Produced by Chris Curnow and the Online Distributed
Proofreading Team at http://www.pgdp.net (This file was
produced from images generously made available by The
Internet Archive)










                            STANDARD MEASURES
                                   OF
                             UNITED STATES,
                       GREAT BRITAIN, AND FRANCE.

                     HISTORY AND ACTUAL COMPARISONS.

                                  WITH
                 APPENDIX ON INTRODUCTION OF THE MÈTRE.

                                   BY
                          ARTHUR S. C. WURTELE,
                     ASS’T ENG., N. Y. C. & H. R. R.

                             [Illustration]

                            E. & F. N. SPON,
                       NEW YORK: 44 MURRAY STREET.
                        LONDON: 16 CHARING CROSS.
                                  1882.

                COPYRIGHT, 1882, BY ARTHUR S. C. WURTELE.




INTRODUCTION.


During the preparation of this investigation of Standard Measures a large
number of authorities were examined, including the following: Kelly’s
“Universal Cambist,” Maunder’s “Weights and Measures,” “Encyclopædia
Britannica,” “Chambers’ Encyclopædia,” Williams’ “Geodesy,” Hymer’s
works, “Smithsonian Reports,” “Coast Survey Reports,” Herschel’s
“Astronomy,” etc. The only concise and clear statement I found was J. E.
Hilgard’s report to the Coast Survey on standards in 1876, which I was
gratified to find coincides with my deductions.

                                                    ARTHUR S. C. WURTELE.

ALBANY, November 26, 1881.




STANDARD MEASURES.


A standard measure of length at first sight appears to be very
simple--merely a bar of metal of any length, according to the unit of any
country; and comparisons of different standards do not seem to present
any difficulty. But on looking further into the thing, we find that
standards are referred to some natural invariable length, and we are at
once confronted with a mass of scientific reductions giving different
values to the same thing, according to successively improved means of
observation. We find, also, that comparisons of one standard with another
differ, as given by reductions carried to great apparent exactness.

Every author appears to assume the right of using his own judgment as to
what reduction is to be considered the most exact, and the result is a
very confusing difference in apparently exact figures, with nothing to
show how these differences arise.

I have endeavored to indicate what may be the cause of this confusion by
giving the figures of actually observed comparisons and reductions; in a
manner, the roots of the figures used as statements of length.

Sir Joseph Whitworth gives 1/40000 of an inch as the smallest length that
can be measured with certainty, with an ultimate possibility of 1/1000000
of an inch; but imperceptible variations of temperature affect these
infinitesimal lengths to such an extent that he believes the limit can
only be reached at a standard temperature of 85° F., to avoid the effect
of heat of the body.

It appears to me that comparisons should be made of double yards and
mètres with the old French toise, as the limit of exactness would be
thereby doubled.

Another great defect in statements of relative values is the omission
of necessary facts--the material of which the bars or standards are
made, the temperature at which comparison was made, and the standard
temperatures used as to the final reduction, with the coefficient of
expansion adopted.

Again, bars of different metals appear in time to sensibly change their
relative length.


ENGLISH STANDARDS OF LENGTH.

The first establishment of a uniform standard appears to have been made
in 1101 by Henry I., who is said to have fixed the ulna (now the yard)
at the length of his arm; but nothing definite was done till 1736, when
the Royal Society took steps toward securing a general standard, and
in 1742 they had a standard yard made by Graham from a comparison of
various yards and ells of Henry VII. and Elizabeth, that were kept in the
Exchequer.

Two copies of the Royal Society standard yard were made by Bird in
1758 for a committee of Parliament, one of which was marked “standard
of 1758,” and the other 1760. But no exact legal standard was yet
established, as shown by comparisons in 1802 of the various standard
measures in use which Pictet, of Geneva, made with an accurate scale by
Troughton, using means exact to the ten thousandth part of an inch, with
the following results at the temperature of 62° F.:

    Troughton Scale                          36·00000 inches.
    Parliamentary Standard (1758, Bird)      36·00023   “
    Royal Society    “     (1760,   “ )      35·99955   “
           “         “     (Graham)          36·00130   “
    Exchequer        “                       35·99330   “
    Tower            “                       36·00400   “
    Gen. Roy         “     (Trig. Survey)    36·00036   “

Parliament finally undertook to reform the measures of England, and
appointed a commission in 1818, under whose authority Capt. Kater
compared the standard yards then in use with the following results, as
referred to the Indian Survey standard:

