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                        THE SEVEN FOLLIES
                            OF SCIENCE

                                A
                POPULAR ACCOUNT OF THE MOST FAMOUS
                    SCIENTIFIC IMPOSSIBILITIES
       AND THE ATTEMPTS WHICH HAVE BEEN MADE TO SOLVE THEM.

         TO WHICH IS ADDED A SMALL BUDGET OF INTERESTING
                PARADOXES, ILLUSIONS, AND MARVELS.

                   WITH NUMEROUS ILLUSTRATIONS


                                BY
                            JOHN PHIN

 AUTHOR OF "HOW TO USE THE MICROSCOPE"; "THE WORKSHOP COMPANION";
   "THE SHAKESPEARE CYCLOPEDIA"; EDITOR MARQUIS OF WORCESTER'S,
                  "CENTURY OF INVENTIONS"; ETC.


                          SECOND EDITION

                             [Device]

                             NEW YORK
                     D. VAN NOSTRAND COMPANY
                   23 MURRAY AND 27 WARREN STS.
                               1906




      COPYRIGHT, 1906,
 BY D. VAN NOSTRAND COMPANY.




PREFACE


In the following pages I have endeavored to give a simple account of
problems which have occupied the attention of the human mind ever since
the dawn of civilization, and which can never lose their interest until
time shall be no more. While to most persons these subjects will have
but an historical interest, yet even from this point of view they are of
more value than the history of empires, for they are the intellectual
battlefields upon which much of our progress in science has been won. To
a few, however, some of them may be of actual practical importance, for
although the schoolmaster has been abroad for these many years, it is an
unfortunate fact that the circle-squarer and the perpetual-motion-seeker
have not ceased out of the land.

In these days of almost miraculous progress it is difficult to realize
that there may be such a thing as a scientific impossibility. I have
therefore endeavored to point out where the line must be drawn, and by
way of illustration I have added a few curious paradoxes and marvels,
some of which show apparent contradictions to known laws of nature, but
which are all simply and easily explained when we understand the
fundamental principles which govern each case.

In presenting the various subjects which are here discussed, I have
endeavored to use the simplest language and to avoid entirely the use of
mathematical formulae, for I know by large experience that these are
the bugbear of the ordinary reader, for whom this volume is specially
intended. Therefore I have endeavored to state everything in such a
simple manner that any one with a mere common school education can
understand it. This, I trust, will explain the absence of everything
which requires the use of anything higher than the simple rules of
arithmetic and the most elementary propositions of geometry. And even
this I have found to be enough for many lawyers, physicians, and
clergymen who, in the ardent pursuit of their professions, have
forgotten much that they learned at college. And as I hope to find many
readers amongst intelligent mechanics, I have in some cases suggested
mechanical proofs which any expert handler of tools can easily carry
out.

As a matter of course, very little originality is claimed for anything
in the book,--the only points that are new being a few illustrations of
well-known principles, some of which had already appeared in "The Young
Scientist" and "Self-education for Mechanics." Whenever the exact words
of an author have been used, credit has always been given; but in regard
to general statements and ideas, I must rest content with naming the
books from which I have derived the greatest assistance. Ozanam's
"Recreations in Science and Natural Philosophy," in the editions of
Hutton (1803) and Riddle (1854), has been a storehouse of matter. Much
has been gleaned from the "Budget of Paradoxes" by Professor De Morgan
and also from Professor W. W. R. Ball's "Mathematical Recreations and
Problems." Those who wish to inform themselves in regard to what has
been done by the perpetual-motion-mongers must consult Mr. Dirck's two
volumes entitled "Perpetuum Mobile" and I have made free use of his
labors. To these and one or two others I acknowledge unlimited credit.

Some of the marvels which are here described, although very old, are not
generally known, and as they are easily put in practice they may afford
a pleasant hour's amusement to the reader and his friends.

                                                             JOHN PHIN

_Paterson, N. J., July, 1905._




CONTENTS


 Preface


 THE SEVEN FOLLIES OF SCIENCE
                                                                      PAGE

     Introductory Note                                                   1
   I Squaring the Circle                                                 9
  II The Duplication of the Cube                                        30
 III The Trisection of an Angle                                         33
  IV Perpetual Motion                                                   36
   V The Transmutation of Metals--Alchemy                               79
  VI The Fixation of Mercury                                            92
 VII The Universal Medicine and the Elixir of Life                      95


 ADDITIONAL FOLLIES

 Perpetual or Ever-burning Lamps                                       100
 The Alkahest or Universal Solvent                                     104
 Palingenesy                                                           106
 The Powder of Sympathy                                                111


 A SMALL BUDGET OF PARADOXES, ILLUSIONS, AND MARVELS
 (WITH APOLOGIES TO PROFESSOR DE MORGAN)

 The Fourth Dimension                                                  117
 How a Space may be apparently Enlarged by merely changing
   its Shape                                                           126
 Can a Man Lift Himself by the Straps of his Boots?                    128
 How a Spider Lifted a Snake                                           130
 How the Shadow may be made to move backward on the Sun-dial           133
 How a Watch may be used as a Compass                                  134
 Micrography or Minute Writing. Writing so fine that the
   whole Bible, if written in characters of the same size,
   might be inscribed twenty-two times on a square inch                136
 Illusions of the Senses                                               149
   Taste and Smell                                                     150
   Sense of Heat                                                       150
   Sense of Hearing                                                    150
   Sense of Touch--One Thing Appearing as Two                          151
 How Objects may be apparently Seen through a Hole in the
   Hand                                                                156
 How to See (apparently) through a Solid Brick                         158


 CURIOUS ARITHMETICAL PROBLEMS

 The Chess-board Problem                                               163
 The Nail Problem                                                      164
 A Question of Population                                              165
 How to Become a Millionaire                                           166
 The Actual Cost and Present Value of the First Folio Shakespeare      168
 Arithmetical Puzzles                                                  170
 Archimedes and His Fulcrum                                            171




THE SEVEN FOLLIES OF SCIENCE


The difficult, the dangerous, and the impossible have always had a
strange fascination for the human mind. We see this every day in the
acts of boys who risk life and limb in the performance of useless but
dangerous feats, and amongst children of larger growth we find
loop-the-loopers, bridge-jumpers, and all sorts of venture-seekers to
whom much of the attraction of these performances is undoubtedly the
mere risk that is involved, although, perhaps, to some extent, notoriety
and money-making may contribute their share. Many of our readers will
doubtless remember the words of James Fitz-James, in "The Lady of the
Lake":

    Or, if a path be dangerous known
    The danger's self is lure alone.

And in commenting on the old-time game laws of England, Froude, the
historian, says: "Although the old forest laws were terrible, they
served only to enhance the excitement by danger."

That which is true of physical dangers holds equally true in regard to
intellectual difficulties. Professor De Morgan tells us, in his "Budget
of Paradoxes," that he once gave a lecture on "Squaring the Circle" and
that a gentleman who was introduced to it by what he said, remarked loud
enough to be heard by all around: "Only prove to me that it is
impossible and I will set about it this very evening."

Therefore it is not to be wondered at that certain very difficult, or
perhaps impossible problems have in all ages had a powerful fascination
for certain minds. In that curious _olla podrida_ of fact and fiction,
"The Curiosities of Literature," D'Israeli gives a list of six of these
problems, which he calls "The Six Follies of Science." I do not know
whether the phrase "Follies of Science" originated with him or not, but
he enumerates the Quadrature of the Circle; the Duplication, or, as he
calls it, the Multiplication of the Cube; the Perpetual Motion; the
Philosophical Stone; Magic, and Judicial Astrology, as those known to
him. This list, however, has no classical standing such as pertains to
the "Seven Wonders of the World," the "Seven Wise Men of Greece," the
"Seven Champions of Christendom," and others. There are some well-known
follies that are omitted, while some authorities would peremptorily
reject Magic and Judicial Astrology as being attempts at fraud rather
than earnest efforts to discover and utilize the secrets of nature. The
generally accepted list is as follows:

 1. The Quadrature of the Circle or, as it is called in
 the vernacular, "Squaring the Circle."

 2. The Duplication of the Cube.

 3. The Trisection of an Angle.

 4. Perpetual Motion.

 5. The Transmutation of the Metals.

 6. The Fixation of Mercury.

 7. The Elixir of Life.

The Transmutation of the Metals, the Fixation of Mercury, and the Elixir
of Life might perhaps be properly classed as one, under the head of the
Philosopher's Stone, and then Astrology and Magic might come in to make
up the mystic number Seven.

The expression "Follies of Science" does not seem a very appropriate
one. Real science has no follies. Neither can these vain attempts be
called _scientific_ follies because their very essence is that they are
unscientific. Each one is really a veritable "Will-o'-the-Wisp" for
unscientific thinkers, and there are many more of them than those that
we have here named. But the expression has been adopted in literature
and it is just as well to accept it. Those on the list that we have
given are the ones that have become famous in history and they still
engage the attention of a certain class of minds. It is only a few
months since a man who claims to be a professional architect and
technical writer put forth an alleged method of "squaring the circle,"
which he claims to be "exact"; and the results of an attempt to make
liquid air a pathway to perpetual motion are still in evidence, as a
minus quantity, in the pockets of many who believed that all things are
possible to modern science. And indeed it is this false idea of the
possibility of the impossible that leads astray the followers of these
false lights. Inventive science has accomplished so much--many of her
achievements being so astounding that they would certainly have seemed
miracles to the most intelligent men of a few generations ago--that the
ordinary mind cannot see the difference between unknown possibilities
and those things which well-established science pronounces to be
impossible, because they contradict fundamental laws which are
thoroughly established and well understood.

