutionary character in more than one
branch of science. The application of the theory by P. Langevin to the
case of molecular magnetism has been noticed above, and there can be
little doubt that in the near future it will contribute to the solution
of other problems which are still obscure.

  See W. Gilbert, _De magnete_ (London, 1600; trans. by P. F. Mottelay,
  New York, 1893, and for the Gilbert Club, London, 1900); M. Faraday,
  _Experimental Researches in Electricity_, 3 vols. (London, 1839, 1844
  and 1855); W. Thomson (Lord Kelvin), _Reprint of Papers on
  Electrostatics and Magnetism_ (London, 1884, containing papers on
  magnetic theory originally published between 1844 and 1855, with
  additions); J. C. Maxwell, _Treatise on Electricity and Magnetism_
  (3rd ed., Oxford, 1892); E. Mascart and J. Joubert, _Leçons sur
  l'électricité et le magnétisme_ (2nd ed., Paris, 1896-1897; trans.,
  not free from errors, by E. Atkinson, London, 1883); J. A. Ewing,
  _Magnetic Induction in Iron and other Metals_ (3rd ed., London,
  1900); J. J. Thomson, _Recent Researches in Electricity and Magnetism_
  (Oxford, 1893); _Elements of Mathematical Theory of Electricity and
  Magnetism_ (3rd ed., Cambridge, 1904); H. du Bois, _The Magnetic
  Circuit_ (trans. by E. Atkinson, London, 1896); A. Gray, _Treatise on
  Magnetism and Electricity_, vol. i. (London, 1898); J. A. Fleming,
  _Magnets and Electric Currents_ (London, 1898); C. Maurain, _Le
  magnétisme du fer_ (Paris, 1899; a lucid summary of the principal
  facts and laws, with special regard to their practical application);
  _Rapports présentés au Congrès international de physique_, vol. ii.
  (Paris, 1900); G. C. Foster and A. W. Porter, _Treatise on Electricity
  and Magnetism_ (London, 1903); A. Winkelmann, _Handbuch der Physik_,
  vol. v. part i. (2nd ed., Leipzig, 1905; the most exhaustive
  compendium of magnetic science yet published, containing references to
  all important works and papers on every branch of the subject).
       (S. Bi.)


FOOTNOTES:

  [1] In London in 1910 the needle pointed about 16° W. of the
    geographical north. (See TERRESTRIAL MAGNETISM.)

  [2] For the relations between magnetism and light see MAGNETO-OPTICS.

  [3] Clerk Maxwell employed German capitals to denote vector
    quantities. J. A. Fleming first recommended the use of blockletters
    as being more convenient both to printers and readers.

  [4] The C.G.S. unit of current = 10 amperes.

  [5] The principal theoretical investigations are summarized in
    Mascart and Joubert's _Electricity and Magnetism_, i. 391-398 and ii.
    646-657. The case of a long iron bar has been experimentally studied
    with great care by C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 509.

  [6] _Wied. Ann._, 1884, 22, 411.

  [7] See C. G. Lamb, _loc. cit._ p. 518.

  [8] Hopkinson specified the retentiveness by the numerical value of
    the "residual induction" (= 4[pi]I).

  [9] For all except ferromagnetic substances the coefficient is
    sensibly equal to [kappa].

  [10] See W. Thomson's _Reprint_, §§ 615, 634-651.

  [11] Ibid. §§ 646, 684.

  [12] Faraday, _Exp. Res._ xxi.

  [13] J. J. Thomson, _Electricity and Magnetism_, § 205.

  [14] Maxwell, _Electricity and Magnetism_, § 431.

  [15] H. du Bois, _Electrician_, 1898, 40, 317.

  [16] M. Faraday, _Exp. Res._ xxii., xxiii.; W. Thomson, _Reprint_, §
    604; J. C. Maxwell, _Treatise_, § 435; E. Mascart and J. Joubert,
    _Electricity and Magnetism_, §§ 384, 396, 1226; A. Winkelmann,
    _Physik_, v. 287.

  [17] See A. Winkelmann, _Physik_, v. 69-94; Mascart and Joubert.
    _Electricity and Magnetism_, ii. 617.

  [18] _Sci. Abs._ A, 1906, 9, 225.

  [19] See C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 517.

  [20] _Soc. Franc. Phys. Séances_, 1904, 1, 27.

  [21] E. G. Warburg, _Wied. Ann._ 1881, 13, 141; Ewing, _Phil.
    Trans._, 1885, 176, 549; Hopkinson, _Phil. Trans._ 1885, 176, 466.
    For a simple proof, see Ewing, _Magnetic Induction_ (1900), p. 99.
    Hopkinson pointed out that the greatest dissipation of energy which
    can be caused by a to-and-fro reversal is approximately represented
    by _Coercive force_ × _maximum induction_ /[pi].

  [22] _Magnetic Induction_, 1900, 378.

  [23] _Phil. Trans._, 1902, 198, 33.

  [24] _Phil. Mag._, 1903, 5, 117.

  [25] Some experiments by F. G. Baily showed that hysteresis ceased to
    increase when B was carried beyond 23,000. This value of B
    corresponds to I = 1640, the saturation point for soft iron.--_Brit.
    Assoc. Rep._, 1895, p. 636.

  [26] _Tokyo Phys.-Math. Soc._, 1904, 2, No. 14.

  [27] _Phil. Mag._, 1873, 46, 140.

  [28] S. Bidwell, _Proc. Roy. Soc._, 1886, 40, 495.

  [29] Since in most practicable experiments H³ is negligible in
    comparison with B², the force may be taken as B²/8[pi] without
    sensible error.

  [30] The same phenomenon is exhibited in a less marked degree when
    soft iron is magnetized in stronger fields (Ewing, _Phil. Trans._,
    1885, 176, 569).

  [31] Principal publications: J. P. Joule, _Scientific Papers_, pp.
    46, 235; A. M. Meyer, _Phil. Mag._, 1873, 46, 177; W. F. Barrett,
    _Nature_, 1882, 26, 585; S. Bidwell, _Phil. Trans._, 1888, 179A, 205;
    _Proc. Roy. Soc._, 1886, 40, 109 and 257; 1888, 43, 406; 1890, 47,
    469; 1892, 51, 495; 1894, 55, 228; 1894, 56, 94; 1904, 74, 60;
    _Nature_, 1899, 60, 222; M. Cantone, _Mem. d. Acc d. Lincei_, 1889,
    6, 487; _Rend. d. Acc. d. Lincei_, 1890, 6, 252; A. Berget, _C.R._,
    1892, 115, 722; S. J. Lochner, _Phil. Mag._, 1893, 36, 498; H.
    Nagaoka, _Phil. Mag._, 1894, 37, 131; _Wied. Ann._, 1894, 53, 487; C.
    G. Knott, _Proc. Roy. Soc. Ed._, 1891, 18, 315; _Phil. Mag._, 1894,
    37, 141; _Trans. Roy. Soc. Ed._, 1896, 38, 527; 1898, 39, 457; C. G.
    Knott and A. Shand, _Proc. Roy. Soc. Ed._, 1892, 19, 85 and 249;
    1894, 20, 295; L. T. More, _Phil. Mag._, 1895, 40, 345; G.
    Klingenberg, _Rostock Univ. Thesis_, Berlin, 1897; E. T. Jones,
    _Phil. Trans._, 1897, 189A, 189; B. B. Brackett, _Phys. Rev._, 1897,
    5, 257; H. Nagaoka and K. Honda, _Phil. Mag._, 1898, 46, 261; 1900,
    49, 329; _Journ. Coll. Sci. Tokyo_, 1900, 13, 57; 1903, 19, art. 11;
    J. S. Stevens, _Phys. Rev._, 1898, 7, 19; E. Rhoads, _Phys. Rev._,
    1898, 7, 5; _Phil. Mag._, 1901, 2, 463; G. A. Shakespear, _Phil.
    Mag._, 1899, 17, 539; K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13,
    77; L. W. Austin, _Phys. Rev._, 1900, 10, 180; _Deutsch. Phys.
    Gesell. Verh._, 1904, 6, 4, 211; K. Honda and S. Shimizu, _Phil.
    Mag._, 1902, 4, 338; 1905, 10, 548.

  [32] The loads were successively applied in decreasing order of
    magnitude. They are indicated in fig. 25 as kilos per sq. cm.

  [33] Joule believed that the volume was unchanged.

  [34] For a discussion of theories of magnetic stress, with copious
    references, see Nagaoka, _Rap. du Congrès International de Physique_
    (Paris, 1900), ii. 545. Also Nagaoka and Jones, _Phil. Mag._, 1896,
    41, 454.

  [35] S. Bidwell, _Phil. Trans._, 1888, 179a, 321.

  [36] _Phil. Mag._, 1895, 40, 345.

  [37] J. C. Maxwell, _Treatise_, § 643.

  [38] See correspondence in _Nature_, 1896, 53, pp. 269, 316, 365,
    462, 533; 1906, 74, pp. 317, 539; B. B. Brackett, _loc. cit._, quotes
    the opinion of H. A. Rowland in support of compressive stress.

  [39] J. A. Ewing, _Phil. Trans._, 1885, 176, 580; 1888, 179, 333;
    _Magnetic Induction_, 1900, ch. ix.; J. A. Ewing and G. C. Cowan,
    _Phil. Trans._, 1888, 179a, 325; C. G. Knott, _Trans. Roy. Soc. Ed._,
    1882-1883, 32, 193; 1889, 35, 377; 1891, 36, 485; _Proc. Roy. Soc.
    Ed._, 1899, 586; H. Nagaoka, _Phil. Mag._, 1889, 27, 117; 1890, 29,
    123; H. Nagaoka and K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13,
    263; 1902, 16, art. 8; _Phil. Mag._, 1898, 46, 261; 1902, 4, 45; K.
    Honda and S. Shimizu, _Ann. d. Phys._, 1904, 14, 791; _Tokyo
    Physico-Math. Soc. Rep._, 1904, 2, No. 13; K. Honda and T. Terada,
    _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4.

  [40] H. Tomlinson found a critical point in the "temporary
    magnetization" of nickel (_Proc. Phys. Soc._, 1890, 10, 367, 445),
    but this does not correspond to a Villari reversal. Its nature is
    made clear by Ewing and Cowan's curves (_Phil. Trans._, 1888, 179,
    plates 15, 16).

  [41] _Wied. Ann._, 1894, 52, 462; _Electrician_, 1894, 34, 143.

  [42] _Phil. Trans._, 1890, 131, 329.

  [43] _Magnetic Induction_, 1900, 222.

  [44] _Phys. Rev._, 1904, 18, 432.

  [45] _Phil. Mag._, 1886, 22, 50.

  [46] _Ibid._ 251.

  [47] _Phil. Mag._, 1891, 32, 383.

  [48] _C.R._, 1896, 122, 1192; 1898, 126, 463.

  [49] _Phil. Mag._, 1889, 27, 117.

  [50] _Journ. Coll. Sci. Tokyo_, 1904, 19, art. 9.

  [51] _Phil. Mag._, 1905, 10, 548; _Tokyo Phys.-Math. Soc. Rep._,
    1904, 2, No. 14; _Journ. Coll. Sci. Tokyo_, 1905, 20, art. 6.

  [52] _C.R._, 1888, 106, 129.

  [53] _Proc. Phys. Soc._, 1888, 9, 181.

  [54] _C.R._, 1892, 115, 805; 1894, 118, 796 and 859.

  [55] _Elekt. Zeits._, 1894, 15, 194.

  [56] _Phil. Mag._, 1900, 50, 1.

  [57] _Phil. Trans._, 1903, 201, 1.

  [58] _Phil. Mag._, 1904, 8, 179.

  [59] A. M. Thiessen (_Phys._, 1899, 8, 65) and G. Claude (C. R.,
    1899, 129, 409) found that for considerable inductions (B = 15,000)
    the permeability and hysteresis-loss remained nearly constant down to
    -186°; for weak inductions both notably diminished with temperature.

  [60] _Proc. Roy. Soc._, 1898, 62, 210.

  [61] _C.R._, 1895, 120, 263.

  [62] _Amer. Journ. Sci._, 1898, 5, 245.

  [63] _Phys. Rev._, 1901, 14, 181.

  [64] _C.R._, 1897, 124, 176 and 1515; 1897, 125, 235; 1898, 126, 738.

  [65] Ibid., 1898, 126, 741.

  [66] Ibid., 1899, 128, 304 and 1395.

  [67] See also J. Hopkinson, _Journ. Inst. Elect. Eng._, 1890, 19, 20,
    and J. A. Ewing, _Phil. Trans._, 1889, 180, 239.

  [68] Many of the figures which, through an error, were inaccurately
    stated in the first paper are corrected in the second.

  [69] The marked effect of silicon in increasing the permeability of
    cast iron has also been noticed by F. C. Caldwell, _Elect. World_,
    1898, 32, 619.

  [70] _Trans. Roy. Dub. Soc._, 1902-4, 8, 1 and 123.

  [71] J. Trowbridge and S. Sheldon, _Phil. Mag._, 1890, 29, 136; W. H.
    Preece, _Journ. Inst. Elec. Eng._, 1890, 19, 62; _Electrician_, 1890,
    25, 546; I. Klemençiç, _Wien. Ber._, 1896, 105, IIa, 635; B. O.
    Peirce, _Am. Journ. Sci._, 1896, 2, 347; A. Abt, _Wied. Ann._, 1898,
    66, 116; F. Osmond, _C. R._, 1899, 128, 1513.

  [72] _Deutsch. phys. Gesell. Verh._, 1903, 5, 220 and 224.

  [73] _Exp. Res._, iii. 440.

  [74] No record can be found of experiments with manganese at the
    temperature of liquid air or hydrogen; probably, however, negative
    results would not be published.

  [75] The critical temperature of iron, for instance, is raised more
    than 100° by the addition of a little carbon and tungsten.

  [76] _Bull. Soc. Int. des Électriciens_, 1906, 6, 301.

  [77] _Proc. Roy. Soc._, 1905, 76A, 271.

  [78] E. H. Hall, _Phil. Mag._, 1880, 9, 225; 1880, 10, 301; 1881, 12,
    157; 1883, 15, 341; 1885, 19, 419.

  [79] The large Hall effect in bismuth was discovered by Righi,
    _Journ. de Phys._, 1884, 3, 127.

  [80] REFERENCES.--(2) A. von Ettinghausen, _Wied. Ann._, 1887, 31,
    737.--(4) H. W. Nernst, ibid., 784.--(i.) and (iv.); A. von
    Ettinghausen and H. W. Nernst, _Wied. Ann._, 1886, 29, 343.--(ii.)
    and (iii.); A. Righi, _Rend. Acc. Linc._, 1887, 3 II, 6 and I, 481;
    and A. Leduc, _Journ. de Phys._, 1887, 6, 78. Additional authorities
    are quoted by Lloyd, _loc. cit._

  [81] P. Drude, _Ann. d. Phys._, 1900, 1, 566; 1900, 3, 369; 1902, 7,
    687. See also E. van Everdingen, _Arch. Néerlandaises_, 1901, 4, 371;
    G. Barlow, _Ann. d. Phys._, 1903, 12, 897; H. Zahn, ibid. 1904, 14,
    886; 1905, 16, 148.

  [82] _Phil. Trans._, 1856, p. 722. According to the nomenclature
    adopted by the best modern authorities, a metal A is said to be
    thermo-electrically positive to another metal B when the
    thermo-current passes from A to B through the cold junction, and from
    B to A through the hot (see THERMO-ELECTRICITY).

  [83] _C.R._, 1893, 116, 997.

  [84] _Journ. de Phys._, 1896, 5, 53.

  [85] _Phil. Trans._, 1887, 177, 373.

  [86] _Proc. Roy. Soc._, 1885, 39, 513.

  [87] _Phys. Rev._, 1902, 15, 321. The sign of the thermo-electric
    effect for nickel, as given by Rhoads, is incorrect.

  [88] _Proc. Roy. Soc._, 1904, 73, 413.

  [89] _C.R._, 1903, 136, 1131.

  [90] _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4. The paper contains
    40 tables and 85 figures.

  [91] This deduction from Ewing's theory appears to have been first
    suggested by J. Swinburne. See _Industries_, 1890, 289.

  [92] R. Beattie (_Phil. Mag._, 1901, 1, 642) has found similar
    effects in nickel and cobalt.

  [93] The charge associated with a corpuscle is the same as that
    carried by a hydrogen atom. G. J. Stoney in 1881 (_Phil. Mag._, 1881,
    11, 387) pointed out that this latter constituted the indivisible
    "atom of electricity" or natural unit charge. Later he proposed
    (_Trans. Roy. Dub. Soc._, 1891, 4, 583) that such unit charge should
    be called an "electron." The application of this term to Thomson's
    corpuscle implies, rightly or wrongly, that notwithstanding its
    apparent mass, the corpuscle is in fact nothing more than an atom of
    electricity. The question whether a corpuscle actually has a material
    gravitating nucleus is undecided, but there are strong reasons for
    believing that its mass is entirely due to the electric charge.

  [94] _Jour. de Phys._, 1905, 4, 678; translated in _Electrician_,
    1905, 56, 108 and 141.

  [95] The quotations are from the translation published by the Gilbert
    Club, London, 1900.

  [96] C. A. Coulomb, _Mem. Acad. Roy. Paris_, 1785, p. 578.

  [97] _Intensitas vis magneticae_, § 21, C. F. Gauss's _Werke_, 5, 79.
    See also J. J. Thomson, _Electricity and Magnetism_, § 132.

  [98] S. D. Poisson, _Mém. de l'Institut_, 1821 and 1822, 5, 247, 488;
    1823, 6, 441; 1838, 16, 479.

  [99] For outlines of the mathematical theory of magnetism and
    references see H. du Bois, _Magnetic Circuit_, chs. iii. and iv.

  [100] Gilbert's _Ann. d. phys._, 1820, 6, 295.

  [101] _Ann. de chim. et de phys._, 1820, 15, 59, 170; _Recueil
    d'observations électrodynamiques_, 1822; _Théories des phénomènes
    électrodynamiques_, 1826.

  [102] _Ann. de chim. et de phys._, 1820, 15, 93.

  [103] _Trans. Soc. Arts_, 1825, 43, 38.

  [104] _Phil. Mag._, 1873, 46, 140; 1874, 48, 321.

  [105] _Phil. Trans._, 1885, 176, 523; _Magnetic Induction_, 1900.

  [106] _Proc. Roy. Soc._, 1890, 48, 342.

  [107] _Phil. Mag._, 1897, 44, 293; 1898, 46, 528.




MAGNETISM, TERRESTRIAL, the science which has for its province the study
of the magnetic phenomena of the earth.


  Historical.

§ 1. Terrestrial magnetism has a long history. Its early growth was
slow, and considerable uncertainty prevails as to its earliest
developments. The properties of the magnet (see MAGNETISM) were to some
small extent known to the Greeks and Romans before the Christian era,
and compasses (see COMPASS) of an elementary character seem to have been
employed in Europe at least as early as the 12th century. In China and
Japan compasses of a kind seem to have existed at a much earlier date,
and it is even claimed that the Chinese were aware of the declination of
the compass needle from the true north before the end of the 11th
century. Early scientific knowledge was usually, however, a mixture of
facts, very imperfectly ascertained, with philosophical imaginings. When
an early writer makes a statement which to a modern reader suggests a
knowledge of the declination of the compass, he may have had no such
definite idea in his mind. So far as Western civilization is concerned,
Columbus is usually credited with the discovery--in 1492 during his
first voyage to America--that the pointing of the compass needle to the
true north represents an exceptional state of matters, and that a
_declination_ in general exists, varying from place to place. The credit
of these discoveries is not, however, universally conceded to Columbus.
G. Hellmann[6][A] considers it almost certain that the departure of the
needle from the true north was known in Europe before the time of
Columbus. There is indirect evidence that the declination of the compass
was not known in Europe in the early part of the 15th century, through
the peculiarities shown by early maps believed to have been drawn solely
by regard to the compass. Whether Columbus was the first to observe the
declination or not, his date is at least approximately that of its
discovery.

The next fundamental discovery is usually ascribed to Robert Norman, an
English instrument maker. In _The Newe Attractive_ (1581) Norman
describes his discovery made some years before of the _inclination_ or
_dip_. The discovery was made more or less by accident, through Norman's
noticing that compass needles which were truly balanced so as to be
horizontal when unmagnetized, ceased to be so after being stroked with a
magnet. Norman devised a form of dip-circle, and found a value for the
inclination in London which was at least not very wide of the mark.

Another fundamental discovery, that of the secular change of the
declination, was made in England by Henry Gellibrand, professor of
mathematics at Gresham College, who described it in his _Discourse
Mathematical on the Variation of the Magneticall Needle together with
its Admirable Diminution lately discovered_ (1635). The history of this
discovery affords a curious example of knowledge long delayed. William
Borough, in his _Discourse on the Variation of the Compas or Magneticall
Needle_ (1581), gave for the declination at Limehouse in October 1580
the value 11°¼ E. approximately. Observations were repeated at
Limehouse, Gellibrand tells us, in 1622 by his colleague Edmund Gunter,
professor of astronomy at Gresham College, who found the much smaller
value 6° 13´. The difference seems to have been ascribed at first to
error on Borough's part, and no suspicion of the truth seems to have
been felt until 1633, when some rough observations gave a value still
lower than that found by Gunter. It was not until midsummer 1634 that
Gellibrand felt sure of his facts, and yet the change of declination
since 1580 exceeded 7°. The delay probably arose from the strength of
the preconceived idea, apparently universally held, that the declination
was absolutely fixed. This idea, it would appear, derived some of its
strength from the positive assertion made on the point by Gilbert of
Colchester in his _De magnete_ (1600).

A third fundamental discovery, that of the diurnal change in the
declination, is usually credited to George Graham (1675-1751), a London
instrument maker. Previous observers, e.g. Gellibrand, had obtained
slightly different values for the declination at different hours of the
day, but it was natural to assign them to instrumental uncertainties. In
those days the usual declination instrument was the compass with pivoted
needles, and Graham himself at first assigned the differences he
observed to friction. The observations on which he based his conclusions
were made in 1722; an account of them was communicated to the Royal
Society and published in the _Philosophical Transactions_ for 1724.

The movements of the compass needle throughout the average day represent
partly a regular diurnal variation, and partly irregular changes in the
declination. The distinction, however, was not at first very clearly
realized. Between 1756 and 1759 J. Canton observed the declination-changes
on some 600 days, and was thus able to deduce their general character. He
found that the most prominent part of the regular diurnal change in
England consisted of a westerly movement of the north-pointing pole from 8
or 9 a.m. to 1 or 2 p.m., followed by a more leisurely return movement to
the east. He also found that the amplitude of the movement was
considerably larger in summer than in winter. Canton further observed that
in a few days the movements were conspicuously irregular, and that aurora
was then visible. This association of magnetic disturbance and aurora had,
however, been observed somewhat before this time, a description of one
conspicuous instance being contributed to the Royal Society in 1750 by
Pehr Vilhelm Wargentin (1717-1783), a Swede.

Another landmark in the history of terrestrial magnetism was the
discovery towards the end of the 18th century that the intensity of the
resultant magnetic force varies at different parts of the earth. The
first observations clearly showing this seem to be those of a Frenchman,
Paul de Lamanon, who observed in 1785-1787 at Teneriffe and Macao, but
his results were not published at the time. The first published
observations seem to be those made by the great traveller Humboldt in
tropical America between 1798 and 1803. The delay in this discovery may
again be attributed to instrumental imperfections. The method first
devised for comparing the force at different places consisted in taking
the time of oscillation of the dipping needle, and even with modern
circles this is hardly a method of high precision. Another discovery
worth chronicling was made by Arago in 1827. From observations made at
Paris he found that the inclination of the dipping needle and the
intensity of the horizontal component of the magnetic force both
possessed a diurnal variation.

§ 2. Whilst Italy, England and France claim most of the early
observational discoveries, Germany deserves a large share of credit for
the great improvement in instruments and methods during the first half
of the 19th century. Measurements of the intensity of the magnetic force
were somewhat crude until Gauss showed how absolute results could be
obtained, and not merely relative data based on observations with some
particular needle. Gauss also devised the bifilar magnetometer, which is
still largely represented in instruments measuring changes of the
horizontal force; but much of the practical success attending the
application of his ideas to instruments seems due to Johann von Lamont
(1805-1879), a Jesuit of Scottish origin resident in Germany.

The institution of special observatories for magnetic work is largely
due to Humboldt and Gauss. The latter's observatory at Göttingen, where
regular observations began in 1834, was the centre of the Magnetic Union
founded by Gauss and Weber for the carrying out of simultaneous magnetic
observations and it was long customary to employ Göttingen time in
schemes of international co-operation.

In the next decade, mainly through the influence of Sir Edward Sabine
(1788-1883), afterwards president of the Royal Society, several magnetic
observatories were established in the British colonies, at St Helena,
Cape of Good Hope, Hobarton (now Hobart) and Toronto. These, with the
exception of Toronto, continued in full action for only a few years; but
their records--from their widely distributed positions--threw much fresh
light on the differences between magnetic phenomena in different regions
of the globe. The introduction of regular magnetic observatories led ere
long to the discovery that there are notable differences between the
amplitudes of the regular daily changes and the frequency of magnetic
disturbances in different years. The discovery that magnetic phenomena
have a period closely similar to, if not absolutely identical with, the
"eleven year" period in sun-spots, was made independently and nearly
simultaneously about the middle of the 19th century by Lamont, Sabine
and R. Wolf.

The last half of the 19th century showed a large increase in the number
of observatories taking magnetic observations. After 1890 there was an
increased interest in magnetic work. One of the contributory causes was
the magnetic survey of the British Isles made by Sir A. Rücker and Sir
T. E. Thorpe, which served as a stimulus to similar work elsewhere;
another was the institution by L. A. Bauer of a magazine. _Terrestrial
Magnetism_, specially devoted to the subject. This increased activity
added largely to the stock of information, sometimes in forms of marked
practical utility; it was also manifested in the publication of a number
of papers of a speculative character. For historical details the writer
is largely indebted to the works of E. Walker[1] and L. A. Bauer.[3]


    Observational Methods and Records.

  § 3. All the more important magnetic observatories are provided with
  instruments of two kinds. Those of the first kind give the absolute
  value of the magnetic elements at the time of observation. The
  unifilar magnetometer (q.v.), for instance, gives the absolute values
  of the declination and horizontal force, whilst the inclinometer
  (q.v.) or dip circle gives the inclination of the dipping needle.
  Instruments of the second kind, termed magnetographs (q.v.), are
  differential and self-recording, and show the changes constantly
  taking place in the magnetic elements. The ordinary form of
  magnetograph records photographically. Light reflected from a fixed
  mirror gives a base line answering to a constant value of the element
  in question; the light is cut off every hour or second hour so that
  the base line also serves to make the time. Light reflected from a
  mirror carried by a magnet gives a curved line answering to the
  changes in position of the magnet. The length of the ordinate or
  perpendicular drawn from any point of the curved line on to the base
  line is proportional to the extent of departure of the magnet from a
  standard position. If then we know the absolute value of the element
  which corresponds to the base line, and the equivalent of 1 cm. of
  ordinate, we can deduce the absolute value of the element answering to
  any given instant of time. In the case of the declination the value of
  1 cm. of ordinate is usually dependent almost entirely on the distance
  of the mirror carried by the magnet from the photographic paper, and
  so remains invariable or very nearly so. In the case of the horizontal
  force and vertical force magnetographs--these being the two force
  components usually recorded--the value of 1 cm. of ordinate alters
  with the strength of the magnet. It has thus to be determined from
  time to time by observing the deflection shown on the photographic
  paper when an auxiliary magnet of known moment, at a measured
  distance, deflects the magnetograph magnet. Means are provided for
  altering the sensitiveness, for instance, by changing the effective
  distance in the bifilar suspension of the horizontal force magnet, and
  by altering the height of a small weight carried by the vertical force
  magnet. It is customary to aim at keeping the sensitiveness as
  constant as possible. A very common standard is to have 1 cm. of
  ordinate corresponding to 10´ of arc in the declination and to
  50[gamma] (1[gamma] = 0.00001 C.G.S.) in the horizontal and vertical
  force magnetographs.

  As an example of how the curves are standardized, suppose that
  absolute observations of declination are taken four times a month, and
  that in a given month the mean of the observed values is 16° 34´.6 W.
  The curves are measured at the places which correspond to the times of
  the four observations, and the mean length of the four ordinates is,
  let us say, 2.52 cms. If 1 cm. answers to 10´, then 2.52 cms.
  represents 25´.2, and thus the value of the base line--i.e. the value
  which the declination would have if the curve came down to the base
  line--is for the month in question 16° 34´.6 less 25´.2 or 16° 9´.4.
  If now we wish to know the declination at any instant in this
  particular month all we have to do is to measure the corresponding
  ordinate and add its value, at the rate of 10´ per cm., to the base
  value 16° 9´.4 just found. Matters are a little more complicated in
  the case of the horizontal and vertical force magnetographs. Both
  instruments usually possess a sensible temperature coefficient, i.e.
  the position of the magnet is dependent to some extent on the
  temperature it happens to possess, and allowance has thus to be made
  for the difference from a standard temperature. In the case of the
  vertical force an "observed" value is derived by combining the
  observed value of the inclination with the simultaneous value of the
  horizontal force derived from the horizontal force magnetograph after
  the base value of the latter has been determined. In themselves the
  results of the absolute observations are of minor interest. Their main
  importance is that they provide the means of fixing the value of the
  base line in the curves. Unless they are made carefully and
  sufficiently often the information derivable from the curves suffers
  in accuracy, especially that relating to the secular change. It is
  from the curves that information is derived as to the regular diurnal
  variation and irregular changes. In some observatories it is customary
  to publish a complete record of the values of the magnetic elements at
  every hour for each day of the year. A useful and not unusual addition
  to this is a statement of the absolutely largest and smallest values
  of each element recorded during each day, with the precise times of
  their occurrence. On days of large disturbance even hourly readings
  give but a very imperfect idea of the phenomena, and it is customary
  at some observatories, e.g. Greenwich, to reproduce the more disturbed
  curves in the annual volume. In calculating the regular diurnal
  variation it is usual to consider each month separately. So far as is
  known at present, it is entirely or almost entirely a matter of
  accident at what precise hours specially high or low values of an
  element may present themselves during an individual highly disturbed
  day; whilst the range of the element on such a day may be 5, 10 or
  even 20 times as large as on the average undisturbed day of the month.
  It is thus customary when calculating diurnal inequalities to omit the
  days of largest disturbance, as their inclusion would introduce too
  large an element of uncertainty. Highly disturbed days are more than
  usually common in some years, and in some months of the year, thus
  their omission may produce effects other than that intended. Even on
  days of lesser disturbance difficulties present themselves. There may
  be to and fro movements of considerable amplitude occupying under an
  hour, and the hour may come exactly at the crest or at the very lowest
  part of the trough. Thus, if the reading represents in every case the
  ordinate at the precise hour a considerable element of chance may be
  introduced. If one is dealing with a mean from several hundred days
  such "accidents" can be trusted to practically neutralize one another,
  but this is much less fully the case when the period is as short as a
  month. To meet this difficulty it is customary at some observatories
  to derive hourly values from a freehand curve of continuous curvature,
  drawn so as to smooth out the apparently irregular movements. Instead
  of drawing a freehand curve it has been proposed to use a planimeter,
  and to accept as the hourly value of the ordinate the mean derived
  from a consideration of the area included between the curve, the base
  line and ordinates at the thirty minutes before and after each hour.

  § 4. Partly on account of the uncertainties due to disturbances, and
  partly with a view to economy of labour, it has been the practice at
  some observatories to derive diurnal inequalities from a comparatively
  small number of undisturbed or quiet days. Beginning with 1890, five
  days a month were selected at Greenwich by the astronomer royal as
  conspicuously quiet. In the selection regard was paid to the
  desirability that the arithmetic mean of the five dates should answer
  to near the middle of the month. In some of the other English
  observatories the routine measurement of the curves was limited to
  these selected quiet days. At Greenwich itself diurnal inequalities
  were derived regularly from the quiet days alone and also from all the
  days of the month, excluding those of large disturbance. If a quiet
  day differed from an ordinary day only in that the diurnal variation
  in the latter was partly obscured by irregular disturbances, then
  supposing enough days taken to smooth out irregularities, one would
  get the same diurnal inequality from ordinary and from quiet days. It
  was found, however, that this was hardly ever the case (see §§ 29 and
  30). The quiet day scheme thus failed to secure exactly what was
  originally aimed at; on the other hand, it led to the discovery of a
  number of interesting results calculated to throw valuable sidelights
  on the phenomena of terrestrial magnetism.

  The idea of selecting quiet days seems due originally to H. Wild. His
  selected quiet days for St Petersburg and Pavlovsk were very few in
  number, in some months not even a single day reaching his standard of
  freedom from disturbance. In later years the International Magnetic
  Committee requested the authorities of each observatory to arrange the
  days of each month in three groups representing the quiet, the
  moderately disturbed and the highly disturbed. The statistics are
  collected and published on behalf of the committee, the first to
  undertake the duty being M. Snellen. The days are in all cases counted
  from Greenwich midnight, so that the results are strictly synchronous.
  The results promise to be of much interest.

  § 5. The intensity and direction of the resultant magnetic force at a
  spot--i.e. the force experienced by a unit magnetic pole--are known if
  we know the three components of force parallel to any set of
  orthogonal axes. It is usual to take for these axes the vertical at
  the spot and two perpendicular axes in the horizontal plane; the
  latter are usually taken in and perpendicular to the geographical
  meridian. The usual notation in mathematical work is X to the north, Y
  to the west or east, and Z vertically downwards. The international
  magnetic committee have recommended that Y be taken positive to the
  east, but the fact that the declination is westerly over most of
  Europe has often led to the opposite procedure, and writers are not
  always as careful as they should be in stating their choice. Apart
  from mathematical calculations, the more usual course is to define the
  force by its horizontal and vertical components--usually termed H and
  V--and by the declination or angle which the horizontal component
  makes with the astronomical meridian. The declination is sometimes
  counted from 0° to 360°, 0° answering to the case when the so-called
  north pole (or north seeking pole) is directed towards geographical
  north, 90° to the case when it is directed to the east, and so on. It
  is more usual, however, to reckon declination only from 0° to 180°,
  characterizing it as easterly or westerly according as the north pole
  points to the east or to the west of the geographical meridian. The
  force is also completely defined by H or V, together with D the
  declination, and I the inclination to the horizon of the dipping
  needle. Instead of H and D some writers make use of N the northerly
  component, and W the westerly (or E the easterly). The resultant force
  itself is denoted sometimes by R, sometimes by T (total force). The
  following relationships exist between the symbols

    X [equiv] N, Y [equiv] W or E, Z [equiv] V, R [equiv] T,

    H [equiv] [root](X² + Y²), R [equiv] [root](X² + Y² + Z²),

    tan D = Y/X, tan I = V/H.

  The term _magnetic element_ is applied to R or any of the components,
  and even to the angles D and I.


  Charts.

§ 6. Declination is the element concerning which our knowledge is most
complete and most reliable. With a good unifilar magnetometer, at a
fixed observatory distant from the magnetic poles, having a fixed mark
of known azimuth, the observational uncertainty in a single observation
should not exceed 0´.5 or at most 1´.0. It cannot be taken for granted
that different unifilars, even by the best makers, will give absolutely
identical values for the declination, but as a matter of fact the
differences observed are usually very trifling. The chief source of
uncertainty in the observation lies in the torsion of the suspension
fibre, usually of silk or more rarely of phosphor bronze or other metal.
A very stout suspension must be avoided at all cost, but the fibre must
not be so thin as to have a considerable risk of breaking even in
skilled hands. Near a magnetic pole the directive force on the
declination magnet is reduced, and the effects of torsion are
correspondingly increased. On the other hand, the regular and irregular
changes of declination are much enhanced. If an observation consisting
of four readings of declination occupies twelve minutes, the chances are
that in this time the range at an English station will not exceed 1´,
whereas at an arctic or antarctic station it will frequently exceed 10´.
Much greater uncertainty thus attaches to declination results in the
Arctic and Antarctic than to those in temperate latitudes. In the case
of secular change data one important consideration is that the
observations should be taken at an absolutely fixed spot, free from any
artificial source of disturbance. In the case of many of the older
observations of which records exist, the precise spot cannot be very
exactly fixed, and not infrequently the site has become unsuitable
through the erection of buildings not free from iron. Apart from
buildings, much depends on whether the neighbourhood is free from
basaltic and other magnetic rocks. If there are no local disturbances of
this sort, a few yards difference is usually without appreciable
influence, and even a few miles difference is of minor importance when
one is calculating the mean secular change for a long period of years.
When, however, local disturbances exist, even a few feet difference in
the site may be important, and in the absence of positive knowledge to
the contrary it is only prudent to act as if the site were disturbed.
Near a magnetic pole the declination naturally changes very rapidly when
one travels in the direction perpendicular to the lines of equal
declination, so that the exact position of the site of observation is
there of special importance.

  The usual method of conveying information as to the value of the
  declination at different parts of the earth's surface is to draw
  curves on a map--the so-called _isogonals_--such that at all points on
  any one curve the declination at a given specified epoch has the same
  value. The information being of special use to sailors, the
  preparation of magnetic charts has been largely the work of naval
  authorities--more especially of the hydrographic department of the
  British admiralty. The object of the admiralty world charts--four of
  which are reproduced here, on a reduced scale, by the kind permission
  of the Hydrographer--is rather to show the general features boldly
  than to indicate minute details. Apart from the immediate necessities
  of the case, this is a counsel of prudence. The observations used have
  mostly been taken at dates considerably anterior to that to which the
  chart is intended to apply. What the sailor wants is the declination
  now or for the next few years, not what it was five, ten or twenty
  years ago. Reliable secular change data, for reasons already
  indicated, are mainly obtainable from fixed observatories, and there
  are enormous areas outside of Europe where no such observatories
  exist. Again, as we shall see presently, the rate of the secular
  change sometimes alters greatly in the course of a comparatively few
  years. Thus, even when the observations themselves are thoroughly
  reliable, the prognostication made for a future date by even the most
  experienced of chart makers may be occasionally somewhat wide of the
  mark. Fig. 1 is a reduced copy of the British admiralty declination
  chart for the epoch 1907. It shows the isogonals between 70° N. and
  65° S. latitude. Beyond the limits of this chart, the number of exact
  measurements of declination is somewhat limited, but the general
  nature of the phenomena is easily inferred. The geographical and the
  magnetic poles--where the dipping needle is vertical--are fundamental
  points. The north magnetic pole is situated in North America near the
  edge of the chart. We have no reason to suppose that the magnetic pole
  is really a fixed point, but for our present purpose we may regard it
  as such. Let us draw an imaginary circle round it, and let us travel
  round the circle in the direction, west, north, east, south, starting
  from a point where the north pole of a magnet (i.e. the pole which in
  Europe or the United States points to the north) is directed exactly
  towards the astronomical north. The point we start from is to the
  geographical south of the magnetic pole. As we go round the circle the
  needle keeps directed to the magnetic pole, and so points first
  slightly to the east of geographical north, then more and more to the
  east, then directly east, then to south of east, then to due south, to
  west of south, to west, to north-west, and finally when we get round
  to our original position due north once more. Thus, during our course
  round the circle the needle will have pointed in all possible
  directions. In other words, isogonals answering to all possible values
  of the declination have their origin in the north magnetic pole. The
  same remark applies of course to the south magnetic pole.

  [Illustration: FIG. 1.--Isogonals, or lines of equal magnetic
  declination.]

  Now, suppose ourselves at the north geographical pole of the earth.
  Neglecting as before diurnal variation and similar temporary changes,
  and assuming no abnormal local disturbance, the compass needle at and
  very close to this pole will occupy a fixed direction relative to the
  ground underneath. Let us draw on the ground through the pole a
  straight line parallel to the direction taken there by the compass
  needle, and let us carry a compass needle round a _small_ circle whose
  centre is the pole. At all points on the circle the positions of the
  needle will be parallel; but whereas the north pole of the magnet will
  point exactly towards the centre of the circle at one of the points
  where the straight line drawn on the ground cuts the circumference, it
  will at the opposite end of the diameter point exactly away from the
  centre. The former part is clearly on the isogonal where the
  declination is 0°, the latter on the isogonal where it is 180°.
  Isogonals will thus radiate out from the north geographical pole (and
  similarly of course from the south geographical pole) in all
  directions. If we travel along an isogonal, starting from the north
  magnetic pole, our course will generally take us, often very
  circuitously, to the north geographical pole. If, for example, we
  select the isogonal of 10° E., we at first travel nearly south, but
  then more and more westerly, then north-westerly across the north-east
  of Asia; the direction then gets less northerly, and makes a dip to
  the south before finally making for the north geographical pole. It is
  possible, however, according to the chart, to travel direct from the
  north magnetic to the south geographical pole, provided we select an
  isogonal answering to a small westerly or easterly declination (from
  about 19° W. to 7° E.).

  Special interest attaches to the isogonals answering to declination
  0°. These are termed _agonic lines_, but sailors often call them
  _lines of no variation_, the term _variation_ having at one time been
  in common use in the sense of declination. If we start from the north
  magnetic pole the agonic line takes us across Canada, the United
  States and South America in a fairly straight course to the south
  geographical pole. A curve continuous with this can be drawn from the
  south geographical to the south magnetic pole at every point of which
  the needle points in the geographical meridian; but here the north
  pole of the needle is pointing south, not north, so that this portion
  of curve is really an isogonal of 180°. In continuation of this there
  emanates from the south magnetic pole a second isogonal of 0°, or
  agonic line, which traverses Australia, Arabia and Russia, and takes
  us to the north geographical pole. Finally, we have an isogonal of
  180°, continuous with this second isogonal of 0° which takes us to the
  north magnetic pole, from which we started. Throughout the whole area
  included within these isogonals of 0° and 180°--excluding locally
  disturbed areas--the declination is westerly; outside this area the
  declination is in general easterly. There is, however, as shown in the
  chart, an isogonal of 0° enclosing an area in eastern Asia inside
  which the declination is westerly though small.