    Col. Lambton Standard (Indian Survey)    36·000000 inches.
    Bird’s Standard (1760)                   36·000659   “
    Sir Geo. Schuckburgh’s Standard          36·000642   “
    Ramsden’s Bar. Ordnance Survey           36·003147   “
    Gen. Roy’s Scale                         36·001537   “
    Royal Society Standard                   36·002007   “

The commission reported in favor of adopting Bird’s standard of 1760, as
it differed so slightly from Sir George Schuckburgh’s standard (which
had been used in deducing the value of the French mètre) that those
values could be assumed as correct. They also established the length of
the seconds pendulum at level of sea in London and in vacuo as 39·13929
inches. The seconds pendulum had been previously fixed by Wollaston and
Playfair in 1814 as 39·13047 inches.

On this report, an Act of Parliament in 1823 declared the only standard
measure of length for the United Kingdom to be the yard as given by the
distance at 32° F. between two points in gold studs on the brass bar,
made by Bird, and marked “Standard of 1760,” and in the keeping of the
Clerk of the House of Commons; also it referred this standard yard to the
natural standard of a pendulum vibrating seconds of mean solar time at
the level of the sea, in vacuo at London and temperature of 32° F., as
in the proportion of 36 to 39·13929; so that a pendulum 36 inches long
ought to make 90088·42 vibrations in 24 hours.

The Royal Society had a copy of the legal standard made by Bailey in
1834; and in the same year the Parliamentary standard was destroyed by
fire at the burning of the Houses of Parliament, leaving the kingdom
again without a legal standard.

All attempts made by a commission consisting of Airy, Bailey, Herschel,
Lubbock, and Sheepshanks, to restore the standard by means of the seconds
pendulum failed in exactness, on account of the many conditions of a
vibrating pendulum, and recourse was had to the Royal Society standard,
which had been carefully compared by Captain Kater in 1818, and from this
in 1838 Bailey and Sheepshanks made six bronze bars, one inch square, and
38 inches long, which in 1855 were legalized by Act of Parliament, and
the English standard of length defined as follows:

“That the straight line on distance between the centres of the transverse
lines in the two gold plugs on the bronze bar deposited in the Exchequer
shall be the genuine standard yard at the temperature of 62° Fahrenheit;
and if lost, it shall be replaced by means of its copies.”

The French metrical system was made legal permissively in 1864, at the
length established by Captain Kater, referred to in Act of Parliament of
1823, of 1 mètre equal to 39·37079 inches, or 3·28089916 feet.

These are the standards now in use in the United Kingdom.


UNITED STATES.

By the Constitution of the United States Congress is charged with fixing
the standard of measures (Art. 1, sec. 8); but as no enactment has been
made by Congress, the standard yard in England, which was legal previous
to 1776 in the Colonies, is the standard yard of the United States, and
does not differ with the English standard yard.

Under resolution of Congress in 1830, Mr. Hassler was employed to examine
the standards in use.

Considerable discrepancies were found, but the mean of all examined
corresponded very nearly with the English standard, and in 1832 the
recommendation of Mr. Hassler was adopted, and the standard yard defined
as the distance between the 27th and 63d inch marks, at the temperature
of 62° F., on the brass scale 82 inches long, being an exact copy of Sir
George Schuckburgh’s standard, made by Troughton, of London, for the
Coast Survey, and deposited in the Office of Weights and Measures at
Washington.

In 1836 an Act of Congress ordered standards to be sent to each Governor
of a State, and the work was done under direction of Mr. Hassler.

In 1856, two copies of the English standard yard, as restored after
destruction of the original standard by fire in 1834, No. 11 of bronze,
and No. 57 of Low Moor wrought iron, were presented to the United States
by Airy.

The United States Troughton standard bar being compared with No. 11
was found to be longer by 0·00085 inch, or in proportion of 1 to
1·0000237216, about 1½ inches in a mile, according to Report of Secretary
of Treasury in 1857.

Later comparisons made by J. E. Hilgard, of the Coast Survey, at the
British Standards Office, between No. 11 and the standard imperial yard,
give No. 11 as 0·000088 inch shorter, or it would be of standard length
at temperature of 62·25° F.

We may infer that the Troughton standard is too long by 0·000762 inch, or
would be standard length at temperature 59·77° F. instead of at 62° by
making expansion reduction with Airy’s coefficient for the bronze of the
imperial standards, 0·000342 inch per yard for 1° F.