Thus any one who would claim that he could make a plane triangle in
which the three angles would measure more than two right angles, would
show by this very claim that he was entirely ignorant of the first
principles of geometry. The same would be true of the man who would
claim that he could give, in exact figures, the diagonal of a square of
which the side is exactly one foot or one yard, and it is also true of
the man who claims that he can give the exact area of a circle of which
either the circumference or the diameter is known with precision. That
they cannot both be known exactly is very well understood by all who
have studied the subject, but that the area, the circumference, and the
diameter of a circle may all be known with an exactitude which is far in
excess of anything of which the human mind can form the least
conception, is quite true, as we shall show when we come to consider the
subject in its proper place.

These problems are not only interesting historically but they are
valuable as illustrating the vagaries of the human mind and the
difficulties with which the early investigators had to contend. They
also show us the barriers over which we cannot pass, and they enforce
the immutable character of the natural laws which govern the world
around us. We hear much of the progress of science and of the changes
which this progress has brought about, but these changes never affect
the fundamental facts and principles upon which all true science is
based. Theories and explanations and even practical applications change
or pass away, so that we know them no more, but nature remains the same
throughout the ages. No new theory of electricity can ever take away
from the voltaic battery its power, or change it in any respect, and no
new discovery in regard to the constitution of matter can ever lessen
the eagerness with which carbon and oxygen combine together. Every
little while we hear of some discovery that is going to upset all our
preconceived notions and entirely change those laws which long
experience has proved to be invariable, but in every case these alleged
discoveries have turned out to be fallacies. For example, the wonderful
properties of radium have led some enthusiasts to adopt the idea that
many of our old notions about the conservation of energy must be
abandoned, but when all the facts are carefully examined it is found
that there is no rational basis for such views. Upon this point Sir
Oliver Lodge says:

    "There is absolutely no ground for the popular and gratuitous
    surmise that radium emits energy without loss or waste of any kind,
    and that it is competent to go on forever. The idea, at one time
    irresponsibly mooted, that it contradicted the principle of the
    conservation of energy, and was troubling physicists with the idea
    that they must overhaul their theories--a thing which they ought
    always to be delighted to do on good evidence--this idea was a
    gratuitous absurdity, and never had the slightest foundation. It is
    reasonable to suppose, however, that radium and the other like
    substances are drawing upon their own stores of internal atomic
    energy, and thereby gradually disintegrating and falling into other
    and ultimately more stable forms of matter."

One would naturally suppose that the extensive diffusion of sound
scientific knowledge which has taken place during the century just past,
would have placed these problems amongst the lumber of past ages; but it
seems that some of them, particularly the squaring of the circle and
perpetual motion, still occupy considerable space in the attention of
the world, and even the futile chase after the "Elixir of Life" has not
been entirely abandoned. Indeed certain professors who occupy prominent
official positions, assert that they have made great progress towards
its attainment. In view of such facts one is almost driven to accept the
humorous explanation which De Morgan has offered and which he bases on
an old legend relating to the famous wizard, Michael Scott. The
generally accepted tradition, as related by Sir Walter Scott in his
notes to the "Lay of the Last Minstrel," is as follows:

    "Michael Scott was, once upon a time, much embarrassed by a spirit
    for whom he was under the necessity of finding constant employment.
    He commanded him to build a 'cauld,' or dam head across the Tweed at
    Kelso; it was accomplished in one night, and still does honor to the
    infernal architect. Michael next ordered that Eildon Hill, which was
    then a uniform cone, should be divided into three. Another night was
    sufficient to part its summit into the three picturesque peaks which
    it now bears. At length the enchanter conquered this indefatigable
    demon, by employing him in the hopeless task of making ropes out of
    sea-sand."

Whereupon De Morgan offers the following exceedingly interesting
continuation of the legend:

    "The recorded story is that Michael Scott, being bound by contract
    to procure perpetual employment for a number of young demons, was
    worried out of his life in inventing jobs for them, until at last he
    set them to make ropes out of sea-sand, which they never could do.
    We have obtained a very curious correspondence between the wizard
    Michael and his demon slaves; but we do not feel at liberty to say
    how it came into our hands. We much regret that we did not receive
    it in time for the British Association. It appears that the story,
    true as far as it goes, was never finished. The demons easily
    conquered the rope difficulty, by the simple process of making the
    sand into glass, and spinning the glass into thread which they
    twisted. Michael, thoroughly disconcerted, hit upon the plan of
    setting some to square the circle, others to find the perpetual
    motion, etc. He commanded each of them to transmigrate from one
    human body into another, until their tasks were done. This explains
    the whole succession of cyclometers and all the heroes of the
    Budget. Some of this correspondence is very recent; it is much
    blotted, and we are not quite sure of its meaning. It is full of
    figurative allusions to driving something illegible down a steep
    into the sea. It looks like a humble petition to be allowed some
    diversion in the intervals of transmigration; and the answer is:

                  "'Rumpat et serpens iter institutum'

    "a line of Horace, which the demons interpret as a direction to come
    athwart the proceedings of the Institute by a sly trick."

And really those who have followed carefully the history of the men who
have claimed that they had solved these famous problems, will be almost
inclined to accept De Morgan's ingenious explanation as something more
than a mere "skit." The whole history of the philosopher's stone, of
machines and contrivances for obtaining perpetual motion, and of
circle-squaring, is permeated with accounts of the most gross and
obvious frauds. That ignorance played an important part in the conduct
of many who have put forth schemes based upon these pretended solutions
is no doubt true, but that a deliberate attempt at absolute fraud was
the mainspring in many cases cannot be denied. Like _Dousterswivel_ in
"The Antiquary," many of the men who advocated these delusions may have
had a sneaking suspicion that there might be some truth in the doctrines
which they promulgated; but most of them knew that their particular
claims were groundless, and that they were put forward for the purpose
of deceiving some confiding patron from whom they expected either money
or the credit and glory of having done that which had been hitherto
considered impossible.

Some of the questions here discussed have been called "scientific
impossibilities"--an epithet which many have considered entirely
inapplicable to any problem, on the ground that all things are possible
to science. And in view of the wonderful things that have been
accomplished in the past, some of my readers may well ask: "Who shall
decide when doctors disagree?"

Perhaps the best answer to this question is that given by Ozanam, the
old historian of these and many other scientific puzzles. He claimed
that "it was the business of the Doctors of the Sorbonne to discuss, of
the Pope to decide, and of a mathematician to go straight to heaven in a
perpendicular line!"

In this connection the words of De Morgan have a deep significance.
Alluding to the difficulty of preventing men of no authority from
setting up false pretensions and the impossibility of destroying the
assertions of fancy speculation, he says: "Many an error of thought and
learning has fallen before a gradual growth of thoughtful and learned
opposition. But such things as the quadrature of the circle, etc., are
never put down. And why? Because thought can influence thought, but
thought cannot influence self-conceit; learning can annihilate learning;
but learning cannot annihilate ignorance. A sword may cut through an
iron bar, and the severed ends will not reunite; let it go through the
air, and the yielding substance is whole again in a moment."




I.

SQUARING THE CIRCLE


Undoubtedly one of the reasons why this problem has received so much
attention from those whose minds certainly have no special leaning
towards mathematics, lies in the fact that there is a general impression
abroad that the governments of Great Britain and France have offered
large rewards for its solution. De Morgan tells of a Jesuit who came all
the way from South America, bringing with him a quadrature of the circle
and a newspaper cutting announcing that a reward was ready for the
discovery in England. As a matter of fact his method of solving the
problem was worthless, and even if it had been valuable, there would
have been no reward.

Another case was that of an agricultural laborer who spent his
hard-earned savings on a journey to London, carrying with him an alleged
solution of the problem, and who demanded from the Lord Chancellor the
sum of one hundred thousand pounds, which he claimed to be the amount of
the reward offered and which he desired should be handed over forthwith.
When he failed to get the money he and his friends were highly indignant
and insisted that the influence of the clergy had deprived the poor man
of his just deserts!

And it is related that in the year 1788, one of these deluded
individuals, a M. de Vausenville, actually brought an action against
the French Academy of Sciences to recover a reward to which he felt
himself entitled. It ought to be needless to say that there never was a
reward offered for the solution of this or any other of the problems
which are discussed in this volume. Upon this point De Morgan has the
following remarks:

    "Montucla says, speaking of France, that he finds three notions
    prevalent among the cyclometers [or circle-squarers]: 1. That there
    is a large reward offered for success; 2. That the longitude problem
    depends on that success; 3. That the solution is the great end and
    object of geometry. The same three notions are equally prevalent
    among the same class in England. No reward has ever been offered by
    the government of either country. The longitude problem in no way
    depends upon perfect solution; existing approximations are
    sufficient to a point of accuracy far beyond what can be wanted. And
    geometry, content with what exists, has long pressed on to other
    matters. Sometimes a cyclometer persuades a skipper, who has made
    land in the wrong place, that the astronomers are in fault for using
    a wrong measure of the circle; and the skipper thinks it a very
    comfortable solution! And this is the utmost that the problem ever
    has to do with longitude."