  § 7. Fig. 2 is a reduced copy of the admiralty chart of inclination or
  dip for the epoch 1907. The places where the dip has the same value
  lie on curves called _isoclinals_. The dip is northerly (north pole
  dips) or southerly (south pole dips) according as the place is north
  or south of the isoclinal of 0°. At places actually on this isoclinal
  the dipping needle is horizontal. The isoclinal of 0° is nowhere very
  far from the geographical equator, but lies to the north of it in Asia
  and Africa, and to the south of it in South America. As we travel
  north from the isoclinal of 0° along the meridian containing the
  magnetic pole the dipping needle's north pole dips more and more,
  until when we reach the magnetic pole the needle is vertical. Going
  still farther north, we have the dip diminishing. The northerly
  inclination is considerably less in Europe than in the same latitudes
  of North America; and correspondingly the southerly inclination is
  less in South America than in the same latitudes of Africa.

  [Illustration: FIG. 2.--Isoclinals, or lines of equal magnetic dip.]

  Fig. 3 is a reduced copy of the admiralty horizontal force chart for
  1907. The curves, called _isomagnetics_, connect the places where the
  horizontal force has the same value; the force is expressed in C.G.S.
  units. The horizontal force vanishes of course at the magnetic poles.
  The chart shows a maximum value of between 0.39 and 0.40 in an oval
  including the south of Siam and the China Sea. The horizontal force is
  smaller in North America than in corresponding latitudes in Europe.

  [Illustration: FIG. 3.--Isomagnetics, lines of equal horizontal
  force.]

  Charts are sometimes drawn for other magnetic elements, especially
  vertical force (fig. 4) and total force. The isomagnetic of zero
  vertical force coincides necessarily with that of zero dip, and there
  is in general considerable resemblance between the forms of lines of
  equal vertical force and those of equal dip. The highest values of the
  vertical force occur in areas surrounding the magnetic poles, and are
  fully 50% larger than the largest values of the horizontal force. The
  total force is least in equatorial regions, where values slightly
  under 0.4 C.G.S. are encountered. In the northern hemisphere there are
  two distinct maxima of total force. One of these so-called _foci_ is
  in Canada, the other in the north-east of Siberia, the former having
  the higher value of the force. There are, however, higher values of
  the total force than at either of these _foci_ throughout a
  considerable area to the south of Australia. In the northern
  hemisphere the lines of equal total force--called _isodynamic_
  lines--form two sets more or less distinct, consisting of closed
  ovals, one set surrounding the Canadian the other the Siberian focus.


    Magnetic Elements and their Secular Change.

  § 8. As already explained, magnetic charts for the world or for large
  areas give only a general idea of the values of the elements. If the
  region is undisturbed, very fairly approximate values are derivable
  from the charts, but when the highest accuracy is necessary the only
  thing to do is to observe at the precise spot. In disturbed areas
  local values often depart somewhat widely from what one would infer
  from the chart, and occasionally there are large differences between
  places only a few miles apart. Magnetic observatories usually publish
  the mean value for the year of their magnetic elements. It has been
  customary for many years to collect and publish these results in the
  annual report of the Kew Observatory (Observatory Department of the
  National Physical Laboratory). The data in Tables I. and II. are
  mainly derived from this source. The observatories are arranged in
  order of latitude, and their geographical co-ordinates are given in
  Table II., longitude being reckoned from Greenwich. Table I. gives the
  mean values of the declination, inclination and horizontal force for
  January 1, 1901; they are in the main arithmetic means of the mean
  annual values for the two years 1900 and 1901. The mean annual secular
  changes given in this table are derived from a short period of
  years--usually 1898 to 1903--the centre of which fell at the beginning
  of 1901. Table II. is similar to Table I., but includes vertical force
  results; it is more extensive and contains more recent data. In it the
  number of years is specified from which the mean secular change is
  derived; in all cases the last year of the period employed was that to
  which the absolute values assigned to the element belong. The great
  majority of the stations have declination west and inclination north;
  it has thus been convenient to attach the + sign to increasing
  westerly (or decreasing easterly) declination and to increasing
  northerly (or decreasing southerly) inclination. In other words, in
  the case of the declination + means that the north end of the needle
  is moving to the west, while in the case of the inclination + means
  that the north end (whether the dipping end or not) is moving towards
  the nadir. In the case, however, of the vertical force + means simply
  _numerical_ increase, irrespective of whether the north or the south
  pole dips. The unit employed in the horizontal and vertical force
  secular changes is 1[gamma], i.e. 0.00001 C.G.S. Even in the
  declination, at the very best observatories, it is hardly safe to
  assume that the apparent change from one year to the next is
  absolutely truthful to nature. This is especially the case if there
  has been any change of instrument or observer, or if any alteration
  has been made to buildings in the immediate vicinity. A change of
  instrument is a much greater source of uncertainty in the case of
  horizontal force or dip than in the case of declination, and dip
  circles and needles are more liable to deterioration than
  magnetometers. Thus, secular change data for inclination and vertical
  force are the least reliable. The uncertainties, of course, are much
  less, from a purely mathematical standpoint, for secular changes
  representing a mean from five or ten years than for those derived from
  successive years' values of the elements. The longer, however, the
  period of years, the greater is the chance that one of the elements
  may in the course of it have passed through a maximum or minimum
  value. This possibility should always be borne in mind in cases where
  a mean secular change appears exceptionally small.

  [Illustration: FIG. 4.--Isomagnetics, lines of equal vertical force.]

  As Tables I. and II. show, the declination needle is moving to the
  east all over Europe, and the rate at which it is moving seems not to
  vary much throughout the continent. The needle is also moving to the
  east throughout the western parts of Asia, the north and east of
  Africa, and the east of North America. It is moving to the west in the
  west of North America, in South America, and in the south and east of
  Asia, including Japan, south-east Siberia, eastern China and most of
  India.

  § 9. The information in figs. 1, 2, 3 and 4 and in Tables I. and II.
  applies only to recent years. Owing to secular change, recent charts
  differ widely from the earliest ones constructed. The first charts
  believed to have been constructed were those of Edmund Halley the
  astronomer. According to L. A. Bauer,[7] who has made a special study
  of the subject, Halley issued two declination charts for the epoch
  1700; one, published in 1701, was practically confined to the Atlantic
  Ocean, whilst the second, published in 1702, contained also data for
  the Indian Ocean and part of the Pacific. These charts showed the
  isogonic lines, but only over the ocean areas. Though the charts for
  1700 were the first published, there are others which apply to earlier
  epochs. W. van Bemmelen[8] has published charts for the epochs 1500,
  1550, 1600, 1650 and 1700, whilst H. Fritsche[9] has more recently
  published charts of declination, inclination and horizontal force for
  1600, 1700, 1780, 1842 and 1915. A number of early declination charts
  were given in Hansteen's Atlas and in G. Hellmann's reprints. _Die
  Altesten Karten der Isogonen, Isoklinen, Isodynamen_ (Berlin, 1895).
  The data for the earlier epochs, especially those prior to 1700, are
  meagre, and in many cases probably of indifferent accuracy, so that
  the reliability of the charts for these epochs is somewhat open to
  doubt.

  If we take either Hansteen's or Fritsche's declination chart for 1600
  we notice a profound difference from fig. 1. In 1600 the agonic line
  starting from the north magnetic pole, after finding its way south to
  the Gulf of Mexico, doubled back to the north-east, and passed across
  or near Iceland. After getting well to the north of Iceland it doubled
  again to the south, passing to the east of the Baltic. The second
  agonic line which now lies to the west of St Petersburg appears in
  1600 to have continued, after traversing Australia, in a nearly
  northerly direction through the extreme east of China. The nature of
  the changes in declination in western Europe will be understood from
  Table III., the data from which, though derived from a variety of
  places in the south-east of England,[10] may be regarded as
  approximately true of London. The earliest result is that obtained by
  Borough at Limehouse. Those made in the 16th century are due to
  Gunter, Gellibrand, Henry Bond and Halley. The observations from 1787
  to 1805 were due to George Gilpin, who published particulars of his
  own and the earlier observations in the _Phil. Trans._ for 1806. The
  data for 1817 and 1820 were obtained by Col. Mark Beaufoy, at Bushey,
  Herts. They seem to come precisely at the time when the needle, which
  had been continuously moving to the west since the earliest
  observations, began to retrace its steps. The data from 1860 onwards
  apply to Kew.

  TABLE I.--Magnetic Elements and their Rate of Secular Change for
  January 1, 1901.

    +----------------+------------------------------+----------------------+
    |                |       Absolute values.       |    Secular change.   |
    |     Place.     +----------+----------+--------+-------+------+-------+
    |                |     D.   |    I.    |   H.   |   D.  |  I.  |   H.  |
    +----------------+----------+----------+--------+-------+------+-------+
    |                |  °  ´    |  °  ´    |        |   ´   |   ´  |[gamma]|
    | Pavlovsk       |  0 39.8E | 70 36.8N | .16553 | - 4.1 | -0.8 |  + 7  |
    | Ekatarinburg   | 10  6.3E | 70 40.5N | .17783 | - 4.6 | +0.5 |  -13  |
    | Copenhagen     | 10 10.4W | 68 38.5N | .17525 |       |      |       |
    | Stonyhurst     | 18 10.3W | 68 48.0N | .17330 | - 4.0 |      |  +22  |
    | Wilhelmshaven  | 12 26.0W | 67 39.7N | .18108 | - 4.1 | -2.1 |  +20  |
    | Potsdam        |  9 54.2W | 66 24.5N | .18852 | - 4.2 | -1.6 |  +16  |
    | Irkutsk        |  2  1.0E | 70 15.8N | .20122 | + 0.5 | +1.6 |  -14  |
    | de Bilt        | 13 48.3W | 66 55.5N | .18516 | - 4.4 | -2.2 |  +14  |
    | Kew            | 16 50.8W | 67 10.6N | .18440 | - 4.2 | -2.2 |  +25  |
    | Greenwich      | 16 27.5W | 67  7.3N | .18465 | - 4.0 | -2.2 |  +23  |
    | Uccle          | 14 11.0W | 66  8.8N | .18954 | - 4.2 | -2.1 |  +23  |
    | Falmouth       | 18 27.3W | 66 44.0N | .18705 | - 3.8 | -2.7 |  +26  |
    | Prague         |  9  4.4W |          | .19956 | - 4.4 |      |  +20  |
    | St Helier      | 16 58.1W | 65 44.1N |        | - 3.5 | -2.7 |       |
    | Parc St Maur   | 14 43.4W | 64 52.3N | .19755\| - 4.0 | -2.2 |  +23  |
    | Val Joyeux     | 15 13.7W | 65  0.0N | .19670/|       |      |       |
    | Munich         | 10 25.8W | 63 18.1N | .20629 | - 4.8 | -2.7 |  +21  |
    | O'Gyalla       |  7 26.1W |          | .21164 | - 4.8 |      |  +13  |
    | Pola           |  9 22.7W | 60 14.5N | .22216 | - 4.0 |      |  +23  |
    | Toulouse       | 14 16.4W | 60 55.9N | .21945 | - 3.9 | -2.5 |  +25  |
    | Perpignan      | 13 34.7W | 59 57.6N | .22453 |       |      |       |
    | Capo di Monte  |  9  8.0W | 56 22.3N |        | - 5.2 | -2.3 |       |
    | Madrid         | 15 39.0W |          |        |       |      |       |
    | Coimbra        | 17 18.1W | 59 22.0N | .22786 | - 3.7 | -4.3 |  +34  |
    | Lisbon         | 17 15.7W | 57 53.0N | .23548 |       |      |       |
    | Athens         |  5 38.2W | 52  7.5N | .26076 |       |      |       |
    | San Fernando   | 15 57.5W | 55  8.8N | .24648 |       |      |       |
    | Tokyo          |  4 34.9W | 49  0.3N | .29932 |       |      |       |
    | Zi-ka-wei      |  2 23.5W | 45 43.5N | .32875 | + 1.5 | -1.5 |  +37  |
    | Helwan         |  3 39.7W | 40 30.8N | .30136 | - 7.0 | -0.4 |  - 7  |
    | Hong-Kong      |  0 17.5E | 31 22.8N | .36753 | + 1.8 | -4.3 |  +45  |
    | Kolaba         |  0 23.2E | 21 26.5N | .37436 | + 2.2 | +7.0 |  - 9  |
    | Manila         |  0 52.2E | 16 13.5N | .38064 | + 0.1 | -5.3 |  +47  |
    | Batavia        |  1  7.3E | 30 35.5S | .36724 | + 3.0 | -7.3 |  -11  |
    | Mauritius      |  9 25.2W | 54  9.4S | .23820 | - 4.7 | +4.6 |  -39  |
    | Rio de Janeiro |  8  2.9W | 13 20.1S | .2501  | +10.4 | -2.3 |       |
    | Melbourne      |  8 25.6E | 67 24.6S | .23295 |       |      |       |
    +----------------+----------+----------+--------+-------+------+-------+

  The rate of movement of the needle to the east at London--and
  throughout Europe generally--fell off markedly subsequent to 1880. The
  change of declination in fact between 1880 and 1895 was only about 75%
  of that between 1865 and 1880, and the mean annual change from 1895 to
  1900 was less than 75% of the mean annual change of the preceding
  fifteen years. Thus in 1902 it was at least open to doubt whether a
  change in the sign of the secular change were not in immediate
  prospect. Subsequent, however, to that date there was little further
  decline in the rate of secular change, and since 1905 there has been
  very distinct acceleration. Thus, if we derive a mean value from the
  eighteen European stations for which declination secular changes are
  given in Tables I. and II. we find

    mean value from table  I. -4.18
      "    "     "    "   II. -5.21

  The epoch to which the data in Table II. refer is somewhat variable,
  but is in all cases more recent than the epoch, January 1, 1901, for
  Table I., the mean difference being about 5 years.

  § 10. At Paris there seems to have been a maximum of easterly
  declination (about 9°) about 1580; the needle pointed to true north
  about 1662, and reached its extreme westerly position between 1812 and
  1814. The phenomena at Rome resembled those at Paris and London, but
  the extreme westerly position is believed to have been attained
  earlier. The rate of change near the turning point seems to have been
  very slow, and as no fixed observatories existed in those days, the
  precise time of its occurrence is open to some doubt.

  Perhaps the most complete observations extant as to the declination
  phenomena near a turning point relate to Kolaba observatory at Bombay;
  they were given originally by N. A. F. Moos,[11] the director of the
  observatory. Some of the more interesting details are given in Table
  IV.; here W denotes movement to be west, and so answers to a numerical
  diminution in the declination, which is easterly.

  Prior to 1880 the secular change at Kolaba was unmistakably to the
  east, and subsequent to 1883 it was clearly to the west; but between
  these dates opinions will probably differ as to what actually
  happened. The fluctuations then apparent in the sign of the annual
  change may be real, but it is at least conceivable that they are of
  instrumental origin. From 1870 to 1875 the mean annual change was
  -1´.2; from 1885 to 1890 it was +1´.5, from 1890 to 1895 it was +2´.0,
  while from 1895 to 1905 it was +2´.35, the + sign denoting movement to
  the west. Thus, in this case the rate of secular change has increased
  fairly steadily since the turning point was reached.

  Table V. contains some data for St Helena and the Cape of Good
  Hope,[12] both places having a long magnetic history. The remarkable
  feature at St Helena is the uniformity in the rate of secular change.
  The figures for the Cape show a reversal in the direction of the
  secular change about 1840, but after a few years the arrested movement
  to the west again became visible. According, however, to J. C.
  Beattie's _Magnetic Survey of South Africa_ the movement to the west
  ceased shortly after 1870. A persistent movement to the east then set
  in, the mean annual change increasing from 1´.8 between 1873 and 1890
  to 3´.8 between 1890 and 1900.

  § 11. Secular changes of declination have been particularly
  interesting in the United States, an area about which information is
  unusually complete, thanks to the labours and publications of the
  United States Coast and Geodetic Survey.[13] At present the agonic
  line passes in a south-easterly direction from Lake Superior to South
  Carolina. To the east of the agonic line the declination is westerly,
  and to the west it is easterly. In 1905 the declination varied from
  about 21° W. in the extreme north-east to about 24° E. in the extreme
  north-west. At present the motion of the agonic line seems to be
  towards the west, but it is very slow. To the east of the agonic line
  westerly declination is increasing, and to the west of the line, with
  the exception of a narrow strip immediately adjacent to it, easterly
  declination is increasing. The phenomena in short suggest a motion
  southwards in the north magnetic pole. Since 1750 declination has
  always been westerly in the extreme east of the States, and always
  easterly in the extreme west, but the position of the agonic line has
  altered a good deal. It was to the west of Richmond, Virginia, from
  1750 to about 1772, then to the east of it until about 1838 when it
  once more passed to the west; since that time it has travelled farther
  to the west. Table VI. is intended to show the nature of the secular
  change throughout the whole country. As before, + denotes that the
  north pole of the magnet is moving to the west,--that it is moving to
  the east.

  The data in Table VI. represent the mean change of declination per
  annum, derived from the period (ten years, except for 1900-1905) which
  ended in the year put at the top of the column. The stations are
  arranged in four groups, the first group representing the extreme
  eastern, the last group the extreme western states, the other two
  groups being intermediate. In each group the stations are arranged, at
  least approximately, in order of latitude. The data are derived from
  the values of the declination given in the Geodetic Survey's _Report_
  for 1906, appendix 4, and _Magnetic Tables and Magnetic Charts_ by L.
  A. Bauer, 1908. The values seem, in most cases, based to some extent
  on calculation, and very probably the secular change was not in
  reality quite so regular as the figures suggest. For the Western
  States the earliest data are comparatively recent, but for some of the
  eastern states data earlier than any in the table appear in the
  _Report of the Coast and Geodetic Survey_ for 1902. These data
  indicate that the easterly movement of the magnet, visible in all the
  earlier figures for the Eastern States in Table VI., existed in all of
  them at least as far back as 1700. There is not very much evidence as
  to the secular change between 1700 and 1650, the earliest date to
  which the Coast and Geodetic Survey's figures refer. The figures show
  a maximum of westerly declination about 1670 in New Jersey and about
  1675 in Maryland. They suggest that this maximum was experienced all
  along the Atlantic border some time in the 17th century, but earlier
  in the extreme north-east than in New York or Maryland.

  Examination of Table VI. shows that the needle continued to move to
  the east for some time after 1750 even in the Eastern States. But the
  rate of movement was clearly diminishing, and about 1765 the extreme
  easterly position was reached in Eastport, Maine, the needle then
  beginning to retrace its steps to the west. The phenomena visible at
  Maine are seen repeating themselves at places more and more to the
  west, in Boston about 1785, in Albany about 1800, in Washington, D.C.,
  about 1805, in Columbus (Ohio) about 1815, in Montgomery (Alabama)
  about 1825, in Bloomington (Ill.) about 1830, in Des Moines (Iowa)
  about 1840, in Santa Rosa (New Mexico) about 1860 and in Salt Lake
  about 1870. In 1885 the needle was moving to the west over the whole
  United States with the exception of a comparatively narrow strip along
  the Pacific coast. Even an acute observer would have been tempted to
  prophesy in 1885 that at no distant date the secular change would be
  pronouncedly westerly right up to the Pacific. But in a few years a
  complete change took place. The movement to the east, which had become
  exceedingly small, if existent, in the Pacific states, began to
  accelerate; the movement to the west continued in the central, as in
  the eastern states, but perceptibly slackened. In 1905 the area
  throughout which the movement to the west still continued had greatly
  contracted and lay to the east of a line drawn from the west end of
  Lake Superior to the west of Georgia. If we take a station like Little
  Rock (Arkansas), we have the secular change to the west lasting for
  about sixty years. Further west the period shortens. At Pueblo
  (Colorado) it is about forty years, at Salt Lake under thirty years,
  at Prescott (Arizona) about twenty years. Considering how fast the
  area throughout which the secular change is easterly has extended to
  the east since 1885, one would be tempted to infer that at no distant
  date it will include the whole of the United States. In the extreme
  north-east, however, the movement of the needle to the west, which had
  slackened perceptibly after 1860 or 1870, is once more accelerating.
  Thus the auspices do not all point one way, and the future is as
  uncertain as it is interesting.

  TABLE II.--Recent Values of the Magnetic Elements and their Rate of
  Secular Change.

    +----------------+-----------------------+----------------------------------------------+-----------------------------------
    |                | Geographical position.|         Absolute Values of Elements.         | Secular change (mean per annum).   |
    |      Place.    +-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+
    |                |           |           |       |         |          |        |        | Interval |      |      |     |     |
    |                | Latitude. | Longitude.| Year. |    D.   |    I.    |   H.   |   V.   | in years.|  D.  |  I.  |  H. |  V. |
    +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+
    |                |   °  ´    |    °  ´   |       |  °  ´   |  °   ´   |        |        |          |  ´   |  ´   |     |     |
    | Pavlovsk       |  59 41N   |   30 29E  | 1906  | 1  4.2E | 70 36.6N | .16528 | .46963 |    5     | -4.5 | +0.1 | - 6 | -14 |
    | Sitka (Alaska) |  57 3N    |  135 20W  | 1906  |30  3.3E | 74 41.7N | .15502 | .56646 |    4     | -3.0 | -1.6 | +18 | -38 |
    | Ekatarinburg   |  56 49N   |   60 38E  | 1906  |10 31.0E | 70 49.5N | .17664 | .50796 |    5     | -4.5 | +1.7 | -23 | +18 |
    | Rude Skov      |           |           |       |         |          |        |        |          |      |      |     |     |
    |  (Copenhagen)  |  55 51N   |   12 27E  | 1908  | 9 43.3W | 68 45N   | .17406 | .44759 |          |      |      |     |     |
    | Stonyhurst     |  53 51N   |    2 28W  | 1909  |17 28.6W | 68 42.8N | .17424 | .44722 |    5     | -5.9 | -1.1 | + 6 | -25 |
    | Hamburg        |  53 33N   |    9 59E  | 1903  |11 10.2W | 67 23.5N | .18126 | .43527 |          |      |      |     |     |
    | Wilhelmshaven  |  53 32N   |    8  9E  | 1909  |11 46.8W |          | .18129 |        |    5     | -5.2 |      | - 7 |     |
    | Potsdam        |  52 23N   |   13  4E  | 1909  | 9 10.6W | 66 20.0N | .18834 | .42971 |    5     | -5.8 | +0.1 | - 9 | -19 |
    | Irkutsk        |  52 16N   |  104 16E  | 1905  | 1 58.1E | 70 25.0N | .20011 | .56250 |    5     | +0.6 | +2.0 | -24 | +39 |
    | de Bilt        |  52  5N   |    5 11E  | 1907  |13 19.0W | 66 49.9N | .18559 | .43368 |    5     | -4.7 | -0.6 | + 2 | -16 |
    | Valencia       |  51 56N   |   10 15W  | 1909  |20 50.3W | 68 15.1N | .17877 | .44812 |    5     | -5.0 | -1.2 | + 7 | -25 |
    | Kew            |  51 28N   |    0 19W  | 1909  |16 10.8W | 66 59.7N | .18506 | .43588 |    5     | -5.4 | -1.1 | + 2 | -35 |
    | Greenwich      |  51 28N   |    0  0   | 1909  |15 47.6W | 66 53.9N | .18526 | .43432 |    5     | -5.5 | -0.7 | + 1 | -20 |
    | Uccle          |  50 48N   |    4 21E  | 1908  |13 36.7W | 66  1.6N | .19061 | .42867 |    4     | -5.3 | -0.8 | - 3 | -35 |
    | Falmouth       |  50  9N   |    5  5W  | 1909  |17 48.4W | 66 30.6N | .18802 | .43266 |    5     | -4.7 | -1.4 | + 9 | -30 |
    | Prague         |  50  5N   |   14 25E  | 1908  | 8 20.9W |          |        |        |    5     | -6.5 |      |     |     |
    | Cracow         |  50  4N   |   19 58E  | 1909  | 5 35.1W | 64 18N   |        |        |    3     | -7.3 |      |     |     |
    | St Helier      |  49 12N   |    2 5W   | 1907  |16 27.4W | 65 34.5N |        |        |    5     | -5.3 | -1.2 |     |     |
    | Val Joyeux     |  48 49N   |    2 1E   | 1909  |14 32.9W | 64 43.9N | .19727 | .41792 |    5     | -5.4 | -1.7 | + 1 | -51 |
    | Vienna         |  48 15N   |   16 21E  | 1898  | 8 24.1W |          |        |        |          |      |      |     |     |
    | Munich         |  48  9N   |   11 37E  | 1906  | 9 59.5W | 63 10.0N | .20657 | .40835 |    5     | -4.8 | -1.3 | + 4 | -31 |
    | O'Gyalla       |  47 53N   |   18 12E  | 1909  | 6 43.9W |          | .21094 |        |    5     | -5.0 |      | -10 |     |
    | Odessa         |  46 26N   |   30 46E  | 1899  | 4 36.7W | 62 18.2N | .21869 | .41660 |          |      |      |     |     |
    | Pola           |  44 52N   |   15 51E  | 1908  | 8 43.2W | 60  6.8N | .22207 | .38640 |    5     | -5.5 | -0.6 | - 4 | -23 |
    | Agincourt      |           |           |       |         |          |        |        |          |      |      |     |     |
    |   (Toronto)    |  43 47N   |   79 16W  | 1906  | 5 45.3W | 74 35.6N | .16397 | .59502 |    4     | +3.4 | +0.9 | -23 | -24 |
    | Nice           |  43 43N   |    7 16E  | 1899  |12  4.0W | 60 11.7N | .22390 | .39087 |          |      |      |     |     |
    | Toulouse       |  43 37N   |    1 28E  | 1905  |13 56.3W | 60 49.1N | .22025 | .39439 |    5     | -4.5 | -1.5 | + 2 | - 2 |
    | Perpignan      |  42 42N   |    2 53E  | 1907  |13  4.4W |          |        |        |    7     | -4.7 |      |     |     |
    | Tiflis         |  41 43N   |   44 48E  | 1905  | 2 41.6E | 56 2.8N  | .25451 | .37799 |    7     | -5.2 | +1.7 | -26 | + 2 |
    | Capo di Monte  |  40 52N   |   14 15E  | 1906  | 8 40.3W | 56 13.5N |        |        |    5     | -5.1 | -1.5 |     |     |
    | Madrid         |  40 25N   |    3 40W  | 1901  |15 35.6W |          |        |        |          |      |      |     |     |
    | Coimbra        |  40 12N   |    8 25W  | 1908  |16 46.2W | 58 57.3N | .22946 | .38120 |    5     | -4.6 | -2.9 | +17 | -45 |
    | Baldwin        |           |           |       |         |          |        |        |          |      |      |     |     |
    |  (Kansas)      |  38 47N   |   95 10W  | 1906  | 8 30.1E | 68 45.1N | .21807 | .56081 |    4     | -1.7 | +1.8 | -36 | - 8 |
    | Cheltenham     |           |           |       |         |          |        |        |          |      |      |     |     |
    |  (Maryland)    |  38 44N   |   76 50W  | 1906  | 5 22.0W | 70 27.3N | .20035 | .56436 |    4     | +3.8 | +1.2 | -38 | -45 |
    | Lisbon         |  38 43N   |    9  9W  | 1900  |17 18.0W | 57 54.8N | .23516 | .37484 |          |      |      |     |     |
    | Athens         |  37 58N   |   21 23E  | 1908  | 4 52.9W | 52 11.7N | .26197 | .33613 |    5     | -5.5 |      |     |     |
    | San Fernando   |  36 28N   |    6 12W  | 1908  |15 25.6W | 54 48.4N | .24829 | .35206 |    5     | -4.6 | -2.8 | +26 | -24 |
    | Tokyo          |  35 41N   |  139 45E  | 1901  | 4 36.1W | 49  0.0N | .29954 | .34459 |          |      |      |     |     |
    | Zi-ka-wei      |  31 12N   |  121 26E  | 1906  | 2 32.0W | 45 35.3N | .33040 | .33726 |    5     | +1.5 | -1.3 | +30 | + 6 |
    | Dehra Dun      |  30 19N   |   78  3E  | 1907  | 2 38.3E | 43 36.1N | .33324 | .31736 |    4     | +0.8 | +5.5 | -26 | +77 |
    | Helwan         |  29 52N   |   31 21E  | 1909  | 2 49.2W | 40 40.4N | .30031 | .25804 |    5     | -5.7 | +1.2 | - 6 | +13 |
    | Havana         |  23  8N   |   82 25W  | 1905  | 2 25.0E | 52 57.4N | .30531 | .40452 |          |      |      |     |     |
    | Barrackpore    |  22 46N   |   88 22E  | 1907  | 1  9.9E | 30 30.2N | .37288 | .21967 |    3     | +4.2 | +3.4 | +21 | +62 |
    | Hong-Kong      |  22 18N   |  114 10E  | 1908  | 0  3.9E | 31  2.5N | .37047 | .22292 |    5     | +1.9 | -1.8 | +43 | - 1 |
    | Honolulu       |  21 19N   |  158  4W  | 1906  | 9 21.7E | 40  1.8N | .29220 | .24545 |    4     | -0.9 | -3.2 | -19 | -62 |
    | Kolaba         |  18 54N   |   72 49E  | 1905  | 0 14.0E | 21 58.5N | .37382 | .15084 |    5     | +2.1 | +7.2 | -11 | +86 |
    | Alibagh        |  18 39N   |   72 52E  | 1909  | 1  0.3E | 23 29.0N | .36845 | .16008 |    3     | +1.7 | +6.8 | -10 | +82 |
    | Vieques        |           |           |       |         |          |        |        |          |      |      |     |     |
    |  (Porto Rico)  |  18  9N   |   65 26W  | 1906  | 1 33.2W | 49 47.7N | .28927 | .34224 |    2     | +7.2 | +6.8 | -49 | +66 |
    | Manila         |  14 35N   |  120 59E  | 1904  | 0 51.4E | 16  0.2N | .38215 | .10960 |    5     | +0.1 | -3.9 | +47 | -34 |
    | Kodaikanal     |  10 14N   |   77 28E  | 1907  | 0 40.7W |  3 27.2N | .37431 | .02259 |    4     | +4.3 | +5.5 | +16 | +61 |
    | Batavia        |   6 11S   |  106 49E  | 1906  | 0 54.1E | 30 48.5S | .36708 | .21889 |    4     | +2.1 | -7.7 | - 2 | +110|
    | Dar es Salaam  |   6 49S   |   39 18E  | 1903  | 7 35.2W |          |        |        |          |      |      |     |     |
    | Mauritius      |  20  6S   |   57 33E  | 1908  | 9 14.3W | 53 44.9S | .23415 | .31932 |    5     | -0.3 | +2.9 | -53 | -131|
    | Rio de Janeiro |  22 55S   |   43 11W  | 1906  | 8 55.5W | 13 57.1S | .24772 | .06164 |    5     | +9.1 | -6.8 | -42 | +44 |
    | Santiago       |           |           |       |         |          |        |        |          |      |      |     |     |
    |  (Chile)       |  33 27S   |   70 42W  | 1906  |14 18.7E | 30 11.8S |        |        |    3     | +6.1 | +9.9 |     |     |
    | Melbourne      |  37 50S   |  144 58E  | 1901  | 8 26.7E | 67 25.0S | .23305 | .56024 |          |      |      |     |     |
    | Christchurch,  |           |           |       |         |          |        |        |          |      |      |     |     |
    |   N.Z.         |  43 32S   |  172 37E  | 1903  |16 18.4E | 67 42.3S | .22657 | .55259 |          |      |      |     |     |
    +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+


  TABLE III.--Declination at London.

    +-------+--------------+-------+--------------+-------+--------------+
    | Date. | Declination. | Date. | Declination. | Date. | Declination. |
    +-------+--------------+-------+--------------+-------+--------------+
    |       |    °     ´   |       |    °     ´   |       |    °    ´    |
    | 1580  |   11    15E  | 1773  |   21     9W  | 1860  |   21   38.9W |
    | 1622  |    6     0   | 1787  |   23    19   | 1865  |   20   58.7  |
    | 1634  |    4     6   | 1795  |   23    57   | 1870  |   20   18.3  |
    | 1657  |    0     0   | 1802  |   24     6   | 1875  |   19   35.6  |
    | 1665  |    1    22W  | 1805  |   24     8   | 1880  |   18   52.1  |
    | 1672  |    2    30   | 1817  |   24    36   | 1885  |   18   19.2  |
    | 1692  |    6     0   | 1818  |   24    38   | 1890  |   17   50.6  |
    | 1723  |   14    17   | 1819  |   24    36   | 1895  |   17   16.8  |
    | 1748  |   17    40   | 1820  |   24    34   | 1900  |   16   52.7  |
    |       |              |       |              | 1905  |   16   32.9  |
    +-------+--------------+-------+--------------+-------+--------------+

  § 12. Table VII. gives particulars of the secular change of horizontal
  force and northerly inclination at London. Prior to the middle of the
  19th century information as to the value of H is of uncertain value.
  The earlier inclination data[14] are due to Norman, Gilbert, Bond,
  Graham, Heberden and Gilpin. The data from 1857 onwards, both for H
  and I, refer to Kew. "London" is rather a vague term, but the
  differences between the values of H and I at Kew and Greenwich--in the
  extreme west and east--are almost nil. For some time after its
  discovery by Robert Norman inclination at London increased. The
  earlier observations are not sufficient to admit of the date of the
  maximum inclination or its absolute value being determined with
  precision. Probably the date was near 1723. This view is supported by
  the fact that at Paris the inclination fell from 72° 15´ in 1754 to
  71° 48´ in 1780. The earlier observations in London were probably of
  no very high accuracy, and the rates of secular change deducible from
  them are correspondingly uncertain. It is not improbable that the
  average annual change 0´.8 derived from the thirteen years 1773-1786
  is too small, and the value 6´.2 derived from the fifteen years
  1786-1801 too large. There is, however, other evidence of unusually
  rapid secular change of inclination towards the end of the 18th
  century in western Europe; for observations in Paris show a fall of
  56´ between 1780 and 1791, and of 90´ between 1791 and 1806. Between
  1801 and 1901 inclination in London diminished by 3° 26´.5, or on the
  average by 2´.1 per annum, while between 1857 and 1900 H increased on
  the average by 22[gamma] a year. These values differ but little from
  the secular changes given in Table I. as applying at Kew for the epoch
  Jan. 1, 1901. Since the beginning, however, of the 20th century a
  notable change has set in, which seems shared by the whole of western
  Europe. This is shown in a striking fashion by contrasting the data
  from European stations in Tables I. and II. There are fifteen of these
  stations which give secular change data for H in both tables, while
  thirteen give secular data for I. The mean values of the secular
  changes derived from these stations are as follows:--

                      I           H

    From Table I.   -2´.35   +21.0[gamma]
    From Table II.  -1.12    +1.6[gamma]

  The difference in epoch between the two sets of results is only about
  5 years, and yet in that short time the mean rate of annual increase
  in H fell to a thirteenth of its original value. During 1908-1909 H
  diminished throughout all Europe except in the extreme west. Whether
  we have to do with merely a temporary phase, or whether a general and
  persistent diminution in the value of H is about to set in over Europe
  it is yet hardly possible to say.

  TABLE IV.--Declination at Kolaba (Bombay).

    +-------+----------------+----------------+
    | Year. |   Declination  | Change since   |
    |       |      East.     | previous year. |
    +-------+----------------+----------------+
    |       |  °    ´   ´´   |    ´    ´´     |
    | 1876  |  0   55   58   |    0   37 E    |
    | 1877  |      56   39   |    0   41 E    |
    | 1878  |      57    6   |    0   27 E    |
    | 1879  |      57   30   |    0   24 E    |
    | 1880  |      57    9   |    0   21 W    |
    | 1881  |  0   57   12   |    0    3 E    |
    | 1882  |  0   56   50   |    0   22 W    |
    | 1883  |      57    2   |    0   12 E    |
    | 1884  |      55   39   |    1   23 W    |
    | 1885  |      55    3   |    0   36 W    |
    +-------+----------------+----------------+

  § 13. It is often convenient to obtain a formula to express the mean
  annual change of an element during a given period throughout an area
  of some size. The usual method is to assume that the change at a place
  whose latitude is l and longitude [lambda] is given by an expression
  of the type c + a(l - l0) + b([lambda] - [lambda]0), where a, b, c are
  constants, l0 and [lambda]0, denoting some fixed latitude and
  longitude which it is convenient to take as point of departure.
  Supposing observational data available from a series of stations
  throughout the area, a, b and c can be determined by least squares. As
  an example, we may take the following slightly modified formula given
  by Ad. Schmidt[15] as applicable to Northern Europe for the period
  1890 to 1900. [Delta]D, [Delta]I and [Delta]H represent the mean
  annual changes during this period in westerly declination, in
  inclination and in horizontal force:--

                ´      ´               ´
    [Delta]D = -5.24 - 0.071(l - 50) + 0.033([lambda] - 10),
    [Delta]I = -1.58 + 0.010(l - 50) + 0.036([lambda] - 10),
    [Delta]H = +23.5 - 0.59 (l - 50) - 0.35 ([lambda] - 10).

  Longitude [lambda] is here counted positive to the east. The central
  position assumed here (lat. 50°, long. 10° E.) falls in the north of
  Bavaria. In the case of the horizontal force unity represents
  1[gamma]. Schmidt found the above formulae to give results in very
  close agreement with the data at the eight stations which he had
  employed in determining the constants. These stations ranged from
  Pavlovsk to Perpignan, and from Stonyhurst to Ekaterinburg in Siberia.
  Formulae involving the second as well as the first powers of l - l0
  and [lambda] - [lambda]0 have also been used, e.g., by A. Tanakadate
  in the Magnetic Survey of Japan.

  Table V.--Declination at St Helena and Cape of Good Hope.

    +----------------------+----------------------+
    |       St Helena.     |  Cape of Good Hope.  |
    +--------+-------------+--------+-------------+
    |  Date. | Declination.|  Date. | Declination.|
    +--------+-------------+--------+-------------+
    |        |    °  ´     |        |    °  ´     |
    |  1610  |    7  13 E  |  1605  |    0  30 E  |
    |  1677  |    0  40    |  1609  |    0  12 W  |
    |  1691  |    1   0 W  |  1675  |    8  14    |
    |  1724  |    7  30    |  1691  |   11   0    |
    |  1775  |   12  18    |  1775  |   21  14    |
    |  1789  |   15  30    |  1792  |   24  31    |
    |  1796  |   15  48    |  1818  |   26  31    |
    |  1806  |   17  18    |  1839  |   29   9    |
    |  1839  |   22  17    |  1842  |   29   6    |
    |  1840  |   22  53    |  1846  |   29   9    |
    |  1846  |   23  11    |  1850  |   29  19    |
    |  1890  |   23  57    |  1857  |   29  34    |
    |        |             |  1874  |   30   4    |
    |        |             |  1890  |   29  32    |
    |        |             |  1903  |   28  44    |
    +--------+-------------+--------+-------------+


  TABLE VI.--Secular Change of Declination in the United States (+ to
  the West).