The mètre was made a legal standard permissively in 1866; the United
States mètre standard being one of the 12 iron mètre bars made and
verified for the French Government in 1799 on the adoption of the
metrical system, and brought to America by Mr. Hassler in 1800, the
relative value being fixed by Act of Congress at 39·37 inches.

The relative value of 39·36850154 United States inches, as obtained by
Mr. Hassler, corrected to 62° F., was used by the Coast Survey till
1868, when it was found advisable to use the relative value of 39·3704
as deduced by Clarke. Since 1800 several standard mètre bars were sent
to the United States by the French Government, and on comparison, there
appearing to be a slight discrepancy, the original iron standard mètre
bar was sent to Dr. F. A. P. Barnard in Paris, and in 1867 it was
compared with the French platinum standard, which is only used once in
ten years to verify other standards.

A difference was found by this comparison of only ·00017 millimètre
or 1/160000 inch, which being only 1/100 of an inch in a mile is
inappreciable.


FRANCE.

The standard of length of the système ancient was the toise of 6 pieds,
divided into 12 pouces of 12 lignes each.

The origin of the toise is not known, but it was probably legally
established by Philip Le Bel, about 1300, as he first appears to have
taken steps toward a uniform system of measures in France. In the 13th
century the toise is mentioned by Ch. Le Rains. In the 14th century
Menongier writes that, in marching, the sight should strike the ground 4
toises in front. In the fifteenth century Pereforest brings in the toise,
and in the sixteenth century the Contume de Berry says, “We use in this
country two toises; one for carpenters of 5 pieds and a half, the other
for masons of 6 pieds.”

Picard used the toise in his measurement of an arc of meridian from
Malvoisin to London in 1669.

The meridians measured by the Academy in 1735 to settle the question of
the figure of the earth were made by means of two standard toises, known
as the “Toise du Nord,” and the “Toise du Sud.”

The first, used by Maupertuis, Clairault, and Le Monnier, in Lapland, was
destroyed by immersion in sea-water, when their ship was wrecked on the
return voyage.

The second, with which La Condamine, Bourgner, and Godin operated in
Peru, was the original of the toise Canivet made in 1768, and of the
standards used in determining the mètre.

The commencement of the move for a scientific standard of length in
France which resulted in the mètre was in 1790, when the revolutionary
government proposed to England the formation of a commission of equal
numbers from the English Royal Society and the French Academy, for the
purpose of fixing the length of the seconds pendulum at latitude 45° as
the basis of a new system of measures. This proposal was not favorably
received, and the Academy, at the request of government, appointed as
a commission Borda, Lagrange, Laplace, Monge, and Condorcet, to decide
whether the seconds pendulum, the quarter of the equator, or the quarter
of a meridian, should be used as the natural standard for the new system
of measures. They settled on the last as best for the purpose, and
resolved that the ten millionth of the meridian quadrant, or distance
from equator to pole, measured at sea level, be taken for basis of the
new system, and be called a mètre.

Delambre and Mechin were at once charged with re-measurement of the
meridian surveyed in 1739 by La Caille and Cassini, from Dunkirk to
Perpignan, and its extension to Barcelona.

Operations were commenced in 1792, and carried on with great accuracy
to completion in 1799; Delambre working between Dunkirk and Paris, and
Mechin between Paris and Barcelona.

The distance measured from Dunkirk to Barcelona was 9° 40´ 24·24´´ of
arc, or 1,075,059 mètres, as reduced to the new standard.

The “toise de Peru” was the standard used in the work at a temperature of
13° R.

Two base-lines were measured with Borda’s compensating bars of brass and
platinum; one at Melun, near Paris, 6076 toises long, and the second at
Perpignan, 6028 toises long, and though over 900,000 mètres apart, the
calculated length differed by only 10 pouces.

This meridian was afterward, in 1806, extended by Gen. Roy to Greenwich,
on the north, and by Biot and Arago to Formentera, on the south. The
results, as given by Laplace in centesimal degrees and mètres, are as
follows:

    Greenwich            57·19753°               ·0 mètres.
    Pantheon, Paris      54·27431°        292,719·3   “
    Formentera           42·96178°      1,423,636·1   “

The middle of the arc being 50·079655° Cent., or 45° 4´ 18·0822´´ Sexa.,
and the middle degree centesimal being very nearly 100,000 mètres.