In the year 1775 the Royal Academy of Sciences of Paris passed a
resolution not to entertain communications which claimed to give
solutions of any of the following problems: The duplication of the cube,
the trisection of an angle, the quadrature of a circle, or any machine
announced as showing perpetual motion. And we have heard that the Royal
Society of London passed similar resolutions, but of course in the case
of neither society did these resolutions exclude legitimate mathematical
investigations--the famous computations of Mr. Shanks, to which we shall
have occasion to refer hereafter, were submitted to the Royal Society of
London and published in their Transactions. Attempts to "square the
circle," when made intelligently, were not only commendable but have
been productive of the most valuable results. At the same time there is
no problem, with the possible exception of that of perpetual motion,
that has caused more waste of time and effort on the part of those who
have attempted its solution, and who have in almost all cases been
ignorant both of the nature of the problem and of the results which have
been already attained. From Archimedes down to the present time some of
the ablest mathematicians have occupied themselves with the quadrature,
or, as it is called in common language, "the squaring of the circle";
but these men are not to be placed in the same class with those to whom
the term "circle-squarers" is generally applied.

As already noted, the great difficulty with most circle-squarers is that
they are ignorant both of the nature of the problem to be solved and of
the results which have been already attained. Sometimes we see it
explained as the drawing of a square inside a circle and at other times
as the drawing of a square around a circle, but both these problems are
amongst the very simplest in practical geometry, the solutions being
given in the sixth and seventh propositions of the Fourth Book of
Euclid. Other definitions have been given, some of them quite absurd.
Thus in France, in 1753, M. de Causans, of the Guards, cut a circular
piece of turf, squared it, and from the result deduced original sin and
the Trinity. He found out that the circle was equal to the square in
which it is inscribed, and he offered a reward for the detection of any
error, and actually deposited 10,000 francs as earnest of 300,000. But
the courts would not allow any one to recover.

In the last number of the Athenæum for 1855 a correspondent says "the
thing is no longer a _problem_ but an _axiom_." He makes the square
equal to a circle by making each side equal to a quarter of the
circumference. As De Morgan says, he does not know that the area of the
circle is greater than that of any other figure of the same circuit.

Such ideas are evidently akin to the poetic notion of the quadrature.
Aristophanes, in the "Birds," introduces a geometer, who announces his
intention to make a _square circle_. And Pope in the "Dunciad" delivers
himself as follows:

    Mad Mathesis alone was unconfined,
    Too mad for mere material chains to bind,--
    Now to pure space lifts her ecstatic stare,
    Now, running round the circle, finds it square.

The author's note explains that this "regards the wild and fruitless
attempts of squaring the circle." The poetic idea seems to be that the
geometers try to make a square circle.

As stated by all recognized authorities, the problem is this: To
describe a square which shall be exactly equal in area to a given
circle.

The solution of this problem may be given in two ways: (1) the
arithmetical method, by which the area of a circle is found and
expressed numerically in square measure, and (2) the geometrical
quadrature, by which a square, equal in area to a given circle, is
described by means of rule and compasses alone.

Of course, if we know the area of the circle, it is easy to find the
side of a square of equal area; this can be done by simply extracting
the square root of the area, provided the number is one of which it is
possible to extract the square root. Thus, if we have a circle which
contains 100 square feet, a square with sides of 10 feet would be
exactly equal to it. But the ascertaining of the area of the circle is
the very point where the difficulty comes in; the dimensions of circles
are usually stated in the lengths of the diameters, and when this is the
case, the problem resolves itself into another, which is: To find the
area of a circle when the diameter is given.

Now Archimedes proved that the area of any circle is equal to that of a
triangle whose base has the same length as the circumference and whose
altitude or height is equal to the radius. Therefore if we can find the
length of the circumference when the diameter is given, we are in
possession of all the points needed to enable us to "square the circle."

In this form the problem is known to mathematicians as that of the
rectification of the curve.

In a practical form this problem must have presented itself to
intelligent workmen at a very early stage in the progress of operative
mechanics. Architects, builders, blacksmiths, and the makers of chariot
wheels and vessels of various kinds must have had occasion to compare
the diameters and circumferences of round articles. Thus in I Kings,
vii, 23, it is said of Hiram of Tyre that "he made a molten sea, ten
cubits from the one brim to the other; it was round all about * * * and
a line of thirty cubits did compass it round about," from which it has
been inferred that among the Jews, at that time, the accepted ratio was
3 to 1, and perhaps, with the crude measuring instruments of that age,
this was as near as could be expected. And this ratio seems to have been
accepted by the Babylonians, the Chinese, and probably also by the
Greeks, in the earliest times. At the same time we must not forget that
these statements in regard to the ratio come to us through historians
and prophets, and may not have been the figures used by trained
mechanics. An error of one foot in a hoop made to go round a tub or
cistern of seven feet in diameter, would hardly be tolerated even in an
apprentice.

The Egyptians seem to have reached a closer approximation, for from a
calculation in the Rhind papyrus, the ratio of 3.16 to 1 seems to have
been at one time in use. It is probable, however, that in these early
times the ratio accepted by mechanics in general was determined by
actual measurement, and this, as we shall see hereafter, is quite
capable of giving results accurate to the second fractional place, even
with very common apparatus.

To Archimedes, however, is generally accorded the credit of the first
attempt to solve the problem in a scientific manner; he took the
circumference of the circle as intermediate between the perimeters of
the inscribed and the circumscribed polygons, and reached the conclusion
that the ratio lay between 3-1/7 and 3-10/71, or between 3.1428 and
3.1408.

This ratio, in its more accurate form of 3.141592.. is now known by the
Greek letter [pi] (pronounced like the common word _pie_), a symbol
which was introduced by Euler, between 1737 and 1748, and which is now
adopted all over the world. I have, however, used the term ratio, or
value of the ratio instead, throughout this chapter, as probably being
more familiar to my readers.

Professor Muir justly says of this achievement of Archimedes, that it is
"a most notable piece of work; the immature condition of arithmetic, at
the time, was the only real obstacle preventing the evaluation of the
ratio to any degree of accuracy whatever."

And when we remember that neither the numerals now in use nor the Arabic
numerals, as they are usually called, nor any system equivalent to our
decimal system, was known to these early mathematicians, such a
calculation as that made by Archimedes was a wonderful feat.

If any of my readers, who are familiar with the Hebrew or Greek numbers,
and the mode of representing them by letters, will try to do any of
those more elaborate sums which, when worked out by modern methods, are
mere child's play in the hands of any of the bright scholars in our
common schools, they will fully appreciate the difficulties under which
Archimedes labored.

Or, if ignorant of Greek and Hebrew, let them try it with the Roman
numerals, and multiply XCVIII by MDLVII, without using Arabic or common
numerals. Professor McArthur, in his article on "Arithmetic" in the
Encyclopædia Britannica, makes the following statement on this point:

    "The methods that preceded the adoption of the Arabic numerals were
    all comparatively unwieldy, and very simple processes involved great
    labor. The notation of the Romans, in particular, could adapt itself
    so ill to arithmetical operations, that nearly all their
    calculations had to be made by the abacus. One of the best and most
    manageable of the ancient systems is the Greek, though that, too, is
    very clumsy."

After Archimedes, the most notable result was that given by Ptolemy, in
the "Great Syntaxis." He made the ratio 3.141552, which was a very close
approximation.

For several centuries there was little progress towards a more accurate
determination of the ratio. Among the Hindoos, as early as the sixth
century, the now well-known value, 3.1416, had been obtained by
Arya-Bhata, and a little later another of their mathematicians came to
the conclusion that the square root of 10 was the true value of the
ratio. He was led to this by calculating the perimeters of the
successive inscribed polygons of 12, 24, 48, and 96 sides, and finding
that the greater the number of sides the nearer the perimeter of the
polygon approached the square root of 10. He therefore thought that the
perimeter or circumference of the circle itself would be the square root
of exactly 10. It is too great, however, being 3.1622 instead of
3.14159... The same idea is attributed to Bovillus, by Montucla.

By calculating the perimeters of the inscribed and circumscribed
polygons, Vieta (1579) carried his approximation to ten fractional
places, and in 1585 Peter Metius, the father of Adrian, by a lucky step
reached the now famous fraction 355/113, or 3.14159292, which is correct
to the sixth fractional place. The error does not exceed one part in
thirteen millions.

At the beginning of the seventeenth century, Ludolph Van Ceulen reached
35 places. This result, which "in his life he found by much labor," was
engraved upon his tombstone in St. Peter's Church, Leyden. The monument
has now unfortunately disappeared.

From this time on, various mathematicians succeeded, by improved
methods, in increasing the approximation. Thus in 1705, Abraham Sharp
carried it to 72 places; Machin (1706) to 100 places; Rutherford (1841)
to 208 places, and Mr. Shanks in 1853, to 607 places. The same computer
in 1873 reached the enormous number of 707 places.