    +---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
    |           Place.          |Epoch | 1760 |  70  |  80  |  90  | 1800 |  10  |  20  |  30  |  40  |  50  |  60  |  70  |  80  |  90  | 1900 |  50  |
    +---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
    |                           |      |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |  ´   |
    | / Eastport, Maine         |      | -1.2 |  0.0 | +1.2 | +2.1 | +3.2 | +4.0 | +4.5 | +4.9 | +5.0 | +5.6 | +4.5 | +3.0 | +2.1 | +1.0 | +1.8 | +2.4 |
    | | Boston, Mass.           |      | -2.7 | -1.9 | -1.0 |  0.0 | +1.1 | +1.9 | +2.7 | +3.5 | +4.2 | +4.4 | +4.0 | +3.3 | +3.1 | +3.0 | +3.2 | +3.4 |
    | | Albany, New York        |      | -4.2 | -3.6 | -2.7 | -1.6 | -0.6 | +0.6 | +1.6 | +2.7 | +3.6 | +4.6 | +4.6 | +3.9 | +4.7 | +2.3 | +3.4 | +3.6 |
    | | Philadelphia, Penn.     |      | -4.6 | -4.2 | -3.5 | -2.3 | -1.3 | +0.1 | +1.3 | +2.5 | +3.4 | +4.3 | +4.2 | +4.6 | +4.4 | +3.4 | +3.5 | +3.4 |
    | | Baltimore, Maryland     |      | -3.9 | -3.4 | -2.7 | -2.0 | -0.9 |  0.0 | +0.9 | +2.0 | +2.7 | +3.4 | +3.9 | +4.0 | +3.9 | +3.6 | +3.5 | +3.2 |
    | | Richmond, Virginia      |      | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 |  0.0 | +0.9 | +1.8 | +2.5 | +3.1 | +3.6 | +3.9 | +3.8 | +3.7 | +3.4 | +3.2 |
    | | Columbia, S. Carolina   |      | -3.7 | -3.4 | -2.9 | -2.2 | -1.3 | -0.5 | +0.5 | +1.3 | +2.2 | +2.9 | +3.4 | +3.8 | +3.8 | +3.8 | +3.6 | +1.8 |
    | | Macon, Georgia          |      | -3.7 | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 |  0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.9 | +3.5 | +3.1 | +1.2 |
    | \ Tampa, Florida          |      | -3.0 | -2.5 | -2.0 | -1.1 | -0.4 | +0.4 | +1.1 | +2.0 | +2.5 | +3.0 | +3.2 | +3.5 | +3.7 | +2.8 | +2.9 | +1.6 |
    |                           |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |
    | / Marquette, Michigan     |      |      |      |      |      |      |      |      |  0.0 | +1.4 | +2.6 | +3.7 | +4.7 | +5.1 | +4.9 | +3.8 | +2.4 |
    | | Columbus, Ohio          |      |      |      |      |      |      | -0.9 |  0.0 | +0.9 | +2.0 | +2.9 | +3.4 | +3.6 | +3.7 | +3.9 | +4.0 | +2.4 |
    | | Bloomington, Illinois   |      |      |      |      |      |      | -2.4 | -1.5 | -0.4 | +0.4 | +1.5 | +2.4 | +2.8 | +4.2 | +3.9 | +2.9 | +1.0 |
    | | Lexington, Kentucky     |      |      |      |      |      |      | -0.9 |  0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.8 | +3.8 | +3.4 | +1.8 |
    | | Chattanooga, Tennessee  |      |      |      |      |      |      | -0.9 |  0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +4.0 | +3.5 | +3.1 | +1.6 |
    | | Little Rock, Arkansas   |      |      |      |      |      |      | -2.3 | -1.5 | -0.9 | +0.1 | +0.8 | +1.7 | +2.0 | +3.6 | +3.7 | +2.3 | -1.2 |
    | | Montgomery, Alabama     |      | -3.6 | -3.5 | -3.1 | -2.8 | -2.2 | -1.5 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +2.8 | +3.8 | +3.9 | +2.6 | +0.2 |
    | \ Alexandria, Louisiana   |      |      |      |      |      |      | -2.1 | -1.6 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +3.6 | +3.3 | +2.0 | -1.4 |
    |                           |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |
    | / Northome, Minnesota     |      |      |      |      |      |      |      |      | -1.7 | -0.6 | +0.6 | +1.7 | +2.8 | +4.2 | +4.4 | +3.5 |  0.0 |
    | | Jamestown, N. Dakota    |      |      |      |      |      |      |      |      |      |      |      | +1.0 | +1.9 | +3.1 | +4.8 | +1.9 | -2.2 |
    | | Des Moines, Iowa        |      |      |      |      |      |      |      |      | -1.5 | -0.6 | +0.6 | +1.5 | +2.5 | +3.8 | +4.5 | +2.7 | -0.6 |
    | | Douglas, Wyoming        |      |      |      |      |      |      |      |      |      |      |      | -0.8 |  0.0 | +1.2 | +2.3 | +0.5 | -1.6 |
    | | Emporia, Kansas         |      |      |      |      |      |      |      |      |      |      |      | +0.6 | +1.6 | +2.7 | +3.8 | +1.7 | -1.8 |
    | | Pueblo, Colorado        |      |      |      |      |      |      |      |      |      |      |      | -0.3 | +0.4 | +1.5 | +3.1 | +0.7 | -2.2 |
    | | Okmulgee, Oklahoma      |      |      |      |      |      |      |      |      |      |      |      | +0.9 | +1.5 | +2.7 | +3.9 | +1.4 | -2.4 |
    | | Santa Rosa, New Mexico  |      |      |      |      |      |      |      |      |      |      |      | -0.4 | +0.4 | +1.4 | +2.6 | +0.4 | -2.4 |
    | \ San Antonio, Texas      |      |      |      |      |      |      |      |      |      | -1.1 | -0.5 | -0.5 | +1.1 | +1.8 | +2.7 | +0.9 | -2.4 |
    |                           |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |
    | / Seattle, Washington     |      |      |      |      | -3.3 | -3.5 | -3.7 | -3.7 | -3.5 | -3.3 | -3.0 | -2.6 | -2.1 | -1.3 | -1.9 | -2.0 | -3.2 |
    | | Wilson Creek, Washington|      |      |      |      |      |      |      |      |      |      |      | -2.1 | -1.5 | -0.4 | -1.0 | -1.6 | -3.2 |
    | | Detroit, Oregon         |      |      |      |      |      |      | -3.8 | -3.9 | -3.9 | -3.7 | -3.4 | -2.9 | -2.5 | -1.8 | -0.8 | -1.8 | -3.8 |
    | | Salt Lake, Utah         |      |      |      |      |      |      |      |      |      |      |      | -1.1 | -0.4 | +1.0 | +1.0 | -0.8 | -2.8 |
    | | Prescott, Arizona       |      |      |      |      |      |      |      |      |      |      |      | -1.4 | -0.7 | +0.4 | +0.4 | -1.2 | -3.2 |
    | | San José, California    |      |      |      |      | -2.6 | -2.9 | -2.9 | -2.9 | -2.7 | -2.5 | -2.3 | -2.0 | -1.5 | -0.8 | -0.4 | -1.9 | -3.8 |
    | \ Los Angeles,   "        |      |      |      |      | -3.4 | -3.4 | -3.5 | -3.2 | -3.0 | -2.7 | -2.1 | -1.6 | -1.1 | -0.9 | -0.3 | -1.6 | -3.6 |
    +---------------------------+------+------+------+--------------------+------+------+------+------+------+------+------+------+------+------+------+

  Formulae are also wanted to show how the value of an element, or the
  rate of change of an element, at a particular place has varied
  throughout a long period. For comparatively short periods it is best
  to use formulae of the type E = a + bt + ct², where E denotes the
  value of an element t years subsequent to some convenient epoch; a, b,
  c are constants to be determined from the observational data. For
  longer periods formulae of the type E = a + b sin (mt + n), where a,
  b, m and n are constants, have been used by Schott[16] and others with
  considerable success. The following examples, due to G. W.
  Littlehales,[17] for the Cape of Good Hope, will suffice for
  illustration:

    Declination (West)  = 14°.63 + 15°.00 sin {0.61(t - 1850) + 77°.8}
    Inclination (South) = 49°.11 +  8°.75 sin {0.8 (t - 1850) + 34°.3}.

  Here t denotes the date. It is perhaps hardly necessary to point out
  that the extension of any of these empirical formulae--whether to
  places outside the surveyed area, or to times not included in the
  period of observation--is fraught with danger, which increases rapidly
  the further the extrapolation is pushed.

  Table VII.--Inclination (northerly) and Horizontal Force at London.

    +------+-------+------+---------+------+---------+--------+------+---------+--------+
    | Date.|   I.  | Date.|    I.   | Date.|    I.   |    H.  | Date.|    I.   |    H.  |
    +------+-------+------+---------+------+---------+--------+------+---------+--------+
    |      |  ° ´  |      |  °  ´   |      |  °  ´   |        |      |  °  ´   |        |
    | 1576 | 71 50 | 1801 | 70 36.0 | 1857 | 68 24.9 | .17474 | 1891 | 67 33.2 | .18193 |
    | 1600 | 72  0 | 1821 | 70  3.4 | 1860 | 69 19.8 | .17550 | 1895 | 67 25.4 | .18278 |
    | 1676 | 73 30 | 1830 | 69 38.0 | 1865 | 68  8.7 | .17662 | 1900 | 67 11.8 | .18428 |
    | 1723 | 74 42 | 1838 | 69 17.3 | 1870 | 67 58.6 | .17791 | 1905 | 67  3.8 | .18510 |
    | 1773 | 72 19 | 1854 | 68 31.1 | 1874 | 67 50.0 | .17903 | 1908 | 67  0.9 | .18515 |
    | 1786 | 72  9 |      |         |      |         |        |      |         |        |
    +------+-------+------+---------+------+---------+--------+------+---------+--------+

  [Illustration: FIG. 5.]

  Bauer has employed a convenient graphical method of illustrating
  secular change. Radii are drawn from the centre of a sphere parallel
  to the direction of the freely dipping needle, and are produced to
  intersect the tangent plane drawn at the point which answers to the
  mean position of the needle during the epoch under consideration. The
  curve formed by the points of intersection shows the character of the
  secular change. Fig. 5 (slightly modified from _Nature_, vol. 57, p.
  181) applies to London. The curve is being described in the clockwise
  direction. This, according to Bauer's[18] own investigation, is the
  normal mode of description. Schott and Littlehales have found,
  however, a considerable number of cases where it is difficult to say
  whether the motion is clockwise or not, while in some stations on both
  the east and west shores of the Pacific it was clearly anti-clockwise.
  Fritsche[19] dealing with the secular changes from 1600 to 1885--as
  given by his calculated values of the magnetic elements--at 204 points
  of intersection of equidistant lines of latitude and longitude, found
  only sixty-three cases in which the motion was unmistakably clockwise,
  while in twenty-one cases it was clearly the opposite.


    Diurnal Variations.

  § 14. All the magnetic elements at any ordinary station show a regular
  variation in the solar day. To separate this from the irregular
  changes, means of the hourly readings must be formed making use of a
  number of days. The amplitude of the diurnal change usually varies
  considerably with the season of the year. Thus a diurnal inequality
  derived from all the days of the year combined, or from a smaller
  number of days selected equally from all the months of the year, can
  give only the average effect throughout the year. Also unless the
  hours of maxima and minima at a given station are but slightly
  variable with the season, the result obtained by combining data from
  all the months of the year may be a hybrid which does not very closely
  resemble the phenomena in the majority of individual months. This
  remark applies in particular to the declination at places within the
  tropics. One consequence is obviously to make the range of a diurnal
  inequality which answers to the year as a whole less than the
  arithmetic mean of the twelve ranges obtained for the constituent
  months. At stations in temperate latitudes, whilst minor differences
  of type do exist between the diurnal inequalities for different months
  of the year, the difference is mainly one of amplitude, and the mean
  diurnal inequality from all the months of the year gives a very fair
  idea of the nature of the phenomena in any individual month.

  Table VIII.--Diurnal Inequality of Declination, mean from whole year (+ to West).

    +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
    | Station. |  Jan Mayen.  |St Petersburg| Greenwich.|     Kew.    |   Parc   |  Tiflis.  |  Kolaba.  |  Batavia. | Mauritius.|  South Vic-   |
    |                         |and Pavlovsk.|           |             | St Maur. |           |           |           |           |  toria Land.  |
    +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
    | Latitude.|  71°  0´ N.  |  59° 41´ N. | 51° 28´ N.|  51° 28´ N. |48° 49´ N.| 41° 43´ N.| 18° 54´ N.|  6° 11´ S.| 20°  6´ S.|   77° 51´ S.  |
    |Longitude.|   8° 28´ W.  |  30° 29´ E. |  0°  0´.  |   0° 19´ W. | 2° 29´ E.| 44° 48´ E.| 72° 49´ E.|106° 49´ E.| 57° 33´ E.|  166° 45´ E.  |
    +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
    |  Period. |  1882-1883.  |  1873-1885. | 1890-1900.|  1890-1900. |1883-1897.| 1888-1898.| 1894-1901.| 1883-1894.| 1876-1890.|   1902-1903.  |
    +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
    |          |   a.  |  q.  |  a.  |  q.  |     a.    |  a.  |  q.  |    a.    |     a.    |     q.    |     a.    |      a.   |   a.  |   q.  |
    +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
    |   Hour.  |    ´  |   ´  |   ´  |   ´  |     ´     |   ´  |   ´  |     ´    |     ´     |     ´     |     ´     |      ´    |   ´   |   ´   |
    |    1     |  -6.6 | -4.2 | -1.3 | -0.7 |   -1.4    | -1.5 | -0.9 |   -1.4   |   -0.7    |   -0.2    |   +0.1    |   +0.1    |  +2.0 |  +0.9 |
    |    2     | -10.5 | -6.4 | -1.2 | -0.8 |   -1.3    | -1.4 | -0.9 |   -1.2   |   -0.6    |   -0.1    |   -0.1    |   +0.1    |  -2.1 |  -1.8 |
    |    3     | -15.2 | -7.8 | -1.2 | -1.0 |   -1.3    | -1.5 | -1.0 |   -1.2   |   -0.6    |   -0.1    |   -0.1    |   +0.1    |  -5.2 |  -4.5 |
    |    4     | -16.9 | -8.4 | -1.4 | -1.3 |   -1.4    | -1.7 | -1.3 |   -1.2   |   -0.5    |   -0.1    |    0.0    |   +0.2    |  -9.4 |  -6.8 |
    |    5     | -17.0 | -8.1 | -1.7 | -1.8 |   -1.7    | -2.1 | -1.8 |   -1.6   |   -0.7    |   -0.1    |    0.0    |   +0.3    | -12.2 |  -9.0 |
    |    6     | -13.7 | -7.0 | -1.9 | -2.3 |   -2.1    | -2.4 | -2.3 |   -1.9   |   -1.2    |   -0.6    |   +0.1    |   +0.4    | -15.3 | -11.7 |
    |    7     |  -9.3 | -5.1 | -2.2 | -2.8 |   -2.4    | -2.7 | -2.8 |   -2.4   |   -1.9    |   -1.0    |   +0.5    |   +0.6    | -17.2 | -15.0 |
    |    8     |  -6.8 | -3.2 | -2.5 | -3.2 |   -2.5    | -2.8 | -3.1 |   -2.7   |   -2.4    |   -1.2    |   +1.3    |   +1.1    | -21.5 | -17.3 |
    |    9     |  -3.7 | -0.6 | -2.3 | -3.0 |   -1.9    | -2.1 | -2.5 |   -2.3   |   -2.3    |   -0.7    |   +1.7    |   +1.8    | -23.5 | -18.1 |
    |   10     |  -2.4 | +2.1 | -1.0 | -1.7 |   -0.2    | -0.3 | -0.7 |   -0.5   |   -0.9    |    0.0    |   +1.5    |   +1.9    | -21.2 | -15.8 |
    |   11     |  -0.5 | +4.6 | +1.0 | +0.4 |   +2.1    | +2.2 | +1.7 |   +2.0   |   +1.0    |   +0.9    |   +0.9    |   +1.3    | -15.3 |  -9.2 |
    |   Noon   |  +2.5 | +6.5 | +3.1 | +2.7 |   +4.2    | +4.3 | +3.9 |   +4.2   |   +2.6    |   +1.4    |   +0.1    |    0.0    |  -9.8 |  -4.9 |
    |    1     |  +3.7 | +7.3 | +4.6 | +4.3 |   +5.1    | +5.3 | +4.8 |   +5.3   |   +3.3    |   +1.2    |   -0.6    |   -1.1    |  -3.2 |  -0.1 |
    |    2     |  +6.4 | +7.1 | +4.9 | +4.5 |   +4.7    | +4.9 | +4.4 |   +4.9   |   +3.1    |   +0.6    |   -1.1    |   -2.0    |  +3.8 |  +5.9 |
    |    3     |  +7.4 | +5.9 | +4.1 | +3.6 |   +3.6    | +3.7 | +3.1 |   +3.7   |   +2.3    |   +0.1    |   -1.3    |   -2.3    | +11.1 |  +9.5 |
    |    4     |  +8.5 | +4.3 | +2.7 | +2.3 |   +2.2    | +2.4 | +1.8 |   +2.3   |   +1.3    |   -0.2    |   -1.2    |   -1.8    | +16.6 | +12.9 |
    |    5     | +10.6 | +3.0 | +1.5 | +1.3 |   +1.1    | +1.2 | +0.7 |   +1.1   |   +0.6    |   -0.1    |   -0.9    |   -0.9    | +19.9 | +14.6 |
    |    6     | +14.2 | +2.3 | +0.6 | +0.7 |   +0.3    | +0.4 | +0.2 |   +0.2   |   +0.2    |    0.0    |   -0.6    |   -0.1    | +22.0 | +15.5 |
    |    7     | +15.2 | +2.2 |  0.0 | +0.4 |   -0.3    | -0.2 | -0.1 |   -0.4   |   +0.1    |   +0.1    |   -0.4    |   +0.1    | +22.0 | +15.9 |
    |    8     | +15.8 | +2.6 | -0.4 | +0.2 |   -0.9    | -0.6 | -0.3 |   -0.9   |   -0.1    |   +0.2    |   -0.2    |   +0.1    | +19.9 | +14.6 |
    |    9     | +13.2 | +2.6 | -1.0 |  0.0 |   -1.2    | -1.0 | -0.5 |   -1.3   |   -0.4    |   +0.1    |    0.0    |   +0.1    | +16.0 | +10.6 |
    |   10     |  +7.4 | +2.0 | -1.4 | -0.2 |   -1.5    | -1.3 | -0.7 |   -1.5   |   -0.6    |    0.0    |   +0.1    |   +0.1    | +11.6 |  +7.2 |
    |   11     |  +1.1 | +0.5 | -1.6 | -0.4 |   -1.6    | -1.4 | -0.8 |   -1.6   |   -0.7    |    0.0    |   +0.1    |   +0.1    |  +7.6 |  +4.2 |
    |   12     |  -3.6 | -1.8 | -1.5 | -0.6 |   -1.6    | -1.5 | -0.9 |   -1.6   |   -0.8    |   -0.1    |   +0.1    |   +0.1    |  +3.3 |  +1.9 |
    +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
    |   Range  |  32.8 | 15.7 |  7.4 |  7.7 |    7.6    |  8.1 |  7.9 |    8.0   |    5.7    |    2.6    |    3.0    |    4.2    |  45.5 |  34.0 |
    +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+

  Tables VIII. to XI. give mean diurnal inequalities derived from all
  the months of the year combined, the figures representing the
  algebraic excess of the hourly value over the mean for the twenty-four
  hours. The + sign denotes in Table VIII. that the north end of the
  needle is to the west of its mean position for the day; in Tables IX.
  to XI. it denotes that the element--the dip being the north or south
  as indicated--is numerically in excess of the twenty-four hour mean.
  The letter "a" denotes that all days have been included except, as a
  rule, those characterized by specially large disturbances. The letter
  "q" denotes that the results are derived from a limited number of days
  selected as being specially quiet, i.e. free from disturbance. In all
  cases the aperiodic or non-cyclic element--indicated by a difference
  between the values found for the first and second midnights of the
  day--has been eliminated in the usual way, i.e. by treating it as
  accumulating at a uniform rate throughout the twenty-four hours. The
  years from which the data were derived are indicated. The
  algebraically greatest and least of the hourly values are printed in
  heavy type; the range thence derived is given at the foot of the
  tables.

  TABLE IX.--Diurnal Inequality of Horizontal Force, mean from whole
  year (Unit 1[gamma] = .00001 C.G.S.)

    +--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+
    |Station.|Jan Mayen.|St Petersburg|Greenwich.|   Kew.   |  Parc    | Tiflis.  | Kolaba.  | Batavia. |Mauritius.|S. Victoria|
    |        |          |and Pavlovsk.|          |          | St Maur. |          |          |          |          |   Land.   |
    +--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+
    | Period.|1882-1883.|  1873-1885. |1890-1900.|1890-1900.|1883-1897.|1888-1898.|1894-1901.|1883-1894.|1883-1890.| 1902-1903.|
    +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
    |        |  a. | q. |  a.  |  q.  |    a.    |    q.    |    a.    |    a.    |    q.    |    a.    |    a.    |    a.     |
    +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
    | Hour.  |     |    |      |      |          |          |          |          |          |          |          |           |
    |   1    | -57 |-22 |  + 4 |  + 5 |   + 4    |   + 4    |   + 5    |   + 3    |   -10    |   -11    |   - 3    |    -12    |
    |   2    | -64 |-24 |  + 4 |  + 4 |   + 3    |   + 4    |   + 5    |   + 3    |   - 9    |   -10    |   - 1    |    -13    |
    |   3    | -74 |-25 |  + 4 |  + 4 |   + 3    |   + 4    |   + 5    |   + 3    |   - 9    |   - 8    |   + 1    |    -14    |
    |   4    | -69 |-24 |  + 4 |  + 4 |   + 3    |   + 4    |   + 5    |   + 4    |   - 9    |   - 7    |   + 2    |    -15    |
    |   5    | -60 |-22 |  + 5 |  + 4 |   + 3    |   + 4    |   + 6    |   + 4    |   - 9    |   - 5    |   + 3    |    -15    |
    |   6    | -37 |-19 |  + 4 |  + 4 |   + 1    |   + 2    |   + 4    |   + 4    |   - 7    |   - 1    |   + 4    |    -12    |
    |   7    | -15 |-15 |  + 2 |  + 2 |   - 3    |   - 1    |   + 1    |   + 2    |   - 1    |   + 5    |   + 7    |    - 9    |
    |   8    | - 1 |-13 |  - 3 |  - 4 |   - 9    |   - 7    |   - 5    |   - 3    |   + 8    |   +14    |   + 9    |    - 7    |
    |   9    | + 8 |-12 |  -10 |  -10 |   -16    |   -13    |   -12    |   - 8    |   -19    |   +24    |   + 9    |    - 3    |
    |  10    | +17 |-12 |  -16 |  -16 |   -20    |   -18    |   -17    |   -10    |   +26    |   +31    |   + 9    |    + 3    |
    |  11    | +32 |-10 |  -19 |  -20 |   -19    |   -18    |   -16    |   - 7    |   +30    |   +35    |   + 9    |    + 7    |
    | Noon   | +49 |- 4 |  -17 |  -18 |   -13    |   -12    |   -12    |   - 1    |   +26    |   +31    |   + 8    |    +12    |
    |   1    | +65 |+ 8 |  -12 |  -13 |   - 7    |   - 7    |   - 7    |   + 4    |   +19    |   +22    |   + 7    |    +18    |
    |   2    | +78 |+22 |  - 6 |  - 6 |   - 1    |   - 2    |   - 4    |   + 5    |   +10    |   +10    |   + 2    |    +20    |
    |   3    | +89 |+37 |    0 |    0 |   + 2    |   + 1    |   - 1    |   + 3    |   + 2    |   - 1    |   - 2    |    +19    |
    |   4    | +83 |+43 |  + 3 |  + 3 |   + 5    |   + 3    |     0    |   - 1    |   - 3    |   - 9    |   - 6    |    +18    |
    |   5    | +68 |+49 |  + 5 |  + 5 |   + 7    |   + 5    |   + 2    |   - 4    |   - 7    |   -13    |   - 7    |    +15    |
    |   6    | +37 |+43 |  + 6 |  + 6 |   + 9    |   + 7    |   + 4    |   - 6    |   - 8    |   -14    |   - 7    |    +11    |
    |   7    | +13 |+30 |  + 7 |  + 7 |   +10    |   + 8    |   + 6    |   - 4    |   - 9    |   -15    |   - 7    |    + 5    |
    |   8    | -11 |+15 |  + 8 |  + 8 |   +10    |   + 8    |   + 7    |   - 1    |   -10    |   -16    |   - 8    |    + 0    |
    |   9    | -33 |+ 1 |  + 9 |  + 9 |   + 8    |   + 7    |   + 7    |   + 1    |   -11    |   -16    |   - 8    |    - 4    |
    |  10    | -36 |-10 |  + 8 |  + 9 |   + 7    |   + 6    |   + 6    |   + 2    |   -11    |   -16    |   - 8    |    - 7    |
    |  11    | -40 |-16 |  + 7 |  + 8 |   + 6    |   + 6    |   + 6    |   + 3    |   -10    |   -15    |   - 7    |    - 9    |
    |  12    | -51 |-20 |  + 6 |  + 6 |   + 5    |   + 5    |   + 6    |   + 3    |   -10    |   -13    |   - 5    |    -11    |
    +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
    | Range  | 163 | 74 |   28 |   29 |    30    |    26    |    24    |    15    |    41    |    51    |    17    |     35    |
    +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+


  TABLE X.--Diurnal Inequality of Vertical Force, mean from whole year
  (Unit 1[gamma]).

    +--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+
    |        |           |St Peters- |Green- |       | Parc St|       |       |        |Maur-  |South    |
    |Station.| Jan Mayen.| burg and  | wich. |  Kew. |  Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria|
    |        |           | Pavlovsk. |       |       |        |       |       |        |       | Land.   |
    +--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+
    | Period.| 1882-1883.| 1873-1885.|1890   |1891   |1883    |1888   |1894   |1883    |1884   | 1902    |
    |        |           |           | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.|  -1903. |
    +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
    |  Hour  |  a. |  q. |  a. |  q. |   a.  |   q.  |   a.   |   a.  |   q.  |   a.   |   a.  |    a.   |
    +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
    |    1   | +65 | + 3 | - 7 | - 1 |  - 3  |  + 1  |    0   |  + 2  |  + 4  |  + 7   |  + 2  |   +13   |
    |    2   | +65 | + 2 | - 7 | - 1 |  - 4  |  + 1  |    0   |  + 2  |  + 4  |  + 5   |  + 2  |   +12   |
    |    3   | +56 | - 1 | - 7 | - 1 |  - 4  |    0  |  - 1   |  + 1  |  + 3  |  + 4   |  + 2  |   +10   |
    |    4   | +37 | - 5 | - 6 |   0 |  - 3  |    0  |    0   |  + 1  |  + 3  |  + 3   |  + 2  |   + 8   |
    |    5   | +16 | - 7 | - 5 |   0 |  - 2  |  + 1  |    0   |  + 2  |  + 5  |  + 2   |  + 2  |   + 3   |
    |    6   | - 7 | - 8 | - 4 |   0 |  - 1  |  + 1  |  + 1   |  + 3  |  + 7  |  + 1   |  + 2  |     0   |
    |    7   | -17 | - 6 | - 3 |   0 |    0  |    0  |  + 1   |  + 3  |  + 6  |    0   |  + 3  |     0   |
    |    8   | -14 | - 4 | - 2 |   0 |    0  |  - 1  |    0   |  + 3  |    0  |  - 3   |  + 4  |   - 2   |
    |    9   | - 9 |   0 | - 3 | - 1 |  - 3  |  - 4  |  - 4   |  - 1  |  - 8  |  -11   |  + 5  |   - 6   |
    |   10   | - 6 | + 5 | - 2 | - 2 |  - 6  |  - 8  |  - 8   |  - 7  |  -14  |  -20   |  + 3  |   -13   |
    |   11   | - 6 | +10 | - 3 | - 4 |  - 9  |  -11  |  -12   |  -11  |  -15  |  -26   |    0  |   -17   |
    |  Noon  | -10 | +16 | - 3 | - 5 |  -10  |  -11  |  -12   |  -11  |  -10  |  -27   |  - 4  |   -20   |
    |    1   | -13 | +21 | - 1 | - 4 |  - 6  |  - 8  |  - 9   |  - 9  |  - 3  |  -21   |  - 7  |   -20   |
    |    2   | -24 | +23 | + 2 | - 1 |    0  |  - 3  |  - 3   |  - 5  |  + 1  |  -13   |  - 9  |   -16   |
    |    3   | -31 | +20 | + 8 | + 2 |  + 5  |  + 2  |  + 2   |  - 1  |  + 4  |  - 4   |  - 8  |   -12   |
    |    4   | -40 | +13 | + 9 | + 3 |  + 8  |  + 5  |  + 6   |  + 1  |  + 3  |  + 4   |  - 5  |   - 6   |
    |    5   | -48 | + 2 | +10 | + 3 |  + 9  |  + 6  |  + 7   |  + 3  |    0  |  +10   |  - 3  |   - 1   |
    |    6   | -53 | - 9 | +10 | + 3 |  +10  |  + 7  |  + 8   |  + 4  |    0  |  +13   |    0  |   + 3   |
    |    7   | -47 | -18 | + 9 | + 3 |  + 9  |  + 6  |  + 7   |  + 3  |    0  |  +14   |    0  |   + 6   |
    |    8   | -36 | -20 | + 8 | + 3 |  + 7  |  + 5  |  + 6   |  + 3  |  + 1  |  +14   |  + 1  |   + 9   |
    |    9   | - 7 | -19 | + 6 | + 2 |  + 5  |  + 5  |  + 5   |  + 3  |  + 2  |  +14   |  + 2  |   +11   |
    |   10   | +18 | -13 | + 3 | + 2 |  + 3  |  + 4  |  + 3   |  + 3  |  + 3  |  +13   |  + 2  |   +12   |
    |   11   | +42 | - 5 | - 2 |   0 |    0  |  + 3  |  + 2   |  + 3  |  + 3  |  +11   |  + 2  |   +12   |
    |   12   | +54 |   0 | - 5 | - 1 |  - 2  |  + 2  |  + 1   |  + 2  |  + 3  |  + 9   |  + 2  |   +13   |
    +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
    | Range  | 118 |  43 |  17 |   8 |   20  |   18  |   20   |   15  |   22  |   41   |   14  |    33   |
    +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+

  When comparing results from different stations, it must be remembered
  that the disturbing forces required to cause a change of 1´ in
  declination and in dip vary directly, the former as the horizontal
  force, the latter as the total force. Near a magnetic pole the
  horizontal force is relatively very small, and this accounts, at least
  partly, for the difference between the declination phenomena at Jan
  Mayen and South Victoria Land on the one hand and at Kolaba, Batavia
  and Mauritius on the other. There is, however, another cause, already
  alluded to, viz. the variability in the type of the diurnal inequality
  in tropical stations. With a view to illustrating this point Table
  XII. gives diurnal inequalities of declination for June and December
  for a number of stations lying between 45° N. and 45° S. latitude.
  Some of the results are represented graphically in fig. 6, plus
  ordinates representing westerly deflection. At the northmost station,
  Toronto, the difference between the two months is mainly a matter of
  amplitude, the range being much larger at midsummer than at midwinter.
  The conspicuous phenomenon at both seasons is the rapid swing to the
  west from 8 or 9 a.m. to 1 or 2 p.m. At the extreme southern station,
  Hobart--at nearly equal latitude--the rapid diurnal movement is to the
  east, and so in the opposite direction to that in the northern
  hemisphere, but it again takes place at nearly the same hours in June
  (midwinter) as in December. If, however, we take a tropical station
  such as Trivandrum or Kolaba, the phenomena in June and December are
  widely different in type. At Trivandrum--situated near the magnetic
  equator in India--we have in June the conspicuous forenoon swing to
  the west seen at Toronto, occurring it is true slightly earlier in the
  day; but in December at the corresponding hours the needle is actually
  swinging to the east, just as it is doing at Hobart. In June the
  diurnal inequality of declination at tropical stations--whether to the
  north of the equator like Trivandrum, or to the south of it like
  Batavia--is on the whole of the general type characteristic of
  temperate regions in the northern hemisphere; whereas in December the
  inequality at these stations resembles that of temperate regions in
  the southern hemisphere. Comparing the inequalities for June in Table
  XII. amongst themselves, and those for December amongst themselves,
  one can trace a gradual transformation from the phenomena seen at
  Toronto to those seen at Hobart. At a tropical station the change from
  the June to the December type is probably in all cases more or less
  gradual, but at some stations the transition seems pretty rapid.

  TABLE XI.--Diurnal Inequality of Inclination mean from whole year.

    +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
    |        |             |  St Peters- |Green- |       | Parc St|       |       |        |Maur-  |South    |
    |Station.|  Jan Mayen. |  burg and   | wich. |  Kew. |  Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria|
    |        |             |  Pavlovsk.  |       |       |        |       |       |        |       | Land.   |
    +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
    |  End   |    North.   |    North.   | North.| North.| North. | North.| North.| South. | South.|  South. |
    |Dipping |             |             |       |       |        |       |       |        |       |         |
    +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
    | Period.|  1882-1883. |  1873-1885. |1890   |1891   |1883    |1888   |1894   |1883    |1884   | 1902    |
    |        |             |             | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.|  -1903. |
    +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
    |        |  a.  |  q.  |  a.  |  q.  |   a.  |   q.  |   a.   |   a.  |   q.  |   a.   |   a.  |    a.   |
    +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
    |  Hour  |  ´   |   ´  |   ´  |   ´  |   ´   |   ´   |    ´   |   ´   |   ´   |    ´   |   ´   |    ´    |
    |    1   | +4.6 | +1.5 | -0.5 | -0.3 | -0.4  | -0.3  | -0.3   | -0.1  | +0.6  | +0.9   | +0.3  |  +0.6   |
    |    2   | +5.0 | +1.6 | -0.5 | -0.3 | -0.3  | -0.2  | -0.3   | -0.1  | +0.6  | +0.8   | +0.2  |  +0.7   |
    |    3   | +5.6 | +1.6 | -0.5 | -0.3 | -0.3  | -0.2  | -0.3   | -0.1  | +0.5  | +0.6   |  0.0  |  +0.7   |
    |    4   | +5.0 | +1.5 | -0.4 | -0.3 | -0.3  | -0.2  | -0.4   | -0.2  | +0.5  | +0.5   | -0.0  |  +0.7   |
    |    5   | +4.2 | +1.4 | -0.5 | -0.3 | -0.2  | -0.2  | -0.4   | -0.2  | +0.7  | +0.3   | -0.1  |  +0.7   |
    |    6   | +2.4 | +1.2 | -0.4 | -0.3 | -0.1  | -0.1  | -0.3   | -0.1  | +0.8  | +0.1   | -0.2  |  +0.5   |
    |    7   | +0.7 | +0.9 | -0.2 | -0.1 | +0.2  | +0.1  |  0.0   |  0.0  | +0.5  | -0.2   | -0.3  |  +0.4   |
    |    8   | -0.1 | +0.8 | +0.1 | +0.3 | +0.6  | +0.4  | +0.4   | +0.3  | -0.2  | -0.8   | -0.4  |  +0.3   |
    |    9   | -0.7 | +0.8 | +0.6 | +0.6 | +1.0  | +0.8  | +0.7   | +0.5  | -1.2  | -1.7   | -0.4  |  +0.1   |
    |   10   | -1.2 | +0.9 | +1.0 | +1.0 | +1.1  | +1.0  | +0.9   | +0.3  | -1.9  | -2.7   | -0.5  |  -0.2   |
    |   11   | -2.2 | +0.8 | +1.2 | +1.2 | +1.0  | +0.9  | +0.7   |  0.0  | -2.1  | -3.3   | -0.6  |  -0.4   |
    |  Noon  | -3.4 | +0.4 | +1.1 | +1.1 | +0.6  | +0.6  | +0.4   | -0.5  | -1.6  | -3.1   | -0.7  |  -0.7   |
    |    1   | -4.5 | -0.2 | +0.7 | +0.7 | +0.3  | +0.2  | +0.2   | -0.6  | -0.8  | -2.4   | -0.8  |  -0.9   |
    |    2   | -5.6 | -1.2 | +0.4 | +0.4 | +0.1  | +0.1  | +0.2   | -0.5  | -0.2  | -1.3   | -0.6  |  -1.0   |
    |    3   | -6.3 | -2.2 | +0.2 | +0.1 |  0.0  |  0.0  | +0.2   | -0.3  | +0.3  | -0.2   | -0.3  |  -1.0   |
    |    4   | -6.1 | -2.9 |  0.0 | -0.1 | -0.1  | -0.1  | +0.2   | +0.1  | +0.3  | +0.7   | +0.1  |  -0.9   |
    |    5   | -5.1 | -3.2 | -0.1 | -0.3 | -0.2  | -0.2  | +0.1   | +0.4  | +0.2  | +1.3   | +0.4  |  -0.7   |
    |    6   | -3.1 | -2.9 | -0.2 | -0.3 | -0.3  | -0.3  |  0.0   | +0.5  | +0.2  | +1.5   | +0.5  |  -0.5   |
    |    7   | -1.7 | -2.2 | -0.3 | -0.4 | -0.4  | -0.4  | -0.2   | +0.4  | +0.3  | +1.6   | +0.5  |  -0.2   |
    |    8   | +0.3 | -1.3 | -0.3 | -0.5 | -0.4  | -0.4  | -0.3   | +0.2  | +0.4  | +1.6   | +0.6  |   0.0   |
    |    9   | +2.0 | -0.3 | -0.4 | -0.6 | -0.4  | -0.4  | -0.3   | +0.1  | +0.5  | +1.6   | +0.6  |  +0.2   |
    |   10   | +2.5 | +0.5 | -0.5 | -0.6 | -0.4  | -0.3  | -0.3   |  0.0  | +0.6  | +1.5   | +0.6  |  +0.4   |
    |   11   | +3.0 | +1.0 | -0.5 | -0.6 | -0.4  | -0.3  | -0.3   |  0.0  | +0.6  | +1.4   | +0.5  |  +0.5   |
    |   12   | +4.0 | +1.3 | -0.5 | -0.4 | -0.4  | -0.3  | -0.3   | -0.1  | +0.6  | +1.2   | +0.4  |  +0.6   |
    +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
    | Range  | 11.9 |  4.8 |  1.7 |  1.8 |  1.5  |  1.4  |  1.3   |  1.1  |  2.9  |  4.9   |  1.4  |   1.7   |
    +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+


  TABLE XII.--Diurnal Inequality of Declination (+ to West).

    +--------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
    |Station.|  Toronto. |  Kolaba.  |Trivandrum.|  Batavia. | St Helena.| Mauritius.|   Cape.   |  Hobart.  |
    +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
    | Month. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |
    +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
    |  Hour  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |  ´  |
    |    1   |-0.4 |-0.1 |-0.3 | 0.0 |-0.3 |-0.1 |+0.1 |+0.1 |-0.1 |-0.4 | 0.0 |+0.1 |-0.4 |-0.7 |+0.8 |+1.1 |
    |    2   |-0.2 |+0.4 |-0.3 |+0.1 |-0.4 |+0.1 |-0.1 |+0.1 |-0.2 |-0.1 |-0.2 |+0.2 |-0.5 |-0.4 |+0.3 |+1.1 |
    |    3   |-0.2 |-0.1 |-0.3 |+0.1 |-0.4 |+0.3 |-0.2 |+0.2 |-0.2 |+0.1 |-0.2 |+0.4 |-0.7 |-0.1 |-0.1 |+1.0 |
    |    4   |-1.2 |-0.4 |-0.3 |+0.3 |-0.5 |+0.5 |-0.3 |+0.3 |-0.3 |+0.3 |-0.2 |+0.7 |-0.6 |+0.3 |-0.1 |+1.1 |
    |    5   |-2.9 |-0.6 |-0.7 |+0.4 |-0.7 |+0.7 |-0.3 |+0.5 |-0.5 |+0.6 |-0.3 |+1.0 |-0.7 |+1.0 | 0.0 |+1.7 |
    |    6   |-5.2 |-0.6 |-1.6 |+0.5 |-1.6 |+1.1 |-0.5 |+1.2 |-1.0 |+0.9 |-0.4 |+1.7 |-1.0 |+2.2 | 0.0 |+2.7 |
    |    7   |-6.2 |-0.9 |-2.2 |+0.7 |-1.7 |+1.4 |-1.1 |+2.0 |-2.2 |+1.9 |-1.1 |+2.6 |-1.6 |+3.3 |-0.1 |+4.4 |
    |    8   |-6.0 |-1.2 |-2.1 |+0.2 |-1.1 |+0.9 |-0.4 |+2.3 |-1.5 |+2.2 |-1.0 |+2.4 |-0.8 |+3.6 |+0.1 |+5.6 |
    |    9   |-4.4 |-1.8 |-1.1 |-0.1 |-0.2 |+0.5 |+0.5 |+2.0 |-0.3 |+1.3 |+0.2 |+2.0 |+0.7 |+3.1 |+0.6 |+5.6 |
    |   10   |-1.5 |-1.1 | 0.0 |-0.2 |+0.6 |+0.3 |+0.9 |+1.3 |+0.3 |+0.2 |+1.2 |+1.1 |+1.6 |+1.6 |+1.2 |+3.6 |
    |   11   |+2.1 |+0.6 |+1.2 | 0.0 |+1.2 |+0.1 |+1.0 |+0.4 |+0.5 |-1.0 |+1.4 | 0.0 |+1.5 |+0.1 |+1.0 |+0.7 |
    |  Noon  |+4.8 |+2.2 |+2.1 | 0.0 |+1.4 |-0.4 |+0.7 |-0.6 |+0.3 |-1.4 |+1.0 |-1.4 |+0.8 |-1.0 |-0.1 |-2.6 |
    |    1   |+6.1 |+3.2 |+2.0 |-0.2 |+1.1 |-0.8 |+0.3 |-1.4 |+0.3 |-1.2 |+0.1 |-2.2 |+0.3 |-1.8 |-1.4 |-5.1 |
    |    2   |+6.1 |+3.2 |+1.6 |-0.3 |+0.7 |-0.9 |-0.2 |-1.8 |+0.2 |-0.4 |-0.9 |-2.5 |-0.3 |-1.9 |-2.2 |-6.2 |
    |    3   |+5.2 |+2.4 |+0.9 |-0.3 |+0.3 |-0.9 |-0.7 |-1.9 |+0.2 |+0.4 |-1.5 |-2.2 |-0.3 |-1.4 |-2.4 |-5.8 |
    |    4   |+3.6 |+1.5 |+0.2 |-0.3 |+0.1 |-0.8 |-0.8 |-1.6 |+0.7 |+0.6 |-1.3 |-1.6 |+0.2 |-0.8 |-1.6 |-4.8 |
    |    5   |+1.8 |+0.5 | 0.0 |-0.2 | 0.0 |-0.4 |-0.5 |-1.2 |+1.1 |+0.4 |-0.3 |-1.0 |+0.5 |-0.8 |-0.7 |-3.3 |
    |    6   |+0.7 |-0.1 |+0.1 |-0.2 |+0.2 |-0.4 |-0.1 |-0.7 |+1.0 |+0.1 |+0.5 |-0.5 |+0.5 |-0.6 |-0.4 |-1.9 |
    |    7   | 0.0 |-0.8 |+0.3 |-0.2 |+0.5 |-0.4 |+0.1 |-0.6 |+0.6 |-0.4 |+0.7 |-0.3 |+0.4 |-0.8 | 0.0 |-1.0 |
    |    8   | 0.0 |-1.2 |+0.4 |-0.1 |+0.5 |-0.3 |+0.2 |-0.5 |+0.5 |-0.7 |+0.7 |-0.3 |+0.3 |-0.9 |+0.5 |-0.3 |
    |    9   |-0.5 |-1.4 |+0.3 |-0.1 |+0.4 |-0.2 |+0.4 |-0.3 |+0.4 |-0.9 |+0.6 |-0.2 |+0.2 |-0.9 |+1.1 | 0.0 |
    |   10   |-0.5 |-1.7 |+0.1 | 0.0 |+0.2 |-0.1 |+0.4 |-0.1 |+0.2 |-1.0 |+0.4 |-0.1 |+0.1 |-1.0 |+1.3 |+0.6 |
    |   11   |-0.7 |-1.1 |-0.1 |-0.1 | 0.0 |-0.1 |+0.3 | 0.0 |+0.1 |-0.8 |+0.3 | 0.0 | 0.0 |-1.0 |+1.3 |+0.9 |
    |   12   |-0.6 |-0.7 |-0.2 |-0.1 |-0.2 |-0.1 |+0.2 |+0.1 |-0.1 |-0.6 |+0.1 |+0.1 |-0.2 |-1.0 |+1.1 |+1.2 |
    +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
    | Range  |12.3 | 5.0 | 4.3 | 1.0 | 3.1 | 2.3 | 2.1 | 4.2 | 3.3 | 3.6 | 2.9 | 5.1 | 3.2 | 5.5 | 3.7 |11.8 |
    +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

  § 15. In the case of the horizontal force there are, as Table IX.
  shows, two markedly different types of diurnal inequality. In the one
  type, exemplified by Pavlovsk or Greenwich, the force is below its
  mean value in the middle of the day; it has a principal minimum about
  10 or 11 a.m., and morning and evening maxima, the latter usually the
  largest. In the other type, exemplified by Kolaba or Batavia, the
  horizontal force is above its mean in the middle of the day, and has
  a maximum about 11 a.m. The second type may be regarded as the
  tropical type. At tropical stations, such as Kolaba, Batavia, Manila
  and St Helena, the type is practically the same in summer as in
  winter, and is the same whether the station is north or south of the
  equator. Similarly, what we may call the temperate type is seen--with
  comparatively slight modifications--both in summer and winter at
  stations such as Greenwich or Pavlovsk. In winter, it is true, the
  pronounced daily minimum is a little later and the early morning
  maximum is relatively more important than in summer. There is not, as
  in the case of the declination, any essential difference between the
  phenomena at temperate stations in the northern and southern
  hemispheres.