The determination of the final result of these geodetic measurements was
referred to a committee of 20 members; 9 named by the French Government,
and the others by the governments of Holland, Savoy, Denmark, Spain,
Tuscany, and of the Cisalpine, Ligurian, and Swiss republics, on the
invitation of France.

This committee established the meridian quadrant at 5,130,740 toises;
making the mètre 0·513074 of the toise, or 36·9413 pouces, or 443·296
lignes, and the toise 1·94903659 mètres.

Iron standard mètre bars, 12 in number were made by Borda, also 2 of
platinum and 4 standard toise bars.

The 12 standard iron mètre bars were sent to different countries, after
being verified by the French Government, and on the 2d of November, 1801,
the mètrical système was legalized by France, and the standard unit of
length declared to be the ten millionth part of a meridian quadrant of
the earth, as defined by the distance at a temperature of 0° Centigrade
(32° F.) between two points on a platinum bar in the keeping of the
Academy of Science at Paris. This standard bar is used only once every
ten years for exact comparisons, as stated by Dr. F. A. P. Barnard.

About 1837 Bessel, by a combination of 11 measured arcs of meridian,
deduced the quadrant of meridian as 5,131,179·81 toises instead
of 5,130,740 toises, as fixed by law. This would make to quadrant
10,000,565·278 legal mètres, or would increase the mètre length from
443·296 lignes to 443·334 lignes, agreeing very nearly with result
obtained by Airy in 1830, from a combination of 13 measured arcs.

The following are the measured arcs used by Bessel and Airy; the
combinations being indicated by initial letters, A and B.

          _Measurer._           _Mid. Lat._       _Arc._        _Length._
  B.--Svanberg, Sweden       +66° 20´ 10·0´´  1° 37´ 19·6´´    593,277 feet
  A.--Maupertuis, Sweden     +66° 19´ 37·0´´  0° 57´ 30·4´´    351,832  “
  A.--Struve, Russia         +58° 17´ 37·0´´  3° 35´  5·2´´  1,309,742  “
  B.--Struve and Tenner,
      Russia                 +56°  3´ 55·5´´  8°  2´ 28·9´´  2,937,439  “
  B.--Bessel and Bayer,
      Prussia                +54° 58´ 26·0´´  1° 30´ 29·0´´    551,073  “
  B.--Schumacher, Denmark    +54°  8´ 13·7´´  1° 31´ 53·3´´    559,121  “
  A, B.--Ganss, Hanover      +52° 32´ 16·6´´  2°  0´ 57·4´´    736,425  “
  A.--Roy and Kater, England +52° 35´ 45·0´´  3° 57´ 13·1´´  1,442,953  “
  B.--    “    “       “     +52°  2´ 19·0´´  2° 50´ 23·5´´  1,036,409  “
  A.--Lacaille and Cassini,
      France                 +46° 52´  2·0´´  8° 20´  0·3´´  3,040,605  “
  A, B.--Delambre and Mechin,
      France                 +44° 51´  2·5´´ 12° 22´ 12·7´´  4,509,832  “
  A.--Boscovich, Rome        +42° 59´   ·0´´  2°  9´ 47·0´´    787,919  “
  A.--Mason and Dixon,
      America                +39° 12´   ·0´´  1° 28´ 45·0´´    538,100  “
  A, B.--Lambton, India      +16°  8´ 21·5´´ 15° 57´ 40·7´´  5,794,598  “
  A, B.--Lambton and Everest,
      India                  +12° 32´ 20·8´´  1° 34´ 56·4´´    574,318  “
  A, B.--Lacondamine, Peru   - 1° 31´  0·4´´  3°  7´  3·5´´  1,131,050  “
  A.--Lacaille, Cape Good
       Hope                  -33° 18´ 30·0´´  1° 13´ 17·5´´    445,506  “
  B.--Maclear,   “    “      -35° 43´ 20·0´´  3° 34´ 34·7´´  1,301,993  “
  A.--Plana and Cartessi,
      Piedmont                --------------  1°  7´ 31·1´´  ------------

The following different lengths of the mètre have been obtained:

    As adopted by France, 1801     443·296   lignes.
    According to Delambre          443·264     “
          “      Bessel            443·33394   “
          “      Airy              443·32387   “
          “      Clarke            443·36146   “
    From Peru Meridian             443·440     “