Printed in type of the same size as that used on this page, these
figures would form a line nearly six feet long.

As a matter of interest I give here the value of the ratio of the
circumference to the diameter, to 127 places:

    3.14159 26535 89793 23846 26433 83279 50288 41971
      69399 37510 58209 74944 59230 78164 06286 20899
      86280 34825 34211 70679 82148 08651 32723 06647
      09384 46+

The degree of accuracy which may be attained by using a ratio carried to
only ten fractional places, far exceeds anything that can be required in
even the finest work, and indeed it is beyond anything attainable by
means of our present tools and instruments. For example: If the length
of a curve of 100 feet radius were determined by a value of ten
fractional places, the result would not err by the one-millionth part of
an inch, a quantity which is quite invisible under the best microscopes
of the present day. This shows us that in any calculations relating to
the dimensions of the earth, such as longitude, etc., we have at our
command, in the 127 places of figures given above, an exactness which
for all practical purposes may be regarded as absolute. This will be
best appreciated by a consideration of the fact that if the earth were a
perfect sphere and if we knew its exact diameter, we could calculate so
exactly the length of an iron hoop which would go round it, that the
difference produced by a change of temperature equal to the millionth of
a millionth part of a degree Fahrenheit, would far exceed the error
arising from the difference between the true ratio and the result thus
reached.

Such minute quantities are far beyond the powers of conception of even
the most thoroughly trained human mind, but when we come to use six and
seven hundred places the results are simply astounding. Professor De
Morgan, in his "Budget of Paradoxes," gives the following illustration
of the extreme accuracy which might be attained by the use of 607
fractional places, the highest number which had been reached when he
wrote:

    "Say that the blood-globule of one of our animalcules is a millionth
    of an inch in diameter.[1] Fashion in thought a globe like our own,
    but so much larger that our globe is but a blood-globule in one of
    its animalcules; never mind the microscope which shows the creature
    being rather a bulky instrument. Call this the first globule above
    us. Let the first globe above us be but a blood-globule, as to size,
    in the animalcule of a still larger globe, which call the second
    globe above us. Go on in this way to the twentieth globe above us.
    Now, go down just as far on the other side. Let the blood-globule
    with which we started be a globe peopled with animals like ours, but
    rather smaller, and call this the first globe below us. This is a
    fine stretch of progression both ways. Now, give the giant of the
    twentieth globe above us the 607 decimal places, and, when he has
    measured the diameter of his globe with accuracy worthy of his size,
    let him calculate the circumference of his equator from the 607
    places. Bring the little philosopher from the twentieth globe below
    us with his very best microscope, and set him to see the small error
    which the giant must make. He will not succeed, unless his
    microscopes be much better for his size than ours are for ours."

It would of course be impossible for any human mind to grasp the range
of such an illustration as that just given. At the same time these
illustrations do serve in some measure to give us an impression, if not
an idea, of the vastness on the one hand and the minuteness on the other
of the measurements with which we are dealing. I therefore offer no
apology for giving another example of the nearness to absolute accuracy
with which the circle has been "squared."

It is common knowledge that light travels with a velocity of about
185,000 miles per second. In other words, light would go completely
round the earth in a little more than one-eighth of a second, or, as
Herschel puts it, in less time than it would take a swift runner to make
a single stride. Taking this distance of 185,000 miles per second as our
unit of measurement, let us apply it as follows:

It is generally believed that our solar system is but an individual unit
in a stellar system which may include hundreds of thousands of suns like
our own, with all their attendant planets and moons. This stellar system
again may be to some higher system what our solar system is to our own
stellar system, and there may be several such gradations of systems, all
going to form one complete whole which, for want of a better name, I
shall call a universe. Now this universe, complete in itself, may be
finite and separated from all other systems of a similar kind by an
empty space, across which even gravitation cannot exert its influence.
Let us suppose that the imaginary boundary of this great universe is a
perfect circle, the extent of which is such that light, traveling at
the rate we have named (185,000 miles per second), would take millions
of millions of years to pass across it, and let us further suppose that
we know the diameter of this mighty space with perfect accuracy; then,
using Mr. Shanks' 707 places of decimal fractions, we could calculate
the circumference to such a degree of accuracy that the error would not
be visible under any microscope now made.

An illustration which may impress some minds even more forcibly than
either of those which we have just given, is as follows:

Let us suppose that in some titanic iron-works a steel armor-plate had
been forged, perfectly circular in shape and having a diameter of
exactly 185,000,000 miles, or very nearly that of the orbit of the
earth, and a thickness of 8000 miles, or about that of the diameter of
the earth. Let us further assume that, owing to the attraction of some
immense stellar body, this huge mass has what we would call a weight
corresponding to that which a plate of the same material would have at
the surface of the earth, and let it be required to calculate the length
of the side of a square plate of the same material and thickness and
which shall be exactly equal to the circular plate.

Using the 707 places of figures of Mr. Shanks, the length of the
required side could be calculated so accurately that the difference in
weight between the two plates (the circle and the square) would not be
sufficient to turn the scale of the most delicate chemical balance ever
constructed.

Of course in assuming the necessary conditions, we are obliged to leave
out of consideration all those more refined details which would
embarrass us in similar calculations on the small scale and confine
ourselves to the purely mathematical aspect of the case; but the
stretch of imagination required is not greater than that demanded by
many illustrations of the kind.

So much, then, for what is claimed by the mathematicians; and the
certainty that their results are correct, as far as they go, is shown by
the predictions made by astronomers in regard to the moon's place in the
heavens at any given time. The error is less than a second of time in
twenty-seven days, and upon this the sailor depends for a knowledge of
his position upon the trackless deep. This is a practical test upon
which merchants are willing to stake, and do stake, billions of dollars
every day.

It is now well established that, like the diagonal and side of a square,
the diameter and circumference of any circle are incommensurable
quantities. But, as De Morgan says, "most of the quadrators are not
aware that it has been fully demonstrated that no two numbers whatsoever
can represent the ratio of the diameter to the circumference, with
perfect accuracy. When, therefore, we are told that either 8 to 25 or 64
to 201 is the true ratio, we know that it is no such thing, without the
necessity of examination. The point that is left open, as not fully
demonstrated to be impossible, is the _geometrical_ quadrature, the
determination of the circumference by the straight line and circle, used
as in Euclid."

But since De Morgan wrote, it has been shown that a Euclidean
construction is actually impossible. Those who desire to examine the
question more fully, will find a very clear discussion of the subject in
Klein's "Famous Problems in Elementary Geometry." (Boston, Ginn & Co.)

There are various geometrical constructions which give approximate
results that are sufficiently accurate for most practical purposes. One
of the oldest of these makes the ratio 3-1/7 to 1. Using this ratio we
can ascertain the circumference of a circle of which the diameter is
given by the following method: Divide the diameter into 7 equal parts by
the usual method. Then, having drawn a straight line, set off on it
three times the diameter and one of the sevenths; the result will give
the circumference with an error of less than the one twenty-five-hundredth
part or one twenty-fifth of one per cent.

If the circumference had been given, the diameter might have been found
by dividing the circumference into twenty-two parts and setting off
seven of them. This would give the diameter. A more accurate method is
as follows:

Given a circle, of which it is desired to find the length of the
circumference: Inscribe in the given circle a square, and to three times
the diameter of the circle add a fifth of the side of the square; the
result will differ from the circumference of the circle by less than
one-seventeen-thousandth part of it. Another method which gives a result
accurate to the one-seventeen-thousandth part is as follows:

[Illustration: Fig. 1.]

Let AD, Fig. 1, be the diameter of the circle, C the center, and CB
the radius perpendicular to AD. Continue AD and make DE equal to the
radius; then draw BE, and in AE, continued, make EF equal to it; if
to this line EF, its fifth part FG be added, the whole line AG will
be equal to the circumference described with the radius CA, within
one-seventeen-thousandth part.

The following construction gives even still closer results: Given the
semi-circle ABC, Fig. 2; from the extremities A and C of its diameter
raise two perpendiculars, one of them CE, equal to the tangent of 30°,
and the other AF, equal to three times the radius. If the line FE be
then drawn, it will be equal to the semi-circumference of the circle,
within one-hundred-thousandth part nearly. This is an error of
one-thousandth of one per cent, an accuracy far greater than any
mechanic can attain with the tools now in use.

[Illustration: Fig. 2.]

When we have the length of the circumference and the length of the
diameter, we can describe a square which shall be equal to the area of
the circle. The following is the method:

Draw a line ACB, Fig. 3, equal to half the circumference and half the
diameter together. Bisect this line in O, and with O as a center and AO
as radius, describe the semi-circle ADB. Erect a perpendicular CD, at C,
cutting the arc in D; CD is the side of the required square which can
then be constructed in the usual manner. The explanation of this is that
CD is a mean proportional between AC and CB.

[Illustration: Fig. 3.]