  [Illustration: FIG. 6.]

  With diminishing latitude, there is a gradual transition from the
  temperate to the tropical type of horizontal force diurnal variation,
  and at stations whose latitude is under 45° there is a very
  appreciable variation in type with the season. The mean diurnal
  variation for the year at Tiflis in Table IX. really represents a
  struggle between the two types, in which on the whole the temperate
  type prevails. If we take the diurnal variations at Tiflis for
  midsummer and midwinter, we find the former essentially of the
  temperate, the latter essentially of the tropical type. A similar
  conflict may be seen in the mean diurnal inequality for the year at
  the Cape of Good Hope, but there the tropical type on the whole
  predominates, and it prevails more at midwinter than at midsummer.
  Toronto and Hobart, though similar in latitude to Tiflis, show a
  closer approach to the temperate type. Still at both stations the
  hours during which the force is below its mean value tend to extend
  back towards midnight, especially at midsummer. The amplitude of the
  horizontal force range appears less at intermediate stations, such as
  Tiflis, than at stations in either higher or lower latitudes. There
  is a very great difference in this respect between the north and the
  south of India.

  § 16. In the case of the vertical force in higher temperate
  latitudes--at Pavlovsk for instance--the diurnal inequalities from
  "all" and from "quiet" days differ somewhat widely in amplitude and
  slightly even in type. In mean latitudes, e.g. at Tiflis, there is
  often a well marked double period in the mean diurnal inequality for
  the whole year; but even at Tiflis this is hardly, if at all, apparent
  in the winter months. In the summer months the double period is
  distinctly seen at Kew and Greenwich, though the evening maximum is
  always pre-eminent. Speaking generally, the time of the minimum, or
  principal minimum, varies much less with the season than that of the
  maximum. At Kew, for instance, on quiet days the minimum falls between
  11 a.m. and noon in almost all the months of the year, but the time of
  the maximum varies from about 4 p.m. in December to 7 p.m. in June. At
  Kolaba the time of the minimum is nearly independent of the season;
  but the changes from positive to negative in the forenoon and from
  negative to positive in the afternoon are some hours later in winter
  than in summer. At Batavia the diurnal inequality varies very little
  in type with the season, and there is little evidence of more than one
  maximum and minimum in the day. At Batavia, as at Kolaba, negative
  values occur near noon; but it must be remembered that while at Kolaba
  and more northern stations vertical force urges the north pole of a
  magnet downwards, the reverse is true of Batavia, as the dip is
  southerly. At St Helena vertical force is below its mean value in the
  forenoon, but the change from - to + occurs at noon, or but little
  later, both in winter and summer. At the Cape of Good Hope the
  phenomena at midsummer are similar to those at Kolaba, the force being
  below its mean value from about 9 a.m. to 3 p.m. and above it
  throughout the rest of the day; but at midwinter there is a
  conspicuous double period, the force being below its mean from 1 a.m.
  to 7 a.m. as well as from 11 a.m. to 3 p.m., and thus resembling the
  all-day annual results at Greenwich. At Hobart vertical force is below
  its mean value from 1 a.m. to 9 a.m. at midsummer, and from 4 a.m. to
  noon at midwinter; while the force is above its mean persistently
  throughout the afternoon both in summer and winter, there is at
  midwinter a well marked secondary minimum about 6 p.m., almost the
  same hour as that at which the maximum for the day is observed in
  summer.

  TABLE XIII.--Range of the Diurnal Inequality of Declination.

    +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
    |    Place.   |   Period.   | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
    +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
    |             |             |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |
    | Pavlovsk    | 1890-1900 a | 4.93 | 6.15 | 8.58 |10.93 |12.18 |12.27 |11.82 |11.38 | 8.70 | 6.87 | 5.54 | 4.63 |
    |    "        |     "     q | 2.96 | 4.20 | 8.73 |11.28 |12.89 |13.28 |12.31 |11.70 | 9.37 | 6.91 | 3.95 | 2.66 |
    | Ekatarinburg| 1890-1900 a | 3.33 | 4.32 | 7.63 |11.19 |11.82 |11.58 |11.09 |10.45 | 8.13 | 5.60 | 3.73 | 3.14 |
    | Greenwich   | 1865-1896 a | 5.87 | 7.07 | 9.40 |11.42 |10.55 |10.90 |10.82 |10.93 | 9.66 | 8.15 | 6.41 | 5.15 |
    | Kew         | 1890-1900 a | 4.92 | 6.06 | 9.08 |10.95 |10.66 |10.92 |10.59 |11.01 | 9.49 | 7.73 | 5.37 | 4.46 |
    |  "          |     "     q | 4.07 | 4.76 | 8.82 |10.57 |10.92 |10.62 |10.18 |11.01 | 9.76 | 7.51 | 4.75 | 3.34 |
    | Toronto     | 1842-1848 a | 5.96 | 6.05 | 9.18 | 9.94 |11.55 |12.34 |12.21 |13.14 |10.76 | 6.96 | 6.32 | 4.97 |
    | Manila      | 1890-1900 a | 1.79 | 1.09 | 2.13 | 3.02 | 3.84 | 3.94 | 4.21 | 4.89 | 4.53 | 1.83 | 0.85 | 1.33 |
    | Trivandrum  | 1853-1864 a | 2.06 | 1.48 | 0.79 | 1.67 | 2.90 | 3.06 | 3.06 | 3.64 | 3.31 | 1.27 | 2.14 | 2.33 |
    | Batavia     | 1884-1899 a | 4.18 | 4.64 | 3.57 | 2.93 | 2.38 | 2.03 | 2.31 | 3.16 | 3.80 | 4.51 | 4.50 | 4.19 |
    | St Helena   | 1842-1847 a | 3.72 | 5.19 | 4.93 | 3.30 | 2.64 | 3.24 | 3.42 | 3.59 | 2.40 | 4.43 | 4.05 | 3.54 |
    | Mauritius   | 1876-1890 a | 5.2  | 6.1  | 6.3  | 4.7  | 4.1  | 2.9  | 3.4  | 4.9  | 5.0  | 5.5  | 5.6  | 5.1  |
    | Cape        | 1841-1846 a | 5.14 | 8.21 | 7.27 | 5.00 | 3.91 | 3.21 | 3.54 | 4.98 | 4.33 | 5.96 | 6.36 | 5.47 |
    | Hobart      | 1841-1848 a |11.66 |11.80 | 9.50 | 7.26 | 4.56 | 3.70 | 4.61 | 5.89 | 8.24 |11.01 |12.05 |11.81 |
    +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+

  § 17. Variations of inclination are connected with those of horizontal
  and vertical force by the relation

    [delta]I = ½ sin 2I {V^-1 [delta]V - H^-1 [delta]H}.

  Thus in temperate latitudes where V is considerably in excess of H,
  whilst diurnal changes in V are usually less than those in H, it is
  the latter which chiefly dominate the diurnal changes in inclination.
  When the H influence prevails, I has its highest values at hours when
  H is least. This explains why the dip is above its mean value near
  midday at stations in Table XI. from Pavlovsk to Parc St Maur. Near
  the magnetic equator the vertical force has the greater influence.
  This alone would tend to make a minimum dip in the late forenoon, and
  this minimum is accentuated owing to the altered type of the
  horizontal force diurnal variation, whose maximum now coincides
  closely with the minimum in the vertical force. This accounts for the
  prominence of the minimum in the diurnal variation of the inclination
  at Kolaba and Batavia, and the large amplitude of the range. Tiflis
  shows an intermediate type of diurnal variation; there is a minimum
  near noon, as in tropical stations, but inclination is also below its
  mean for some hours near midnight. The type really varies at Tiflis
  according to the season of the year. In June--as in the mean equality
  from the whole year--there is a well marked double period; there is a
  principal minimum at 2 p.m. and a secondary one about 4 a.m.; a
  principal maximum about 9 a.m. and a secondary one about 6 p.m. In
  December, however, only a single period is recognizable, with a
  minimum about 8 a.m. and a maximum about 7 p.m. The type of diurnal
  inequality seen at the Cape of Good Hope does not differ much from
  that seen at Batavia. Only a single period is clearly shown. The
  maximum occurs about 8 or 9 p.m. throughout the year. The time of the
  minimum is more variable; at midsummer it occurs about 11 a.m., but at
  midwinter three or four hours later. At Hobart the type varies
  considerably with the season. In June (midwinter) a double period is
  visible. The principal minimum occurs about 8 a.m., as at the Cape.
  But, corresponding to the evening maximum seen at the Cape, there is
  now only a secondary maximum, the principal maximum occurring about 1
  p.m. At midsummer the principal maximum is found--as at Kew or
  Greenwich--about 10 or 11 a.m., the principal minimum about 4 p.m.

  § 18. Even at tropical stations a considerable seasonal change is
  usually seen in the amplitude of the diurnal inequality in at least
  one of the magnetic elements. At stations in Europe, and generally in
  temperate latitudes, the amplitude varies notably in all the elements.
  Table XIII. gives particulars of the inequality range of declination
  derived from hourly readings at selected stations, arranged in order
  of latitude from north to south. The letters "a" and "q" are used in
  the same sense as before. At temperate stations in either
  hemisphere--e.g. Pavlovsk, Greenwich or Hobart--the range is
  conspicuously larger in summer than in winter. In northern temperate
  stations a decided minimum is usually apparent in December. There is,
  on the other hand, comparatively little variation in the range from
  April to August. Sometimes, as at Kew and Greenwich, there is at least
  a suggestion of a secondary minimum at midsummer. Manila and
  Trivandrum show a transition from the December minimum, characteristic
  of the northern stations, to the June minimum characteristic of the
  southern, there being two conspicuous minima in February or March and
  in November or October. At St Helena there are two similar minima in
  May and September, while a third apparently exists in December. It
  will be noticed that at both Pavlovsk and Kew the annual variation in
  the range is specially prominent in the quiet day results.

  Table XIV. gives a smaller number of data analogous to those of Table
  XIII., comprising inequality ranges for horizontal force, vertical
  force and inclination. In some cases the number of years from which
  the data were derived seems hardly sufficient to give a smooth annual
  variation. It should also be noticed that unless the same group of
  years is employed the data from two stations are not strictly
  comparable. The difference between the all and quiet day vertical
  force data at Pavlovsk is remarkably pronounced. The general tendency
  in all the elements is to show a reduced range at midwinter; but in
  some cases there is also a distinct reduction in the range at
  midsummer. This double annual period is particularly well marked at
  Batavia.

  TABLE XIV.--Ranges in the Diurnal Inequalities.

    +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+
    |                               | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
    +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+
    |       H (unit 1[gamma])       |      |      |      |      |      |      |      |      |      |      |      |      |
    | Pavlovsk          1890-1900 a |  12  |  20  |  32  |  46  |  47  |  49  |  49  |  44  |  39  |  32  |  17  |  11  |
    |    "                  "     q |  12  |  17  |  31  |  42  |  45  |  45  |  42  |  40  |  37  |  31  |  17  |  10  |
    | Ekatarinburg          "     a |  11  |  15  |  29  |  37  |  40  |  40  |  39  |  36  |  33  |  27  |  13  |   9  |
    | Kew                   "     q |  15  |  17  |  26  |  36  |  38  |  39  |  38  |  38  |  35  |  27  |  20  |  11  |
    | Toronto           1843-1848 a |  23  |  21  |  24  |  28  |  29  |  29  |  26  |  28  |  41  |  25  |  21  |  20  |
    | Batavia           1883-1898 a |  49  |  47  |  54  |  60  |  51  |  48  |  50  |  53  |  58  |  52  |  43  |  40  |
    | St Helena         1843-1847 a |  43  |  41  |  48  |  53  |  46  |  40  |  40  |  45  |  41  |  40  |  40  |  32  |
    | Mauritius         1883-1890 a |  21  |  15  |  21  |  23  |  20  |  21  |  20  |  22  |  20  |  21  |  21  |  20  |
    | Cape of Good Hope 1841-1846 a |  13  |  10  |  13  |  13  |  15  |  16  |  14  |  18  |  21  |  14  |  17  |  20  |
    | Hobart            1842-1848 a |  42  |  43  |  34  |  28  |  19  |  17  |  22  |  23  |  23  |  35  |  39  |  42  |
    |                               |      |      |      |      |      |      |      |      |      |      |      |      |
    |       V (unit 1[gamma])       |      |      |      |      |      |      |      |      |      |      |      |      |
    | Pavlovsk          1890-1900 a |  15  |  27  |  29  |  24  |  26  |  20  |  23  |  19  |  23  |  20  |  18  |  14  |
    |    "                  "     q |   4  |   5  |  9   |  13  |  13  |  12  |  13  |  10  |   9  |   7  |   5  |   4  |
    | Ekatarinburg          "     a |  10  |  15  |  17  |  21  |  22  |  19  |  20  |  16  |  14  |  13  |  11  |   9  |
    | Kew               1891-1900 q |   7  |  10  |  20  |  25  |  31  |  27  |  28  |  23  |  20  |  15  |   9  |   6  |
    | Toronto           1843-1848 a |  12  |  14  |  17  |  23  |  26  |  14  |  27  |  32  |  34  |  25  |  19  |  18  |
    | Batavia           1883-1898 a |  42  |  48  |  48  |  45  |  31  |  31  |  32  |  29  |  41  |  50  |  40  |  33  |
    | St Helena         1843-1847 a |  16  |  13  |  12  |  14  |  13  |  11  |  17  |  11  |  17  |  11  |  15  |  18  |
    | Mauritius         1884-1890 a |  12  |  16  |  18  |  15  |  14  |  13  |  15  |  21  |  20  |  16  |  13  |  11  |
    | Cape of Good Hope 1841-1846 a |  29  |  47  |  41  |  38  |  21  |  12  |  14  |  19  |  19  |  35  |  33  |  28  |
    | Hobart            1842-1848 a |  25  |  27  |  22  |  23  |  24  |  21  |  22  |  28  |  26  |  22  |  23  |  27  |
    |                               |      |      |      |      |      |      |      |      |      |      |      |      |
    |         _Inclination_         |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |
    | Pavlovsk          1890-1900 a | 0.97 | 1.24 | 2.07 | 2.79 | 2.72 | 2.88 | 2.85 | 2.64 | 2.52 | 2.18 | 1.20 | 0.89 |
    | Ekatarinburg          "     a | 0.79 | 0.94 | 1.70 | 2.08 | 2.25 | 2.19 | 2.18 | 2.08 | 2.00 | 1.70 | 0.88 | 0.69 |
    | Kew                   "     q | 0.98 | 1.01 | 1.38 | 1.86 | 2.05 | 2.02 | 2.05 | 2.15 | 1.98 | 1.57 | 1.27 | 0.63 |
    | Toronto           1843-1848 a | 1.15 | 0.94 | 1.19 | 1.23 | 1.31 | 1.37 | 1.13 | 1.26 | 1.87 | 1.16 | 1.09 | 1.05 |
    | Batavia           1883-1898 a | 4.88 | 5.22 | 5.56 | 5.62 | 4.21 | 4.05 | 4.24 | 4.17 | 5.13 | 5.58 | 4.51 | 3.85 |
    | Cape of Good Hope 1842-1846 a | 1.55 | 2.29 | 2.23 | 2.23 | 1.60 | 1.41 | 1.54 | 1.70 | 1.86 | 2.03 | 1.55 | 2.04 |
    | Hobart            1842-1848 a | 1.95 | 2.16 | 1.72 | 1.62 | 1.23 | 1.16 | 1.28 | 1.42 | 1.39 | 1.75 | 2.04 | 2.10 |
    +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+

  § 19. When discussing diurnal inequalities it is sometimes convenient
  to consider the components of the horizontal force in and
  perpendicular to the astronomical meridian, rather than the horizontal
  force and declination. If N and W be the components of H to
  astronomical north and west, and D the westerly declination, N = H
  cos D, W = H sin D. Thus corresponding small variations in N, W, H and
  D are connected by the relations:--

    [delta]N = cos D[delta]H - H sin D[delta]D,
    [delta]W = sin D[delta]H + H cos D[delta]D.

  If [delta]H and [delta]D denote the departures of H and D at any hour
  of the day from their mean values, then [delta]N and [delta]W
  represent the corresponding departures of N and W from their mean
  values. In this way diurnal inequalities may be calculated for N and W
  when those for H and D are known. The formulae suppose [delta]D to be
  expressed in absolute measure, i.e. 1´ of arc has to be replaced by
  0.0002909. If we take as an example a station at which H is .185 then
  H[delta]D = .0000538 (number of minutes in [delta]D). In other words,
  employing 1[gamma] as unit of force, one replaces H[delta]D by
  5.38[delta]D, where [delta]D represents declination change expressed
  as usual in minutes of arc. In calculating diurnal inequalities for N
  and W, one ought, strictly speaking, to assign to H and D the exact
  mean values belonging to these elements for the month or the year
  being dealt with. For practical purposes, however, a slight departure
  from the true mean values is immaterial, and one can make use of a
  constant value for several successive years without sensible error. As
  an example, Table XV. gives the mean diurnal inequality for the whole
  year in N and W at Falmouth, as calculated from the 12 years 1891 to
  1902. The unit employed is 1[gamma].

  The data in Table XV. are closely similar to corresponding Kew data,
  and are presumably fairly applicable to the whole south of England for
  the epoch considered. At Falmouth there is comparatively little
  seasonal variation in the type of the diurnal variation in either N or
  W. The amplitude of the diurnal range varies, however, largely with
  the season, as will appear from Table XVI., which is based on the same
  12 years as Table XV.

  Diurnal inequalities in N and W lend themselves readily to the
  construction of what are known as _vector diagrams_. These are curves
  showing the direction and intensity at each hour of the day of the
  horizontal component of the disturbing force to which the diurnal
  inequality may be regarded as due. Figs. 7 and 8, taken from the
  _Phil. Trans._ vol. 204A, will serve as examples. They refer to the
  mean diurnal inequalities for the months stated at Kew (1890 to 1900)
  and Falmouth (1891 to 1902), thick lines relating to Kew, thin to
  Falmouth. NS and EW represent the geographical north-south and
  east-west directions; their intersection answers to the origin (thick
  lines for Kew, thin for Falmouth). The line from the origin to M
  represents the magnetic meridian. The line from the origin to any
  cross--the number indicating the corresponding hour counted from
  midnight as 0--represents the magnitude and direction at that hour of
  the horizontal component of the disturbing force to which the diurnal
  inequality may be assigned. The cross marks the point whose
  rectangular co-ordinates are the values of [delta]N and [delta]W
  derived from the diurnal inequalities of these elements. In figs. 7
  and 8 the distances of the points N, E, S, W from their corresponding
  origin represents 10[gamma]. The tendency to form a loop near
  midnight, seen in the November and December curves, is
  characteristic of the winter months at Kew and Falmouth. The shape is
  less variable in summer than in winter; but even in summer the portion
  answering to the hours 6 p.m. to 6 a.m. varies a good deal. The object
  of presenting the Kew and Falmouth curves side by side is to emphasize
  the close resemblance between the magnetic phenomena at places in
  similar latitudes, though over 200 miles apart and exhibiting widely
  different ranges for their meteorological elements. With considerable
  change of latitude however the shape of vector diagrams changes
  largely.

  TABLE XV.--Diurnal Inequalities in N. and W. at Falmouth (unit
  1[gamma]).

    +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
    |  Hour.  |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9  | 10  | 11  | 12  |
    +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
    |N. /a.m. | + 6 | + 5 | + 5 | + 5 | + 6 | + 6 | + 5 | + 1 | - 6 | -14 | -20 | -20 |
    |   \p.m. | -17 | -12 | - 6 | - 1 | + 3 | + 6 | + 9 | + 9 | + 9 | + 8 | + 7 | + 7 |
    |W. /a.m. | - 2 | - 2 | - 3 | - 4 | - 6 | - 9 | -13 | -17 | -19 | -13 | - 3 | +11 |
    |   \p.m. | +20 | +22 | +17 | +11 | + 6 | + 4 | + 2 | + 1 |   0 | - 1 | - 2 | - 2 |
    +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+


    Fourier Series.

  § 20. Any diurnal inequality can be analysed into a series of harmonic
  terms whose periods are 24 hours and submultiples thereof. The series
  may be expressed in either of the equivalent forms:--

    a1 cos t + b1 sin t + a2 cos 2t + b2 sin 2t + ...  (i)

    c1 sin (t + [alpha]1) + c2 sin (2t + [alpha]2) + ....  (ii)

  TABLE XVI.--Ranges in Diurnal Inequalities at Falmouth (unit
  1[gamma]).

    +----+------+------+------+------+------+------+------+------+------+------+------+------+
    |    | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
    +----+------+------+------+------+------+------+------+------+------+------+------+------+
    | N. |  21  |  23  |  30  |  39  |  39  |  37  |  37  |  39  |  36  |  32  |  24  |  15   |
    | W. |  20  |  24  |  46  |  54  |  55  |  55  |  54  |  56  |  51  |  39  |  24  |  15   |
    +----+------+------+------+------+------+------+------+------+------+------+------+------+

  In both forms t denotes time, counted usually from midnight, one hour
  of time being interpreted as 15° of angle. Form (i) is that utilized
  in actually calculating the constants a, b, ... Once the a, b, ...
  constants are known, the c, [alpha], ... constants are at once
  derivable from the formulae:--

    tan [alpha]_n = a_n/b_n;
    c_n = a_n/sin [alpha]_n = b_n/cos [alpha]_n = [root](a_n² + b_n²).

  The a, b, c, [alpha] constants are called sometimes Fourier, sometimes
  Bessel coefficients.

  [Illustration: (From _Phil. Trans._)

  FIG. 7.]

  By taking a sufficient number of terms a series can always be obtained
  which will represent any set of diurnal inequality figures; but unless
  one can obtain a close approach to the observational figures from the
  terms possessing the periods 24, 12, 8 and 6 hours the physical
  significance and general utility of the analysis is somewhat
  problematical. In the case of the magnetic elements, the 24 and 12
  hour terms are usually much the more important; the 24-hour term is
  generally, but by no means always, the larger of the two. The c
  constants give the amplitudes of the harmonic terms or waves, the
  [alpha] constants the phase angles. An advance of 1 hour in the time
  of occurrence of the first (and subsequent, if any) maximum and
  minimum answers to an _increase_ of 15° in [alpha]1 of 30° in
  [alpha]2, of 45° in [alpha]3, of 60° in [alpha]4 and so on. In the
  case of magnetic elements the phase angles not infrequently possess a
  somewhat large annual variation. It is thus essential for a minute
  study of the phenomena at any station to carry out the analysis for
  the different seasons of the year, and preferably for the individual
  months. If the a and b constants are known for all the individual
  months of one year, or for all the Januarys of a series of years, we
  have only to take their arithmetic means to obtain the corresponding
  constants for the mean diurnal inequality of the year, or for the
  diurnal inequality of the average January of the series of years.
  This, however, is obviously not true of the c or [alpha] constants,
  unless the phase angle is absolutely unchanged throughout the
  contributory months or years. This is a point requiring careful
  attention, because when giving values of c and [alpha] for the whole
  year some authorities give the arithmetic mean of the c's and
  [alpha]'s calculated from the diurnal inequalities of the individual
  months of the year, others give the values obtained for c and [alpha]
  from the mean diurnal inequality of the whole year. The former method
  inevitably supplies a larger value for c than the latter, supposing
  [alpha] to vary with the season. At some observatories, e.g. Greenwich
  and Batavia, it has long been customary to publish every year values
  of the Fourier coefficients for each month, and to include other
  elements besides the declination. For a thoroughly satisfactory
  comparison of different stations, it is necessary to have data from
  one and the same epoch; and preferably that epoch should include at
  least one 11-year period. There are, however, few stations which can
  supply the data required for such a comparison and we have to make the
  best of what is available. Information is naturally most copious for
  the declination. For this element E. Engelenburg[20] gives values of
  C1, C2, C3, C4, and of [alpha]1, [alpha]2, [alpha]3, [alpha]4 for each
  month of the year for about 50 stations, ranging from Fort Rae (62° 6´
  N. lat.) to Cape Horn (55° 5´ S. lat.). From the results for
  individual stations, Engelenburg derives a series of means which he
  regards as representative of 11 different zones of latitude. His data
  for individual stations refer to different epochs, and some are based
  on only one year's observations. The original observations also differ
  in reliability; thus the results are of somewhat unequal value. The
  mean results for Engelenburg's zones must naturally have some of the
  sources of uncertainty reduced; but then the fundamental idea
  represented by the arrangement in zones is open to question. The
  majority of the data in Table XVII. are taken from Engelenburg, but
  the phase angles have been altered so as to apply to westerly
  declination. The stations are arranged in order of latitude from north
  to south; in a few instances results are given for quiet days. The
  figures represent in all cases arithmetic means derived from the 12
  monthly values. In the table, so far as is known, the local mean time
  of the observatory has been employed. This is a point requiring
  attention, because most observatories employ Greenwich time, or time
  based on Greenwich or some other national observatory, and any
  departure from local time enters into the values of the constants. The
  data for Victoria Land refer to the "Discovery's" 1902-1903 winter
  quarters, where the declination, taken westerly, was about 207°.5.

  As an example of the significance of the phase angles in Table XVII.,
  take the ordinary day data for Kew. The times of occurrence of the
  maxima are given by t + 234° = 450° for the 24-hour term, 2t + 39°.7 =
  90° or = 450° for the 12-hour term, and so on, taking an hour in t as
  equivalent to 15°.

  Thus the times of the maxima are:--

  24-hour term, 2 h. 24 m. p.m.; 12-hour term, 1 h. 41 m. a.m. and p.m.

  8-hour term, 4 h. 41 m. a.m., 0 h. 41 m. p.m., and 8 h. 41 m. p.m.

  6-hour term, 0 h. 33 m. a.m. and p.m., and 6 h. 33 m. a.m. and p.m.

  The minima, or extreme easterly positions in the waves, lie midway
  between successive maxima. All four terms, it will be seen, have
  maxima at some hour between 0h. 30m. and 2h. 30m. p.m. They thus
  reinforce one another strongly from 1 to 2 p.m., accounting for the
  prominence of the maximum in the early afternoon.

  [Illustration: (_From Phil. Trans._)

  FIG. 8.]

  The utility of a Fourier analysis depends largely on whether the
  several terms have a definite physical significance. If the 24-hour
  and 12-hour terms, for instance, represent the action of forces whose
  distribution over the earth or whose seasonal variation is essentially
  different, then the analysis helps to distinguish these forces, and
  may assist in their being tracked to their ultimate source. Suppose,
  for example, one had reason to think the magnetic diurnal variation
  due to some meteorological phenomenon, e.g. heating of the earth's
  atmosphere, then a comparison of Fourier coefficients, if such
  existed, for the two sets of phenomena would be a powerful method of
  investigation.

  TABLE XVII.--Amplitudes and Phase Angles for Diurnal Inequality of
  Declination.

    +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |       Place.        |   Epoch.  |  c1.  |  c2.  |  c3.  |  c4.  | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
    +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |                     |           |   ´   |   ´   |   ´   |   ´   |     °     |     °     |     °     |     °     |
    | Fort Rae (all)      | 1882-1883 | 18.49 |  8.22 |  1.99 |  2.07 |   156.5   |    41.9   |    308    |    104    |
    |    "     (quiet)    |    "      |  9.09 |  4.51 |  1.32 |  0.73 |   166.5   |    37.5   |    225    |    350    |
    | Ekatarinburg        | 1841-1862 |  2.57 |  1.81 |  0.73 |  0.22 |   223.3   |     7.4   |    204    |    351    |
    | Potsdam             | 1890-1899 |  2.81 |  1.90 |  0.83 |  0.31 |   239.9   |    32.6   |    237    |     49    |
    | Kew (ordinary)      | 1890-1900 |  2.91 |  1.79 |  0.79 |  0.27 |   234.0   |    39.7   |    239    |     57    |
    | Kew (quiet)         |     "     |  2.37 |  1.82 |  0.90 |  0.30 |   227.3   |    42.1   |    240    |     55    |
    | Falmouth (quiet)    | 1891-1902 |  2.18 |  1.82 |  0.91 |  0.29 |   226.2   |    40.5   |    238    |     56    |
    | Parc St Maur        | 1883-1899 |  2.70 |  1.87 |  0.85 |  0.30 |   238.6   |    32.5   |    235    |     95    |
    | Toronto             | 1842-1848 |  2.65 |  2.34 |  1.00 |  0.33 |   213.7   |    34.9   |    238    |    350    |
    | Washington          | 1840-1842 |  2.38 |  1.86 |  0.65 |  0.33 |   223.0   |    26.6   |    223    |     53    |
    | Manila              | 1890-1900 |  0.53 |  0.58 |  0.43 |  0.17 |   266.3   |    50.7   |    226    |     89    |
    | Trivandrum          | 1853-1864 |  0.54 |  0.46 |  0.29 |  0.10 |   289.0   |    49.6   |           |    114    |
    | Batavia             | 1883-1899 |  0.80 |  0.88 |  0.43 |  0.13 |   332.0   |   163.2   |      5    |    236    |
    | St. Helena          | 1842-1847 |  0.68 |  0.61 |  0.63 |  0.34 |   275.8   |   171.4   |     27    |    244    |
    | Mauritius           | 1876-1890 |  0.86 |  1.11 |  0.76 |  0.22 |    21.6   |   172.7   |    350    |    161    |
    | C. of G. Hope       | 1841-1846 |  1.15 |  1.13 |  0.80 |  0.35 |   287.7   |   156.0   |    351    |    193    |
    | Melbourne           | 1858-1863 |  2.52 |  2.45 |  1.23 |  0.35 |    27.4   |   176.7   |      9    |    193    |
    | Hobart              | 1841-1848 |  2.29 |  2.15 |  0.87 |  0.32 |    33.6   |   170.8   |    349    |    185    |
    | S. Georgia          | 1882-1883 |  2.13 |  1.28 |  0.76 |  0.31 |    30.3   |   185.3   |      7    |    180    |
    | Victoria Land (all) | 1902-1903 | 20.51 |  4.81 |  1.21 |  1.32 |   158.7   |   306.9   |    292    |    303    |
    |     "     (quieter) |     "     | 15.34 |  4.05 |  1.24 |  1.18 |   163.8   |   312.9   |    261    |           |
    +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+

  § 21. Fourier coefficients of course often vary much with the season
  of the year. In the case of the declination this is especially true of
  the phase angles at tropical stations. To enter on details for a
  number of stations would unduly occupy space. A fair idea of the
  variability in the case of declination in temperate latitudes may be
  derived from Table XVIII., which gives monthly values for Kew derived
  from ordinary days of an 11-year period 1890-1900.

  Fourier analysis has been applied to the diurnal inequalities of the
  other magnetic elements, but more sparingly. Such results are
  illustrated by Table XIX., which contains data derived from quiet days
  at Kew from 1890 to 1900. _Winter_ includes November to February,
  _Summer_ May to August, and _Equinox_ the remaining four months. In
  this case the data are derived from mean diurnal inequalities for the
  season specified. In the case of the c or amplitude coefficients the
  unit is 1´ for I (inclination), and 1[gamma] for H and V (horizontal
  and vertical force). At Kew the seasonal variation in the amplitude is
  fairly similar for all the elements. The 24-hour and 12-hour terms
  tend to be largest near midsummer, and least near midwinter; but the
  8-hour and 6-hour terms have two well-marked maxima near the
  equinoxes, and a clearly marked minimum near midsummer, in addition
  to one near midwinter. On the other hand, the phase angle phenomena
  vary much for the different elements. The 24-hour term, for instance,
  has its maximum earlier in winter than in summer in the case of the
  declination and vertical force, but the exact reverse holds for the
  inclination and the horizontal force.

  TABLE XVIII.--Kew Declination: Amplitudes and Phase Angles (local mean
  time).

    +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |  Month.  |  C1.  |  C2.  |  C3.  |  C4.  | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
    +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |          |   ´   |  ´    |  ´    |   ´   |    °      |     °     |     °     |     °     |
    | January  |  1.79 |  0.86 |  0.41 |  0.27 |   251.2   |    29.8   |    254    |    64     |
    | February |  2.41 |  1.11 |  0.57 |  0.30 |   242.0   |    27.7   |    235    |    39     |
    | March    |  3.05 |  1.98 |  1.11 |  0.45 |   233.2   |    36.1   |    223    |    49     |
    | April    |  3.35 |  2.48 |  1.17 |  0.39 |   224.8   |    39.2   |    228    |    61     |
    | May      |  3.57 |  2.38 |  0.87 |  0.17 |   221.3   |    50.8   |    245    |    89     |
    | June     |  3.83 |  2.39 |  0.74 |  0.05 |   212.6   |    46.7   |    239    |    72     |
    | July     |  3.72 |  2.30 |  0.77 |  0.11 |   214.6   |    48.1   |    233    |     8     |
    | August   |  3.64 |  2.43 |  1.05 |  0.18 |   228.2   |    57.2   |    244    |    51     |
    | September|  3.35 |  2.02 |  1.04 |  0.35 |   236.9   |    55.3   |    245    |    70     |
    | October  |  2.69 |  1.69 |  0.92 |  0.48 |   240.1   |    35.6   |    235    |    65     |
    | November |  1.94 |  1.06 |  0.51 |  0.32 |   248.3   |    28.3   |    247    |    61     |
    | December |  1.61 |  0.81 |  0.35 |  0.20 |   255.1   |    22.0   |    243    |    56     |
    +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+


    Annual Inequality.

  § 22. If secular change proceeded uniformly throughout the year, the
  value E_n of any element at the middle of the nth month of the year
  would be connected with E, the mean value for the whole year, by the
  formula E_n = E + (2n - 13)s/24, where s is the secular change per
  annum. For the present purpose, difference in the lengths of the
  months may be neglected. If one applies to E_n - E the correction -(2n
  - 13)s/24 one eliminates a regularly progressive secular change; what
  remains is known as the _annual inequality_. If only a short period of
  years is dealt with, irregularities in the secular change from year to
  year, or errors of observation, may obviously simulate the effect of a
  real annual inequality. Even when a long series of years is included,
  there is always a possibility of a spurious inequality arising from
  annual variation in the instruments, or from annual change in the
  conditions of observation. J. Liznar,[21] from a study of data from a
  number of stations, arrived at certain mean results for the annual
  inequalities in declination and inclination in the northern and
  southern hemispheres, and J. Hann[22] has more recently dealt with
  Liznar's and newer results. Table XX. gives a variety of data,
  including the mean results given by Liznar and Hann. In the case of
  declination + denotes westerly position; in the case of inclination it
  denotes a larger dip (whether the inclination be north or south).
  According to Liznar declination in summer is to the west of the normal
  position in both hemispheres. The phenomena, however, at Parc St Maur
  are, it will be seen, the exact opposite of what Liznar regards as
  normal; and whilst the Potsdam results resemble his mean in type, the
  range of the inequality there, as at Parc St Maur, is relatively
  small. Of the three sets of data given for Kew the first two are
  derived in a similar way to those for other stations; the first set
  are based on quiet days only, the second on all but highly disturbed
  days. Both these sets of results are fairly similar in type to the
  Parc St Maur results, but give larger ranges; they are thus even more
  opposed to Liznar's normal type. The last set of data for Kew is of a
  special kind. During the 11 years 1890 to 1900 the Kew declination
  magnetograph showed to within 1´ the exact secular change as derived
  from the absolute observations; also, if any annual variation existed
  in the position of the base lines of the curves it was exceedingly
  small. Thus the accumulation of the daily non-cyclic changes shown by
  the curves should closely represent the combined effects of secular
  change and annual inequality. Eliminating the secular change, we
  arrive at an annual inequality, based on all days of the year
  including the highly disturbed. It is this annual inequality which
  appears under the heading s. It is certainly very unlike the annual
  inequality derived in the usual way. Whether the difference is to be
  wholly assigned to the fact that highly disturbed days contribute in
  the one case, but not in the other, is a question for future research.

  TABLE XIX.--Kew Diurnal Inequality: Amplitudes and Phase Angles (local
  mean time).

    +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |    Month.   |  C1.  |  C2.  |  C3.  |  C4.  | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
    +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
    |             |   ´   |   ´   |   ´   |   ´   |     °     |     °     |     °     |     °     |
    |    /Winter  | 0.240 | 0.222 | 0.104 | 0.076 |   250.0   |    91.8   |    344    |    194    |
    | I < Equinox | 0.601 | 0.290 | 0.213 | 0.127 |   290.3   |   135.5   |      4    |    207    |
    |    \Summer  | 0.801 | 0.322 | 0.172 | 0.070 |   312.5   |   155.5   |     39    |    238    |
    |             |       |       |       |       |           |           |           |           |
    |    /Winter  |  3.62 | 3.86  | 1.81  | 1.13  |    82.9   |   277.3   |    154    |      6    |
    | H < Equinox | 10.97 | 5.87  | 3.32  | 1.84  |   109.6   |   303.5   |    167    |     16    |
    |    \Summer  | 14.85 | 6.23  | 2.35  | 0.95  |   130.3   |   316.5   |    199    |     41    |
    |             |       |       |       |       |           |           |           |           |
    |    /Winter  |  2.46 | 1.67  | 0.86  | 0.42  |   153.9   |   300.8   |    108    |    280    |
    | V < Equinox |  6.15 | 4.70  | 2.51  | 0.94  |   117.2   |   272.3   |     99    |    289    |
    |    \Summer  |  8.63 | 6.45  | 2.24  | 0.55  |   122.0   |   272.4   |    100    |    285    |
    +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+

  In the case of the inclination, Liznar found that in both hemispheres
  the dip (north in the northern, south in the southern hemisphere) was
  larger than the normal when the sun was in perihelion, corresponding
  to an enhanced value of the horizontal force in summer in the northern
  hemisphere.

  In the case of annual inequalities, at least that of the declination,
  it is a somewhat suggestive fact that the range seems to become less
  as we pass from older to more recent results, or from shorter to
  longer periods of years. Thus for Paris from 1821 to 1830 Arago
  deduced a range of 2´ 9´´. Quiet days at Kew from 1890 to 1894 gave a
  range of 1´.2, while at Potsdam Lüdeling got a range 30% larger than
  that in Table XX. when considering the shorter period 1891-1899. Up to
  the present, few individual results, if any, can claim a very high
  degree of certainty. With improved instruments and methods it may be
  different in the future.

  TABLE XX.--Annual Inequality.

    +---------------------------------------------------------------------------------------------+-------------------------------------+
    |                                           Declination.                                      |              Inclination.           |
    +-----------+---------+-----------+-----------+-----------------------+-----------+-----------+---------+---------+---------+-------+
    |           | Liznar, |  Potsdam, |  Parc St  |    Kew (1890-1900).   |  Batavia, |           | Liznar &|         | Parc St.|       |
    |           | N. Hemi-| 1891-1906.|   Maur,   +-------+-------+-------+ 1883-1893.| Mauritius.|  Hann's | Potsdam.|   Maur. |  Kew. |
    |           | sphere. |           | 1888-1897.|   q.  |   o.  |   s.  |           |           |   mean. |         |         |       |
    +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+
    |           |   ´     |     ´     |     ´     |   ´   |   ´   |   ´   |     ´     |     ´     |    ´    |    ´    |    ´    |   ´   |
    | January   |  -0.25  |   +0.04   |   +0.01   | +0.08 | +0.03 | +0.32 |   +0.23   |   +0.06   |  +0.49  |  +0.32  |  +0.44  | -0.03 |
    | February  |  -0.54  |   -0.11   |    0.00   | +0.48 | +0.25 | -0.20 |   +0.19   |   +0.29   |  +0.39  |  +0.56  |  +0.29  | -0.07 |
    | March     |  -0.27  |   +0.04   |   +0.17   | +0.03 | +0.05 | -1.02 |   -0.12   |   +0.27   |  +0.20  |  +0.38  |  +0.13  | +0.53 |
    | April     |  -0.03  |   +0.10   |   +0.12   | -0.31 | -0.14 | -0.90 |   -0.11   |   +0.30   |  -0.08  |  -0.02  |  -0.13  | +0.18 |
    | May       |  +0.19  |   +0.07   |   -0.11   | -0.39 | -0.28 | +0.29 |   -0.30   |   +0.08   |  -0.43  |  -0.29  |  -0.37  | -0.15 |
    | June      |  +0.46  |   +0.13   |   -0.14   | -0.47 | -0.39 | +0.78 |   -0.13   |   -0.19   |  -0.70  |  -0.77  |  -0.59  | -0.35 |
    | July      |  +0.48  |   +0.14   |   -0.17   | -0.30 | -0.13 | +0.44 |   -0.08   |   -0.44   |  -0.72  |  -0.67  |  -0.27  | -0.13 |
    | August    |  +0.47  |   +0.11   |   +0.01   | +0.08 | +0.05 | +0.52 |   -0.18   |   -0.38   |  -0.47  |  -0.23  |  -0.05  | -0.19 |
    | September |  +0.31  |   +0.01   |    0.00   | +0.29 | +0.24 | -0.02 |   +0.06   |   -0.06   |  -0.06  |  +0.16  |  +0.01  | +0.20 |
    | October   |  -0.07  |   -0.11   |   +0.09   | +0.06 | +0.01 | -0.26 |   +0.03   |   -0.04   |  +0.31  |  +0.27  |  +0.19  |  0.00 |
    | November  |  -0.30  |   -0.28   |   -0.05   | +0.17 | +0.11 | -0.02 |   +0.08   |   -0.01   |  +0.51  |  +0.30  |  +0.43  | +0.18 |
    | December  |  -0.36  |   -0.14   |   +0.05   | +0.26 | +0.23 | +0.05 |   +0.35   |   +0.06   |  +0.55  |  +0.19  |  +0.24  | -0.29 |
    +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+
    | Range     |   1.02  |    0.42   |    0.34   |  0.95 |  0.64 |  1.80 |    0.65   |    0.74   |   1.27  |   1.33  |   1.03  |  0.88 |
    +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+


    Annual Variation Fourier Coefficients.