The length of a pendulum vibrating 100,000 times in a mean solar day was
determined in numerous careful experiments by Biot, Arago, and Mathieu,
in mètres of 443·296 lignes, as follows:

    Dunkirk        56·67 lat. Cent.   0 above sea   0·7419076 mètres.
    Paris          54·26      “      65     “       0·7418870   “
      “  by Borda  54·26      “       0     “       0·7416274   “
    Bordeau        49·82      “       0     “       0·7412615   “
    Formentera     42·96      “     196     “       0·7412061   “

Borda also determined the length of the seconds pendulum at Paris, in
vacuo:

    First result      440·5595 lignes = 0·9938267 mètre.
    Second result        “        “   = 0·9938460   “
    As given by Ganot    “        “   = 0·9935      “

In 1812 the système usuelle was established, of which the unit was one
third of the mètre, with the old name of pied, and duodecimally divided
into pouces and lignes.

This system continued in use till 1840, when it was abolished by law, and
the names of pied, pouce, and ligne forbidden under penalties. So the
mètre, decimally divided, remains the only legal measure of length in
France.


COMPARISONS OF UNITED STATES AND ENGLISH STANDARDS.

In 1832, under resolution of Congress, Mr. Hassler compared the different
standard yards in America, with the following results, using the yard
between the twenty-seventh and sixty-third inches on the scale made of
bronze by Troughton, of London, for the United States Coast Survey, as
the reference, that being identical with Sir George Schuckburg’s standard:

    Troughton Scale, mid. yard                   36·0000000 inches.
         “        “  between platinum points     35·9989758   “
    Jones yard in State Department               35·9990285   “
    Iron yard in Engineer Department             35·9987760   “
    Brass yard, Albany, Sec. of State            36·0002465   “
    Gilbert yard, University of Virginia         35·9952318   “

In 1856 the Troughton standard bronze scale was compared with the bronze
standard yard No. 11, which was sent over by Airy as a copy of the
English imperial standard, as restored after destruction of the original
standard by fire in 1834, and the United States standard was found to be
longer by 0·00085 inch.

Later comparisons by J. E. Hilgard, of the Coast Survey, of the bronze
standard No. 11 with the imperial standard yard, at the British Standards
Office, gave No. 11 as 0·000088 shorter than the imperial standard.

Hassler’s reduction of the mètre, as deduced by Beach at 62° F.,
39·36850154, compared with the English reduction of the mètre, 39·37079
inches, gives an excess to the United States Standard of 0·002029 inch.

The following reductions have been given for the United States yard in
English inches:

    Report of Sec. of Treas., 1857      36·00087    = 1·00002416
    Chambers’ Encyclopædia, 1872        36·00087
       “            “         “         36·0020892  = 1·0000580334
    Trautwine                           36·0020894  = 1·000058038
    Mathewson, U. S. surveyor           36·00208944 = 1·00005804
    Hassler and Beach                   36·002092   = 1·00005811
    J. E. Hilgard, Coast Survey         36·00076    = 1·000021

To Mr. Hassler’s reduction the name of United States inch has been
applied; but his reduction is not correct, as he used a rate of expansion
for brass deduced by himself of 0·0003783 inch in one yard for 1° F.,
and later experiments show that the smaller rate of 0·000342, deduced by
Airy, is more correct.

By correcting Hassler’s reduction with the later rate of expansion, J. E.
Hilgard shows that the difference would be very small, or only 36·0002286
= 1·00000635, or about ⅖ of an inch in a mile.

In Coast Survey report for 1876, J. E. Hilgard calls attention to another
difficulty in the matter of extreme accuracy, in the uncertainty with
regard to the permanence in the length of a bar, and states that the
bronze standard bar No. 11 and the Low Moor iron standard bar No. 57,
presented to the United States by Great Britain, are found to have
changed their relative length by 0·00025 inch in 25 years; the bronze bar
being now relatively shorter by that amount. This subject, he states, is
undergoing further investigation.


COMPARISON OF UNITED STATES AND FRENCH STANDARDS.

In 1817 Mr. Hassler examined the French standards in America, for the
Coast Survey, using the Troughton bronze standard scale, which is
identical with Sir George Schuckburg’s standard, as the reference, with
the following results, all being reduced to temperature of 32° F.