De Morgan says: "The following method of finding the circumference of a
circle (taken from a paper by Mr. S. Drach in the 'Philosophical
Magazine,' January, 1863, Suppl.), is as accurate as the use of eight
fractional places: From three diameters deduct eight-thousandths and
seven-millionths of a diameter; to the result, add five per cent. We
have then not quite enough; but the shortcoming is at the rate of about
an inch and a sixtieth of an inch in 14,000 miles."

For obtaining the side of a square which shall be equal in area to a
given circle, the empirical method, given by Ahmes in the Rhind papyrus
4000 years ago, is very simple and sufficiently accurate for many
practical purposes. The rule is: Cut off one-ninth of the diameter and
construct a square upon the remainder.

This makes the ratio 3.16.. and the error does not exceed one-third of
one per cent.

There are various mechanical methods of measuring and comparing the
diameter and the circumference of a circle, and some of them give
tolerably accurate results. The most obvious device and that which was
probably the oldest, is the use of a cord or ribbon for the curved
surface and the usual measuring rule for the diameter. With an
accurately divided rule and a thin metallic ribbon which does not
stretch, it is possible to determine the ratio to the second fractional
place, and with a little care and skill the third place may be
determined quite closely.

An improvement which was no doubt introduced at a very early day is the
measuring wheel or circumferentor. This is used extensively at the
present day by country wheelwrights for measuring tires. It consists of
a wheel fixed in a frame so that it may be rolled along or over any
surface of which the measurement is desired.

This may of course be used for measuring the circumference of any circle
and comparing it with the diameter. De Morgan gives the following
instance of its use: A squarer, having read that the circular ratio was
undetermined, advertised in a country paper as follows: "I thought it
very strange that so many great scholars in all ages should have failed
in finding the true ratio and have been determined to try myself." He
kept his method secret, expecting "to secure the benefit of the
discovery," but it leaked out that he did it by rolling a twelve-inch
disk along a straight rail, and his ratio was 64 to 201 or 3.140625
exactly. As De Morgan says, this is a very creditable piece of work; it
is not wrong by 1 in 3000.

Skilful machinists are able to measure to the one-five-thousandth of an
inch; this, on a two-inch cylinder, would give the ratio correct to five
places, provided we could measure the curved line as accurately as we
can the straight diameter, but it is difficult to do this by the usual
methods. Perhaps the most accurate plan would be to use a fine wire and
wrap it round the cylinder a number of times, after which its length
could be measured. The result would of course require correction for the
angle which the wire would necessarily make if the ends did not meet
squarely and also for the diameter of the wire. Very accurate results
have been obtained by this method in measuring the diameters of small
rods.

A somewhat original way of finding the area of a circle was adopted by
one squarer. He took a carefully turned metal cylinder and having
measured its length with great accuracy he adopted the Archimedean
method of finding its cubical contents, that is to say, he immersed it
in water and found out how much it displaced. He then had all the data
required to enable him to calculate the area of the circle upon which
the cylinder stood.

Since the straight diameter is easily measured with great accuracy, when
he had the area he could readily have found the circumference by working
backward the rule announced by Archimedes, viz.: that the area of a
circle is equal to that of a triangle whose base has the same length as
the circumference and whose altitude is equal to the radius.

One would almost fancy that amongst circle-squarers there prevails an
idea that some kind of ban or magical prohibition has been laid upon
this problem; that like the hidden treasures of the pirates of old it
is protected from the attacks of ordinary mortals by some spirit or
demoniac influence, which paralyses the mind of the would-be solver and
frustrates his efforts.

It is only on such an hypothesis that we can account for the wild
attempts of so many men, and the persistence with which they cling to
obviously erroneous results in the face not only of mathematical
demonstration, but of practical mechanical measurements. For even when
working in wood it is easy to measure to the half or even the one-fourth
of the hundredth of an inch, and on a ten-inch circle this will bring
the circumference to 3.1416 inches, which is a corroboration of the
orthodox ratio (3.14159) sufficient to show that any value which is
greater than 3.142 or less than 3.141 cannot possibly be correct.

And in regard to the area the proof is quite as simple. It is easy to
cut out of sheet metal a circle 10 inches in diameter, and a square of
7.85 on the side, or even one-thousandth of an inch closer to the
standard 7.854. Now if the work be done with anything like the accuracy
with which good machinists work, it will be found that the circle and
the square will exactly balance each other in weight, thus proving in
another way the correctness of the accepted ratio.

But although even as early as before the end of the eighteenth century,
the value of the ratio had been accurately determined to 152 places of
decimals, the nineteenth century abounded in circle-squarers who brought
forward the most absurd arguments in favor of other values. In 1836, a
French well-sinker named Lacomme, applied to a professor of mathematics
for information in regard to the amount of stone required to pave the
circular bottom of a well, and was told that it was impossible "to give
a correct answer, because the exact ratio of the diameter of a circle to
its circumference had never been determined"! This absolutely true but
very unpractical statement by the professor, set the well-sinker to
thinking; he studied mathematics after a fashion, and announced that he
had discovered that the circumference was exactly 3-1/8 times the length
of the diameter! For this discovery (?) he was honored by several medals
of the first class, bestowed by Parisian societies.

Even as late as the year 1860, a Mr. James Smith of Liverpool, took up
this ratio 3-1/8 to 1, and published several books and pamphlets in
which he tried to argue for its accuracy. He even sought to bring it
before the British Association for the Advancement of Science.
Professors De Morgan and Whewell, and even the famous mathematician, Sir
William Rowan Hamilton, tried to convince him of his error, but without
success. Professor Whewell's demonstration is so neat and so simple that
I make no apology for giving it here. It is in the form of a letter to
Mr. Smith: "You may do this: calculate the side of a polygon of 24 sides
inscribed in a circle. I think you are mathematician enough to do this.
You will find that if the radius of the circle be one, the side of the
polygon is .264, etc. Now the arc which this side subtends is, according
to your proposition, 3.125/12 = .2604, and, therefore, the chord is
greater than its arc, which, you will allow, is impossible."

This must seem, even to a school-boy, to be unanswerable, but it did not
faze Mr. Smith, and I doubt if even the method which I have suggested
previously, viz., that of cutting a circle and a square out of the same
piece of sheet metal and weighing them, would have done so. And yet by
this method even a common pair of grocer's scales will show to any
common-sense person the error of Mr. Smith's value and the correctness
of the accepted ratio.

Even a still later instance is found in a writer who, in 1892, contended
in the New York "Tribune" for 3.2 instead of 3.1416, as the value of the
ratio. He announces it as the re-discovery of a long lost secret, which
consists in the knowledge of a certain line called "the Nicomedean
line." This announcement gave rise to considerable discussion, and even
towards the dawn of the twentieth century 3.2 had its advocates as
against the accepted ratio 3.1416.

Verily the slaves of the mighty wizard, Michael Scott, have not yet
ceased from their labors!


FOOTNOTES:

[1] What follows is an exceedingly forcible illustration of an important
mathematical truth, but at the same time it may be worth noting that the
size of the blood-globules or corpuscles has no relation to the size of
the animal from which they are taken. The blood corpuscle of the tiny
mouse is larger than that of the huge ox. The smallest blood corpuscle
known is that of a species of small deer, and the largest is that of a
lizard like reptile found in our southern waters--the amphiuma.

These facts do not at all affect the force or value of De Morgan's
mathematical illustration, but I have thought it well to call the
attention of the reader to this point, lest he should receive an
erroneous physiological idea.




II

THE DUPLICATION OF THE CUBE


This problem became famous because of the halo of mythological romance
with which it was surrounded. The story is as follows:

About the year 430 B.C. the Athenians were afflicted by a terrible
plague, and as no ordinary means seemed to assuage its virulence, they
sent a deputation of the citizens to consult the oracle of Apollo at
Delos, in the hope that the god might show them how to get rid of it.

The answer was that the plague would cease when they had doubled the
size of the altar of Apollo in the temple at Athens. This seemed quite
an easy task; the altar was a cube, and they placed beside it another
cube of exactly the same size. But this did not satisfy the conditions
prescribed by the oracle, and the people were told that the altar must
consist of one cube, the size of which must be exactly twice the size of
the original altar. They then constructed a cubic altar of which the
side or edge was twice that of the original, but they were told that the
new altar was eight times and not twice the size of the original, and
the god was so enraged that the plague became worse than before.

According to another legend, the reason given for the affliction was
that the people had devoted themselves to pleasure and to sensual
enjoyments and pursuits, and had neglected the study of philosophy, of
which geometry is one of the higher departments--certainly a very sound
reason, whatever we may think of the details of the story. The people
then applied to the mathematicians, and it is supposed that their
solution was sufficiently near the truth to satisfy Apollo, who
relented, and the plague disappeared.

In other words, the leading citizens probably applied themselves to the
study of sewerage and hygienic conditions, and Apollo (the Sun) instead
of causing disease by the festering corruption of the usual filth of
cities, especially in the East, dried up the superfluous moisture, and
promoted the health of the inhabitants.

It is well known that the relation of the area and the cubical contents
of any figure to the linear dimensions of that figure are not so
generally understood as we should expect in these days when the
schoolmaster is supposed to be "abroad in the land." At an examination
of candidates for the position of fireman in one of our cities, several
of the applicants made the mistake of supposing that a two-inch pipe and
a five-inch pipe were equal to a seven-inch pipe, whereas the combined
capacities of the two small pipes are to the capacity of the large one
as 29 to 49.