  § 23. The inequalities in Table XX. may be analysed--as has in fact
  been done by Hann--in a series of Fourier terms, whose periods are the
  year and its submultiples. Fourier series can also be formed
  representing the annual variation in the amplitudes of the regular
  diurnal inequality, and its component 24-hour, 12-hour, &c. waves, or
  of the amplitude of the absolute daily range (§ 24). To secure the
  highest theoretical accuracy, it would be necessary in calculating the
  Fourier coefficients to allow for the fact that the "months" from
  which the observational data are derived are not of uniform length.
  The mid-times, however, of most months of the year are but slightly
  displaced from the position they would occupy if the 12 months were
  exactly equal, and these displacements are usually neglected. The loss
  of accuracy cannot be but trifling, and the simplification is
  considerable.

  The Fourier series may be represented by

    P1 sin (t + [theta]1) + P2 sin (2t + [theta]2) + ...,

  where t is time counted from the beginning of the year, one month
  being taken as the equivalent of 30°, P1, P2 represent the amplitudes,
  and [theta]1, [theta]2 the phase angles of the first two terms, whose
  periods are respectively 12 and 6 months. Table XXI. gives the values
  of these coefficients in the case of the range of the regular diurnal
  inequality for certain specified elements and periods at Kew[23] and
  Falmouth.[23a] In the case of P1 and P2 the unit is 1´ for D and I,
  and 1[gamma] for H and V. M denotes the mean value of the range for
  the 12 months. The letters q and o represent quiet and ordinary day
  results. S max. means the years 1892-1895, with a mean sun spot
  frequency of 75.0. S min. for Kew means the years 1890, 1899 and 1900
  with a mean sun spot frequency of 9.6; for Falmouth it means the years
  1899-1902 with a mean sun spot frequency of 7.25.

  Increase in [theta]1 or [theta]2 means an earlier occurrence of the
  maximum or maxima, 1° answering roughly to one day in the case of the
  12-month term, and to half a day in the case of the 6-month term. P1/M
  and P2/M both increase decidedly as we pass from years of many to
  years of few sun spots; i.e. _relatively_ considered the range of the
  regular diurnal inequality is more variable throughout the year when
  sun spots are few than when they are many.

  The tendency to an earlier occurrence of the maximum as we pass from
  quiet days to ordinary days, or from years of sun spot minimum to
  years of sun spot maximum, which appears in the table, appears also
  in the case of the horizontal force--at least in the case of the
  annual term--both at Kew and Falmouth. The phenomena at the two
  stations show a remarkably close parallelism. At both, and this is
  true also of the absolute ranges, the maximum of the annual term falls
  in all cases near midsummer, the minimum near midwinter. The maxima of
  the 6-month terms fall near the equinoxes.

  TABLE XXI.--Annual Variation of Diurnal Inequality Range. Fourier
  Coefficients.

    +---------------------+--------+--------+-----------+-----------+-------+-------+
    |                     |   P1.  |   P2.  | [theta]1. | [theta]2. | P1/M. | P2/M. |
    +-----------+---------+--------+--------+-----------+-----------+-------+-------+
    | Kew       |   D_0   |  3.36  |  0.94  |   279°    |    280°   |  0.40 |  0.11 |
    | 1890-1900 |   D_q   |  3.81  |  1.22  |   275°    |    273°   |  0.47 |  0.15 |
    |           |   I_q   |  0.67  |  0.16  |   264°    |    269°   |  0.42 |  0.10 |
    |           |   H_q   | 13.6   |  3.0   |   269°    |    261°   |  0.48 |  0.11 |
    |           |   V_q   | 11.7   |  2.2   |   282°    |    242°   |  0.63 |  0.12 |
    +-----------+---------+--------+--------+-----------+-----------+-------+-------+
    | S max.    | Kew     |  4.50  |  1.26  |   277°    |    282°   |  0.47 |  0.13 |
    |   D_q     | Falmouth|  4.10  |  1.40  |   277°    |    286°   |  0.43 |  0.15 |
    +-----------+---------+--------+--------+-----------+-----------+-------+-------+
    | S min.    | Kew     |  3.35  |  1.10  |   274°    |    269°   |  0.49 |  0.16 |
    |   D_q     | Falmouth|  3.19  |  1.14  |   275°    |    277°   |  0.49 |  0.17 |
    +-----------+---------+--------+--------+-----------+-----------+-------+-------+


    Absolute Range.

  § 24. Allusion has already been made in § 14 to one point which
  requires fuller discussion. If we take a European station such as Kew,
  the general character of, say, the declination does not vary very much
  with the season, but still it does vary. The principal minimum of the
  day, for instance, occurs from one to two hours earlier in summer than
  in winter. Let us suppose for a moment that all the days of a month
  are exactly alike, the difference in type between successive months
  coming in _per saltum._ Suppose further that having formed twelve
  diurnal inequalities from the days of the individual months of the
  year, we deduce a mean diurnal inequality for the whole year by
  combining these twelve inequalities and taking the mean. The hours of
  maximum and minimum being different for the twelve constituents, it is
  obvious that the resulting maximum will normally be less than the
  arithmetic mean of the twelve maxima, and the resulting minimum
  (arithmetically) less than the arithmetic mean of the twelve minima.
  The range--or algebraic excess of the maximum over the minimum--in the
  mean diurnal inequality for the year is thus normally less than the
  arithmetic mean of the twelve ranges from diurnal inequalities for the
  individual months. Further, as we shall see later, there are
  differences in type not merely between the different months of the
  year, but even between the same months in different years. Thus the
  range of the mean diurnal inequality for, say, January based on the
  combined observations of, say, eleven Januarys may be and generally
  will be slightly less than the arithmetic mean of the ranges obtained
  from the Januarys separately. At Kew, for instance, taking the
  ordinary days of the 11 years 1890-1900, the arithmetic mean of the
  diurnal inequality ranges of declination from the 132 months treated
  independently was 8´.52, the mean range from the 12 months of the year
  (the eleven Januarys being combined into one, and so on) was 8´.44,
  but the mean range from the whole 4,000 odd days superposed was only
  8´.03. Another consideration is this: a diurnal inequality is usually
  based on hourly readings, and the range deduced is thus an
  under-estimate unless the absolute maximum and minimum both happen to
  come exactly at an hour. These considerations would alone suffice to
  show that the _absolute range_ in individual days, i.e. the difference
  between the algebraically largest and least values of the element
  found any time during the 24 hours, must on the average exceed the
  range in the mean diurnal inequality for the year, however this
  latter is formed. Other causes, moreover, are at work tending in the
  same direction. Even in central Europe, the magnetic curves for
  individual days of an ordinary month often differ widely amongst
  themselves, and show maxima and minima at different times of the day.
  In high latitudes, the variation from day to day is sometimes so great
  that mere eye inspection of magnetograph curves may leave one with but
  little idea as to the probable shape of the resultant diurnal curve
  for the month. Table XXII. gives the arithmetic mean of the absolute
  daily ranges from a few stations. The values which it assigns to the
  year are the arithmetic means of the 12 monthly values. The Mauritius
  data are for different periods, viz. declination 1875, 1880 and 1883
  to 1890, horizontal force 1883 to 1890, vertical force 1884 to 1890.
  The other data are all for the period 1890 to 1900.

  TABLE XXII.--Mean Absolute Daily Ranges (Units 1´ for Declination,
  1[gamma] for H and V).

    +--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
    |                    |  Jan. |  Feb. |  Mar. | April.|  May. | June. | July. |  Aug. | Sept. |  Oct. |  Nov. |  Dec. | Year. |
    |                    +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
    | _Declination._     |       |       |       |       |       |       |       |       |       |       |       |       |       |
    | Pavlovsk           | 13.42 | 17.20 | 18.22 | 17.25 | 17.76 | 15.91 | 16.89 | 16.57 | 16.75 | 15.70 | 13.87 | 12.37 | 15.99 |
    | Ekatarinburg       |  7.33 |  9.54 | 11.90 | 12.89 | 13.63 | 13.03 | 12.78 | 12.21 | 11.23 |  9.44 |  7.86 |  6.85 | 10.72 |
    | Kew.  All days     | 11.16 | 13.69 | 15.93 | 15.00 | 14.90 | 13.65 | 14.13 | 14.22 | 14.57 | 14.07 | 11.71 |  9.80 | 13.57 |
    |  "    Ordinary days| 10.14 | 11.87 | 14.19 | 14.24 | 13.85 | 13.26 | 13.47 | 13.67 | 13.71 | 13.10 | 10.40 |  9.00 | 12.58 |
    |  "    Quiet     "  |  6.12 |  7.57 | 10.59 | 11.84 | 12.09 | 11.95 | 11.60 | 11.93 | 10.86 |  9.16 |  6.54 |  5.08 |  9.61 |
    | Zi-ka-wei          |  3.88 |  3.25 |  6.22 |  7.04 |  7.15 |  7.40 |  7.77 |  8.06 |  6.73 |  4.68 |  2.91 |  2.52 |  5.63 |
    | Mauritius          |  6.93 |  7.79 |  7.11 |  5.75 |  4.87 |  4.03 |  4.36 |  6.00 |  6.28 |  6.71 |  6.99 |  6.78 |  6.13 |
    |                    |       |       |       |       |       |       |       |       |       |       |       |       |       |
    | _Horizontal force._|       |       |       |       |       |       |       |       |       |       |       |       |       |
    | Pavlovsk           | 52.4  | 74.5  | 79.1  | 80.1  | 86.2  | 79.0  | 86.7  | 77.6  | 76.7  | 67.3  | 55.7  | 45.9  | 71.8  |
    | Ekatarinburg       | 33.2  | 43.1  | 48.4  | 51.7  | 56.2  | 54.1  | 56.7  | 51.7  | 49.3  | 44.1  | 34.1  | 29.3  | 46.0  |
    | Mauritius          | 37.9  | 35.0  | 36.2  | 37.6  | 35.0  | 34.1  | 33.8  | 34.5  | 36.6  | 37.4  | 37.8  | 35.3  | 35.9  |
    |                    |       |       |       |       |       |       |       |       |       |       |       |       |       |
    | _Vertical force._  |       |       |       |       |       |       |       |       |       |       |       |       |       |
    | Pavlovsk           | 27.0  | 50.4  | 54.7  | 43.2  | 45.3  | 34.8  | 42.1  | 35.5  | 42.5  | 37.5  | 33.5  | 25.5  | 39.3  |
    | Ekatarinburg       | 17.4  | 26.6  | 29.2  | 30.1  | 29.6  | 27.6  | 29.6  | 26.1  | 25.2  | 22.1  | 19.6  | 16.4  | 24.9  |
    | Mauritius          | 17.1  | 19.5  | 20.1  | 17.3  | 16.5  | 15.5  | 17.1  | 22.0   |22.7  | 19.4  | 16.7  | 15.2  | 18.2  |
    +--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+

  A comparison of the absolute ranges in Table XXII. with the inequality
  ranges for the same stations derivable from Tables VIII. to X. is most
  instructive. At Mauritius the ratio of the absolute to the inequality
  range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the
  corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and
  2.05 for V. The declination data for Kew in Table XXII. illustrate
  other points. The first set of data are derived from all days of the
  year. The second omit the highly disturbed days. The third answer to
  the 5 days a month selected as typically quiet. The yearly mean
  absolute range from ordinary days at Kew in Table XXII. is 1.49 times
  the mean inequality range in Table VIII.; comparing individual months
  the ratio of the absolute to the inequality range varies from 2.06 in
  January to 1.21 in June. Even confining ourselves to the quiet days at
  Kew, which are free from any but the most trifling disturbances, we
  find that the mean absolute range for the year is 1.20 times the
  arithmetic mean of the inequality ranges for the individual months of
  the year, and 1.22 times the range from the mean diurnal inequality
  for the year. In this case the ratio of the absolute to the inequality
  range varies from 1.55 in December to only 1.09 in May.

  § 25. The variability of the absolute daily range of declination is
  illustrated by Table XXIII., which contains data for Kew[24] derived
  from all days of the 11-year period 1890-1900. It gives the total
  number of times during the 11 years when the absolute range lay within
  the limits specified at the heads of the first nine columns of
  figures. The two remaining columns give the arithmetic means of the
  five largest and the five least absolute ranges encountered each
  month. The mean of the twelve monthly diurnal inequality ranges from
  ordinary days was only 8´.44, but the absolute range during the 11
  years exceeded 20´ on 492 days, 15´ on 1196 days, and 10´ on 2784
  days, i.e. on 69 days out of every 100.

  Table XXIII.--Absolute Daily Range of Declination at Kew.

    +------------------------------------------------------------------------------------------------------------------+---------------------+
    |                                                                                                                  |   Means from the 5  |
    |                                                                                                                  | largest and 5 least |
    |                         Number of occasions during 11 years when absolute range was:--                           | ranges of the month |
    |                                                                                                                  | on the average of   |
    |                                                                                                                  | 11 years.           |
    +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+
    |           |0´ to 5´.|5´ to 10´.|10´ to 15´.|15´ to 20´.|20´ to 25´.|25´ to 30´.|30´ to 35´.|35´ to 40´.|over 40´.| 5 largest.| 5 least.|
    +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+
    |           |         |          |           |           |           |           |           |           |         |     ´     |    ´    |
    | January   |   51    |   145    |     69    |    37     |     24    |     7     |     4     |     3     |    1    |   22.90   |   5.07  |
    | February  |   26    |    99    |     84    |    51     |    226    |    10     |     4     |     2     |    8    |   27.21   |   6.55  |
    | March     |    1    |    72    |    138    |    61     |    232    |    21     |     8     |     1     |    7    |   29.87   |   8.93  |
    | April     |    0    |    43    |    167    |    73     |    227    |    10     |     6     |     3     |    1    |   23.69   |  10.31  |
    | May       |    0    |    57    |    157    |    85     |    220    |    12     |     3     |     0     |    7    |   25.36   |   9.50  |
    | June      |    0    |    56    |    185    |    67     |    215    |     1     |     3     |     1     |    2    |   19.92   |   9.89  |
    | July      |    0    |    59    |    185    |    70     |    214    |     5     |     2     |     2     |    4    |   22.49   |   9.96  |
    | August    |    0    |    37    |    202    |    75     |    222    |     1     |     2     |     0     |    2    |   21.27   |  10.05  |
    | September |    1    |    68    |    153    |    71     |    219    |     5     |     4     |     5     |    4    |   24.55   |   9.52  |
    | October   |    3    |   103    |    111    |    67     |    234    |    10     |     11    |     2     |    0    |   23.92   |   8.01  |
    | November  |   42    |   140    |     81    |    28     |    214    |     9     |     8     |     5     |    3    |   23.58   |   5.64  |
    | December  |   64    |   166    |     56    |    29     |    214    |     7     |     1     |     1     |    3    |   20.43   |   4.36  |
    +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+
    | Totals    |  188    |  1045    |   1588    |   714     |    261    |    98     |    56     |    25     |   42    |           |         |
    +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+


    Relations to Sun-spot Frequency.

  § 26. Magnetic phenomena, both regular and irregular, at any station
  vary from year to year. The extent of this variation is illustrated in
  Tables XXIV. and XXV., both relating to the period 1890 to 1900.[25]
  Table XXIV. gives the amplitudes of the regular diurnal inequality in
  the elements stated at the head of the columns. The ordinary day
  declination data (D0) for Kew represent arithmetic means from the
  twelve months of the year; the other data all answer to the mean
  diurnal inequality for the whole year. Table XXV. gives the arithmetic
  means for each year of the absolute daily range, of the monthly range
  (or difference between the highest and lowest values in the month),
  and of the yearly range (or difference between the highest and lowest
  values of the year). The numerals attached to the years in these
  tables indicate their order as regards sun-spot frequency according to
  Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest
  frequency, and 1890 that of least. The difference in sun-spot
  frequency between 1897 and 1898 was microscopic; the differences
  between 1890, 1900 and 1899 were small, and those between 1893, 1894
  and 1892 were not very large.

  The years 1892-1895 represent high sun-spot frequency, while 1890,
  1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to
  1895 were in all cases distinguished by the large size of the
  inequality ranges, and 1890, 1899 and 1900 by the small size. The
  range in 1893 is usually the largest, and though the H and V ranges
  at Ekaterinburg are larger in 1892 than in 1893, the excess is
  trifling. The phenomena apparent in Table XXIV. are fairly
  representative; other stations and other periods associate large
  inequality ranges with high sun-spot frequency. The diurnal inequality
  range it should be noticed is comparatively little influenced by
  irregular disturbances. Coming to Table XXV., we have ranges of a
  different character. The absolute range at Kew on quiet days is almost
  as little influenced by irregularities as is the range of the diurnal
  inequality, and in its case the phenomena are very similar to those
  observed in Table XXIV. As we pass from left to right in Table XXV.,
  the influence of disturbance increases. Simultaneously with this, the
  parallelism with sun-spot frequency is less close. The entries
  relating to 1892 and 1894 become more and more prominent compared to
  those for 1893. The yearly range may depend on but a single magnetic
  storm, the largest disturbance of the year possibly far outstripping
  any other. But taking even the monthly ranges the values for 1893 are,
  speaking roughly, only half those for 1892 and 1894, and very similar
  to those of 1898, though the sun-spot frequency in the latter year was
  less than a third of that in 1893. Ekatarinburg data exactly analogous
  to those for Pavlovsk show a similar prominence in 1892 and 1894 as
  compared to 1893. The retirement of 1893 from first place, seen in the
  absolute ranges at Kew, Pavlovsk and Ekatarinburg, is not confined to
  the northern hemisphere. It is visible, for instance, in the
  amplitudes of the Batavia disturbance results. Thus though the
  variation from year to year in the amplitude of the absolute ranges is
  relatively not less but greater than that of the inequality ranges,
  and though the general tendency is for all ranges to be larger in
  years of many than in years of few sun-spots, still the parallelism
  between the changes in sun-spot frequency and in magnetic range is not
  so close for the absolute ranges and for disturbances as for the
  inequality ranges.

  TABLE XXIV.--Ranges of Diurnal Inequalities.

    +----------+-------------------------+-----------------------------------+---------------------------------+
    |          |         Pavlovsk.       |            Ekatarinburg.          |               Kew.              |
    +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+
    |          |   D.  |   I.  |    H.   |   D.  |   I.  |    H.   |    V.   |  D_q. |  I_q. |   H_q.  |  D_0. |
    |          +-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+
    |          |   ´   |   ´   | [gamma] |   ´   |   ´   | [gamma] | [gamma] |   ´   |   ´   | [gamma] |   ´   |
    | 1890_11  |  6.32 |  1.33 |    22   |  5.83 |  1.05 |    18   |     9   |  6.90 |       |    20   |  7.32 |
    | 1891_6   |  7.31 |  1.79 |    30   |  6.85 |  1.38 |    25   |    14   |  8.04 |  1.52 |    28   |  8.48 |
    | 1892_3   |  8.75 |  2.21 |    37   |  7.74 |  1.72 |    32   |    19   |  9.50 |  1.66 |    31   |  9.85 |
    | 1893_1   |  9.64 |  2.24 |    38   |  8.83 |  1.80 |    31   |    17   | 10.06 |  1.96 |    35   | 10.74 |
    | 1894_2   |  8.58 |  2.17 |    38   |  7.80 |  1.73 |    30   |    17   |  9.32 |  1.94 |    34   |  9.80 |
    | 1895_4   |  8.22 |  2.08 |    33   |  7.29 |  1.64 |    28   |    15   |  8.59 |  1.66 |    30   |  9.54 |
    | 1896_5   |  7.39 |  1.77 |    29   |  6.50 |  1.38 |    25   |    15   |  7.77 |  1.31 |    25   |  8.50 |
    | 1897_6   |  6.79 |  1.59 |    26   |  6.01 |  1.16 |    21   |    12   |  6.71 |  1.14 |    22   |  7.76 |
    | 1898_7   |  6.25 |  1.56 |    26   |  5.76 |  1.19 |    21   |    11   |  6.85 |  1.07 |    21   |  7.59 |
    | 1899_9   |  6.02 |  1.44 |    24   |  5.33 |  1.12 |    20   |    11   |  6.69 |  1.01 |    21   |  7.30 |
    | 1900_10  |  6.20 |  1.28 |    22   |  5.88 |  0.93 |    17   |     8   |  6.52 |  1.06 |    21   |  6.83 |
    +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+

  TABLE XXV.--Absolute Ranges.

    +---------+-----------------------+-----------------------------------------------------------------------------------+
    |         |    Kew Declination.   |                                     Pavlovsk.                                     |
    |         |         Daily.        +---------------------------+---------------------------+---------------------------+
    |         |                       |           Daily.          |          Monthly.         |          Yearly.          |
    +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+
    |         |   q.  |   o.  |   a.  |   D.  |    H.   |    V.   |   D.  |    H.   |    V.   |   D.  |    H.   |    V.   |
    |         +-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+
    |         |   ´   |   ´   |   ´   |   ´   | [gamma] | [gamma] |   ´   | [gamma] | [gamma] |   ´   | [gamma] | [gamma] |
    | 1890_11 |  8.3  | 10.5  | 10.7  | 12.1  |    49   |    21   | 28.2  |   118   |    80   |  42.1 |   169   |   179   |
    | 1891_6  | 10.0  | 12.8  | 13.7  | 16.0  |    70   |    39   | 46.3  |   218   |   233   |  92.3 |   550   |   614   |
    | 1892_3  | 12.3  | 15.4  | 17.7  | 21.0  |   111   |    73   | 93.6  |   698   |   575   | 194.0 |  2416   |  1385   |
    | 1893_1  | 11.8  | 15.2  | 15.6  | 17.8  |    79   |    41   | 48.3  |   241   |   210   |  87.1 |   514   |   457   |
    | 1894_2  | 11.3  | 14.7  | 16.5  | 20.4  |    97   |    62   | 84.1  |   493   |   493   | 145.6 |  1227   |   878   |
    | 1895_4  | 10.6  | 14.8  | 15.6  | 18.1  |    80   |    46   | 47.4  |   220   |   223   |  73.9 |   395   |   534   |
    | 1896_5  |  9.5  | 12.9  | 14.5  | 17.5  |    74   |    43   | 52.4  |   232   |   236   |  88.7 |   574   |   608   |
    | 1897_8  |  8.2  | 11.5  | 12.1  | 14.6  |    61   |    30   | 43.8  |   201   |   170   | 101.1 |   449   |   480   |
    | 1898_7  |  8.2  | 11.2  | 12.3  | 14.7  |    67   |    35   | 46.6  |   276   |   242   | 118.9 |  1136   |   888   |
    | 1899_9  |  7.9  | 10.5  | 11.3  | 13.1  |    58   |    27   | 38.3  |   178   |   150   |  63.8 |   382   |   527   |
    | 1900_10 |  7.4  |  8.9  |  9.2  | 10.5  |    44   |    16   | 32.8  |   134   |    89   |  94.2 |   457   |   365   |
    +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+
    |  Means  |  9.6  | 12.6  | 13.6  | 16.0  |    72   |    39   | 51.1  |   274   |   246   | 100.2 |   752   |   629   |
    +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+

  § 27. The relationship between magnetic ranges and sun-spot frequency
  has been investigated in several ways. W. Ellis[26] has employed a
  graphical method which has advantages, especially for tracing the
  general features of the resemblance, and is besides independent of any
  theoretical hypothesis. Taking time for the axis of abscissae, Ellis
  drew two curves, one having for its ordinates the sun-spot frequency,
  the other the inequality range of declination or of horizontal force
  at Greenwich. The value assigned in the magnetic curve to the ordinate
  for any particular month represents a mean from 12 months of which it
  forms a central month, the object being to eliminate the regular
  annual variation in the diurnal inequality. The sun-spot data derived
  from Wolf and Wolfer were similarly treated. Ellis originally dealt
  with the period 1841 to 1877, but subsequently with the period 1878 to
  1896, and his second paper gives curves representing the phenomena
  over the whole 56 years. This period covered five complete sun-spot
  periods, and the approximate synchronism of the maxima and minima, and
  the general parallelism of the magnetic and sun-spot changes is patent
  to the eye. Ellis[27] has also applied an analogous method to
  investigate the relationship between sun-spot frequency and the number
  of days of magnetic disturbance at Greenwich. A decline in the number
  of the larger magnetic storms near sun-spot minimum is recognizable,
  but the application of the method is less successful than in the case
  of the inequality range. Another method, initiated by Professor Wolf
  of Zurich, lends itself more readily to the investigation of numerical
  relationships. He started by supposing an exact proportionality
  between corresponding changes in sun-spot frequency and magnetic
  range. This is expressed mathematically by the formula

    R = a + bS [equiv] a{1 + (b/a)S},

  where R denotes the magnetic range, S the corresponding sun-spot
  frequency, while a and b are constants. The constant a represents the
  range for zero sun-spot frequency, while b/a is the proportional
  increase in the range accompanying unit rise in sun-spot frequency.
  Assuming the formula to be true, one obtains from the observed values
  of R and S numerical values for a and b, and can thus investigate
  whether or not the sun-spot influence is the same for the different
  magnetic elements and for different places. Of course, the usefulness
  of Wolf's formula depends largely on the accuracy with which it
  represents the facts. That it must be at least a rough approximation
  to the truth in the case of the diurnal inequality at Greenwich might
  be inferred from Ellis's curves. Several possibilities should be
  noticed. The formula may apply with high accuracy, a and b having
  assigned values, for one or two sun-spot cycles, and yet not be
  applicable to more remote periods. There are only three or four
  stations which have continuous magnetic records extending even 50
  years back, and, owing to temperature correction uncertainties, there
  is perhaps no single one of these whose earlier records of horizontal
  and vertical force are above criticism. Declination is less exposed to
  uncertainty, and there are results of eye observations of declination
  before the era of photographic curves. A change, however, of 1´ in
  declination has a significance which alters with the intensity of the
  horizontal force. During the period 1850-1900 horizontal force in
  England increased about 5%, so that the force requisite to produce a
  declination change of 19´ in 1900 would in 1850 have produced a
  deflection of 20´. It must also be remembered that secular changes of
  declination must alter the angle between the needle and any disturbing
  force acting in a fixed direction. Thus secular alteration in a and b
  is rather to be anticipated, especially in the case of the
  declination. Wolf's formula has been applied by Rajna[28] to the
  yearly mean diurnal declination ranges at Milan based on readings
  taken twice daily from 1836 to 1894, treating the whole period
  together, and then the period 1871 to 1894 separately. During two
  sub-periods, 1837-1850 and 1854-1867, Rajna's calculated values for
  the range differ very persistently in one direction from those
  observed; Wolf's formula was applied by C. Chree[25] to these two
  periods separately. He also applied it to Greenwich inequality ranges
  for the years 1841 to 1896 as published by Ellis, treating the whole
  period and the last 32 years of it separately, and finally to all (a)
  and quiet (q) day Greenwich ranges from 1889 to 1896. The results of
  these applications of Wolf's formula appear in Table XXVI.

  The Milan results are suggestive rather of heterogeneity in the
  material than of any decided secular change in a or b. The Greenwich
  data are suggestive of a gradual fall in a, and rise in b, at least in
  the case of the declination.

  Table XXVII. gives values of a, b and b/a in Wolf's formula calculated
  by Chree[25] for a number of stations. There are two sets of data, the
  first set relating to the range from the mean diurnal inequality for
  the year, the second to the arithmetic mean of the ranges in the mean
  diurnal inequalities for the twelve months. It is specified whether
  the results were derived from all or from quiet days.

  TABLE XXVI.--Values of a and b in Wolf's Formula.

    +--------------------------+------------------------------------------------+
    |           Milan.         |                   Greenwich.                   |
    |---------+----------------+------------+----------------+------------------+
    |         |  Declination   |            |   Declination  | Horizontal Force |
    |         |   (unit 1´).   |            |    (unit 1´).  | (unit 1[gamma]). |
    |  Epoch. |--------+-------+   Epoch.   +--------+-------+---------+--------+
    |         |    a.  |   b.  |            |   a.   |   b.  |    a.   |   b.   |
    +---------+--------+-------+------------+--------+-------+---------+--------+
    | 1836-94 |  5.31  | .047  | 1841-96    |  7.29  | .0377 |   26.4  |  .190  |
    | 1871-94 |  5.39  | .047  | 1865-96    |  7.07  | .0396 |   23.6  |  .215  |
    | 1837-50 |  6.43  | .041  | 1889-96(a) |  6.71  | .0418 |   23.7  |  .218  |
    | 1854-67 |  4.62  | .047  | 1889-96(q) |  6.36  | .0415 |   25.0  |  .213  |
    +---------+--------+-------+------------+--------+-------+---------+--------+

  As explained above, a would represent the range in a year of no
  sun-spots, while 100 b would represent the excess over this shown by
  the range in a year when Wolf's sun-spot frequency is 100. Thus b/a
  seems the most natural measure of sun-spot influence. Accepting it, we
  see that sun-spot influence appears larger at most places for
  inclination and horizontal force than for declination. In the case of
  vertical force there is at Pavlovsk, and probably in a less measure at
  other northern stations, a large difference between all and quiet
  days, which is not shown in the other elements. The difference between
  the values of b/a at different stations is also exceptionally large
  for vertical force. Whether this last result is wholly free from
  observational uncertainties is, however, open to some doubt, as the
  agreement between Wolf's formula and observation is in general
  somewhat inferior for vertical force. In the case of the declination,
  the mean numerical difference between the observed values and those
  derived from Wolf's formula, employing the values of a and b given in
  Table XXVII., represented on the average about 4% of the mean value of
  the element for the period considered, the probable error representing
  about 6% of the difference between the highest and lowest values
  observed. The agreement was nearly, if not quite, as good as this for
  inclination and horizontal force, but for vertical force the
  corresponding percentages were nearly twice as large.

  TABLE XXVII.--Values of a and b in Wolf's Formula.

    +---------------------------------+----------------------+----------------------+----------------------+----------------------+
    |                                 |     Declination      |     Inclination      |   Horizontal Force   |   Vertical Force     |
    |                                 |      (unit 1´).      |      (unit 1´).      |    (unit 1[gamma]).  |   (unit 1[gamma]).   |
    +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+
    | Diurnal Inequality for the Year.|  a.  |  b.  |100 b/a.|  a.  |  b.  |100 b/a.|  a.  |  b.  |100 b/a.|  a.  |  b.  |100 b/a.|
    +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+
    | Pavlovsk, 1890-1900       all   | 5.74 |.0400 |  .70   | 1.24 |.0126 |  1.01  | 20.7 | .211 |  1.02  |  8.1 | .265 |  3.26  |
    | Pavlovsk, 1890-1900       quiet | 6.17 |.0424 |  .69   |  ..  | ..   |   ..   | 20.6 | .195 |  0.95  |  5.9 | .027 |  0.46  |
    | Ekatarinburg, 1890-1900   all   | 5.29 |.0342 |  .65   | 0.93 |.0105 |  1.13  | 16.8 | .182 |  1.09  |  8.6 | .117 |  1.37  |
    | Irkutsk         "    "    all   | 4.82 |.0358 |  .74   | 0.97 |.0087 |  0.90  | 18.2 | .190 |  1.04  |  6.5 | .071 |  1.09  |
    | Kew             "    "    quiet | 6.10 |.0433 |  .71   | 0.87 |.0125 |  1.45  | 18.1 | .194 |  1.07  | 14.3 | .081 |  0.56  |
    | Falmouth, 1891-1902       quiet | 5.90 |.0451 |  .76   |  ..  | ..   |   ..   | 20.1 | .233 |  1.16  |  ..  |  ..  |   ..   |
    | Kolaba, 1894-1901         quiet | 2.37 |.0066 |  .28   |  ..  | ..   |   ..   | 31.6 | .281 |  0.89  | 19.4 | .072 |  0.37  |
    | Batavia, 1887-1898        all   | 2.47 |.0179 |  .72   | 3.60 |.0218 |  0.61  | 38.7 | .274 |  0.71  | 30.1 | .156 |  0.52  |
    | Mauritius / 1875-1880 \   all   | 4.06 |.0164 |  .40   |  ..  | ..   |   ..   | 15.0 | .096 |  0.64  | 11.9 | .069 |  0.58  |
    |           \ 1883-1890 /         |      |      |        |      |      |        |      |      |        |      |      |        |
    +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+
    | _Mean from individual months:--_|      |      |        |      |      |        |      |      |        |      |      |        |
    | Pavlovsk, 1890-1900       all   | 6.81 |.0446 |  .66   | 1.44 |.0151 |  1.05  | 22.8 | .243 |  1.07  |  9.7 | .287 |  2.97  |
    |     "      "    "         quiet | 6.52 |.0442 |  .68   |  ..  | ..   |   ..   | 22.2 | .208 |  0.94  |  7.0 | .044 |  0.63  |
    | Ekatarinburg, 1890-1900   all   | 6.18 |.0355 |  .58   | 1.12 |.0120 |  1.06  | 19.2 | .195 |  1.01  |  9.2 | .156 |  1.70  |
    | Greenwich, 1865-1896      all   | 7.07 |.0396 |  .56   |  ..  | ..   |   ..   | 23.6 | .215 |  0.91  |  ..  |  ..  |   ..   |
    | Kew, 1890-1900            all   | 6.65 |.0428 |  .64   |  ..  | ..   |   ..   |  ..  |  ..  |   ..   |  ..  |  ..  |   ..   |
    |  "    "    "              quiet | 6.49 |.0410 |  .63   | 1.17 |.0130 |  1.11  | 21.5 | .191 |  0.89  | 16.0 | .072 |  0.45  |
    | Falmouth, 1891-1902       quiet | 6.16 |.0450 |  .73   |  ..  | ..   |   ..   | 20.9 | .236 |  1.13  |  ..  |  ..  |   ..   |
    +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+

  Applying Wolf's formula to the diurnal ranges for different months of
  the year, Chree found, as was to be anticipated, that the constant a
  had an annual period, with a conspicuous minimum at midwinter; but
  whilst b also varied, it did so to a much less extent, the consequence
  being that b/a showed a minimum at midsummer. The annual variation in
  b/a alters with the place, with the element, and with the type of day
  from which the magnetic data are derived. Thus, in the case of
  Pavlovsk declination, whilst the mean value of 100 b/a for the 12
  months is, as shown in Table XXVII., 0.66 for all and 0.68 for quiet
  days--values practically identical--if we take the four midwinter and
  the four midsummer months separately, we have 100 b/a, varying from
  0.81 in winter to 0.52 in summer on all days, but from 1.39 in winter
  to 0.52 in summer on quiet days. In the case of horizontal force at
  Pavlovsk the corresponding figures to these are for all days--winter
  1.77, summer 0.98, but for quiet days--winter 1.83, summer 0.71.

  Wolf's formula has also been applied to the absolute daily ranges, to
  monthly ranges, and to various measures of disturbance. In these cases
  the values found for b/a are usually larger than those found for
  diurnal inequality ranges, but the accordance between observed values
  and those calculated from Wolf's formula is less good. If instead of
  the range of the diurnal inequality we take the sum of the 24-hourly
  differences from the mean for the day--or, what comes to the same
  thing, the average departure throughout the 24 hours from the mean
  value for the day--we find that the resulting Wolf's formula gives at
  least as good an agreement with observation as in the case of the
  inequality range itself. The formulae obtained in the case of the 24
  differences, at places as wide apart as Kew and Batavia, agreed in
  giving a decidedly larger value for b/a than that obtained from the
  ranges. This indicates that the inequality curve is relatively less
  peaked in years of many than in years of few sun-spots.

  § 28. The applications of Ellis's and Wolf's methods relate directly
  only to the amplitude of the diurnal changes. There is, however, a
  change not merely in amplitude but in type. This is clearly seen when
  we compare the values found in years of many and of few sun-spots for
  the Fourier coefficients in the diurnal inequality. Such a comparison
  is carried out in Table XXVIII. for the declination on ordinary days
  at Kew. Local mean time is used. The heading S max. (sun-spot maximum)
  denotes mean average results from the four years 1892-1895, having a
  mean sun-spot frequency of 75.0, whilst S min. (sun-spot minimum)
  applies similarly to the years 1890, 1899 and 1900, having a mean
  sun-spot frequency of only 9.6. The data relate to the mean diurnal
  inequality for the whole year or for the season stated. It will be
  seen that the difference between the c, or amplitude, coefficients in
  the S max. and S min. years is greater for the 24-hour term than for
  the 12-hour term, greater for the 12-hour than for the 8-hour term,
  and hardly apparent in the 6-hour term. Also, _relatively considered_,
  the difference between the amplitudes in S max. and S min. years is
  greatest in winter and least in summer. Except in the case of the
  6-hour term, where the differences are uncertain, the phase angle is
  larger, i.e. maxima and minima occur earlier in the day, in years of S
  min. than in years of S max. Taking the results for the whole year in
  Table XXVIII., this advance of phase in the S min. years represents in
  time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour
  term, and 14.7 minutes for the 8-hour term. The difference in the
  phase angles, as in the amplitudes, is greatest in winter. Similar
  phenomena are shown by the horizontal force, and at Falmouth[24] as
  well as Kew.

  TABLE XXVIII.--Fourier Coefficients in Years of many and few
  Sun-spots.

    +---------+-------------+-------------+-------------+-------------+
    |         |     Year.   |   Winter.   |   Equinox.  |   Summer.   |
    |         +------+------+------+------+------+------+------+------+
    |         |S max.|S min.|S max.|S min.|S max.|S min.|S max.|S min.|
    +---------+------+------+------+------+------+------+------+------+
    |         |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |   ´  |
    |    c1   | 3.47 | 2.21 | 2.41 | 1.43 | 3.76 | 2.41 | 4.38 | 2.98 |
    |    c2   | 2.04 | 1.51 | 1.15 | 0.78 | 2.33 | 1.71 | 2.73 | 2.06 |
    |    c3   | 0.89 | 0.72 | 0.55 | 0.42 | 1.16 | 0.97 | 0.97 | 0.77 |
    |    c4   | 0.28 | 0.27 | 0.30 | 0.27 | 0.42 | 0.42 | 0.11 | 0.11 |
    +---------+------+------+------+------+------+------+------+------+
    |         |   °  |   °  |   °  |   °  |   °  |   °  |   °  |   °  |
    |[alpha]1 | 228.5| 232.4| 243.0| 256.0| 231.3| 233.7| 218.2| 220.3|
    |[alpha]2 |  41.7|  46.6|  23.5|  36.9|  40.6|  43.9|  50.6|  52.5|
    |[alpha]3 | 232.6| 243.6| 234.0| 257.6| 228.4| 236.2| 236.8| 245.4|
    |[alpha]4 |  58.0|  57.3|  52.3|  60.8|  62.0|  58.2|  57.4|  45.2|
    +---------+------+------+------+------+------+------+------+------+


    Quiet Day Phenomena.

  § 29. There have already been references to _quiet_ days, for instance
  in the tables of diurnal inequalities. It seems to have been
  originally supposed that quiet days differed from other days only in
  the absence of irregular disturbances, and that mean annual values, or
  secular change data, or diurnal inequalities, derived from them might
  be regarded as truly normal or representative of the station. It was
  found, however, by P. A. Müller[29] that mean annual values of the
  magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885
  derived from quiet days alone differed in a systematic fashion from
  those derived from all days, and analogous results were obtained by
  Ellis[30] at Greenwich for the period 1889-1896. The average excesses
  for the quiet-day over the all-day means in these two cases were as
  follows:--

    +---------------+--------------+--------------+------------+-------------+
    |               |   Westerly   | Inclination. | Horizontal |   Vertical  |
    |               | Declination. |              |   Force.   |    Force.   |
    +---------------+--------------+--------------+------------+-------------+
    | St Petersburg |    +0.24     |    -0.23     | +3.2[gamma]| -0.8[gamma] |
    | Greenwich     |    +0.08     |              | +3.2[gamma]| -0.9[gamma] |
    +---------------+--------------+--------------+------------+-------------+

  The sign of the difference in the case of D, I and H was the same in
  each year examined by Müller, and the same was true of H at Greenwich.
  In the case of V, and of D at Greenwich, the differences are small
  and might be accidental. In the case of D at Greenwich 1891 differed
  from the other years, and of two more recent years examined by
  Ellis[31] one, 1904, agreed with 1891. At Kew, on the average of the
  11 years 1890 to 1900, the quiet-day mean annual value of declination
  exceeded the ordinary day value, but the apparent excess 0´.02 is too
  small to possess much significance.


    Non-cyclic Change.

  Another property more recently discovered in quiet days is the
  non-cyclic change. The nature of this phenomenon will be readily
  understood from the following data from the 11-year period 1890 to
  1900 at Kew[32]. The mean daily change for all days is calculated from
  the observed annual change.