    Original Iron Mètre, 1799             39·381022708 inches.
    Lenoir   Iron Mètre, Coast Survey     39·37972015     “
      “      Brass  “         “           39·380247972    “
      “       “     “    Eng. Dept.       39·38052739     “
    Canivet  Iron Toise, 1768             76·74334472     “
    Lenoir    “     “                     76·74192710     “

In 1814 Troughton had compared with his own scale in London two of the
above.

    Lenoir Iron Mètre, C. S.              39·3802506 inches.
      “    Brass  “      “                39·3803333   “

In 1832, under resolution of Congress, Hassler again compared the French
standards in the United States, using as before the Troughton scale, and
reducing all to temperature of 32° F. as follows:

    Original Iron Mètre,   1799                 39·3808643 inches.
    Lenoir        “         “  C. S.            39·3799120   “
      “      Brass Mètre    C. S.               39·380447    “
      “           “         Eng. Dept.          39·3801714   “
      “           “             “     in 1829   39·3807095   “
    Fortin        “         State Dept.         39·3796084   “
                  “         Treas.  “           39·3795983   “
             Iron Mètre       “      “          39·3807827   “
    Gilbert       “         Univ. of Virg.      39·365408    “
             Platinum Mètre                     39·3803278   “
                  “         (Nicollet)          39·380511    “
    Canivet  Iron Toise,    1768                76·74290511  “
    Lenoir        “         1799                76·74047599  “

From the mean of his comparisons between the United States brass
Troughton standard yard and the authentic French standard mètres used by
the Coast Survey, Hassler, in 1832, deduced the value of the mètre at
39·3809172 inches, at 32° F., and by correction for expansion to United
States standard temperature of 62° F., he made the mètre at 32° equal to
39·36850154 inches at 62° F.

The British imperial standard and the United States Troughton standard
differ by only 0·000762 inch, which applied to the English reduction
of 39·37079, would give 39·36996 as the relative value according to
Troughton standard.

The difference between these reductions is probably to be attributed
to the use of different rates of expansion, in correcting for standard
temperatures, which vary considerably, according to high authority as
follows for brass at 1° F.

    Whitworth, 1876     0·00000956  = 0·00034416 in. per yard.
    Borda, 1799         0·000009913 = 0·00035687        “
    Smeaton, 1750       0·000010417 = 0·00037501        “
    Hassler             0·000010508 = 0·0003783         “
    Ramsden, 1760       0·000010516 = 0·0003786         “
    Faraday, 1830       0·00001059  = 0·00038124        “

And for the bronze of which the British imperial standards are made:

    Airy and Sheepshanks   0·0000095  = 0·000342 in. per yard.
    Fizeau                 0·00000975 = 0·000351         “

The correction at Ramsden’s rate is nearly identical with Hassler’s,
and gives 39·3684933; at Whitworth’s rate it would give 39·36962, very
nearly the same as deduced from the difference between the British
Imperial standard and the United States Troughton standard. The results
of Sir Joseph Whitworth were obtained by use of all late improvements for
scientific precision, and they must be accepted as most reliable.

It would appear preferable to give comparisons at the same temperature in
connection with the corrected result, so that international comparisons
of scientific measurements may not be vitiated by accidental variations.


COMPARISON OF ENGLISH AND FRENCH STANDARDS.

When the mètre standard was established in France, 1799, it was compared
with Sir George Schuckburg’s standard yard by Captain Kater. The
quadrant of 10,000,000 mètres, or 5,130,740 toises, was determined to
be 32,808,992 English feet, giving the mètre equal to 3·2808992 English
feet, or 39·37079 inches, and the toise equal to 6·3945925921 English
feet.

In 1814 Wollaston and Playfair, by comparison with the platinum mètre
standard at 55° F., deduced the mètre as equal to 39·3828 English inches.

During the geodetic operations of General Roy in 1802, who used 60° F.
as standard temperature, Pictet’s comparisons, using means capable of
measuring the 10,000th part of an inch, gave the mètre standard, which is
used at 32° F. as standard temperature, at 39·3828 English inches; this
corrected for temperature by Dr. Young, gave 39·371 English inches at 62°
F.; which result was confirmed by Bird, Maskelyne and Laudale.

In 1823, by Act of Parliament on report of committee, the mètre is fixed
as 39·37079 English inches.

In 1800 the Royal Society, by comparison with two toise standards sent by
Lalande to Maskelyne, deduced the mètre as 39·3702 English inches.

Later comparisons by Clarke in the Ordnance Survey Office at Southampton,
in 1866, give the mètre as 39·37043 inches.