This reminds us of a story which Sir Frederick Bramwell, the engineer,
used to tell of a water company using water from a stream flowing
through a pipe of a certain diameter. The company required more water,
and after certain negotiations with the owner of the stream, offered
double the sum if they were allowed a supply through a pipe of double
the diameter of the one then in use. This was accepted by the owner, who
evidently was not aware of the fact that a pipe of double the diameter
would carry _four_ times the supply.

A square whose side is twice the length of another, and a circle whose
diameter is twice that of another will each have an area four times that
of the original. And in the case of solids: A ball of twice the diameter
will weigh eight times as much as the original, and a ball of three
times the diameter will weigh twenty-seven times as much as the
original.

In attempting to calculate the side of a cube which shall have twice the
volume of a given cube, we meet the old difficulty of incommensurability,
and the solution cannot be effected geometrically, as it requires the
construction of two mean proportionals between two given lines.




III

THE TRISECTION OF AN ANGLE


This problem is not so generally known as that of squaring the circle,
and consequently it has not received so much attention from amateur
mathematicians, though even within little more than a year a small book,
in which an attempted solution is given, has been published. When it is
first presented to an uneducated reader, whose mind has a mathematical
turn, and especially to a skilful mechanic, who has not studied
theoretical geometry, it is apt to create a smile, because at first
sight most persons are impressed with an idea of its simplicity, and the
ease with which it may be solved. And this is true, even of many persons
who have had a fair general education. Those who have studied only what
is known as "practical geometry" think at once of the ease and accuracy
with which a right angle, for example, may be divided into three equal
parts. Thus taking the right angle ACB, Fig. 4, which may be set off
more easily and accurately than any other angle except, perhaps, that of
60°, and knowing that it contains 90°, describe an arc ADEB, with C for
the center and any convenient radius. Now every school-boy who has
played with a pair of compasses knows that the radius of a circle will
"step" round the circumference exactly six times; it will therefore
divide the 360° into six equal parts of 60° each. This being the case,
with the radius CB, and B for a center, describe a short arc crossing
the arc ADEB in D, and join CD. The angle DCB will be 60°, and as the
angle ACB is 90°, the angle ACD must be 30°, or one-third part of the
whole. In the same way lay off the angle ACE of 60°, and ECB must be
30°, and the remainder DCE must also be 30°. The angle ACB is therefore
easily divided into three equal parts, or in other words, it is
trisected. And with a slight modification of the method, the same may be
done with an angle of 45°, and with some others. These however are only
special cases, and the very essence of a geometrical solution of any
problem is that it shall be applicable to _all_ cases so that we require
a method by which _any_ angle may be divided into three equal parts by a
pure Euclidean construction. The ablest mathematicians declare that the
problem cannot be solved by such means, and De Morgan gives the
following reasons for this conclusion: "The trisector of an angle, if he
demand attention from any mathematician, is bound to produce from his
construction, an expression for the sine or cosine of the third part of
any angle, in terms of the sine or cosine of the angle itself, obtained
by the help of no higher than the square root. The mathematician knows
that such a thing cannot be; but the trisector virtually says it can be,
and is bound to produce it to save time. This is the misfortune of most
of the solvers of the celebrated problems, that they have not knowledge
enough to present those consequences of their results by which they can
be easily judged."

[Illustration: Fig. 4.]

De Morgan gives an account of a "terrific" construction by a friend of
Dr. Wallich, which he says is "so nearly true, that unless the angle be
very obtuse, common drawing, applied to the construction, will not
detect the error." But geometry requires _absolute_ accuracy, not a mere
approximation.




IV

PERPETUAL MOTION


It is probable that more time, effort, and money have been wasted in the
search for a perpetual-motion machine than have been devoted to attempts
to square the circle or even to find the philosopher's stone. And while
it has been claimed in favor of this delusion that the pursuit of it has
given rise to valuable discoveries in mechanics and physics, some even
going so far as to urge that we owe the discovery of the great law of
the conservation of energy to the suggestions made by the
perpetual-motion seekers, we certainly have no evidence to show anything
of the kind. Perpetual motion was declared to be an impossibility upon
purely mechanical and mathematical grounds long before the law of the
conservation of energy was thought of, and it is very certain that this
delusion had no place in the thoughts of Rumford, Black, Davy, Young,
Joule, Grove, and others when they devoted their attention to the laws
governing the transformation of energy. Those who pursued such a
will-o'-the-wisp, were not the men to point the way to any scientific
discovery.

The search for a perpetual-motion machine seems to be of comparatively
modern origin; we have no record of the labors of ancient inventors in
this direction, but this may be as much because the records have been
lost, as because attempts were never made. The works of a mechanical
inventor rarely attracted much attention in ancient times, while the
mathematical problems were regarded as amongst the highest branches of
philosophy, and the search for the philosopher's stone and the elixir of
life appealed alike to priest and layman. We have records of attempts
made 4000 years ago to square the circle, and the history of the
philosopher's stone is lost in the mists of antiquity; but it is not
until the eleventh or twelfth century that we find any reference to
perpetual motion, and it was not until the close of the sixteenth and
the beginning of the seventeenth century that this problem found a
prominent place in the writings of the day.

By perpetual motion is meant a machine which, without assistance from
any external source except gravity, shall continue to go on moving until
the parts of which it is made are worn out. Some insist that in order to
be properly entitled to the name of a perpetual-motion machine, it must
evolve more power than that which is merely required to run it, and it
is true that almost all those who have attempted to solve this problem
have avowed this to be their object, many going so far as to claim for
their contrivances the ability to supply unlimited power at no cost
whatever, except the interest on a small investment, and the trifling
amount of oil required for lubrication. But it is evident that a machine
which would of itself maintain a regular and constant motion would be of
great value, even if it did nothing more than move itself. And this
seems to have been the idea upon which those men worked, who had in view
the supposed reward offered for such an invention as a means for finding
the longitude. And it is well known that it was the hope of attaining
such a reward that spurred on very many of those who devoted their time
and substance to the subject.

There are several legitimate and successful methods of obtaining a
practically perpetual motion, provided we are allowed to call to our aid
some one of the various natural sources of power. For example, there are
numerous mountain streams which have never been known to fail, and which
by means of the simplest kind of a water-wheel would give constant
motion to any light machinery. Even the wind, the emblem of fickleness
and inconstancy, may be harnessed so that it will furnish power, and it
does not require very much mechanical ingenuity to provide means whereby
the surplus power of a strong gale may be stored up and kept in reserve
for a time of calm. Indeed this has frequently been done by the raising
of weights, the winding up of springs, the pumping of water into storage
reservoirs and other simple contrivances.

The variations which are constantly occurring in the temperature and the
pressure of the atmosphere have also been forced into this service. A
clock which required no winding was exhibited in London towards the
latter part of the eighteenth century. It was called a perpetual motion,
and the working power was derived from variations in the quantity, and
consequently in the weight of the mercury, which was forced up into a
glass tube closed at the upper end and having the lower end immersed in
a cistern of mercury after the manner of a barometer. It was fully
described by James Ferguson, whose lectures on Mechanics and Natural
Philosophy were edited by Sir David Brewster. It ran for years without
requiring winding, and is said to have kept very good time. A similar
contrivance was employed in a clock which was possessed by the Academy
of Painting at Paris. It is described in Ozanam's work, Vol. II, page
105, of the edition of 1803.

The changes which are constantly taking place in the temperature of all
bodies, and the expansion and contraction which these variations
produce, afford a very efficient power for clocks and small machines.
Professor W. W. R. Ball tells us that "there was at Paris in the latter
half of last century a clock which was an ingenious illustration of such
perpetual motion. The energy, which was stored up in it to maintain the
motion of the pendulum, was provided by the expansion of a silver rod.
This expansion was caused by the daily rise of temperature, and by means
of a train of levers it wound up the clock. There was a disconnecting
apparatus, so that the contraction due to a fall of temperature produced
no effect, and there was a similar arrangement to prevent overwinding. I
believe that a rise of eight or nine degrees Fahrenheit was sufficient
to wind up the clock for twenty-four hours."

Another indirect method of winding a watch is thus described by
Professor Ball:

    "I have in my possession a watch, known as the Lohr patent, which
    produces the same effect by somewhat different means. Inside the
    case is a steel weight, and if the watch is carried in a pocket this
    weight rises and falls at every step one takes, somewhat after the
    manner of a pedometer. The weight is moved up by the action of the
    person who has it in his pocket, and in falling the weight winds up
    the spring of the watch. On the face is a small dial showing the
    number of hours for which the watch is wound up. As soon as the hand
    of this dial points to fifty-six hours, the train of levers which
    wind up the watch disconnects automatically, so as to prevent
    overwinding the spring, and it reconnects again as soon as the watch
    has run down eight hours. The watch is an excellent time-keeper, and
    a walk of about a couple of miles is sufficient to wind it up for
    twenty-four hours."