    +------------------------------+--------+--------+--------------+--------------+
    |                              |    D.  |   I.   |      H.      |       V.     |
    +------------------------------+--------+--------+--------------+--------------+
    |                              |    ´   |   ´    |              |              |
    | Mean annual change           | -5.79  | -2.38  | +25.9[gamma] | -22.6[gamma] |
    | Mean daily change, all days  | -0.016 | -0.007 | +0.07[gamma] | -0.06[gamma] |
    | Mean daily change, quiet days| +0.044 | -0.245 | +3.34[gamma] | -0.84[gamma] |
    +------------------------------+------------------+-------------+--------------+

  Thus the changes during the representative quiet day differed from
  those of the average day. Before accepting such a phenomenon as
  natural, instrumental peculiarities must be carefully considered. The
  secular change is really based on the absolute instruments, the
  diurnal changes on the magnetographs, and the first idea likely to
  occur to a critical mind is that the apparent abnormal change on quiet
  days represents in reality change of zero in the magnetographs. If,
  however, the phenomenon were instrumental, it should appear equally on
  days other than quiet days, and we should thus have a shift of zero
  amounting in a year to over 1,200[gamma] in H, and to about 90´ in I.
  Under such circumstances the curve would be continually drifting off
  the sheet. In the case of the Kew magnetographs, a careful
  investigation showed that if any instrumental change occurred in the
  declination magnetograph during the 11 years it did not exceed a few
  tenths of a minute. In the case of the H and V magnetographs at Kew
  there is a slight drift, of instrumental origin, due to weakening of
  the magnets, but it is exceedingly small, and in the case of H is in
  the opposite direction to the non-cyclic change on quiet days. It only
  remains to add that the hypothesis of instrumental origin was
  positively disproved by measurement of the curves on ordinary days.

  It must not be supposed that every quiet day agrees with the average
  quiet day in the order of magnitude, or even in the sign, of the
  non-cyclic change. In fact, in not a few months the sign of the
  non-cyclic change on the mean of the quiet days differs from that
  obtained for the average quiet day of a period of years. At Kew,
  between 1890 and 1900, the number of months during which the mean
  non-cyclic change for the five quiet days selected by the astronomer
  royal (Sir W. H. M. Christie) was plus, zero, or minus, was as
  follows:--

    +-----------+------+------+------+------+
    |  Element. |  D.  |  I.  |  H.  |  V.  |
    +-----------+------+------+------+------+
    | Number +  |  63  |   13 |  112 |  47  |
    |    "   0  |  14  |   16 |   11 |   9  |
    |    "   -  |  55  |  101 |    9 |  74  |
    +-----------+------+------+------+------+

  The + sign denotes westerly movement in the declination, and
  increasing dip of the north end of the needle. In the case of I and H
  the excess in the number of months showing the normal sign is
  overwhelming. The following mean non-cyclic changes on quiet days are
  from other sources:--

    +-----------+--------------+-------------+--------------+
    |           |   Greenwich  |   Falmouth  |    Kolaba    |
    |  Element. | (1890-1895). | (1898-1902).| (1894-1901). |
    +-----------+--------------+-------------+--------------+
    |           |      ´       |      ´      |      ´       |
    |     D     | + 0.03       | + 0.05      | + 0.07       |
    |     H     | + 4.3[gamma] | + 3.0[gamma]| + 3.9[gamma] |
    +-----------+--------------+-------------+--------------+

  The results are in the same direction as at Kew, + meaning in the case
  of D movement to the west. At Falmouth[32], as at Kew, the non-cyclic
  change showed a tendency to be small in years of few sun-spots.

  § 30. In calculating diurnal inequalities from quiet days the
  non-cyclic effect must be eliminated, otherwise the result would
  depend on the hour at which the "day" is supposed to commence. If the
  value recorded at the second midnight of the average day exceeds that
  at the first midnight by N, the elimination is effected by applying to
  each hourly value the correction N(12 - n)/24, where n is the hour
  counted from the first midnight (0 hours). This assumes the change to
  progress uniformly throughout the 24 hours. Unless this is practically
  the case--a matter difficult either to prove or disprove--the
  correction may not secure exactly what is aimed at. This method has
  been employed in the previous tables. The fact that differences do
  exist between diurnal inequalities derived from quiet days and all
  ordinary days was stated explicitly in § 4, and is obvious in Tables
  VIII. to XI. An extreme case is represented by the data for Jan Mayen
  in these tables. Figs. 9 and 10 are vector diagrams for this station,
  for all and for quiet days during May, June and July 1883, according
  to data got out by Lüdeling. As shown by the arrows, fig. 10 (quiet
  days) is in the main described in the normal or clockwise direction,
  but fig. 9 (all days) is described in the opposite direction. Lüdeling
  found this peculiar difference between all and quiet days at all the
  north polar stations occupied in 1882-1883 except Kingua Fjord, where
  both diagrams were described clockwise.

  [Illustration: FIG. 9.]

  [Illustration: FIG. 10.]

  In temperate latitudes the differences of type are much less, but
  still they exist. A good idea of their ordinary size and character in
  the case of declination may be derived from Table XXIX., containing
  data for Kew, Greenwich and Parc St Maur.

  The data for Greenwich are due to W. Ellis[30], those for Parc St Maur
  to T. Moureaux[33]. The quantity tabulated is the algebraic excess of
  the all or ordinary day mean hourly value over the corresponding quiet
  day value in the mean diurnal inequality for the year. At Greenwich
  and Kew days of extreme disturbance have been excluded from the
  ordinary days, but apparently not at Parc St Maur. The number of
  highly disturbed days at the three stations is, however, small, and
  their influence is not great. The differences disclosed by Table XXIX.
  are obviously of a systematic character, which would not tend to
  disappear however long a period was utilized. In short, while the
  diurnal inequality from quiet days may be that most truly
  representative of undisturbed conditions, it does not represent the
  average state of conditions at the station. To go into full details
  respecting the differences between all and quiet days would occupy
  undue space, so the following brief summary of the differences
  observed in declination at Kew must suffice. While the inequality
  range is but little different for the two types of days, the mean of
  the hourly differences from the mean for the day is considerably
  reduced in the quiet days. The 24-hour term in the Fourier analysis is
  of smaller amplitude in the quiet days, and its phase angle is on the
  average about 6°.75 smaller than on ordinary days, implying a
  retardation of about 27 minutes in the time of maximum. The diurnal
  inequality range is more variable throughout the year in quiet days
  than on ordinary days, and the same is true of the absolute ranges.
  The tendency to a secondary minimum in the range at midsummer is
  considerably more decided on ordinary than on quiet days. When the
  variation throughout the year in the diurnal inequality range is
  expressed in Fourier series, whose periods are the year and its
  submultiples, the 6-month term is notably larger for ordinary than for
  quiet days. Also the date of the maximum in the 12-month term is about
  three days earlier for ordinary than for quiet days. The exact size of
  the differences between ordinary and quiet day phenomena must depend
  to some extent on the criteria employed in selecting quiet days and in
  excluding disturbed days. This raises difficulties when it comes to
  comparing results at different stations. For stations near together
  the difficulty is trifling. The astronomer royal's quiet days have
  been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew,
  as well as at Greenwich. But when stations are wide apart there are
  two obvious difficulties: first, the difference of local time;
  secondly, the fact that a day may be typically quiet at one station
  but appreciably disturbed at the other.

  If the typical quiet day were simply the antithesis of a disturbed
  day, it would be natural to regard the non-cyclic change on quiet days
  as a species of recoil from some effect of disturbance. This view
  derives support from the fact, pointed out long ago by Sabine[34],
  that the horizontal force usually, though by no means always, is
  lowered by magnetic disturbances. Dr van Bemmelen[35] who has examined
  non-cyclic phenomena at a number of stations, seems disposed to regard
  this as a sufficient explanation. There are, however, difficulties in
  accepting this view. Thus, whilst the non-cyclic effect in horizontal
  force and inclination at Kew and Falmouth appeared on the whole
  enhanced in years of sun-spot maximum, the difference between years
  such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other,
  was by no means proportional to the excess of disturbance in the
  former years. Again, when the average non-cyclic change of declination
  was calculated at Kew for 207 days, selected as those of most marked
  irregular disturbance between 1890 and 1900, the sign actually proved
  to be the same as for the average quiet day of the period.

  TABLE XXIX.--All or Ordinary, less Quiet Day Hourly Values (+ to the
  West).

    +-----+--------------------------------------+-------------------------------------+
    |     |               Forenoon.              |              Afternoon.             |
    |Hour.+------------+-----------+-------------+-----------+-----------+-------------+
    |     |    Kew     | Greenwich |Parc St Maur |    Kew    | Greenwich |Parc St Maur |
    |     | 1890-1900. | 1890-1894.|  1883-1897. | 1890-1900.| 1890-1894.|  1893-1897. |
    +-----+------------+-----------+-------------+-----------+-----------+-------------+
    |     |     ´      |     ´     |      ´      |     ´     |     ´     |      ´      |
    |  1  |   -0.58    |   -0.59   |    -0.63    |   +0.42   |   +0.44   |    +0.40    |
    |  2  |   -0.54    |   -0.47   |    -0.47    |   +0.52   |   +0.45   |    +0.50    |
    |  3  |   -0.51    |   -0.31   |    -0.32    |   +0.57   |   +0.52   |    +0.59    |
    |  4  |   -0.41    |   -0.23   |    -0.16    |   +0.60   |   +0.51   |    +0.55    |
    |  5  |   -0.28    |   -0.10   |    -0.01    |   +0.46   |   +0.34   |    +0.38    |
    |  6  |   -0.08    |   +0.12   |    +0.18    |   +0.21   |   +0.04   |    +0.07    |
    |  7  |   +0.13    |   +0.30   |    +0.34    |   -0.06   |   -0.24   |    -0.25    |
    |  8  |   +0.29    |   +0.48   |    +0.47    |   -0.27   |   -0.50   |    -0.54    |
    |  9  |   +0.40    |   +0.56   |    +0.53    |   -0.47   |   -0.68   |    -0.74    |
    | 10  |   +0.44    |   +0.58   |    +0.51    |   -0.61   |   -0.78   |    -0.79    |
    | 11  |   +0.48    |   +0.50   |    +0.44    |   -0.62   |   -0.77   |    -0.79    |
    | 12  |   +0.45    |   +0.44   |    +0.38    |   -0.54   |   -0.61   |    -0.67    |
    +-----+------------+-----------+-------------+-----------+-----------+-------------+


    Magnetic Disturbances.

  § 31. A satisfactory definition of magnetic disturbance is about as
  difficult to lay down as one of heterodoxy. The idea in its generality
  seems to present no difficulty, but it is a very different matter when
  one comes to details. Amongst the chief disturbances recorded since
  1890 are those of February 13-14 and August 12, 1892; July 20 and
  August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903;
  February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On
  such days as these the oscillations shown by the magnetic curves are
  large and rapid, aurora is nearly always visible in temperate
  latitudes, earth currents are prominent, and there is
  interruption--sometimes very serious--in the transmission of telegraph
  messages both in overhead and underground wires. At the other end of
  the scale are days on which the magnetic curves show practically no
  movement beyond the slow regular progression of the regular diurnal
  inequality. But between these two extremes there are an infinite
  variety of intermediate cases. The first serious attempt at a precise
  definition of disturbance seems due to General Sabine[35a]. His method
  had once an extensive vogue, and still continues to be applied at some
  important observatories. Sabine regarded a particular observation as
  disturbed when it differed from the mean of the observations at that
  hour for the whole month by not less than a certain limiting value.
  His definition takes account only of the extent of the departure from
  the mean, whether the curve is smooth at the time or violently
  oscillating makes no difference. In dealing with a particular station
  Sabine laid down separate limiting values for each element. These
  limits were the same, irrespective of the season of the year or of the
  sun-spot frequency. A departure, for example, of 3´.3 at Kew from the
  mean value of declination for the hour constituted a disturbance,
  whether it occurred in December in a year of sun-spot minimum, or in
  June in a year of sun-spot maximum, though the regular diurnal
  inequality range might be four times as large in the second case as in
  the first. The limiting values varied from station to station, the
  size depending apparently on several considerations not very clearly
  defined. Sabine subdivided the disturbances in each element into two
  classes: the one tending to increase the element, the other tending to
  diminish it. He investigated how the numbers of the two classes varied
  throughout the day and from month to month. He also took account of
  the aggregate value of the disturbances of one sign, and traced the
  diurnal and annual variations in these aggregate values. He thus got
  two sets of diurnal variations and two sets of annual variations of
  disturbance, the one set depending only on the number of the disturbed
  hours, the other set considering only the aggregate value of the
  disturbances. Generally the two species of disturbance variations were
  on the whole fairly similar. The aggregates of the + and -
  disturbances for a particular hour of the day were seldom equal, and
  thus after the removal of the disturbed values the mean value of the
  element for that hour was generally altered. Sabine's complete scheme
  supposed that after the criterion was first applied, the hourly means
  would be recalculated from the undisturbed values and the criterion
  applied again, and that this process would be repeated until the
  disturbed observations all differed by not less than the accepted
  limiting value from the final mean based on undisturbed values alone.
  If the disturbance limit were so small that the disturbed readings
  formed a considerable fraction of the whole number, the complete
  execution of Sabine's scheme would be exceedingly laborious. As a
  matter of fact, his disturbed readings were usually of the order of 5%
  of the total number, and unless in the case of exceptionally large
  magnetic storms it is of little consequence whether the first choice
  of disturbed readings is accepted as final or is reconsidered in the
  light of the recalculated hourly means.

  Sabine applied his method to the data obtained during the decade 1840
  to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to
  data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C.
  Chambers[36] applied it to data from Bombay. The yearly publication of
  the Batavia observatory gives corresponding results for that station,
  and Th. Moureaux [33] has published similar data for Parc St Maur.
  Tables XXX. to XXXII. are based on a selection of these data. Tables
  XXX. and XXXI. show the annual variation in Sabine's disturbances, the
  monthly values being expressed as percentages of the arithmetic mean
  value for the 12 months. The Parc St Maur and Batavia data, owing to
  the long periods included, are especially noteworthy. Table XXX. deals
  with the east (E) and west (W) disturbances of declination separately.
  Table XXXI., dealing with disturbances in horizontal and vertical
  force, combines the + and - disturbances, treated numerically. At Parc
  St Maur the limits required to qualify for disturbance were 3´.0 in D,
  20[gamma] in H, and 12[gamma] in V; the corresponding limits for
  Batavia were 1´.3, 11[gamma] and 11[gamma]. The limits for D at
  Toronto, Bombay and Hobart were respectively 3´.6, 1´.4 and 2´.4.

  At Parc St Maur the disturbance data from all three elements give
  distinct maxima near the equinoxes; a minimum at midwinter is clearly
  shown, and also one at midsummer, at least in D and H. A decline in
  disturbance at midwinter is visible at all the stations, but at
  Batavia the equinoctial values for D and V are inferior to those at
  midsummer.

  TABLE XXX.--Annual Variation of Disturbances (Sabine's numbers).

    +-----------+-------------+-------------+-------------+-------------+-------------+
    |           | Parc St Maur|   Toronto   |    Bombay   |   Batavia   |    Hobart   |
    |           |   1883-97.  |   1841-48.  |   1859-65.  |   1883-99.  |   1843-48.  |
    +-----------+------+------+------+------+------+------+------+------+------+------+
    |   Month.  |  E.  |  W.  |  E.  |  W.  |  E.  |  W.  |  E.  |  W.  |  E.  |  W.  |
    +-----------+------+------+------+------+------+------+------+------+------+------+
    | January   |  78  |  60  |  55  |  66  |  89  |  89  | 180  | 223  | 165  | 182  |
    | February  | 116  |  92  |  75  |  86  |  94  |  67  | 138  | 144  | 121  | 116  |
    | March     | 126  | 107  |  92  |  94  | 129  |  97  | 102  |  87  | 114  | 104  |
    | April     | 105  | 113  | 115  | 114  | 106  | 129  |  67  |  73  | 110  | 102  |
    | May       | 101  | 118  | 101  | 101  |  63  |  99  |  72  |  71  |  62  |  53  |
    | June      |  77  |  89  |  95  |  72  |  78  |  81  |  45  |  27  |  32  |  37  |
    | July      |  82  | 104  | 140  | 126  | 121  | 173  |  62  |  46  |  50  |  49  |
    | August    |  88  | 113  | 137  | 133  | 154  | 131  |  69  |  69  |  86  |  78  |
    | September | 134  | 137  | 163  | 139  | 111  | 108  | 135  | 144  | 135  | 114  |
    | October   | 119  | 115  | 101  | 111  | 140  | 128  |  95  |  88  | 124  | 123  |
    | November  |  99  |  94  |  73  |  85  |  43  |  43  | 106  |  91  |  79  | 111  |
    | December  |  75  |  58  |  51  |  72  |  72  |  55  | 124  | 137  | 123  | 130  |
    +-----------+------+------+------+------+------+------+------+------+------+------+

  Table XXXII. shows in some cases a most conspicuous diurnal variation
  in Sabine's disturbances. The data are percentages of the totals for
  the whole 24 hours. But whilst at Batavia the easterly and westerly
  disturbances in D vary similarly, at Parc St Maur they follow opposite
  laws, the easterly showing a prominent maximum near noon, the westerly
  a still more prominent maximum near midnight. The figures in the
  second last line of the table, if divided by 0.24, will give the
  percentage of hours which show the species of disturbance indicated.
  For instance, at Parc St Maur, out of 100 hours, 3 show disturbances
  to the west and 3.7 to the east; or in all 6.7 show disturbances of
  declination. The last line gives the average size of a disturbance of
  each type, the unit being 1´ in D and 1[gamma] in H and V.

  TABLE XXXI.--Annual Variation of Disturbances.

    +-----------+-------------+-------------+---------------------------+
    |           |Parc St Maur.|   Toronto.  |          Batavia.         |
    +-----------+-------------+-------------+-------------+-------------+
    |   Month.  |   Numbers.  | Aggregates. |   Numbers.  | Aggregates. |
    +-----------+------+------+------+------+------+------+------+------+
    |           |  H.  |  V.  |  H.  |  V.  |  H.  |  V.  |  H.  |  V.  |
    |           +------+------+------+------+------+------+------+------+
    | January   |  81  |  51  |  58  |  56  |  96  | 151  |  89  | 154  |
    | February  |  96  | 133  |  94  |  74  | 105  | 123  | 110  | 125  |
    | March     | 126  | 118  |  94  | 108  | 116  | 105  | 117  | 103  |
    | April     |  94  | 111  | 150  | 149  | 104  |  76  | 105  |  73  |
    | May       | 108  | 133  |  90  | 112  | 101  |  92  | 105  |  95  |
    | June      |  90  |  85  |  36  |  50  |  82  |  69  |  79  |  66  |
    | July      |  99  | 128  |  61  |  71  |  90  |  83  |  95  |  81  |
    | August    | 113  |  92  |  75  | 108  |  91  |  91  |  98  |  91  |
    | September | 119  | 122  | 171  | 160  | 113  | 111  | 114  | 115  |
    | October   | 101  |  94  | 148  | 129  | 114  |  89  | 104  |  86  |
    | November  | 104  |  81  |  98  |  75  |  99  | 102  | 100  | 101  |
    | December  |  70  |  51  | 128  | 100  |  89  | 108  |  84  | 110  |
    +-----------+------+------+------+------+------+------+------+------+

  At Batavia disturbances increasing and decreasing the element are
  about equally numerous, but this is exceptional. Easterly disturbances
  of declination predominated at Toronto, Point Barrow, Fort Kennedy,
  Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse
  was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and
  Parc St Maur the ratios borne by the eastern to the western
  disturbances were 1.19 and 1.23 respectively, and so not much in
  excess of unity; but the preponderance of easterly disturbances at the
  North American[37] stations was considerably larger than this.

  TABLE XXXII.--Diurnal Variation of Disturbances (Sabine's numbers).

    +-------------+-----------------------------------------+-----------------------------------------+
    |             |              Parc St Maur.              |                 Batavia.                |
    |             +-------------+-------------+-------------+-------------+-------------+-------------+
    |    Hour.    |      D.     |      H.     |      V.     |      D.     |      H.     |      V.     |
    |             +------+------+------+------+------+------+------+------+------+------+------+------+
    |             |  E.  |  W.  |   +  |   -  |   +  |   -  |  E.  |  W.  |   +  |   -  |   +  |   -  |
    +-------------+------+------+------+------+------+------+------+------+------+------+------+------+
    |    0-3      | 10.1 | 20.3 |  9.0 |  8.3 |  5.7 | |9.2 |  1.1 |  5.8 | 13.1 |  6.6 |  4.0 |  7.4 |
    |    3-6      | 12.3 |  8.2 |  8.4 |  8.0 |  6.4 | 10.4 |  7.6 |  7.3 | 14.2 |  4.8 |  6.3 | 10.0 |
    |    6-9      | 15.7 |  3.8 | 14.1 | 12.5 |  7.2 |  9.0 | 24.9 | 16.8 | 12.1 |  9.9 | 21.2 | 21.7 |
    |    9-noon   | 16.2 |  5.1 | 18.0 | 15.6 | 12.9 | 15.4 | 38.5 | 33.0 |  8.6 | 15.8 | 19.8 | 16.4 |
    |    noon-3   | 19.3 |  6.7 | 15.3 | 16.5 | 18.2 | 18.3 | 18.8 | 24.7 | 16.8 | 21.1 | 23.5 | 22.1 |
    |    3-6      | 14.8 |  9.7 | 12.5 | 15.4 | 22.9 | 21.8 |  6.4 |  5.4 | 13.3 | 16.9 | 12.6 | 12.7 |
    |    6-9      |  5.7 | 21.2 | 11.4 | 13.2 | 18.9 | 11.2 |  2.3 |  3.4 |  9.9 | 13.6 |  7.1 |  4.1 |
    |    9-12     |  5.9 | 25.0 | 11.2 | 10.5 |  7.8 |  4.7 |  0.4 |  3.8 | 12.0 | 11.1 |  5.6 |  5.4 |
    +-------------+------+------+------+------+------+------+------+------+------+------+------+------+
    | Mean number |      |      |      |      |      |      |      |      |      |      |      |      |
    |   per day   |  0.88|  0.72|  1.15|  1.56|  1.04|  0.96|  0.46|  0.44|  1.62|  1.61|  1.19|  1.13|
    | Mean size   |  ..  |  ..  |  ..  |  ..  |  ..  |  ..  |  1.72|  1.69|  18.0| 19.5 | 16.7 | 15.5 |
    +-------------+------+------+------+------+------+------+------+------+------+------+------+------+

  § 32. From the point of view of the surveyor there is a good deal to
  be said for Sabine's definition of disturbance, but it is less
  satisfactory from other standpoints. One objection has been already
  indicated, viz. the arbitrariness of applying the same limiting value
  at a station irrespective of the size of the normal diurnal range at
  the time. Similarly it is arbitrary to apply the same limit between 10
  a.m. and noon, when the regular diurnal variation is most rapid, as
  between 10 p.m. and midnight, when it is hardly appreciable. There
  seems a distinct difference of phase between the diurnal inequalities
  on different types of days at the same season; also the phase angles
  in the Fourier terms vary continuously throughout the year, and much
  more rapidly at some stations and at some seasons than at others. Thus
  there may be a variety of phenomena which one would hesitate to regard
  as disturbances which contribute to the annual and diurnal variations
  in Tables XXX. to XXXII.

  Sabine, as we have seen, confined his attention to the departure of
  the hourly reading from the mean for that hour. Another and equally
  natural criterion is the apparent character of the magnetograph curve.
  At Potsdam curves are regarded as "1" quiet, "2" moderately disturbed,
  or "3" highly disturbed. Any hourly value to which the numeral 3 is
  attached is treated as disturbed, and the annual Potsdam publication
  contains tables giving the annual and diurnal variations in the number
  of such disturbed hours for D, H and V. According to this point of
  view, the extent to which the hourly value departs from the mean for
  that hour is immaterial to the results. It is the greater or less
  sinuosity and irregularity of the curve that counts. Tables XXXIII.
  and XXXIV. give an abstract of the mean Potsdam results from 1892 to
  1901. The data are percentages: in Table XXXIII. of the mean monthly
  total, in Table XXXIV. of the total for the day. So far as the annual
  variation is concerned, the results in Table XXXIII. are fairly
  similar to those in Table XXX. for Parc St Maur. There are pronounced
  maxima near the equinoxes, especially the spring equinox. The diurnal
  variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus
  in the case of H the largest disturbance numbers at Parc St Maur
  occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur
  between 4 p.m. and midnight. Considering the comparative proximity of
  Parc St Maur and Potsdam, one must conclude that the apparent
  differences between the results for these two stations are due almost
  entirely to the difference in the definition of disturbance.

  TABLE XXXIII.--Annual Variation of Potsdam Disturbances.

    +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
    | Element.| Jan.| Feb.| Mar.| April.| May.| June.| July.| Aug.| Sept.| Oct.|  Nov.| Dec.|
    +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
    |    D    | 129 | 170 | 149 |   90  |  86 |  57  |  62  |  64 |  59  | 118 |  94  |  82 |
    |    H    | 109 | 133 | 131 |  102  | 109 |  82  |  94  |  91 |  89  | 101 |  75  |  84 |
    |    V    | 106 | 171 | 170 |  108  | 121 |  56  |  64  |  74 |  93  |  87 |  78  |  70 |
    +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
    |   Mean  | 115 | 158 | 150 |  100  | 105 |  65  |  73  |  76 |  94  | 102 |  82  |  79 |
    +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+

  TABLE XXXIV.--Diurnal Variation of Potsdam Disturbances.

    +--------+------+------+-----+---------+------+------+------+-------+
    | Hours. | 1-3. | 4-6. | 7-9.| 10-noon.| 1-3. | 4-6. | 7-9. | 10-12.|
    +--------+------+------+-----+---------+------+------+------+-------+
    |    D   | 14.9 | 11.1 | 8.0 |   5.2   |  5.7 | 13.1 | 22.5 |  19.5 |
    |    H   | 10.5 |  8.4 | 8.0 |   8.5   | 11.3 | 17.6 | 19.2 |  16.5 |
    |    V   | 13.5 |  9.7 | 5.7 |   4.7   |  8.5 | 17.2 | 21.5 |  19.2 |
    +--------+------+------+-----+---------+------+------+------+-------+
    |  Mean  | 13.0 |  9.7 | 7.2 |   6.1   |  8.5 | 16.0 | 21.1 |  18.4 |
    +--------+------+------+-----+---------+------+------+------+-------+

  TABLE XXXV.--Disturbed Day less ordinary Day Inequality (Unit 1´, + to West).

    +------+------+------+------+------+------+------+------+------+------+------+------+------+
    | Hour.|   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |  11  |  12  |
    +------+------+------+------+------+------+------+------+------+------+------+------+------+
    | a.m. | -3.4 | -2.6 | -2.0 | -0.3 | +1.6 | +1.9 | +2.3 | +2.0 | +2.1 | +2.0 | +1.6 | +1.8 |
    | p.m. | +1.8 | +2.2 | +2.1 | +1.7 | +1.4 |  0.0 | -1.3 | -2.8 | -3.5 | -2.6 | -3.5 | -2.4 |
    +------+------+------+------+------+------+------+------+------+------+------+------+------+

  One difficulty in the Potsdam procedure is the maintenance of a
  uniform standard. Unless very frequent reference is made to the curves
  of some standard year there must be a tendency to enter under "3" in
  quiet years a number of hours which would be entered under "2" in a
  highly disturbed year. Still, such a source of uncertainty is unlikely
  to have much influence on the diurnal, or even on the annual,
  variation.

  § 33. A third method of investigating a diurnal period in disturbances
  is to form a diurnal inequality from disturbed days alone, and compare
  it with the corresponding inequalities from ordinary or from quiet
  days. Table XXXV. gives some declination data for Kew, the quantity
  tabulated being the algebraic excess of the disturbed day hourly value
  over that for the ordinary day in the mean diurnal inequality for the
  year, as based on the 11 years 1890 to 1900.

  [Illustration: FIG. 11.]

  The disturbed day inequality was corrected for non-cyclic change in
  the usual way. Fig. 11 shows the results of Table XXXV. graphically.
  The irregularities are presumably due to the limited number, 209, of
  disturbed days employed; to get a smooth curve would require probably
  a considerably longer period of years. The differences between
  disturbed and ordinary days at Kew are of the same general character
  as those between ordinary and quiet days in Table XXIX.; they are,
  however, very much larger, the range in Table XXXV. being fully 5½
  times that in Table XXIX. If quiet days had replaced ordinary days in
  Table XXXV., the algebraic excess of the disturbed day would have
  varied from +2´.7 at 2 p.m. to -4´.1 at 11 p.m., or a range of 6´.8.

  § 34. When the mean diurnal inequality in declination for the year at
  Kew is analysed into Fourier waves, the chief difference, it will be
  remembered, between ordinary and quiet days was that the amplitude of
  the 24-hour term was enhanced in the ordinary days, whilst its phase
  angle indicated an earlier occurrence of the maximum. Similarly, the
  chief difference between the Fourier waves for the disturbed and
  ordinary day inequalities at Kew is the increase in the amplitude of
  the 24-hour term in the former by over 70%, and the earlier occurrence
  of its maximum by about 1 hour 50 minutes. It is clear from these
  results for Kew, and it is also a necessary inference from the
  differences obtained by Sabine's method between east and west or + and
  - disturbances, that there is present during disturbances some
  influence which affects the diurnal inequality in a regular systematic
  way, tending to make the value of the element higher during some hours
  and lower during others than it is on days relatively free from
  disturbance. At Kew the consequence is a notable increase in the range
  of the regular diurnal inequality on disturbed days; but whether this
  is the general rule or merely a local peculiarity is a subject for
  further research.

  § 35. There are still other ways of attacking the problem of
  disturbances. W. Ellis[27] made a complete list of disturbed days at
  Greenwich from 1848 onwards, arranging them in classes according to
  the amplitude of the disturbance shown on the curves. Of the 18,000
  days which he considered, Ellis regarded 2,119, or only about 12%, as
  undisturbed. On 11,898 days, or 66%, the disturbance movement in
  declination was under 10´; on 3614, or 20%, the disturbance, though
  exceeding 10´, was under 30´; on 294 days it lay between 30´ and 60´;
  while on 75 days it exceeded 60´. Taking each class of disturbances
  separately, Ellis found, except in the case of his "minor"
  disturbances--those under 10´--a distinct double annual period, with
  maxima towards the equinoxes. Subsequently C. W. Maunder,[38] making
  use of these same data, and of subsequent data up to 1902, put at his
  disposal by Ellis, came to similar conclusions. Taking all the days
  with disturbances of declination over 10´, and dealing with 15-day
  periods, he found the maxima of frequency to occur the one a little
  before the spring equinox, the other apparently after the autumnal
  equinox; the two minima were found to occur early in June and in
  January. When the year is divided into three seasons--winter (November
  to February), summer (May to August), and equinox--Maunder's figures
  lead to the results assigned to Greenwich disturbed days in Table
  XXXVI. The frequency in winter, it will be noticed, though less than
  at equinox, is considerably greater than in summer. This greater
  frequency in winter is only slightly apparent in the disturbances over
  60´, but their number is so small that this may be accidental. The
  next figures in Table XXXVI. relate to highly disturbed days at Kew.
  The larger relative frequency at Kew in winter as compared to summer
  probably indicates no real difference from Greenwich, but is simply a
  matter of definition. The chief criterion at Kew for classifying the
  days was not so much the mere amplitude of the largest movement, as
  the general character of the day's curve and its departure from the
  normal form. The data in Table XXXVI. as to magnetic storms at
  Greenwich are based on the lists given by Maunder[39] in the _Monthly
  Notices_, R.A.S. A storm may last for any time from a few hours to
  several days, and during part of its duration the disturbance may not
  be very large; thus it does not necessarily follow that the
  frequencies of magnetic storms and of disturbed days will follow the
  same laws. The table shows, however, that so far as Greenwich is
  concerned the annual variations in the two cases are closely alike. In
  addition to mean data for the whole 56 years, 1848 to 1903, Table
  XXXVI. contains separate data for the 14 years of that period which
  represented the highest sun-spot frequency, and the 15 years which
  represented lowest sun-spot frequency. It will be seen that relatively
  considered the seasonal frequencies of disturbance are more nearly
  equal in the years of many than in those of few sun-spots. Storms are
  more numerous as a whole in the years of many sun-spots, and this
  preponderance is especially true of storms of the largest size. This
  requires to be borne in mind in any comparisons between larger and
  smaller storms selected promiscuously from a long period. An unduly
  large proportion of the larger storms will probably come from years of
  large sun-spot frequency, and there is thus a risk of assigning to
  differences between the laws obeyed by large and small storms
  phenomena that are due in whole or in part to differences between the
  laws followed in years of many and of few sun-spots. The last data in
  Table XXXVI. are based on statistics for Batavia given by W. van
  Bemmelen,[40] who considers separately the storms which commence
  suddenly and those which do not. These sudden movements are recorded
  over large areas, sometimes probably all over the earth, if not
  absolutely simultaneously, at least too nearly so for differences in
  the time of occurrence to be shown by ordinary magnetographs. It is
  ordinarily supposed that these sudden movements, and the storms to
  which they serve as precursors, arise from some source extraneous to
  the earth, and that the commencement of the movement intimates the
  arrival, probably in the upper atmosphere, of some form of energy
  transmitted through space. In the storms which commence gradually the
  existence of a source external to the earth is not so prominently
  suggested, and it has been sometimes supposed that there is a
  fundamental difference between the two classes of storms. Table XXXVI.
  shows, however, no certain difference in the annual variation at
  Batavia. At the same time, this possesses much less significance than
  it would have if Batavia were a station like Greenwich, where the
  annual variation in magnetic storms is conspicuous.

  Besides the annual period, there seems to be also a well-marked
  diurnal period in magnetic disturbances. This is apparent in Tables
  XXXVII. and XXXVIII., which contain some statistics for Batavia due to
  van Bemmelen, and some for Greenwich derived from the data in
  Maunder's papers referred to above. Table XXXVII. gives the relative
  frequency of occurrence for two hour intervals, starting with
  midnight, treating separately the storms of gradual (g) and sudden (s)
  commencement. In Table XXXVIII. the day is subdivided into three equal
  parts. Batavia and Greenwich agree in showing maximum frequency of
  beginnings about the time of minimum frequency of endings and
  conversely; but the hours at which the respective maxima and minima
  occur at the two places differ rather notably.

  § 36. There are peculiarities in the sudden movements ushering in
  magnetic storms which deserve fuller mention. According to van
  Bemmelen the impulse consists usually at some stations of a sudden
  slight jerk of the magnet in one direction, followed by a larger
  decided movement in the opposite direction, the former being often
  indistinctly shown. Often we have at the very commencement but a faint
  outline, and thereafter a continuous movement which is only sometimes
  distinctly indicated, resulting after some minutes in the displacement
  of the trace by a finite amount from the position it occupied on the
  paper before the disturbance began. This may mean, as van Bemmelen
  supposes, a small preliminary movement in the opposite direction to
  the clearly shown displacement; but it may only mean that the magnet
  is initially set in vibration, swinging on both sides of the position
  of equilibrium, the real displacement of the equilibrium position
  being all the time in the direction of the displacement apparent after
  a few minutes. To prevent misconception, the direction of the
  displacement apparent after a few minutes has been termed the
  direction of the first _decided_ movement in Table XXXIX., which
  contains some data as to the direction given by Ellis[41] and van
  Bemmelen.[40] The + sign means an increase, the - sign a decrease of
  the element. The sign is not invariably the same, it will be
  understood, but there are in all cases a marked preponderance of
  changes in the direction shown in the table. The fact that all the
  stations indicated an increase in horizontal force is of special
  significance.

  TABLE XXXVI.--Disturbances, and their Annual Distribution.

    +-------------------------------+-------+---------------------------+
    |                               | Total |        Percentages.       |
    |                               |Number.+--------+---------+--------+
    |                               |       | Winter.| Equinox.| Summer.|
    +-------------------------------+-------+--------+---------+--------+
    | Greenwich disturbed days,     |       |        |         |        |
    |   all, 1848-1902              | 4,214 |  33.9  |   39.2  |  26.9  |
    | Greenwich disturbed days,     |       |        |         |        |
    |   range 10´ to 30´, 1848-1902 | 3,830 |  33.9  |   39.0  |  27.1  |
    | Greenwich disturbed days,     |       |        |         |        |
    |   range 30´ to 60´, 1848-1902 |   307 |  34.5  |   41.0  |  24.4  |
    | Greenwich disturbed days,     |       |        |         |        |
    |   range over 60´, 1848-1902   |    77 |  29.9  |   41.6  |  28.6  |
    | Kew highly disturbed days,    |       |        |         |        |
    |   1890-1900                   |   209 |  38.3  |   41.6  |  20.1  |
    | Greenwich magnetic storms,    |       |        |         |        |
    |   all, 1848-1903              |   726 |  32.1  |   42.3  |  25.6  |
    | Greenwich magnetic storms,    |       |        |         |        |
    |   range 20´ to 30´, 1848-1903 |   392 |  30.1  |   43.6  |  26.3  |
    | Greenwich magnetic storms,    |       |        |         |        |
    |   range over 30´, 1848-1903   |   334 |  34.4  |   40.7  |  24.9  |
    | Greenwich magnetic storms,    |       |        |         |        |
    |   all, 14 years of S. max.    |   258 |  35.3  |   38.0  |  26.7  |
    | Greenwich magnetic storms,    |       |        |         |        |
    |   all, 15 years of S. min.    |   127 |  28.4  |   48.0  |  23.6  |
    | Batavia magnetic storms,      |       |        |         |        |
    |   all, 1883-1899              | 1,008 |  32.9  |   34.9  |  32.2  |
    | Batavia magnetic storms of    |       |        |         |        |
    |   gradual commencement        |   679 |  32.4  |   34.8  |  32.8  |
    | Batavia magnetic storms of    |       |        |         |        |
    |   sudden commencement         |   329 |  33.7  |   35.3  |  31.0  |
    +-------------------------------+-------+--------+---------+--------+

  TABLE XXXVII.--Batavia Magnetic Storms, Diurnal Distribution
  (percentages).

    +--------------+----+----+----+----+----+----+----+----+----+----+----+----+
    |    Hour.     |  0 |  2 |  4 |  6 |  8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |
    +--------------+----+----+----+----+----+----+----+----+----+----+----+----+
    | Beginning /g |  5 |  5 |  5 |  6 | 20 | 16 |  7 |  5 |  6 |  9 |  8 |  8 |
    |           \s |  7 |  5 |  7 | 10 | 10 | 11 | 10 |  8 |  8 |  9 |  8 |  7 |
    | Maximum   /g | 12 | 10 |  6 |  5 |  4 |  9 |  9 |  6 |  6 |  6 | 12 | 15 |
    |           \s | 14 |  7 |  5 |  2 |  2 |  9 |  9 |  5 |  8 | 10 | 13 | 16 |
    | End      all | 15 | 16 | 19 | 13 |  5 |  3 |  6 |  5 |  4 |  5 |  4 |  5 |
    +--------------+----+----+----+----+----+----+----+----+----+----+----+----+

  TABLE XXXVIII.--Greenwich Magnetic Storms, Diurnal Distribution.

    +------------------------+--------+-------+-----------------------------+
    |                        |        |       |         Percentages.        |
    |         Epoch.         | Class. | Total +---------+---------+---------+
    |                        |        |Number.| 1-8 p.m.| 9 p.m.- | 5 a.m.- |
    |                        |        |       |         |  4 a.m. |  noon.  |
    +------------------------+--------+-------+---------+---------+---------+
    |            / 1848-1903 |   all  |  721  |   60.1  |   21.9  |   18.0  |
    | Beginning <  1882-1903 |    "   |  276  |   58.0  |   18.8  |   23.2  |
    |            \   "    "  | sudden |   77  |   45.4  |   27.3  |   27.3  |
    |                        |        |       |         |         |         |
    |            / 1848-1903 |   all  |  720  |    9.4  |   44.6  |   46.0  |
    | End       <  1882-1903 |    "   |  276  |    7.2  |   41.7  |   51.1  |
    |            \   "    "  | sudden |   77  |   11.7  |   35.1  |   53.2  |
    +------------------------+--------+-------+---------+---------+---------+

  § 37. That large magnetic disturbances occur simultaneously over large
  areas was known in the time of Gauss, on whose initiative observations
  were taken at 5-minute intervals at a number of stations on
  prearranged _term days_. During March 1879 and August 1880 some large
  magnetic storms occurred, and the magnetic curves showing these at a
  number of stations fitted with Kew pattern magnetographs were compared
  by W. G. Adams.[42] He found the more characteristic movements to be,
  so far as could be judged, simultaneous at all the stations. At
  comparatively near stations such as Stonyhurst and Kew, or Coimbra and
  Lisbon, the curves were in general almost duplicates. At Kew and St
  Petersburg there were usually considerable differences in detail, and
  the movements were occasionally in opposite directions. The
  differences between Toronto, Melbourne or Zi-ka-wei and the European
  stations were still more pronounced. In 1896, on the initiative of M.
  Eschenhagen,[43] eye observations of declination and horizontal force
  were taken at 5-second intervals during prearranged hours at Batavia,
  Manila, Melbourne and nine European stations. The data from one of
  these occasions when appreciable disturbance prevailed were published
  by Eschenhagen, and were subsequently analysed by Ad. Schmidt.[44]
  Taking the stations in western Europe, Schmidt drew several series of
  lines, each series representing the disturbing forces at one instant
  of time as deduced from the departure of the elements at the several
  stations from their undisturbed value. The lines answering to any one
  instant had a general sameness of direction with more or less
  divergence or convergence, but their general trend varied in a way
  which suggested to Schmidt the passage of a species of vortex with
  large but finite velocity.

  TABLE XXXIX.--Direction of First Decided Movement.