The French Academy of Sciences by comparison with Sir George Schuckburg’s
standard at temperature of 32° F., deduced the mètre as 39·3824 English
inches, which reduced to standard temperature of 62° F., would be
39·3711, or slightly in excess of the value deduced by Dr. Young from
Pictet’s comparisons.

The legal value in England is one mètre equal to 39·37079, and the latest
reduction is 39·37043 inches by Clarke in 1866, which is probably the
most exact reduction.

DIFFERENT REDUCTIONS OF THE FRENCH TOISE INTO ENGLISH FEET.

    Captain Kater, 1799     6·3945925921 feet.
    Hassler, 1832           6·3951409     “
    Chambers’ Encyclopædia  6·39456       “
       “      Mathematics   6·394662      “
    Wallace                 6·39462       “
    Nystrom                 6·39625       “
    Alexander               6·39435       “
    Dana                    6·3946        “

The following table of reductions as used shows clearly how great a
confusion exists in the matter of comparisons:

MÈTRE IN INCHES.

    Phœnixville Hand-book                39·368       inches.
    Hassler                              39·36850154    “
      “                                  39·370788      “
      “                                  39·3809172     “
    Trautwine                            39·368505      “
        “                                39·37079       “
    Silliman                             39·368505      “
        “                                39·37079       “
    Chambers’ Encyclopædia               39·36850535    “
        “           “                    39·3707904     “
    Act of United States Congress, 1866  39·37          “
    Smithsonian Report                   39·37          “
    Youmans                              39·37          “
    Davies                               39·37          “
    Homan’s Encyclopædia                 39·37008       “
    Weale                                39·3702        “
    Ordnance Survey (England, 1866)      39·37043       “
    Clerk Maxwell                        39·37043       “
    Capt. Clarke                         39·3704316     “
    J. M. Rankine (1870)                 39·3704316     “
          “       (1866)                 39·3707904     “
    Alexander (weights and measures)     39·37068       “
    Ganot                                39·370788      “
    Vose                                 39·370788      “
    Act of British Parliament, 1823      39·37079       “
    Encyclopædia Britannica              39·37079       “
    Hymer                                39·37079       “
    Davies and Peck                      39·37079       “
    J. W. Clarke                         39·37079       “
    Dana                                 39·37079       “
    Whittaker                            39·37079       “
    Sommerville                          39·3707904     “
    Chambers’ Mathematics                39·3707904     “
    Gwilt’s Encyclopædia                 39·3707904     “
    Gillespie                            39·3707904     “
    Capt. Kater                          39·3708        “
    Appleton’s Encyclopædia              39·37079       “
    Van Nostrand                         39·3708        “
    D’Aubuisson                          39·3708        “
    Johnson (draftsman)                  39·3708        “
    Encyclopædia Americana               39·371         “
    Jameson’s Dictionary                 39·371         “
    Herbert’s Encyclopædia               39·371         “
    Popular        “                     39·371         “
    Molesworth                           39·371         “
    Dr. Young (1802)                     39·371         “
    Wallace (engineer)                   39·371         “
    Nystrom                              39·38091       “
    Hencke                               39·3809172     “
    Act of Canadian Parliament, 1873     39·3819        “
    Paris Academy                        39·3824        “

LENGTH OF THE SECONDS PENDULUM AS GIVEN BY DIFFERENT WRITERS.

    NEW YORK.--Hencke                       39·1012 inches.
               Bartlet                      39·11256   “
               Nystrom                      39·1017    “
               Ganot                        39·1012    “
               Byrne                        39·10153   “
               Wallace                      39·10153   “

      LONDON.--Hencke                       39·13908   “
               Gillespie                    39·13929   “
               Chambers’ Encyclopædia       39·13929   “
               Williams’ Geodesy            39·13929   “
               Act of Parliament, 1823      39·13929   “
               Wallace (engineer)           39·1393    “
               Chambers’ Mathematics        39·1393    “
               Hymer Astronomy              39·13734   “
               Bartlet                      39·13908   “
               Vose                         39·1393    “
               Sommerville                  39·1393    “
               Nystrom                      39·1393    “
               Davies and Peck              39·13908   “
               Ganot                        39·1398    “
               Wollaston (1814)             39·13047   “
               Galbraith                    39·139     “
               Byrne                        39·1393    “
               Capt. Kater                  39·13829   “

       PARIS.--Hencke                       39·12843   “
               Ganot                        39·1285    “
               Galbraith                    39·128     “
               Byrne                        39·12843   “
               Wallace                      39·12843   “




APPENDIX.