Dr. Hooper, in his "Rational Recreations," has described a method of
driving a clock by the motion of the tides, and it would not be
difficult to contrive a very simple arrangement which would obtain from
that source much more power than is required for that purpose. Indeed
the probability is that many persons now living will see the time when
all our railroads, factories, and lighting plants will be operated by
the tides of the ocean. It is only a question of return for capital, and
it is well known that that has been falling steadily for years. When the
interest on investments falls to a point sufficiently low, the tides
will be harnessed and the greater part of the heat, light, and power
that we require will be obtained from the immense amount of energy that
now goes to waste along our coasts.

Another contrivance by which a seemingly perpetual motion may be
obtained is the dry pile or column of De Luc. The pile consists of a
series of disks of gilt and silvered paper placed back to back and
alternating, all the gilt sides facing one way and all the silver sides
the other. The so-called gilding is really Dutch metal or copper, and
the silver is tin or zinc, so that the two actually form a voltaic
couple. Sometimes the paper is slightly moistened with a weak solution
of molasses to insure a certain degree of dampness; this increases the
action, for if the paper be artificially dried and kept in a perfectly
dry atmosphere, the apparatus will not work. A pair of these piles, each
containing two or three thousand disks the size of a quarter of a
dollar, may be arranged side by side, vertically, and two or three
inches apart. At the lower ends they are connected by a brass plate, and
the upper ends are each surmounted by a small metal bell and between
these bells a gilt ball, suspended by a silk thread, keeps vibrating
perpetually. Many years ago I made a pair of these columns which kept a
ball in motion for nearly two years, and Professor Silliman tells us
that "a set of these bells rang in Yale College laboratory for six or
eight years unceasingly." How much longer the columns would have
continued to furnish energy sufficient to cause the balls to vibrate, it
might be difficult to determine. The amount of energy required is
exceedingly small, but since the columns are really nothing but a
voltaic pile, it is very evident that after a time they would become
exhausted.

Such a pair of columns, covered with a tall glass shade, form a very
interesting piece of bric-a-brac, especially if the bells have a sweet
tone, but the contrivance is of no practical use except as embodied in
Bohnenberger's electroscope.

Inventions of this kind might be multiplied indefinitely, but none of
these devices can be called a perpetual motion because they all depend
for their action upon energy derived from external sources other than
gravity. But the authors of these inventions are not to be classed with
the regular perpetual-motion-mongers. The purposes for which these
arrangements were invented were legitimate, and the contrivances
answered fully the ends for which they were intended. The real
perpetual-motion-seekers are men of a different stamp, and their schemes
readily fall into one of these three classes: 1. ABSURDITIES, 2.
FALLACIES, 3. FRAUDS. The following is a description of the most
characteristic machines and apparatus of which accounts have been
published.


1. ABSURDITIES

In this class may be included those inventions which have been made or
suggested by honest but ignorant persons in direct violation of the
fundamental principles of mechanics and physics. Such inventions if
presented to any expert mechanic or student of science, would be at once
condemned as impracticable, but as a general rule, the inventors of
these absurd contrivances have been so confident of success, that they
have published descriptions and sketches of them, and even gone so far
as to take out patents before they have tested their inventions by
constructing a working machine. It is said, that at one time the United
States Patent Office issued a circular refusal to all applicants for
patents of this kind, but at present instead of sending such a circular,
the applicant is quietly requested to furnish a _working_ model of his
invention and that usually ends the matter. While I have no direct
information on the subject, I suspect that the circular was withdrawn
because of the amount of useless correspondence, in the shape of foolish
replies and arguments, which it drew forth. To require a working model
is a reasonable request and one for which the law duly provides, and
when a successful model is forthcoming, a patent will no doubt be
granted; but until that is presented the officials of the Patent Office
can have no positive information in regard to the practicability of the
invention.

The earliest mechanical device intended to produce perpetual motion is
that known as the overbalancing wheel. This is described in a sketch
book of the thirteenth century by Wilars de Honecourt, an architect of
the period, and since then it has been re-invented hundreds of times. In
its simplest forms it is thus described and figured by Ozanam:

    "Fig. 5 represents a large wheel, the circumference of which is
    furnished, at equal distances, with levers, each bearing at its
    extremity a weight, and movable on a hinge so that in one direction
    they can rest upon the circumference, while on the opposite side,
    being carried away by the weight at the extremity, they are obliged
    to arrange themselves in the direction of the radius continued. This
    being supposed, it is evident that when the wheel turns in the
    direction ABC, the weights A, B, and C will recede from the center;
    consequently, as they act with more force, they will carry the wheel
    towards that side; and as a new lever will be thrown out, in
    proportion as the wheel revolves, it thence follows, say they, that
    the wheel will continue to move in the same direction. But
    notwithstanding the specious appearance of this reasoning,
    experience has proved that the machine will not go; and it may
    indeed be demonstrated that there is a certain position in which the
    center of gravity of all these weights is in the vertical plane
    passing through the point of suspension, and that therefore it must
    stop."

[Illustration: Fig. 5.]

[Illustration: Fig. 6.]

Another invention of a similar kind is thus described by the same
author:

    "In a cylindric drum, in perfect equilibrium on its axis, are formed
    channels as seen in Fig. 6, which contain balls of lead or a certain
    quantity of quicksilver. In consequence of this disposition, the
    balls or quicksilver must, on the one side, ascend by approaching
    the center, and on the other must roll towards the circumference.
    The machine ought, therefore, to turn incessantly towards that
    side."

In his "Course of Lectures on Natural Philosophy," Dr. Thomas Young
speaks of these contrivances as follows:

    "One of the most common fallacies, by which the superficial
    projectors of machines for obtaining perpetual motion have been
    deluded, has arisen from imagining that any number of weights
    ascending by a certain path, on one side of the center of motion and
    descending on the other at a greater distance, must cause a constant
    preponderance on the side of the descent: for this purpose the
    weights have either been fixed on hinges, which allow them to fall
    over at a certain point, so as to become more distant from the
    center, or made to slide or roll along grooves or planes which lead
    them to a more remote part of the wheel, from whence they return as
    they ascend; but it will appear on the inspection of such a machine,
    that although some of the weights are more distant from the center
    than others, yet there is always a proportionately smaller number
    of them on that side on which they have the greatest power, so that
    these circumstances precisely counterbalance each other."

[Illustration: Fig. 7.]

He then gives the illustration (Fig. 7), shown on the preceding page, of
"a wheel supposed to be capable of producing a perpetual motion; the
descending balls acting at a greater distance from the center, but being
fewer in number than the ascending. In the model, the balls may be kept
in their places by a plate of glass covering the wheel."

[Illustration: Fig. 8.]

A more elaborate arrangement embodying the same idea is figured and
described by Ozanam. The machine, which is shown in Fig. 8, consists of
"a kind of wheel formed of six or eight arms, proceeding from a center
where the axis of motion is placed. Each of these arms is furnished with
a receptacle in the form of a pair of bellows: but those on the opposite
arms stand in contrary directions, as seen in the figure. The movable
top of each receptacle has affixed to it a weight, which shuts it in one
situation and opens it in the other. In the last place, the bellows of
the opposite arms have a communication by means of a canal, and one of
them is filled with quicksilver.

"These things being supposed, it is visible that the bellows on the one
side must open, and those on the other must shut; consequently, the
mercury will pass from the latter into the former, while the contrary
will be the case on the opposite side."

Ozanam naïvely adds: "It might be difficult to point out the deficiency
of this reasoning; but those acquainted with the true principles of
mechanics will not hesitate to bet a hundred to one, that the machine,
when constructed, will not answer the intended purpose."

That this bet would have been a perfectly safe one must be quite evident
to any person who has the slightest knowledge of practical mechanics,
and yet the fundamental idea which is embodied in this and the other
examples which we have just given, forms the basis of almost all the
attempts which have been made to produce a perpetual motion by purely
mechanical means.

The hydrostatic paradox by which a few ounces of liquid may apparently
balance many pounds, or even tons, has frequently suggested a form of
apparatus designed to secure a perpetual motion. Dr. Arnott, in his
"Elements of Physics," relates the following anecdote: "A projector
thought that the vessel of his contrivance, represented here (Fig. 9),
was to solve the renowned problem of the perpetual motion. It was
goblet-shaped, lessening gradually towards the bottom until it became a
tube, bent upwards at _c_ and pointing with an open extremity into the
goblet again. He reasoned thus: A pint of water in the goblet _a_ must
more than counterbalance an ounce which the tube _b_ will contain, and
must, therefore, be constantly pushing the ounce forward into the vessel
again at _a_, and keeping up a stream or circulation, which will cease
only when the water dries up. He was confounded when a trial showed him
the same level in _a_ and in _b_."

[Illustration: Fig. 9.]

This suggestion has been adopted over and over again by sanguine
inventors. Dircks, in his "Perpetuum Mobile," tells us that a
contrivance, on precisely the same principle, was proposed by the Abbé
de la Roque, in "Le Journal des Sçavans," Paris, 1686. The instrument
was a U tube, one leg longer than the other and bent over, so that any
liquid might drop into the top end of the short leg, which he proposed
to be made of wax, and the long one of iron. Presuming the liquid to be
more condensed in the metal than the wax tube, it would flow from the
end into the wax tube and so continue.