    +-----------+-------------+------------------+----------------+
    |   Place.  | Declination.| Horizontal Force.| Vertical Force.|
    +-----------+-------------+------------------+----------------+
    | Pavlovsk  |    West     |         +        |       +        |
    | Potsdam   |    West     |         +        |       -        |
    | Greenwich |    West     |         +        |       +        |
    | Zi-ka-wei |    East     |         +        |       -        |
    | Kolaba    |    East     |         +        |       -        |
    | Batavia   |    West     |         +        |       -        |
    | Mauritius |    East     |         +        |       +        |
    | Cape Horn |    West     |         +        |       -        |
    +-----------+-------------+------------------+----------------+

  The conclusion that magnetic disturbances tend to follow one another
  at nearly equal intervals of time has been reached by several
  independent observers. J. A. Broun[45] pronounced for a period of
  about 26 days, and expressed a belief that a certain zone, or zones,
  of the sun's surface might exert a prepotent influence on the earth's
  magnetism during several solar rotations. Very similar views were
  advanced in 1904 by E. W. Maunder,[39] who was wholly unaware of
  Broun's work. Maunder concluded that the period was 27.28 days,
  coinciding with the sun's rotation period relative to an observer on
  the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he
  found the interval between the commencement of successive storms to
  approach closely to the above period in a considerably larger number
  of instances than one would have expected from mere chance. He found
  several successions of three or four storms, and in one instance of as
  many as six storms, showing his interval. In a later paper Maunder
  reached similar results for magnetic storms at Greenwich from 1848 to
  1881. Somewhat earlier than Maunder, Arthur Harvey[46] deduced a
  period of 27.246 days from a consideration of magnetic disturbances at
  Toronto. A. Schuster,[47] examining Maunder's data mathematically,
  concluded that they afforded rather strong evidence of a period of
  about ½ (27.28) or 13.6 days. Maunder regarded his results as
  _demonstrating_ that magnetic disturbances originate in the sun. He
  regarded the solar action as arising from active areas of limited
  extent on the sun's surface, and as propagated along narrow, well
  defined streams. The active areas he believed to be also the seats of
  the formation of sun-spots, but believed that their activity might
  precede and outlive the visible existence of the sun-spot.

  Maunder did not discuss the physical nature of the phenomenon, but his
  views are at least analogous to those propounded somewhat earlier by
  Svante Arrhenius,[48] who suggested that small negatively charged
  particles are driven from the sun by the repulsion of light and reach
  the earth's atmosphere, setting up electrical currents, manifest in
  aurora and magnetic disturbances. Arrhenius's calculations, for the
  size of particle which he regarded as most probable, make the time of
  transmission to the earth slightly under two days. Amongst other
  theories which ascribe magnetic storms to direct solar action may be
  mentioned that of Kr. Birkeland,[49] who believes the vehicle to be
  cathode rays. Ch. Nordmann[50] similarly has suggested Röntgen rays.
  Supposing the sun the ultimate source, it would be easier to
  discriminate between the theories if the exact time of the originating
  occurrence could be fixed. For instance, a disturbance that is
  propagated with the velocity of light may be due to Röntgen rays, but
  not to Arrhenius's particles. In support of his theory, Nordmann
  mentions several cases when conspicuous visual phenomena on the sun
  have synchronized with magnetic movements on the earth--the best known
  instance being the apparent coincidence in time of a magnetic
  disturbance at Kew on the 1st of September 1859 with a remarkable
  solar outburst seen by R. C. Carrington. Presumably any electrical
  phenomenon on the sun will set up waves in the aether, so transmission
  of electric and magnetic disturbances from the sun to the earth with
  the velocity of light is a certainty rather than a hypothesis; but it
  by no means follows that the energy thus transmitted can give rise to
  sensible magnetic disturbances. Also, when considering Nordmann's
  coincidences, it must be remembered that magnetic movements are so
  numerous that it would be singular if no apparent coincidences had
  been noticed. Another consideration is that the movements shown by
  ordinary magnetographs are seldom very rapid. During some storms,
  especially those accompanied by unusually bright and rapidly varying
  auroral displays, large to and fro movements follow one another in
  close succession, the changes being sometimes too quick to be
  registered distinctly on the photographic paper. This, however, is
  exceptional, even in polar regions where disturbances are largest and
  most numerous. As a rule, even when the change in the direction of
  movement in the declination needle seems quite sudden, the movement in
  one direction usually lasts for several minutes, often for 10, 15 or
  30 minutes. Thus the cause to which magnetic disturbances are due
  seems in many cases to be persistent in one direction for a
  considerable time.

  § 38. Attempts have been made to discriminate between the theories as
  to magnetic storms by a critical examination of the phenomena. A
  general connexion between sun-spot frequency and the amplitude of
  magnetic movements, regular and irregular, is generally admitted. If
  it is a case of cause and effect, and the interval between the solar
  and terrestrial phenomena does not exceed a few hours, then there
  should be a sensible connexion between corresponding daily values of
  the sun-spot frequency and the magnetic range. Even if only some
  sun-spots are effective, we should expect when we select from a series
  of years two groups of days, the one containing the days of most
  sun-spots, the other the days of least, that a prominent difference
  will exist between the mean values of the absolute daily magnetic
  ranges for the two groups. Conversely, if we take out the days of
  small and the days of large magnetic range, or the days that are
  conspicuously quiet and those that are highly disturbed, we should
  expect a prominent difference between the corresponding mean sun-spot
  areas. An application of this principle was made by Chree[23] to the
  five quiet days a month selected by the astronomer royal between 1890
  and 1900. These days are very quiet relative to the average day and
  possess a much smaller absolute range. One would thus have expected on
  Birkeland's or Nordmann's theory the mean sun-spot frequency derived
  from Wolfer's provisional values for these days to be much below his
  mean value, 41.22, for the eleven years. It proved, however, to be
  41.28. This practical identity was as visible in 1892 to 1895, the
  years of sun-spot maximum, as it was in the years of sun-spot minimum.
  Use was next made of the Greenwich _projected_ sun-spot areas, which
  are the result of exact measurement. The days of each month were
  divided into three groups, the first and third--each normally of ten
  days--containing respectively the days of largest and the days of
  least sun-spot area. The mean sun-spot area from group 1 was on the
  average about five times that for group 3. It was then investigated
  how the astronomer royal's quiet days from 1890 to 1900, and how the
  most disturbed days of the period selected from the Kew[24] magnetic
  records, distributed themselves among the three groups of days.
  Nineteen months were excluded, as containing more than ten days with
  no sun-spots. The remaining 113 months contained 565 quiet and 191
  highly disturbed days, whose distribution was as follows:

    +----------------+---------+---------+---------+
    |                | Group 1.| Group 2.| Group 3.|
    |                +---------+---------+---------+
    | Quiet days     |   179   |   195   |   191   |
    | Disturbed days |    68   |    65   |    58   |
    +----------------+---------+---------+---------+

  The group of days of largest sun-spot area thus contained slightly
  under their share of quiet days and slightly over their share of
  disturbed days. The differences, however, are not large, and in three
  years, viz. 1895, 1897 and 1899, the largest number of disturbed days
  actually occurred in group 3, while in 1895, 1896 and 1899 there were
  fewer quiet days in group 3 than in group 1. Taking the same
  distribution of days, the mean value of the absolute daily range of
  declination at Kew was calculated for the group 1 and the group 3 days
  of each month. The mean range from the group 1 days was the larger in
  57% of the individual months as against 43% in which it was the
  smaller. When the days of each month were divided into groups
  according to the absolute declination range at Kew, the mean sun-spot
  area for the group 1 days (those of largest range) exceeded that for
  the group 3 days (those of least range) in 55% of the individual
  months, as against 45% of cases in which it was the smaller.

  Taking next the five days of largest and the five days of least range
  in each month, sun-spot areas were got out not merely for these days
  themselves, but also for the next subsequent day and the four
  immediately preceding days in each case. On Arrhenius's theory we
  should expect the magnetic range to vary with the sun-spot area, not
  on the actual day but two days previously. The following figures give
  the percentage excess or deficiency of the mean sun-spot area for the
  respective groups of days, relative to the average value for the whole
  epoch dealt with. n denotes the day to which the magnetic range
  belongs, n + 1 the day after, n - 1 the day before, and so on.
  Results are given for 1894 and 1895, the years which were on the whole
  the most favourable and the least favourable for Arrhenius's
  hypothesis, as well as for the whole eleven years.

  TABLE XL.

    +-------------------------+-------+-------+-------+-------+--------+-------+
    |           Day.          | n - 4 | n - 3 | n - 2 | n - 1 |   n    | n + 1 |
    +-------------------------+-------+-------+-------+-------+--------+-------+
    | Five days of \  1894    |  +12  |  + 9  |  +11  |  +12  |  +11   |  + 6  |
    | largest range > 1895    |  -16  |  -17  |  -15  |  -12  |  -11   |  -10  |
    |              /  11 yrs. |  + 9  |  + 8  |  + 8  |  + 7  |  + 5   |  + 0.5|
    | Five days of \  1894    |  -15  |  -17  |  -19  |  -21  |  -21   |  -19  |
    | least range   > 1895    |  +17  |  +10  |  + 1  |  - 2  |  - 2   |  - 4  |
    |              /  11 yrs. |  - 4  |  - 4  |  - 7  |  - 7  |  - 7   |  - 6  |
    +-------------------------+-------+-------+-------+-------+--------+-------+

  Taking the 11-year-means we have the sun-spot area practically normal
  on the day subsequent to the representative day of large magnetic
  range, but sensibly above its mean on that day and still more so on
  the four previous days. This suggests an emission from the sun taking
  a highly variable time to travel to the earth. The 11-year mean data
  for the five days of least range seem at first sight to point to the
  same conclusion, but the fact that the deficiency in sun-spot area is
  practically as prominent on the day after the representative day of
  small magnetic range as on that day itself, or the previous days,
  shows that the phenomenon is probably a secondary one. On the whole,
  taking into account the extraordinary differences between the results
  from individual years, we seem unable to come to any very positive
  conclusion, except that in the present state of our knowledge little
  if any clue is afforded by the extent of the sun's spotted area on any
  particular day as to the magnetic conditions on the earth on that or
  any individual subsequent day. Possibly some more definite information
  might be extracted by considering the extent of spotted area on
  different zones of the sun. On theories such as those of Arrhenius or
  Maunder, effective bombardment of the earth would be more or less
  confined to spotted areas in the zones nearest the centre of the
  visible hemisphere, whilst all spots on this hemisphere contribute to
  the total spotted area. Still the _projected_ area of a spot rapidly
  diminishes as it approaches the edge of the visible hemisphere, i.e.
  as it recedes from the most effective position, so that the method
  employed above gives a preponderating weight to the central zones. One
  rather noteworthy feature in Table XL. is the tendency to a sequence
  in the figures in any one row. This seems to be due, at least in large
  part, to the fact that days of large and days of small sun-spot area
  tend to occur in groups. The same is true to a certain extent of days
  of large and days of small magnetic range, but it is unusual for the
  range to be much above the average for more than 3 or 4 successive
  days.


    Pulsations.

  § 39. The records from ordinary magnetographs, even when run at the
  usual rate and with normal sensitiveness, not infrequently show a
  repetition of regular or nearly regular small rhythmic movements,
  lasting sometimes for hours. The amplitude and period on different
  occasions both vary widely. Periods of 2 to 4 minutes are the most
  common. W. van Bemmelen[51] has made a minute examination of these
  movements from several years' traces at Batavia, comparing the results
  with corresponding statistics sent him from Zi-ka-wei and Kew. Table
  XLI. shows the diurnal variation in the frequency of occurrence of
  these small movements--called _pulsations_ by van Bemmelen--at these
  three stations. The Batavia results are from the years 1885 and 1892
  to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the
  years 1897, 1898 and 1900, as given by van Bemmelen, while (ii)
  answers to the period 1900-1905, as given in the Zi-ka-wei _Bulletin_
  for 1905. The Kew data are for 1897. The results are expressed as
  percentages of the total for the 24 hours. There is a remarkable
  contrast between Batavia and Zi-ka-wei on the one hand and Kew on the
  other, pulsations being much more numerous by night than by day at the
  two former stations, whereas at Kew the exact reverse holds. Van
  Bemmelen decided that almost all the occasions of pulsation at
  Zi-ka-wei were also occasions of pulsations at Batavia. The hours of
  commencement at the two places usually differed a little, occasionally
  by as much as 20 minutes; but this he ascribed to the fact that the
  earliest oscillations were too small at one or other of the stations
  to be visible on the trace. Remarkable coincidence between pulsations
  at Potsdam and in the north of Norway has been noted by Kr.
  Birkeland.[49]

  With magnetographs of greater sensitiveness and more open time scales,
  waves of shorter period become visible. In 1882 F. Kohlrausch[52]
  detected waves with a period of about 12 seconds. Eschenhagen[53]
  observed a great variety of short period waves, 30 seconds being
  amongst the most common. Some of the records he obtained suggest the
  superposition of regular sine waves of different periods. Employing a
  very sensitive galvanometer to record changes of magnetic induction
  through a coil traversed by the earth's lines of force, H. Ebert[54]
  has observed vibrations whose periods are but a small fraction of a
  second. The observations of Kohlrausch and Eschenhagen preceded the
  recent great development of applications of electrical power, while
  longer period waves are shown in the Kew curves of 50 years ago, so
  that the existence of natural waves with periods of from a few seconds
  up to several minutes can hardly be doubted. Whether the much shorter
  period waves of Ebert are also natural is more open to doubt, as it is
  becoming exceedingly difficult in civilized countries to escape
  artificial disturbances.

  TABLE XLI.--Diurnal Distribution of Pulsations.

    +---------------+-----+-----+-----+--------+--------+-----+-----+------+
    | Hours.        | 0-3.| 3-6.| 6-9.| 9-Noon.| Noon-3.| 3-6.| 6-9.| 9-12.|
    +---------------+-----+-----+-----+--------+--------+-----+-----+------+
    | Batavia       |  28 |  9  |  2  |    6   |    8   |  6  |  13 |  28  |
    | Zi-ka-wei (i) |  33 |  5  |  2  |    7   |    4   |  4  |  10 |  35  |
    |    "     (ii) |  23 |  6  |  8  |   11   |    7   |  5  |  14 |  26  |
    | Kew           |   4 |  8  | 19  |   14   |   22   | 18  |  11 |   4  |
    +---------------+-----+-----+-----+--------+--------+-----+-----+------+


    Lunar Influence.

  § 40. The fact that the moon exerts a small but sensible effect on the
  earth's magnetism seems to have been first discovered in 1841 by C.
  Kreil. Subsequently Sabine[55] investigated the nature of the lunar
  diurnal variation in declination at Kew, Toronto, Pekin, St Helena,
  Cape of Good Hope and Hobart. The data in Table XLII. are mostly due
  to Sabine. They represent the mean lunar diurnal inequality in
  declination for the whole year. The unit employed is 0´.001, and as in
  our previous tables + denotes movement to the _west_. By "mean
  departure" is meant the arithmetic mean of the 24 hourly departures
  from the mean value for the lunar day; the range is the difference
  between the algebraically greatest and least of the hourly values. Not
  infrequently the mean departure gives the better idea of the
  importance of an inequality, especially when as in the present case
  two maxima and minima occur in the day. This double daily period is
  unusually prominent in the case of the lunar diurnal inequality, and
  is seen in the other elements as well as in the declination.

  TABLE XLII.--Lunar Diurnal Inequality of Declination (unit 0´.001).

    +----------+-----------+-----------+-----------+-----------+-----------+-----------+
    |  Lunar   |    Kew.   |  Toronto. |  Batavia. | St Helena.|    Cape.  |   Hobart. |
    |   Hour.  | 1858-1862.| 1843-1848.| 1883-1899.| 1843-1847.| 1842-1846.| 1841-1848.|
    +----------+-----------+-----------+-----------+-----------+-----------+-----------+
    |    0     |   +103    |   +315    |    -70    |   - 43    |   -148    |   - 98    |
    |    1     |   +160    |   +275    |    -63    |   -  5    |   -107    |   -138    |
    |    2     |   +140    |   +158    |    -39    |   + 37    |   - 35    |   -142    |
    |    3     |   + 33    |   +  2    |    - 8    |   + 70    |   + 43    |   -107    |
    |    4     |   + 10    |   -153    |    +38    |   + 85    |   +108    |   - 45    |
    |    5     |   - 67    |   -265    |    +63    |   + 77    |   +140    |   + 27    |
    |    6     |   -150    |   -302    |    +87    |   + 48    |   +132    |   + 88    |
    |    7     |   -188    |   -255    |    +77    |   +  5    |   + 82    |   +122    |
    |    8     |   -160    |   -137    |    +40    |   - 43    |   +  5    |   +120    |
    |    9     |   - 78    |   +  7    |    - 4    |   - 82    |   - 78    |   + 82    |
    |    10    |   +  2    |   +178    |    -45    |   -102    |   -143    |   + 17    |
    |    11    |   + 92    |   +288    |    -80    |   - 98    |   -177    |   - 57    |
    |    12    |   +160    |   +323    |    -87    |   - 73    |   -165    |   -120    |
    |    13    |   +188    |   +272    |    -68    |   - 32    |   -112    |   -152    |
    |    14    |   +158    |   +148    |    -43    |   + 13    |   - 30    |   -147    |
    |    15    |   + 90    |   - 17    |    - 8    |   + 52    |   + 58    |   -105    |
    |    16    |   + 10    |   -180    |    +30    |   + 73    |   +132    |   - 35    |
    |    17    |   - 85    |   -297    |    +62    |   + 73    |   +172    |   + 45    |
    |    18    |   -142    |   -337    |    +72    |   + 52    |   +168    |   +112    |
    |    19    |   -163    |   -290    |    +68    |   + 17    |   +122    |   +152    |
    |    20    |   -147    |   -170    |    +52    |   - 25    |   + 45    |   +152    |
    |    21    |   -123    |   -  7    |    + 8    |   - 58    |   - 40    |   +113    |
    |    22    |   - 40    |   +155    |    -28    |   - 73    |   -112    |   + 47    |
    |    23    |   + 27    |   +265    |    -56    |   - 68    |   -153    |   - 30    |
    +----------+-----------+-----------+-----------+-----------+-----------+-----------+
    | Mean De-\|           |           |           |           |           |           |
    | parture /|    105    |    200    |     50    |     54    |    104    |     93    |
    +----------+-----------+-----------+-----------+-----------+-----------+-----------+
    | Range    |    376    |    660    |    174    |    187    |    349    |    304    |
    +----------+-----------+-----------+-----------+-----------+-----------+-----------+

  Lunar action has been specially studied in connexion with observations
  from India and Java. Broun[56] at Trivandrum and C. Chambers[57] at
  Kolaba investigated lunar action from a variety of aspects. At Batavia
  van der Stok[58] and more recently S. Figee[59] have carried out
  investigations involving an enormous amount of computation. Table
  XLIII. gives a summary of Figee's results for the mean lunar diurnal
  inequality at Batavia, for the two half-yearly periods April to
  September (Winter or W.), and October to March (S.). The + sign
  denotes movement to the west in the case of declination, but numerical
  increase in the case of the other elements. In the case of H and T
  (total force) the results for the two seasons present comparatively
  small differences, but in the case of D, I and V the amplitude and
  phase both differ widely. Consequently a mean lunar diurnal variation
  derived from all the months of the year gives at Batavia, and
  presumably at other tropical stations, an inadequate idea of the
  importance of the lunar influence. In January Figee finds for the
  range of the lunar diurnal inequality 0´.62 in D, 3.1[gamma] in H and
  3.5[gamma] in V, whereas the corresponding ranges in June are only
  0´.13, 1.1[gamma] and 2.2[gamma] respectively. The difference between
  summer and winter is essentially due to solar action, thus the lunar
  influence on terrestrial magnetism is clearly a somewhat complex
  phenomenon. From a study of Trivandrum data, Broun concluded that the
  action of the moon is largely dependent on the solar hour at the time,
  being on the average about twice as great for a day hour as for a
  night hour. Figee's investigations at Batavia point to a similar
  conclusion. Following a method suggested by Van der Stok, Figee
  arrives at a numerical estimate of the "lunar activity" for each hour
  of the solar day, expressed in terms of that at noon taken as 100. In
  summer, for instance, in the case of D he finds the "activity" varying
  from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in
  the case of H are 139 at 10 a.m. and 54 at 6 a.m.

  TABLE XLIII.--Lunar Diurnal Inequality at Batavia in Winter and Summer.

    +----------+---------------+----------------+----------------+----------------+----------------+
    |          |  Declination  | Inclination, S.|    H. (unit    |    V. (unit    |    T. (unit    |
    |          | (unit 0´.001).| (unit 0´.001). |  0.01[gamma]). |  0.01[gamma]). |  0.01[gamma]). |
    +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+
    |   Lunar  |       |       |        |       |        |       |        |       |        |       |
    |   Hour.  |   W.  |   S.  |    W.  |   S.  |    W.  |   S.  |    W.  |   S.  |    W.  |   S.  |
    +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+
    |     0    |  +30  | -170  |   - 1  |  +25  |  -15   | - 56  |  - 9   |  + 4  |  - 17  |  -47  |
    |     1    |  +21  | -147  |   -23  |  +49  |  -40   | - 87  |  -54   |  +20  |  - 61  |  -67  |
    |     2    |  + 5  | - 83  |   -49  |  +69  |  -25   | -107  |  -82   |  +37  |  - 62  |  -76  |
    |     3    |  - 5  | - 12  |   -51  |  +47  |  -21   | - 76  |  -83   |  +24  |  - 59  |  -55  |
    |     4    |  + 1  | + 76  |   -37  |  +43  |  -13   | - 59  |  -58   |  +18  |  - 39  |  -38  |
    |     5    |  - 8  | +134  |   -23  |  +12  |  +10   | -  9  |  -27   |  +11  |  -  4  |  - 3  |
    |     6    |  - 7  | +181  |   - 2  |  -21  |  +21   | + 43  |  + 9   |  - 6  |  + 23  |  +35  |
    |     7    |  -10  | +164  |   +30  |  -12  |  +23   | + 45  |  +55   |  + 8  |  + 47  |  +43  |
    |     8    |  - 7  | + 86  |   +36  |  -21  |  +38   | + 52  |  +71   |  - 1  |  + 68  |  +45  |
    |     9    |  - 8  |    0  |   +28  |  -23  |  +46   | + 30  |  +64   |  -16  |  + 71  |  +19  |
    |    10    |  - 5  | - 85  |   +34  |  -20  |  +13   | + 13  |  +54   |  -21  |  + 38  |  + 1  |
    |    11    |  -15  | -144  |   +27  |  -11  |  -12   | -  6  |  +31   |  -19  |  +  5  |  -15  |
    |    12    |  - 9  | -164  |   +19  |  - 5  |  -47   | - 23  |    0   |  -19  |  - 41  |  -29  |
    |    13    |  + 1  | -136  |   - 3  |  +17  |  -59   | - 46  |  -36   |  - 2  |  - 69  |  -41  |
    |    14    |  - 7  | - 79  |   -13  |  +27  |  -66   | - 44  |  -55   |  +14  |  - 84  |  -32  |
    |    15    |  - 8  | -  8  |   -32  |  +25  |  -53   | - 37  |  -74   |  +14  |  - 82  |  -26  |
    |    16    |  -12  | + 72  |   -37  |  +25  |  -34   | - 17  |  -70   |  +26  |  - 64  |  - 2  |
    |    17    |  -13  | +137  |   -33  |  + 4  |  - 1   | + 28  |  -47   |  +21  |  - 24  |  +35  |
    |    18    |  -21  | +165  |   - 2  |  -10  |  +20   | + 47  |  + 8   |  +12  |  + 21  |  +47  |
    |    19    |  -12  | +147  |   +21  |  -42  |  +44   | + 81  |  +53   |  -14  |  + 64  |  +64  |
    |    20    |  +10  | + 95  |   +21  |  -62  |  +75   | +107  |  +71   |  -28  |  +100  |  +80  |
    |    21    |  +13  | +  4  |   +26  |  -70  |  +65   | + 98  |  +72   |  -44  |  + 92  |  +65  |
    |    22    |  +25  | - 82  |   +35  |  -41  |  +35   | + 35  |  +68   |  -38  |  + 64  |  +12  |
    |    23    |  +36  | -147  |   +34  |  - 4  |  - 7   | - 14  |  +44   |  -13  |  + 15  |  -19  |
    +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+
    | Mean De-\|       |       |        |       |        |       |        |       |        |       |
    | parture /|  12   |  150  |    26  |   29  |   33   |   48  |   50   |   18  |    51  |   37  |
    +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+
    | Range    |  57   |  351  |    87  |  139  |  141   |  214  |  155   |   81  |   184  |  156  |
    +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+


  The question whether lunar influence increases with sun-spot frequency
  is obviously of considerable theoretical interest. Balfour Stewart in
  the 9th edition of this encyclopaedia gave some data indicating an
  appreciably enhanced lunar influence at Trivandrum during years of
  sun-spot maximum, but he hesitated to accept the result as finally
  proved. Figee recently investigated this point at Batavia, but with
  inconclusive results. Attempts have also been made to ascertain how
  lunar influence depends on the moon's declination and phase, and on
  her distance from the earth. The difficulty in these investigations is
  that we are dealing with a small effect, and a very long series of
  data would be required satisfactorily to eliminate other periodic
  influences.


    Planetary Influence.

  § 41. From an analysis of seventeen years data at St Petersburg and
  Pavlovsk, Leyst[60] concluded that all the principal planets sensibly
  influence the earth's magnetism. According to his figures, all the
  planets except Mercury--whose influence he found opposite to that of
  the others--when nearest the earth tended to deflect the declination
  magnet at St Petersburg to the west, and also increased the range of
  the diurnal inequality of declination, the latter effect being the
  more conspicuous. Schuster,[61] who has considered the evidence
  advanced by Leyst from the mathematical standpoint, considers it to be
  inconclusive.


    Magnetic Surveys.

  § 42. The best way of carrying out a magnetic survey depends on where
  it has to be made and on the object in view. The object that probably
  still comes first in importance is a knowledge of the declination, of
  sufficient accuracy for navigation in all navigable waters. One might
  thus infer that magnetic surveys consist mainly of observations at
  sea. This cannot however be said to be true of the past, whatever it
  may be of the future, and this for several reasons. Observations at
  sea entail the use of a ship, specially constructed so as to be free
  from disturbing influence, and so are inherently costly; they are
  also apt to be of inferior accuracy. It might be possible in quiet
  weather, in a large vessel free from vibration, to observe with
  instruments of the highest precision such as a unifilar magnetometer,
  but in the ordinary surveying ship apparatus of less sensitiveness has
  to be employed. The declination is usually determined with some form
  of compass. The other elements most usually found directly at sea are
  the inclination and the total force, the instrument employed being a
  special form of inclinometer, such as the Fox circle, which was
  largely used by Ross in the Antarctic, or in recent years the
  Lloyd-Creak. This latter instrument differs from the ordinary
  dip-circle fitted for total force observations after H. Lloyd's method
  mainly in that the needles rest in pivots instead of on agate edges.
  To overcome friction a projecting pin on the framework is scratched
  with a roughened ivory plate.

  The most notable recent example of observations at sea is afforded by
  the cruises of the surveying ships "Galilee" and "Carnegie" under the
  auspices of the Carnegie Institution of Washington, which includes in
  its magnetic programme a general survey. To see where the ordinary
  land survey assists navigation, let us take the case of a country with
  a long seaboard. If observations were taken every few miles along the
  coast results might be obtained adequate for the ordinary wants of
  coasting steamers, but it would be difficult to infer what the
  declination would be 50 or even 20 miles off shore at any particular
  place. If, however, the land area itself is carefully surveyed, one
  knows the trend of the lines of equal declination, and can usually
  extend them with considerable accuracy many miles out to sea. One also
  can tell what places if any on the coast suffer from local
  disturbances, and thus decide on the necessity of special
  observations. This is by no means the only immediately useful purpose
  which is or may be served by magnetic surveys on land. In Scandinavia
  use has been made of magnetic observations in prospecting for iron
  ore. There are also various geological and geodetic problems to whose
  solution magnetic surveys may afford valuable guidance. Among the most
  important recent surveys may be mentioned those of the British Isles
  by A. Rücker and T. E. Thorpe,[62] of France and Algeria by
  Moureaux,[63] of Italy by Chistoni and Palazzo,[64] of the Netherlands
  by Van Ryckevorsel,[65] of South Sweden by Carlheim Gyllenskiöld,[66]
  of Austria-Hungary by Liznar,[67] of Japan by Tanakadate,[68] of the
  East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A
  survey of the United States has been proceeding for a good many years,
  and many results have appeared in the publications of the U.S. Coast
  and Geodetic Survey, especially Bauer's _Magnetic Tables and Magnetic
  Charts_, 1908. Additions to our knowledge may also be expected from
  surveys of India, Egypt and New Zealand.

  For the satisfactory execution of a land survey, the observers must
  have absolute instruments such as the unifilar magnetometer and dip
  circle, suitable for the accurate determination of the magnetic
  elements, and they must be able to fix the exact positions of the
  spots where observations are taken. If, as usual, the survey occupies
  several years, what is wanted is the value of the elements not at the
  actual time of observation, but at some fixed epoch, possibly some
  years earlier or later. At a magnetic observatory, with standardized
  records, the difference between the values of a magnetic element at
  any two specified instants can be derived from the magnetic curves.
  But at an ordinary survey station, at a distance from an observatory,
  the information is not immediately available. Ordinarily the reduction
  to a fixed epoch is done in at least two stages, a correction being
  applied for secular change, and a second for the departure from the
  mean value for the day due to the regular diurnal inequality and to
  disturbance.

  The reduction to a fixed epoch is at once more easy and more accurate
  if the area surveyed contains, or has close to its borders, a well
  distributed series of magnetic observatories, whose records are
  comparable and trustworthy. Throughout an area of the size of France
  or Germany, the secular change between any two specified dates can
  ordinarily be expressed with sufficient accuracy by a formula of the
  type

    [delta] = [delta]0 + a(l - l0) + b([lambda] - [lambda]0)  (i),

  where [delta] denotes secular change, l latitude and [lambda]
  longitude, the letters with suffix _0_ relating to some convenient
  central position. The constants [delta]0, a, b are to be determined
  from the observed secular changes at the fixed observatories whose
  geographical co-ordinates are accurately known. Unfortunately, as a
  rule, fixed observatories are few in number and not well distributed
  for survey purposes; thus the secular change over part at least of the
  area has usually to be found by repeating the observations after some
  years at several of the field stations. The success attending this
  depends on the exactitude with which the sites can be recovered, on
  the accuracy of the observations, and on the success with which
  allowance is made for diurnal changes, regular and irregular. It is
  thus desirable that the observations at repeat stations should be
  taken at hours when the regular diurnal changes are slow, and that
  they should not be accepted unless taken on days that prove to be
  magnetically quiet. Unless the secular change is exceptionally rapid,
  it will usually be most convenient in practice to calculate it from or
  to the middle of the month, and then to allow for the difference
  between the mean value for the month and the value at the actual hour
  of observation. There is here a difficulty, inasmuch as the latter
  part of the correction depends on the diurnal inequality, and so on
  the local time of the station. No altogether satisfactory method of
  surmounting this difficulty has yet been proposed. Rücker and Thorpe
  in their British survey assumed that the divergence from the mean
  value at any hour at any station might be regarded as made up of a
  regular diurnal inequality, identical with that at Kew when both were
  referred to _local_ time, and of a disturbance element identical with
  that existing at the same absolute time at Kew. Suppose, for instance,
  that at hour h G.M.T. the departure at Kew from the mean value for the
  month is d, then the corresponding departure from the mean at a
  station [lambda] degrees west of Kew is d - e, where e is the increase
  in the element at Kew due to the regular diurnal inequality between
  hour h - [lambda]/15 and hour h. This procedure is simple, but is
  exposed to various criticisms. If we define a diurnal inequality as
  the result obtained by combining hourly readings from all the days of
  a month, we can assign a definite meaning to the diurnal inequality
  for a particular month of a particular year, and after the curves have
  been measured we can give exact numerical figures answering to this
  definition. But the diurnal inequality thus obtained differs, as has
  been pointed out, from that derived from a limited number of the
  quietest days of the month, not merely in amplitude but in phase, and
  the view that the diurnal changes on any individual day can be
  regarded as made up of a regular diurnal inequality of definite
  character and of a disturbance element is an hypothesis which is
  likely at times to be considerably wide of the mark. The extent of the
  error involved in assuming the regular diurnal inequality the same in
  the north of Scotland, or the west of Ireland, as in the south-east of
  England remains to be ascertained. As to the disturbance element, even
  if the disturbing force were of given magnitude and direction all over
  the British Isles--which we now know is often very far from the
  case--its effects would necessarily vary very sensibly owing to the
  considerable variation in the direction and intensity of the local
  undisturbed force. If observations were confined to hours at which the
  regular diurnal changes are slow, and only those taken on days of
  little or no disturbance were utilized, corrections combining the
  effects of regular and irregular diurnal changes could be derived from
  the records of fixed observations, supposed suitably situated,
  combined in formulae of the same type as (i).

  § 43. The field results having been reduced to a fixed epoch, it
  remains to combine them in ways likely to be useful. In most cases the
  results are embodied in charts, usually of at least two kinds, one set
  showing only general features, the other the chief local
  peculiarities. Charts of the first kind resemble the world charts
  (figs. 1 to 4) in being free from sharp twistings and convolutions. In
  these the declination for instance at a fixed geographical position on
  a particular isogonal is to be regarded as really a mean from a
  considerable surrounding area.

  Various ways have been utilized for arriving at these _terrestrial
  isomagnetics_--as Rücker and Thorpe call them--of which an elaborate
  discussion has been made by E. Mathias.[69] From a theoretical
  standpoint the simplest method is perhaps that employed by Liznar for
  Austria-Hungary. Let l and [lambda] represent latitude and longitude
  relative to a certain central station in the area. Then assume that
  throughout the area the value E of any particular magnetic element is
  given by a formula

    E = E0 + al + b[lambda] + cl² + d[lambda]² + el[lambda],

  where E0, a, b, c, d, e are absolute constants to be determined from
  the observations. When determining the constants, we write for E in
  the equation the observed value of the element (corrected for secular
  change, &c.) at each station, and for l and [lambda] the latitude and
  longitude of the station relative to the central station. Thus each
  station contributes an equation to assist in determining the six
  constants. They can thus be found by least squares or some simpler
  method. In Liznar's case there were 195 stations, so that the labour
  of applying least squares would be considerable. This is one objection
  to the method. A second is that it may allow undesirably large weight
  to a few highly disturbed stations. In the case of the British Isles,
  Rücker and Thorpe employed a different method. The area was split up
  into _districts_. For each district a mean was formed of the observed
  values of each element, and the mean was assigned to an imaginary
  central station, whose geographical co-ordinates represented the mean
  of the geographical co-ordinates of the actual stations. Want of
  uniformity in the distribution of the stations may be allowed for by
  weighting the results. Supposing E0 the value of the element found for
  the central station of a district, it was assumed that the value E at
  any actual station whose latitude and longitude exceeded those of the
  central station by l and [lambda] was given by E = E0 + al +
  b[lambda], with a and b constants throughout the district. Having
  found E0, a and b, Rücker and Thorpe calculated values of the element
  for points defined by whole degrees of longitude (from Greenwich) and
  half degrees of latitude. Near the common border of two districts
  there would be two calculated values, of which the arithmetic mean was
  accepted.

  The next step was to determine by interpolation where isogonals--or
  other isomagnetic lines--cut successive lines of latitude. The curves
  formed by joining these successive points of intersection were called
  _district_ lines or curves. Rücker and Thorpe's next step was to
  obtain formulae by trial, giving smooth curves of continuous
  curvature--terrestrial isomagnetics--approximating as closely as
  possible to the district lines. The curves thus obtained had somewhat
  complicated formulae. For instance, the isogonals south of 54°.5
  latitude were given for the epoch Jan. 1, 1891 by

    D = 18° 37´ + 18´.5(l - 49.5) - 3´.5 cos {45°(l - 49.5)}
      + {26´.3 + 1´.5(l - 49.5)} ([lambda] - 4)
      + 0´.01([lambda] - 4)² (l - 54.5)²,

  where D denotes the westerly declination. Supposing, what is at least
  approximately true, that the secular change in Great Britain since
  1891 has been uniform south of lat. 54°.5, corresponding formulae for
  the epochs Jan. 1, 1901, and Jan. 1, 1906, could be obtained by
  substituting for 18° 37´ the values 17° 44´ and 17° 24´ respectively.
  In their very laborious and important memoir E. Mathias and B.
  Baillaud[69] have applied to Rücker and Thorpe's observations a method
  which is a combination of Rücker and Thorpe's and of Liznar's. Taking
  Rücker and Thorpe's nine districts, and the magnetic data found for
  the nine imaginary central stations, they employed these to determine
  the six constants of Liznar's formula. This is an immense
  simplification in arithmetic. The declination formula thus obtained
  for the epoch Jan. 1, 1891, was

    D = 20° 45´.89 + .53474[lambda] + .34716l + .000021[lambda]²
      + .000343l[lambda] - .000239l²,

  where l + (53° 30´.5) represents the latitude, and ([lambda] + 5°
  35´.2) the west longitude of the station. From this and the
  corresponding formulae for the other elements, values were calculated
  for each of Rücker and Thorpe's 882 stations, and these were compared
  with the observed values. A complete record is given of the
  differences between the observed and calculated values, and of the
  corresponding differences obtained by Rücker and Thorpe from their own
  formulae. The mean numerical (calculated ~ observed) differences from
  the two different methods are almost exactly the same--being
  approximately 10´ for declination, 5´½ for inclination, and 70[gamma]
  for horizontal force. The applications by Mathias[69] of his method to
  the survey data of France obtained by Moureaux, and those of the
  Netherlands obtained by van Rïjckevorsel, appear equally successful.
  The method dispenses entirely with district curves, and the parabolic
  formulae are perfectly straightforward both to calculate and to apply;
  they thus appear to possess marked advantages. Whether the method
  could be applied equally satisfactorily to an area of the size of
  India or the United States actual trial alone would show.


    Local Disturbances.

  § 44. Rücker and Thorpe regarded their terrestrial isomagnetics and
  the corresponding formulae as representing the normal field that would
  exist in the absence of disturbances peculiar to the neighbourhood.
  Subtracting the forces derived from the formulae from those observed,
  we obtain forces which may be ascribed to regional disturbance.

  When the vertical disturbing force is downwards, or the observed
  vertical component larger than the calculated, Rücker and Thorpe
  regard it as positive, and the loci where the largest positive values
  occur they termed _ridge lines_. The corresponding loci where the
  largest negative values occur were called _valley lines_. In the
  British Isles Rücker and Thorpe found that almost without exception,
  in the neighbourhood of a ridge line, the horizontal component of the
  disturbing force pointed towards it, throughout a considerable area on
  both sides. The phenomena are similar to what would occur if ridge
  lines indicated the position of the summits of underground masses of
  magnetic material, magnetized so as to attract the north-seeking pole
  of a magnet. Rücker and Thorpe were inclined to believe in the real
  existence of these subterranean magnetic mountains, and inferred that
  they must be of considerable extent, as theory and observation alike
  indicate that thin basaltic sheets or dykes, or limited masses of trap
  rock, produce no measurable magnetic effect except in their immediate
  vicinity. In support of their conclusions, Rücker and Thorpe dwell on
  the fact that in the United Kingdom large masses of basalt such as
  occur in Skye, Mull, Antrim, North Wales or the Scottish coalfield,
  are according to their survey invariably centres of attraction for the
  north-seeking pole of a magnet. Various cases of repulsion have,
  however, been described by other observers in the northern hemisphere.

  § 45. Rücker and Thorpe did not make a very minute examination of
  disturbed areas, so that purely local disturbances larger than any
  noticed by them may exist in the United Kingdom. But any that exist
  are unlikely to rival some that have been observed elsewhere, notably
  those in the province of Kursk in Russia described by Moureaux[70] and
  by E. Leyst.[71] In Kursk Leyst observed declinations varying from 0°
  to 360°, inclinations varying from 39°.1 to 90°; he obtained values of
  the horizontal force varying from 0 to 0.856 C.G.S., and values of the
  vertical force varying from 0.371 to 1.836. Another highly disturbed
  Russian district Krivoi Rog (48° N. lat. 33° E. long.) was
  elaborately surveyed by Paul Passalsky.[72] The extreme values
  observed by him differed, the declination by 282° 40´, the inclination
  by 41° 53´, horizontal force by 0.658, and vertical force by 1.358. At
  one spot a difference of 116°½ was observed between the declinations
  at two positions only 42 metres apart. In cases such as the last
  mentioned, the source of disturbance comes presumably very near the
  surface. It is improbable that any such enormously rapid changes of
  declination can be experienced anywhere at the surface of a deep
  ocean. But in shallow water disturbances of a not very inferior order
  of magnitude have been met with. Possibly the most outstanding case
  known is that of an area, about 3 m. long by 1¼ m. at its widest, near
  Port Walcott, off the N.W. Australian coast. The results of a minute
  survey made here by H.M.S. "Penguin" have been discussed by Captain E.
  W. Creak.[73] Within the narrow area specified, declination varied
  from 26° W. to 56° E., and inclination from 50° to nearly 80°, the
  observations being taken some 80 ft. above sea bottom. Another
  noteworthy case, though hardly comparable with the above, is that of
  East Loch Roag at Lewis in the Hebrides. A survey by H.M.S. "Research"
  in water about 100 ft. deep--discussed by Admiral A. M.
  Field[74]--showed a range of 11° in declination. The largest observed
  disturbances in horizontal and vertical force were of the order 0.02
  and 0.05 C.G.S. respectively. An interesting feature in this case was
  that vertical force was reduced, there being a well-marked valley
  line.

  In some instances regional magnetic disturbances have been found to be
  associated with geodetic anomalies. This is true of an elongated area
  including Moscow, where observations were taken by Fritsche.[75]
  Again, Eschenhagen[76] detected magnetic anomalies in an area
  including the Harz Mountains in Germany, where deflections of the
  plumb line from the normal had been observed. He found a magnetic
  ridge line running approximately parallel to the line of no deflection
  of the plumb line.