Having shown in the preceding pages that in the point of view of
scientific accuracy the yard, mètre, and toise standards are on a
common level, and that in the matter of comparisons there is no extreme
accuracy, I will now refer to the proposed change of our standard from
the yard to the mètre.

Theoretically the mètre is the 10,000,000th part of the earth’s quadrant,
and the yard the 36/39·13929th part of a seconds pendulum at London.
Practically, neither the mètre nor yard could be recovered with exactness
from their natural basis. The legal French mètre differs from the
latest reduction enough to give an excess of over three miles to the
circumference of the earth. In fact, the mètre and yard are only the
lengths of bars of metal kept in certain offices, from which copies are
made. Decimally considered, it is as easy to divide one as the other into
tenths, hundredths, etc., and the yard standard is often so divided.

As to nomenclature, the metrical system is overloaded with Greek and
Latin prefixes, which are in no way so easy and convenient in expression
as the short, sharp Anglo-Saxon words yard, foot, inch.

In all sciences Latin and Greek names are given for easier purposes
of classification; but the different peoples invariably keep their
own household names for daily purposes, leaving prefix and affix to
specialists, probably with advantage to both parties.

The units used for different purposes are entirely distinct from the
base of any system, and though always referable to such base, are not
practically so referred. It therefore seems useless to burden the people
with long scientific names in the ordinary transactions of daily life.

For long distances the units in the yard and metrical systems are
respectively the mile and the kilomètre.

The mile has a definite meaning in our minds, being associated, from the
days of youth, with the measured distances in race-courses, speed in
walking, railway and steamer travel, length of surveyed lots--the same
being in use among about 100,000,000 people.

For mechanical structures, the units are respectively the foot and the
mètre. The foot is used instead of the yard, as being the most convenient
in practice, and is fixed in the minds of the people by constant
association with length of foot-rules, size of buildings, doors, windows,
etc., all of which are always before us.

For commercial purposes the units are respectively the yard and the
mètre. The yard is associated with length of yard-sticks, distance
between brass nails on counters, so many finger-lengths by ladies.
Probably three fourths of the business of the world is conducted on the
yard standard.

For machine and shop work the English unit is the inch and fractions,
and countries having the metrical standard have universally adopted the
millimètre.

The inch is well fixed in the minds of all mechanics by constant use, and
the ease with which the fractions are had by halving only renders the
system very convenient.

As more figures must be used to indicate a size by millimètres than by
inches and fractions, it appears that the metrical system cannot shorten
the work of arithmetical computation in shop work, and is therefore of no
advantage to the mechanic or draftsman, but rather the reverse. This is
the opinion of Coleman Sellers, the distinguished Philadelphia engineer
and manufacturer, who, after a trial of the millimètre in his shops for
some years, returned to the use of the inch, and writes in _Engineering
News_: “The loss from the use of a small unit requiring many figures
to express what is needed, takes away from the other advantages of the
system when considered from a labor-saving point of view.”

In France itself the metrical system is not wholly decimal in actual
practice, as we find the following measures in use in addition to the
decimal divisions: double decamètre, demi-decamètre, double mètre,
demi-mètre, and double decimètre.

The metrical system has been adopted in the following countries: France
and colonies, Holland and colonies, Belgium, Spain and colonies,
Portugal, Italy, Germany, Greece, Roumania, British India, Mexico,
New Granada, Ecuador, Peru, Brazil, Uruguay, Argentine Confederacy,
Chili, Venezuela; and partially in Wurtemburg, Bavaria, Baden, Hesse,
Switzerland, Denmark, Austria, and Turkey.

In the past centuries all the work and records of English-speaking
peoples--now numbering about 100,000,000, and increasing and progressing
faster than all other nationalities, as well as being closely connected
by descent and business--have been done and recorded under the yard
standard, and any change now would inevitably render necessary continual
reductions, to the great detriment and inconvenience of the mass of our
people, and with little or no practical benefit, except perhaps to a
small class of scientific and pseudo-scientific men, who can and do amuse
themselves with the fancied uniformity of the mètre.

All our numerous text-books and tables, mechanical and scientific, would
be rendered entirely useless by the change, and this is a serious final
consideration.