  § 46. A question of interest, about which however not very much is
  known, is the effect of local disturbance on secular change and on the
  diurnal inequality. The determination of secular change in a highly
  disturbed locality is difficult, because an unintentional slight
  change in the spot where the observations are made may wholly falsify
  the conclusions drawn. When the disturbed area is very limited in
  extent, the magnetic field may reasonably be regarded as composed of
  the normal field that would have existed in the absence of local
  disturbance, plus a disturbance field arising from magnetic material
  which approaches nearly if not quite to the surface. Even if no
  sensible change takes place in the disturbance field, one would hardly
  expect the secular change to be wholly normal. The changes in the
  rectangular components of the force may possibly be the same as at a
  neighbouring undisturbed station, but this will not give the same
  change in declination and inclination. In the case of the diurnal
  inequality, the presumption is that at least the declination and
  inclination changes will be influenced by local disturbance. If, for
  example, we suppose the diurnal inequality to be due to the direct
  influence of electric currents in the upper atmosphere, the
  declination change will represent the action of the component of a
  force of given magnitude which is perpendicular to the position of the
  compass needle. But when local disturbance exists, the direction of
  the needle and the intensity of the controlling field are both altered
  by the local disturbance, so it would appear natural for the
  declination changes to be influenced also. This conclusion seems borne
  out by observations made by Passalsky[72] at Krivoi Rog, which showed
  diurnal inequalities differing notably from those experienced at the
  same time at Odessa, the nearest magnetic observatory. One station
  where the horizontal force was abnormally low gave a diurnal range of
  declination four times that at Odessa; on the other hand, the range of
  the horizontal force was apparently reduced. It would be unsafe to
  draw general conclusions from observations at two or three stations,
  and much completer information is wanted, but it is obviously
  desirable to avoid local disturbance when selecting a site for a
  magnetic observatory, assuming one's object is to obtain data
  reasonably applicable to a large area. In the case of the older
  observatories this consideration seems sometimes to have been lost
  sight of. At Mauritius, for instance, inside of a circle of only 56
  ft. radius, having for centre the declination pillar of the absolute
  magnetic hut of the Royal Alfred Observatory, T. F. Claxton[77] found
  that the declination varied from 4° 56´ to 13° 45´ W., the inclination
  from 50° 21´ to 58° 34´ S., and the horizontal force from 0.197 to
  0.244 C.G.S. At one spot he found an alteration of 1°1/3 in the
  declination when the magnet was lowered from 4 ft. above the ground to
  2. Disturbances of this order could hardly escape even a rough
  investigation of the site.


    Gaussian Potential and Constants.

  § 47. If we assume the magnetic force on the earth's surface derivable
  from a potential V, we can express V as the sum of two series of solid
  spherical harmonics, one containing negative, the other positive
  integral powers of the radius vector r from the earth's centre. Let
  [lambda] denote east longitude from Greenwich, and let µ = cos(½[pi] -
  l), where l is latitude; and also let
                           _                                          _
                          |          (n - m)(n - m - 1)                |
    H_n^m = (1 - µ²)^(½m) |µ^(n-m) - ------------------ µ^(n-m-2) + ...|,
                          |_              2(2n - 1)                   _|

  where n and m denote any positive integers, m being not greater than
  n. Then denoting the earth's radius by R, we have

    V/R = [Sigma](R/r)^(n+1) [H_n^m (g_n^m cos m[lambda] + h_n^m sin m[lambda])]
        + [Sigma](r/R)^n [H_n^m (g_(-n)^m cos m[lambda] + h_(-n)^m sin m[lambda])],

  where [Sigma] denotes summation of m from 0 to n, followed by
  summation of n from 0 to [infinity]. In this equation g_n^m, &c. are
  constants, those with positive suffixes being what are generally
  termed _Gaussian constants_. The series with negative powers of r
  answers to forces with a source internal to the earth, the series with
  positive powers to forces with an external source. Gauss found that
  forces of the latter class, if existent, were very small, and they are
  usually left out of account. There are three Gaussian constants of the
  first order, g1^0, g1¹, h1¹, five of the second order, seven of the
  third, and so on. The coefficient of a Gaussian constant of the n^th
  order is a spherical harmonic of the n^th degree. If R be taken as
  unit length, as is not infrequent, the first order terms are given by

    V1 = r^(-2) [g1^0 sin l + (g1¹ cos [lambda] + h1¹ sin [lambda]) cos l].

  The earth is in reality a spheroid, and in his elaborate work on the
  subject J. C. Adams[78] develops the treatment appropriate to this
  case. Here we shall as usual treat it as spherical. We then have for
  the components of the force at the surface

    X = -R^(-1)(1 - µ²)^½ (dV/dµ)      towards the astronomical north,
    Y = -R^(-1)(1 - µ²)^-½ (dV/d[lambda])  "    "        "      west,
    Z = -dV/dr vertically downwards.

  Supposing the Gaussian constants known, the above formulae would give
  the force all over the earth's surface. To determine the Gaussian
  constants we proceed of course in the reverse direction, equating the
  observed values of the force components to the theoretical values
  involving g_n^m, &c. If we knew the values of the component forces at
  regularly distributed stations all over the earth's surface, we could
  determine each Gaussian constant independently of the others. Our
  knowledge however of large regions, especially in the Arctic and
  Antarctic, is very scanty, and in practice recourse is had to methods
  in which the constants are not determined independently. The
  consequence is unfortunately that the values found for some of the
  constants, even amongst the lower orders, depend very sensibly on how
  large a portion of the polar regions is omitted from the calculations,
  and on the number of the constants of the higher orders which are
  retained.

  TABLE XLIV.--Gaussian Constants of the First Order.

    +------+---------+---------+---------+---------+---------+---------+---------+
    |      |   1829  |         |         |         |         |         |         |
    |      |  Erman- |   1830  |   1845  |   1880  |  1885   |   1885  |  1885   |
    |      |Petersen.|  Gauss. |  Adams. |  Adams. |Neumayer.| Schmidt.|Fritsche.|
    +------+---------+---------+---------+---------+---------+---------+---------+
    | g1^0 | +.32007 | +.32348 | +.32187 | +.31684 | +.31572 | +.31735 | +.31635 |
    | g1^1 | +.02835 | +.03111 | +.02778 | +.02427 | +.02481 | +.02356 | +.02414 |
    | h1^1 | -.06011 | -.06246 | -.05783 | -.06030 | -.06026 | -.05984 | -.05914 |
    +------+---------+---------+---------+---------+---------+---------+---------+

  Table XLIV. gives the values obtained for the Gaussian constants of
  the first order in some of the best-known computations, as collected
  by W. G. Adams.[79]

  § 48. Allowance must be made for the difference in the epochs, and for
  the fact that the number of constants assumed to be worth retaining
  was different in each case. Gauss, for instance, assumed 24 constants
  sufficient, whilst in obtaining the results given in the table J. C.
  Adams retained 48. Some idea of the uncertainty thus arising may be
  derived from the fact that when Adams assumed 24 constants sufficient,
  he got instead of the values in the table the following:--

                  g1^0       g1¹       h1¹

    1842-1845   +.32173   +.02833   -.05820
    1880        +.31611   +.02470   -.06071

  Some of the higher constants were relatively much more affected. Thus,
  on the hypotheses of 48 and of 24 constants respectively, the values
  obtained for g2^0 in 1842-1845 were -.00127 and -.00057, and those
  obtained for h3¹ in 1880 were +.00748 and +.00573. It must also be
  remembered that these values assume that the series in positive powers
  of r, with coefficients having negative suffixes, is absolutely
  non-existent. If this be not assumed, then in any equation determing X
  or Y, g_n^m must be replaced by g_n^m + g_(-n)^m, and in any equation
  determining Z by g_n^m - n/(n + 1) g_n^m; similar remarks apply to
  h_n^m and h_(-n)^m. It is thus theoretically possible to check the
  truth of the assumption that the positive power series is non-existent
  by comparing the values obtained for g_n^m and h_n^m from the X and Y
  or from the Z equations, when g_(-n)^m and h_(-n)^m are assumed zero.
  If the values so found differ, values can be found for g_(-n)^m and
  h_(-n)^m which will harmonize the two sets of equations. Adams gives
  the values obtained from the X, Y and the Z equations separately for
  the Gaussian constants. The following are examples of the values
  thence deducible for the coefficients of the positive power series:--

                g_(-1)^0   g_(-1)^1   h_(-1)^1   g_(-4)^0   g_(-5)^0   g_(-6)^0

    1842-1845    +.0018     -.0002     -.0014     +.0064     +.0072     +.0124
    1880         -.0002     -.0012     +.0015     -.0043     -.0021     -.0013

  Compared to g4^0, g5^0 and g6^0 the values here found for g_(-4)^0,
  g_(-5)^0 and g_(-6)^0 are far from insignificant, and there would be
  no excuse for neglecting them if the observational data were
  sufficient and reliable. But two outstanding features claim attention,
  first the smallness of g_(-1)^0, g_(-1)^1 and h_(-1)^1, the
  coefficients least likely to be affected by observational
  deficiencies, and secondly the striking dissimilarity between the
  values obtained for the two epochs. The conclusion to which these and
  other facts point is that observational deficiencies, even up to the
  present date, are such that no certain conclusion can be drawn as to
  the existence or non-existence of the positive power series. It is
  also to be feared that considerable uncertainties enter into the
  values of most of the Gaussian constants, at least those of the higher
  orders. The introduction of the positive power series necessarily
  improves the agreement between observed and calculated values of the
  force, but it is more likely than not to be disadvantageous
  physically, if the differences between observed values and those
  calculated from the negative power series alone arise in large measure
  from observational deficiencies.

  TABLE XLV.--Axis and Moment of First Order Gaussian Coefficients.

    +-------+-------------------+-----------+------------+--------------+
    | Epoch.|   Authority for   |   North   |    West    |    M/R³ in   |
    |       |    Constants.     | Latitude. | Longitude. | G.C.S. units.|
    +-------+-------------------+-----------+------------+--------------+
    |       |                   |  °    ´   |   °    ´   |              |
    | 1650  | H. Fritsche       |  82   50  |   42   55  |    .3260     |
    | 1836  |      "            |  78   27  |   63   35  |    .3262     |
    | 1845  | J. C. Adams       |  78   44  |   64   20  |    .3282     |
    | 1880  |      "            |  78   24  |   68    4  |    .3234     |
    | 1885  | Neumayer-Petersen |           |            |              |
    |       |   and Bauer       |  78    3  |   67    3  |    .3224     |
    | 1885  | Neumayer, Schmidt |  78   34  |   68   31  |    .3230     |
    +-------+-------------------+-----------+------------+--------------+

  § 49. The first order Gaussian constants have a simple physical
  meaning. The terms containing them represent the potential arising
  from the uniform magnetization of a sphere parallel to a fixed axis,
  the moment M of the spherical magnet being given by

    M = R³{(g1^0)² + (g1^1)² + (h1^1)²}^½,

  where R is the earth's radius. The position of the north end of the
  axis of this uniform magnetization and the values of M/R^3, derived
  from the more important determinations of the Gaussian constants, are
  given in Table XLV. The data for 1650 are of somewhat doubtful value.
  If they were as reliable as the others, one would feel greater
  confidence in the reality of the apparent movement of the north end of
  the axis from east to west. The table also suggests a slight
  diminution in M since 1845, but it is open to doubt whether the
  apparent change exceeds the probable error in the calculated values.
  It should be carefully noticed that the data in the table apply only
  to the first order Gaussian terms, and so only to a portion of the
  earth's magnetization, and that the Gaussian constants have been
  calculated on the assumption that the negative power series alone
  exists. The field answering to the first order terms--or what Bauer
  has called the _normal_ field--constitutes much the most important
  part of the whole magnetization. Still what remains is very far from
  negligible, save for rough calculations. It is in fact one of the weak
  points in the Gaussian analysis that when one wishes to represent the
  observed facts with high accuracy one is obliged to retain so many
  terms that calculation becomes burdensome.


    Earth-air Currents.

  § 50. The possible existence of a positive power series is not the
  only theoretical uncertainty in the Gaussian analysis. There is the
  further possibility that part of the earth's magnetic field may not
  answer to a potential at all. Schmidt[80] in his calculation of
  Gaussian constants regarded this as a possible contingency, and the
  results he reached implied that as much as 2 or 3% of the entire field
  had no potential. If the magnetic force F on the earth's surface comes
  from a potential, then the line integral [int]F ds taken round any
  closed circuit s should vanish. If the integral does not vanish, it
  equals 4[pi]I, where I is the total electric current traversing the
  area bounded by s. A + sign in the result of the integration means
  that the current is downwards (i.e. from air to earth) or upwards,
  according as the direction of integration round the circuit, as viewed
  by an observer above ground, has been clockwise or anti-clockwise. In
  applications of the formula by W. von Bezold[81] and Bauer[82] the
  integral has been taken along parallels of latitude in the direction
  west to east. In this case a + sign indicates a resultant upward
  current over the area between the parallel of latitude traversed and
  the north geographical pole. The difference between the results of
  integration round two parallels of latitude gives the total vertical
  current over the zone between them. Schmidt's final estimate of the
  average intensity of the earth-air current, irrespective of sign, for
  the epoch 1885 was 0.17 ampere per square kilometre. Bauer employing
  the same observational data as Schmidt, reached somewhat similar
  conclusions from the differences between integrals taken round
  parallels of latitude at 5° intervals from 60° N. to 60° S. H.
  Fritsche[83] treating the problem similarly, but for two epochs, 1842
  and 1885, got conspicuously different results for the two epochs,
  Bauer[84] has more recently repeated his calculations, and for three
  epochs, 1842-1845 (Sabine's charts), 1880 (Creak's charts), and 1885
  (Neumayer's charts), obtaining the mean value of the current per sq.
  km. for 5° zones. Table XLVI. is based on Bauer's figures, the unit
  being 0.001 ampere, and + denoting an _upwardly_ directed current.

  TABLE XLVI.--Earth-air Currents, after Bauer.

    +-------------+----------------------+---------------------+
    |             | Northern Hemisphere. | Southern Hemisphere.|
    |  Latitude.  +--------+------+------+-------+------+------+
    |             | 1842-5.| 1880.| 1885.|1842-5.| 1880.| 1885.|
    +-------------+--------+------+------+-------+------+------+
    |  0° to  15° |  - 1   | -32  | -34  |  +66  | + 30 | + 36 |
    | 15°  "  30° |  -70   | -59  | -68  |  + 2  | - 62 | - 63 |
    | 30°  "  45° |  + 3   | +14  | -22  |  +26  | - 11 | - 14 |
    | 45°  "  60° |  -31   | -21  | +78  |  + 5  | +276 | +213 |
    +-------------+--------+------+------+-------+------+------+

  In considering the significance of the data in Table XLVI., it should
  be remembered that the currents must be regarded as mean values
  derived from all hours of the day, and all months of the year.
  Currents which were upwards during certain hours of the day, and
  downwards during others, would affect the diurnal inequality; while
  currents which were upwards during certain months, and downwards
  during others, would cause an annual inequality in the absolute
  values. Thus, if the figures be accepted as real, we must suppose that
  between 15° N. and 30° N. there are preponderatingly downward
  currents, and between 0° S. and 15° S. preponderatingly upward
  currents. Such currents might arise from meteorological conditions
  characteristic of particular latitudes, or be due to the relative
  distribution of land and sea; but, whatever their cause, any
  considerable real change in their values between 1842 and 1885 seems
  very improbable. The most natural cause to which to attribute the
  difference between the results for different epochs in Table XLVI. is
  unquestionably observational deficiencies. Bauer himself regards the
  results for latitudes higher than 45° as very uncertain, but he seems
  inclined to accept the reality of currents of the average intensity of
  1/30 ampere per sq. km. between 45° N. and 45° S.

  Currents of the size originally deduced by Schmidt, or even those of
  Bauer's latest calculations, seem difficult to reconcile with the
  results of atmospheric electricity (q.v.).

  § 51. There is no single parallel of latitude along the whole of which
  magnetic elements are known with high precision. Thus results of
  greater certainty might be hoped for from the application of the line
  integral to well surveyed countries. Such applications have been made,
  e.g. to Great Britain by Rücker,[85] and to Austria by Liznar,[86] but
  with negative results. The question has also been considered in detail
  by Tanakadate[68] in discussing the magnetic survey of Japan. He makes
  the criticism that the taking of a line integral round the _boundary_
  of a surveyed area amounts to utilizing the values of the magnetic
  elements where least accurately known, and he thus considers it
  preferable to replace the line integral by the surface integral.

    4[pi]I = [int][int] (dY/dx - dX/dy) dx dy.

  He applied this formula not merely to his own data for Japan, but also
  to British and Austrian data of Rücker and Thorpe and of Liznar. The
  values he ascribes to X and Y are those given by the formulae
  calculated to fit the observations. The result reached was "a line of
  no current through the middle of the country; in Japan the current is
  upward on the Pacific side and downward on the Siberian side; in
  Austria it is upward in the north and downward in the south; in Great
  Britain upward in the east and downward in the west." The results
  obtained for Great Britain differed considerably according as use was
  made of Rücker and Thorpe's own district equations or of a series of
  general equations of the type subsequently utilized by Mathias.
  Tanakadate points out that the fact that his investigations give in
  each case a line of no current passing through the middle of the
  surveyed area, is calculated to throw doubt on the reality of the
  supposed earth-air currents, and he recommends a suspension of
  judgment.

  § 52. A question of interest, and bearing a relationship to the
  Gaussian analysis, is the law of variation of the magnetic elements
  with height above sea-level. If F represent the value at sea-level,
  and F + [delta]F that at height h, of any component of force answering
  to Gaussian constants of the n^th order, then 1 + [delta]F/F = (1 +
  h/R)^(-n-2), where R is the earth's radius. Thus at heights of only a
  few miles we have very approximately [delta]F/F = -(n + 2)h/R. As we
  have seen, the constants of the first order are much the most
  important, thus we should expect as a first approximation [delta]X/X =
  [delta]Y/Y = [delta]Z/Z = -3h/R. This equation gives the same rate of
  decrease in all three components, and so no change in declination or
  inclination. Liznar[86a] compared this equation with the observed
  results of his Austrian survey, subdividing his stations into three
  groups according to altitude. He considered the agreement not
  satisfactory. It must be remembered that the Gaussian analysis,
  especially when only lower order terms are retained, applies only to
  the earth's field freed from local disturbances. Now observations at
  individual high level stations may be seriously influenced not merely
  by regional disturbances common to low level stations, but by magnetic
  material in the mountain itself. A method of arriving at the vertical
  change in the elements, which theoretically seems less open to
  criticism, has been employed by A. Tanakadate.[68] If we assume that a
  potential exists, or if admitting the possibility of earth-air
  currents we assume their effort negligible, we have dX/dz = dZ/dx,
  dY/dz = dZ/dy. Thus from the observed rates of change of the vertical
  component of force along the parallels of latitude and longitude, we
  can deduce the rate of change in the vertical direction of the two
  rectangular components of horizontal force, and thence the rates of
  change of the horizontal force and the declination. Also we have dZ/dz
  = 4[pi][rho] - (dX/dx + dY/dy), where [rho] represents the density of
  free magnetism at the spot. The spot being above ground we may neglect
  [rho], and thus deduce the variation in the vertical direction of the
  vertical component from the observed variations of the two horizontal
  components in their own directions. Tanakadate makes a comparison of
  the vertical variations of the magnetic elements calculated in the two
  ways, not merely for Japan, but also for Austria-Hungary and Great
  Britain. In each country he took five representative points, those for
  Great Britain being the central stations of five of Rücker and
  Thorpe's districts. Table XLVII. gives the mean of the five values
  obtained. By method (i.) is meant the formula involving 3h/R, by
  method (ii.) Tanakadate's method as explained above. H, V, D, and I
  are used as defined in § 5. In the case of H and V unity represents
  1[gamma].

  TABLE XLVII.--Change per Kilometre of Height.

    +---------+-----------------+-----------------+-----------------+
    |         |  Great Britain. | Austria-Hungary.|      Japan.     |
    +---------+-------+---------+-------+---------+-------+---------+
    | Method. |  (i.) |  (ii.)  |  (i.) |  (ii.)  |  (i.) |  (ii.)  |
    +---------+-------+---------+-------+---------+-------+---------+
    | H       | - 8.1 | - 6.7   | -10.1 | - 8.7   | -13.9 | -14.0   |
    | V       | -21.2 | -19.4   | -19.0 | -18.1   | -17.1 | -17.4   |
    | D (west)|   ..  | - 0´.04 |   ..  | + 0´.10 |   ..  | - 0´.27 |
    | I       |   ..  | - 0´.05 |   ..  | - 0´.06 |   ..  | - 0´.01 |
    +---------+-------+---------+-------+---------+-------+---------+

  The - sign in Table XLVII. denotes a decrease in the numerical values
  of H, V and I, and a diminution in westerly declination. If we except
  the case of the westerly component of force--not shown in the
  table--the accordance between the results from the two methods in the
  case of Japan is extraordinarily close, and there is no very marked
  tendency for the one method to give larger values than the other. In
  the case of Great Britain and Austria the differences between the two
  sets of calculated values though not large are systematic, the 3h/R
  formula invariably showing the larger reduction with altitude in both
  H and V. Tanakadate was so satisfied with the accordance of the two
  methods in Japan, that he employed his method to reduce all observed
  Japanese values to sea-level. At a few of the highest Japanese
  stations the correction thus introduced into the value of H was of
  some importance, but at the great majority of the stations the
  corrections were all insignificant.


    Schuster's Diurnal Variation Potential.

  § 53. Schuster[87] has calculated a potential analogous to the
  Gaussian potential, from which the regular diurnal changes of the
  magnetic elements all over the earth may be derived. From the mean
  summer and winter diurnal variations of the northerly and easterly
  components of force during 1870 at St Petersburg, Greenwich, Lisbon
  and Bombay, he found the values of 8 constants analogous to Gaussian
  constants; and from considerations as to the hours of occurrence of
  the maxima and minima of vertical force, he concluded that the
  potential, unlike the Gaussian, must proceed in positive powers of r,
  and so answer to forces external to the earth. Schuster found,
  however, that the calculated amplitudes of the diurnal vertical force
  inequality did not accord well with observation; and his conclusion
  was that while the original cause of the diurnal variation is
  external, and consists probably of electric currents in the
  atmosphere, there are induced currents inside the earth, which
  increase the horizontal components of the diurnal inequality while
  diminishing the vertical. The problem has also been dealt with by H.
  Fritsche,[88] who concludes, in opposition to Schuster, that the
  forces are partly internal and partly external, the two sets being of
  fairly similar magnitude. Fritsche repeats the criticism (already made
  in the last edition of this encyclopaedia) that Schuster's four
  stations were too few, and contrasts their number with the 27 from
  which his own data were derived. On the other hand, Schuster's data
  referred to one and the same year, whereas Fritsche's are from epochs
  varying from 1841 to 1896, and represent in some cases a single year's
  observations, in other cases means from several years. It is clearly
  desirable that a fresh calculation should be made, using synchronous
  data from a considerable number of well distributed stations; and it
  should be done for at least two epochs, one representing large, the
  other small sun-spot frequency. The year 1870 selected by Schuster
  had, as it happened, a sun-spot frequency which has been exceeded
  only once since 1750; so that the magnetic data which he employed were
  far from representative of average conditions.


    Magnetization of Vases, &c.

  § 54. It was discovered by Folgheraiter[89] that old vases from
  Etruscan and other sources are magnetic, and from combined observation
  and experiment he concluded that they acquired their magnetization
  when cooling after being baked, and retained it unaltered. From
  experiments, he derived formulae connecting the magnetization shown by
  new clay vases with their orientation when cooling in a magnetic
  field, and applying these formulae to the phenomena observed in the
  old vases he calculated the magnetic dip at the time and place of
  manufacture. His observations led him to infer that in Central Italy
  inclination was actually southerly for some centuries prior to 600
  B.C., when it changed sign. In 400 B.C. it was about 20°N.; since 100
  B.C. the change has been relatively small. L. Mercanton[90] similarly
  investigated the magnetization of baked clay vases from the lake
  dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800
  B.C. The results he obtained were, however, closely similar to those
  observed in recent vases made where the inclination was about 63°N.,
  and he concluded in direct opposition to Folgheraiter that inclination
  in southern Europe has not undergone any very large change during the
  last 2500 years. Folgheraiter's methods have been extended to natural
  rocks. Thus B. Brunhes[91] found several cases of clay metamorphosed
  by adjacent lava flows and transformed into a species of natural
  brick. In these cases the clay has a determinate direction of
  magnetization agreeing with that of the volcanic rock, so it is
  natural to assume that this direction coincided with that of the dip
  when the lava flow occurred. In drawing inferences, allowance must of
  course be made for any tilting of the strata since the volcanic
  outburst. From one case in France in the district of St Flour, where
  the volcanic action is assigned to the Miocene Age, Brunhes inferred a
  southerly dip of some 75°. Until a variety of cases have been
  critically dealt with, a suspension of judgment is advisable, but if
  the method should establish its claims to reliability it obviously may
  prove of importance to geology as well as to terrestrial magnetism.


    Polar Phenomena.

  § 55. Magnetic phenomena in the polar regions have received
  considerable attention of late years, and the observed results are of
  so exceptional a character as to merit separate consideration. One
  feature, the large amplitude of the regular diurnal inequality, is
  already illustrated by the data for Jan Mayen and South Victoria Land
  in Tables VIII. to XI. In the case, however, of declination allowance
  must be made for the small size of H. If a force F perpendicular to
  the magnetic meridian causes a change [Delta]D in D then [Delta]D =
  F/H. Thus at the "Discovery's" winter quarters in South Victoria Land,
  where the value of H is only about 0.36 of that at Kew, a change of
  45´ in D would be produced by a force which at Kew would produce a
  change of only 16´. Another feature, which, however, may not be
  equally general, is illustrated by the data for Fort Rae and South
  Victoria Land in Table XVII. It will be noticed that it is the 24-hour
  term in the Fourier analysis of the regular diurnal inequality which
  is specially enhanced. The station in South Victoria Land--the winter
  quarters of the "Discovery" in 1902-1904--was at 77° 51´ S. lat.; thus
  the sun did not set from November to February (midsummer), nor rise
  from May to July (midwinter). It might not thus have been surprising
  if there had been an outstandingly large seasonal variation in the
  type of the diurnal inequality. As a matter of fact, however, the type
  of the inequality showed exceptionally small variation with the
  season, and the amplitude remained large throughout the whole year.
  Thus, forming diurnal inequalities for the three midsummer months and
  for the three midwinter months, we obtain the following amplitudes for
  the range of the several elements[92]:--

                 D.        H.        V.       I.

    Midsummer  64´.1   57[gamma]  58[gamma]  2´.87
    Midwinter  26´.8   25[gamma]  18[gamma]  1´.23

  The most outstanding phenomenon in high latitudes is the frequency and
  large size of the disturbances. At Kew, as we saw in § 25, the
  absolute range in D exceeds 20´ on only 12% of the total number of
  days. But at the "Discovery's" winter quarters, about sun-spot
  minimum, the range exceeded 1° on 70%, 2° on 37%, and 3° on fully 15%
  of the total number of days. One day in 25 had a range exceeding 4°.
  During the three midsummer months, only one day out of 111 had a range
  under 1°, and even at midwinter only one day in eight had a range as
  small as 30´. The H range at the "Discovery's" station exceeded
  100[gamma] on 40% of the days, and the V range exceeded 100[gamma] on
  32% of the days.

  The special tendency to disturbance seen in equinoctial months in
  temperate latitudes did not appear in the "Discovery's" records in the
  Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days,
  but on 40% of midsummer days. The preponderance of large movements at
  midsummer was equally apparent in the other elements. Thus the
  percentage of days having a V range over 200[gamma] was 21 at
  midsummer, as against 3 in the four equinoctial months.

  At the "Discovery's" station small oscillations of a few minutes'
  duration were hardly ever absent, but the character of the larger
  disturbances showed a marked variation throughout the 24 hours. Those
  of a very rapid oscillatory character were especially numerous in the
  morning between 4 and 9 a.m. In the late afternoon and evening
  disturbances of a more regular type became prominent, especially in
  the winter months. In particular there were numerous occurrences of a
  remarkably regular type of disturbance, half the total number of cases
  taking place between 7 and 9 p.m. This "special type of disturbance"
  was divisible into two phases, each lasting on the average about 20
  minutes. During the first phase all the elements diminished in value,
  during the second phase they increased. In the case of D and H the
  rise and fall were about equal, but the rise in V was about 3½ times
  the preceding fall. The disturbing force--on the north pole--to which
  the first phase might be attributed was inclined on the average about
  5°½ below the horizon, the horizontal projection of its line of action
  being inclined about 41°½ to the north of east. The amplitude and
  duration of the disturbances of the "special type" varied a good deal;
  in several cases the disturbing force considerably exceeded
  200[gamma]. A somewhat similar type of disturbance was observed by Kr.
  Birkeland[93] at Arctic stations also in 1902-1903, and was called by
  him the "polar elementary" storm. Birkeland's record of disturbances
  extends only from October 1902 to March 1903, so it is uncertain
  whether "polar elementary" storms occur during the Arctic summer.
  Their usual time of occurrence seems to be the evening. During their
  occurrence Birkeland found that there was often a great difference in
  amplitude and character between the disturbances observed at places so
  comparatively near together as Iceland, Nova Zembla and Spitzbergen.
  This led him to assign the cause to electric currents in the Arctic,
  at heights not exceeding a few hundred kilometres, and he inferred
  from the way in which the phenomena developed that the seat of the
  disturbances often moved westward, as if related in some way to the
  sun's position. Contemporaneously with the "elementary polar" storms
  in the Arctic Birkeland found smaller but distinct movements at
  stations all over Europe; these could generally be traced as far as
  Bombay and Batavia, and sometimes as far as Christchurch, New Zealand.
  Chree,[92] on the other hand, working up the 1902-1904 Antarctic
  records, discovered that during the larger disturbances of the
  "special type" corresponding but much smaller movements were visible
  at Christchurch, Mauritius, Kolaba, and even at Kew. He also found
  that in the great majority of cases the Antarctic curves were
  specially disturbed during the times of Birkeland's "elementary polar"
  storms, the disturbances in the Arctic and Antarctic being of the same
  order of magnitude, though apparently of considerably different type.

  Examining the more prominent of the sudden commencements of magnetic
  disturbances in 1902-1903 visible simultaneously in the curves from
  Kew, Kolaba, Mauritius and Christchurch, Chree found that these were
  all represented in the Antarctic curves by movements of a considerably
  larger size and of an oscillatory character. In a number of cases
  Birkeland observed small simultaneous movements in the curves of his
  co-operating stations, which appeared to be at least sometimes
  decidedly larger in the equatorial than the northern temperate
  stations. These he described as "equatorial" perturbations, ascribing
  them to electric currents in or near the plane of the earth's magnetic
  equator, at heights of the order of the earth's radius. It was found,
  however, by Chree that in many, if not all, of these cases there were
  synchronous movements in the Antarctic, similar in type to those which
  occurred simultaneously with the sudden commencements of magnetic
  storms, and that these Antarctic movements were considerably larger
  than those described by Birkeland at the equatorial stations. This
  result tends of course to suggest a somewhat different explanation
  from Birkeland's. But until our knowledge of facts has received
  considerable additions all explanations must be of a somewhat
  hypothetical character.


    Magnetic Poles.

  In 1831 Sir James Ross[94] observed a dip of 89° 59´ at 70° 5´ N., 96°
  46´ W., and this has been accepted as practically the position of the
  north magnetic pole at the time. The position of the south magnetic
  pole in 1840 as deduced from the Antarctic observations made by the
  "Erebus" and "Terror" expedition is shown in Sabine's chart as about
  73° 30´ S., 147° 30´ E. In the more recent chart in J. C. Adams's
  _Collected Papers_, vol. 2, the position is shown as about 73° 40´ S.,
  147° 7´ E. Of late years positions have been obtained for the south
  magnetic pole by the "Southern Cross" expedition of 1898-1900 (A), by
  the "Discovery" in 1902-1904 (B), and by Sir E. Shackleton's
  expedition 1908-1909 (C). These are as follow:

    (A) 72° 40´ S., 152° 30´ E.
    (B) 72° 51´ S., 156° 25´ E.
    (C) 72° 25´ S., 155° 16´ E.

  Unless the diurnal inequality vanishes in its neighbourhood, a
  somewhat improbable contingency considering the large range at the
  "Discovery's" winter quarters, the position of the south magnetic pole
  has probably a diurnal oscillation, with an average amplitude of
  several miles, and there is not unlikely a larger annual oscillation.
  Thus even apart from secular change, no single spot of the earth's
  surface can probably claim to be a magnetic pole in the sense
  popularly ascribed to the term. If the diurnal motion were absolutely
  regular, and carried the point where the needle is vertical round a
  closed curve, the centroid of that curve--though a spot where the
  needle is never absolutely vertical--would seem to have the best
  claim to the title. It should also be remembered that when the dip is
  nearly 90° there are special observational difficulties. There are
  thus various reasons for allowing a considerable uncertainty in
  positions assigned to the magnetic poles. Conclusions as to change of
  position of the south magnetic pole during the last ten years based on
  the more recent results (A), (B) and (C) would, for instance, possess
  a very doubtful value. The difference, however, between these recent
  positions and that deduced from the observations of 1840-1841 is more
  substantial, and there is at least a moderate probability that a
  considerable movement towards the north-east has taken place during
  the last seventy years.

  See publications of individual magnetic observatories, more especially
  the Russian (_Annales de l'Observatoire Physique Central_), the French
  (_Annales du Bureau Central Météorologique de France_), and those of
  Kew, Greenwich, Falmouth, Stonyhurst, Potsdam, Wilhelmshaven, de Bilt,
  Uccle, O'Gyalla, Prague, Pola, Coimbra, San Fernando, Capo di Monte,
  Tiflis, Kolaba, Zi-ka-wei, Hong-Kong, Manila, Batavia, Mauritius,
  Agincourt (Toronto), the observatories of the U.S. Coast and Geodetic
  Survey, Rio de Janeiro, Melbourne.

  In the references below the following abbreviations are used: B.A. =
  _British Association Reports_; Batavia = _Observations made at the
  Royal ... Observatory at Batavia_; M.Z. = _Meteorologische
  Zeitschrift_, edited by J. Hann and G. Hellman; P.R.S. = _Proceedings
  of the Royal Society of London_; P.T. = _Philosophical Transactions_;
  R. = _Repertorium für Meteorologie_, St Petersburg; T.M. =
  _Terrestrial Magnetism_, edited by L. A. Bauer; R.A.S. Notices =
  _Monthly Notices of the Royal Astronomical Society_. Treatises are
  referred to by the numbers attached to them; e.g. (1) p. 100 means p.
  100 of Walker's _Terrestrial Magnetism_.


FOOTNOTES:

  [A] For explanation of these numbers, see end of article.

  [1] E. Walker, _Terrestrial and Cosmical Magnetism_ (Cambridge and
    London, 1856).

  [1a]: H. Lloyd, _A Treatise on Magnetism General and Terrestrial_
    (London, 1874). [2] E. Mascart, _Traité de magnétisme terrestre_
    (Paris, 1900).

  [3] L. A. Bauer, _United States Magnetic Declination Tables and
    Isogonic Charts, and Principal Facts relating to the Earth's
    Magnetism_ (Washington, 1902).

  [4] Balfour Stewart, "Terrestrial Magnetism" (under "Meteorology"),
    _Ency. brit._ 9th ed.

  [5] C. Chree, "Magnetism, Terrestrial," _Ency. brit._ 10th ed.

  [6] _M.Z._ 1906, 23, p. 145.

  [7] (3) p. 62.

  [8] _K. Akad. van Wetenschappen_ (Amsterdam, 1895; Batavia, 1899,
    &c.).

  [9] _Atlas des Erdmagnetismus_ (Riga, 1903).

  [10] (1) p. 16, &c.

  [11] _Kolaba (Colaba) Magnetical and Meteorological Observations_,
    1896. Appendix Table II.

  [12] (1) p. 21.

  [13] _Report_ for 1906, App. 4, see also (3) p. 102.

  [14] (1) p. 166.

  [15] _Ergebnisse der mag. Beobachtungen in Potsdam_, 1901, p. xxxvi.

  [16] _U.S. Coast and Geodetic Survey Report_ for 1895, App. 1, &c.

  [17] _T.M._ 1, pp. 62, 89, and 2, p. 68.

  [18] (3) p. 45.

  [19] _Die Elemente des Erdmagnetismus_, pp. 104.108.

  [20] _Zur täglichen Variation der mag. Deklination (aus Heft II. des
    Archivs des Erdmagnetismus)_ (Potsdam, 1906).

  [21] _M.Z._ 1888, 5, p. 225.

  [22] _M.Z._ 1904, 21, p. 129.

  [23] _P.T._ 202 A, p. 335.

  [23a] _Comb. Phil. Soc. Trans._ 20, p. 165.

  [24] _P.T._ 208 A, p. 205.

  [25] _P.T._ 203 A, p. 151.

  [26] _P.T._ 171. p. 541; _P.R.S._ 63, p. 64.

  [27] _R.A.S. Notices_ 60, p. 142.

  [28] _Rendiconti del R. Ist. Lomb._ 1902, Series II. vol. 35.

  [29] _R._ 1889, vol. 12, no. 8.

  [30] _B.A. Report_, 1898, p. 80.

  [31] _P.R.S._ (A) 79, p. 151.

  [32] _P.T._ 204 A, p. 373.

  [33] _Ann. du Bureau Central Météorologique, année 1897_, 1 Mem. p.
    B65.

  [34] _P.T._ 161, p. 307.

  [35] _M.Z._ 1895, 12, p. 321.

  [35a] _P.T._ 1851, p. 123; and 1852, p. 103, see also (4) § 38.

  [36] _P.T._ 159, p. 363.

  [37] (1) p. 92.

  [38] _R.A.S. Notices_ 65, p. 666.

  [39] _R.A.S. Notices_, 65, pp. 2 and 538.

  [40] _K. Akad. van Wetenschappen_ (Amsterdam, 1906) p. 266.

  [41] _R.A.S. Notices_ 65, p. 520.

  [42] _B.A. Reports_, 1880, p. 201 and 1881, p. 463.

  [43] _Anhang Ergebnisse der mag. Beob. in Potsdam_, 1896.

  [44] _M.Z._ 1899, 16, p. 385.

  [45] _P.T._ 166, p. 387.

  [46] _Trans. Can. Inst._ 1898-1899, p. 345, and Proc. Roy. Ast. Soc.
    of Canada, 1902-1903, p. 74, 1904, p. xiv., &c.

  [47] _R.A.S. Notices_ 65, p. 186.

  [48] _T.M._ 10, p. 1.

  [49] _Expédition norvégienne de 1899-1900_ (Christiania, 1901).

  [50] _Thèses présentées à la Faculté des Sciences_ (Paris, 1903).

  [51] _Nat. Tijdschrift voor Nederlandsch-Indië_, 1902, p. 71.

  [52] _Wied. Ann._ 1882, p. 336.

  [53] _Sitz. der k. preuss. Akad. der Wiss._, 24th June 1897, &c.

  [54] _T.M._ 12, p. 1.

  [55] _P.T._ 143, p. 549; _St Helena Observations_, vol. ii., p.
    cxlvi., &c., (1) § 62.

  [56] _Trans. R.S.E._ 24, p. 669.

  [57] _P.T._ 178 A, p. 1.

  [58] _Batavia_, vol. 16, &c.

  [59] _Batavia_, Appendix to vol. 26.

  [60] _R._ vol. 17, no. 1.

  [61] _T.M._ 3, p. 1, &c.

  [62] _P.T._ 181 A, p. 53 and 188 A.

  [63] _Ann. du Bureau Central Mét._ vol. i. for years 1884 and 1887 to
    1895.

  [64] _Ann. dell' Uff. Centrale Met. e Geod._ vol. 14, pt. i. p. 57.

  [65] _A Magnetic Survey of the Netherlands for the Epoch 1st Jan.
    1891_ (Rotterdam, 1895).

  [66] _Kg. Svenska Vet. Akad. Handlingar_, 1895, vol. 27, no. 7.

  [67] _Denkschriften der math. naturwiss. Classe der k. Akad. des
    Wiss._ (Wien), vols. 62 and 67.

  [68] _Journal of the College of Science, Tokyo_, 1904, vol. 14.

  [69] _Ann. de l'observatoire ... de Toulouse_, 1907, vol. 7.

  [70] _Ann. du Bureau Central Mét._ 1897, I. p. B36.

  [71] _T.M._ 7, p. 74.

  [72] _Bull. Imp. Univ. Odessa_ 85, p. 1, and _T.M._ 7, p. 67.

  [73] _P.T._ 187 A, p. 345.

  [74] _P.R.S._ 76 A, p. 181.

  [75] _Bull. Soc. Imp. des Naturalistes de Moskau_, 1893, no. 4, p.
    381, and _T.M._ 1, p. 50.

  [76] _Forsch. zur deut. Landes- u. Volkskunde_, 1898, Bd. xi, 1, and
    _T.M._ 3, p. 77.

  [77] _P.R.S._ 76 A, p. 507.

  [78] Adams, _Scientific Papers_, II. p. 446.

  [79] _B.A. Report_ for 1898, p. 109.

  [80] _Abhand. der bayer, Akad. der Wiss._, 1895, vol. 19.

  [81] _Sitz. k. Akad. der Wiss_. (Berlin), 1897, no. xviii., also
    _T.M._ 3, p. 191.

    [82] _T.M._ 2, p. 11.

  [83] _Die Elemente des Erdmagnetismus_ (St Petersburg, 1899), p.
    103.

  [84] _T.M._ 9, p. 113.

  [85] _T.M._ 1, p. 77, and Nature, 57, pp. 160 and 180.

  [86] _M.Z._ 15, p. 175.

  [86a] _Sitz, der k. k. Akad. der Wiss. Wien, math. nat. Classe_,
    1898, Bd. cvii., Abth. ii.

  [87] _P.T._ (A) 180, p. 467.

  [88] _Die Tägliche Periode der erdmagnetischen Elemente_ (St
    Petersburg, 1902).

  [89] _R. Accad. Lincei Atti_, viii. 1899, pp. 69, 121, 176, 269 and
    previous volumes, see also _Séances de la Soc. Franc. de Physique_,
    1899, p. 118.

  [90] _Bull. Soc. Vaud., Sc. Nat._ 1906, 42, p. 225.

  [91] _Comptes rendus_, 1905, 141, p. 567.

  [92] _National Antarctic Expedition 1901-1904_, "Magnetic
    Observations."

  [93] _The Norwegian Aurora Polaris Expedition 1902-1903_, vol. i.

  [94] (1) p. 163.

      (C. Ch.)