This is a typical case. A man of learning and of high position is
so confident that his theory is right that he does not think it
worth while to test it experimentally, but rushes into print and
immortalizes himself as the author of a blunder. It is safe to say
that this absurd invention will do more to perpetuate his name than
all his learning and real achievements. And there are others in the
same predicament--circle-squarers who, a quarter of a century hence,
will be remembered for their errors when all else connected with them
will be forgotten.

To every miller whose mill ceased working for want of water, the idea
has no doubt occurred that if he could only pump the water back again
and use it a second or a third time he might be independent of dry or
wet seasons. Of course no practical miller was ever so far deluded as to
attempt to put such a suggestion into practice, but innumerable machines
of this kind, and of the most crude arrangement, have been sketched and
described in magazines and papers. Figures of wheels driving an ordinary
pump, which returns to an elevated reservoir the water which has driven
the wheel, are so common that it is not worth while to reproduce any of
them. In the following attempt, however, which is copied from Bishop
Wilkins' famous book, "Mathematical Magic" (1648), the well-known
Archimedean screw is employed instead of a pump, and the naïveté of the
good bishop's description and conclusion are well worth the space they
will occupy.

After an elaborate description of the screw, he says: "These things,
considered together, it will hence appear how a perpetual motion may
seem easily contrivable. For, if there were but such a water-wheel made
on this instrument, upon which the stream that is carried up may fall
in its descent, it would turn the screw round, and by that means convey
as much water up as is required to move it; so that the motion must
needs be continual since the same weight which in its fall does turn the
wheel, is, by the turning of the wheel, carried up again. Or, if the
water, falling upon one wheel, would not be forcible enough for this
effect, why then there might be two, or three, or more, according as the
length and elevation of the instrument will admit; by which means the
weight of it may be so multiplied in the fall that it shall be
equivalent to twice or thrice that quantity of water which ascends; as
may be more plainly discerned by the following diagram (Fig. 10):

"Where the figure LM at the bottom does represent a wooden cylinder with
helical cavities cut in it, which at AB is supposed to be covered over
with tin plates, and three waterwheels, upon it, HIK; the lower cistern,
which contains the water, being CD. Now, this cylinder being turned
round, all the water which from the cistern ascends through it, will
fall into the vessel at E, and from that vessel being conveyed upon the
water-wheel H, shall consequently give a circular motion to the whole
screw. Or, if this alone should be too weak for the turning of it, then
the same water which falls from the wheel H, being received into the
other vessel F, may from thence again descend on the wheel I, by which
means the force of it will be doubled. And if this be yet insufficient,
then may the water, which falls on the second wheel I, be received into
the other vessel G, and from thence again descend on the third wheel at
K; and so for as many other wheels as the instrument is capable of. So
that besides the greater distance of these three streams from the center
or axis by which they are made so much heavier; and besides that the
fall of this outward water is forcible and violent, whereas the ascent
of that within is natural--besides all this, there is twice as much
water to turn the screw as is carried up by it.

[Illustration: Fig. 10.]

"But, on the other side, if all the water falling upon one wheel would
be able to turn it round, then half of it would serve with two wheels,
and the rest may be so disposed of in the fall as to serve unto some
other useful, delightful ends.

"When I first thought of this invention, I could scarce forbear, with
Archimedes, to cry out 'Eureka! Eureka!' it seeming so infallible a way
for the effecting of a perpetual motion that nothing could be so much as
probably objected against it; but, upon trial and experience, I find it
altogether insufficient for any such purpose, and that for these two
reasons:

"1. The water that ascends will not make any considerable stream in the
fall.

"2. This stream, though multiplied, will not be of force enough to turn
about the screw."

How well it would have been for many of those inventors, who supposed
that they had discovered a successful perpetual motion, if they had only
given their contrivances a fair and unprejudiced test as did the good
old bishop!

A modification of this device, in which mercury is used instead of
water, is thus described by a correspondent of "The Mechanic's
Magazine." (London.)

    "In Fig. 11, A is the screw turning on its two pivots GG; B is a
    cistern to be filled above the level of the lower aperture of the
    screw with mercury, which I conceive to be preferable to water on
    many accounts, and principally because it does not adhere or
    evaporate like water; C is a reservoir, which, when the screw is
    turned round, receives the mercury which falls from the top; there
    is a pipe, which, by the force of gravity, conveys the mercury from
    the reservoir C on to (what for want of a better term may be called)
    the float-board E, fixed at right angles to the center [axis] of the
    screw, and furnished at its circumference with ridges or floats to
    intercept the mercury, the moment and weight of which will cause the
    float-board and screw to revolve, until, by the proper inclination
    of the floats, the mercury falls into the receiver F, from whence it
    again falls by its spout into the cistern G, where the constant
    revolution of the screw takes it up again as before."

He then suggests some difficulties which the ball, seen just under the
letter E, is intended to overcome, but he confesses that he has never
tried it, and to any practical mechanic it is very obvious that the
machine will not work. But we give the description in the language of
the inventor, as a fair type of this class of perpetual-motion machines.

[Illustration: Fig. 11.]

In the year 1790 a Doctor Schweirs took out a patent for a machine in
which small metal balls were used instead of a liquid, and they were
raised by a sort of chain pump which delivered them upon the
circumference of a large wheel, which was thus caused to revolve. It was
claimed for this invention that it kept going for some months, but any
mechanic who will examine the Doctor's drawing must see that it could
not have continued in motion after the initial impulse had been
expended.

That property of liquids known as capillary attraction has been
frequently called to the aid of perpetual-motion seekers, and the fact
that although water will, in capillary tubes and sponges, rise several
inches above the general level, it will not overflow, has been a
startling surprise to the would-be inventors. Perhaps the most notable
instance of a mistake of this kind occurred in the case of the famous
Sir William Congreve, the inventor of the military rockets that bore his
name, and the author of certain improvements in matches which were
called after him. It was thus described and figured in an article which
appeared in the "Atlas" (London) and was copied into "The Mechanic's
Magazine" (London) for 1827:

    "The celebrated Boyle entertained an idea that perpetual motion
    might be obtained by means of capillary attraction; and, indeed,
    there seems but little doubt that nature has employed this force in
    many instances to produce this effect.

    "There are many situations in which there is every reason to believe
    that the sources of springs on the tops and sides of mountains
    depend on the accumulation of water created at certain elevations by
    the operation of capillary attraction, acting in large masses of
    porous material, or through laminated substances. These masses being
    saturated, in process of time become the sources of springs and the
    heads of rivers; and thus by an endless round of ascending and
    descending waters, form, on the great scale of nature, an incessant
    cause of perpetual motion, in the purest acceptance of the term, and
    precisely on the principle that was contemplated by Boyle. It is
    probable, however, that any imitation of this process on the limited
    scale practicable by human art would not be of sufficient magnitude
    to be effective. Nature, by the immensity of her operations, is able
    to allow for a slowness of process which would baffle the attempts
    of man in any direct and simple imitation of her works. Working,
    therefore, upon the same causes, he finds himself obliged to take a
    more complicated mode to produce the same effect.

    "To amuse the hours of a long confinement from illness, Sir William
    Congreve has recently contrived a scheme of perpetual motion,
    founded on this principle of capillary attraction, which, it is
    apprehended, will not be subject to the general refutation
    applicable to those plans in which the power is supposed to be
    derived from gravity only. Sir William's perpetual motion is as
    follows:

    [Illustration: Fig. 12.]

    "Let ABC, Fig. 12, be three horizontal rollers fixed in a frame;
    aaa, etc., is an endless band of sponge, running round these
    rollers; and bbb, etc., is an endless chain of weights, surrounding
    the band of sponge, and attached to it, so that they must move
    together; every part of this band and chain being so accurately
    uniform in weight that the perpendicular side AB will, in all
    positions of the band and chain, be in equilibrium with the
    hypothenuse AC, on the principle of the inclined plane. Now, if the
    frame in which these rollers are fixed be placed in a cistern of
    water, having its lower part immersed therein, so that the water's
    edge cuts the upper part of the rollers BC, then, if the weight and
    quantity of the endless chain be duly proportioned to the thickness
    and breadth of the band of sponge, the band and chain will, on the
    water in the cistern being brought to the proper level, begin to
    move round the rollers in the direction AB, by the force of
    capillary attraction, and will continue so to move. The process is
    as follows:

    "On the side AB of the triangle, the weights bbb, etc., hanging
    perpendicularly alongside the band of sponge, the band is not
    compressed by them, and its pores being left open, the water at the
    point x, at which the band meets its surface, will rise to a certain
    height y, above its level, and thereby create a load, which load
    will not exist on the ascending side CA, because on this side the
    chain of weights compresses the band at the water's edge, and
    squeezes out any water that may have previously accumulated in it;
    so that the band rises in a dry state, the weight of the chain
    having been so proportioned to the breadth and thickness of the band
    as to be sufficient to produce this effect. The load, therefore, on
    the descending side AB, not being opposed by any similar load on the
    ascending side, and the equilibrium of the other parts not being
    disturbed by the alternate expansion and compression of the sponge,
    the band will begin to move in the direction AB; and as it moves
    downwards, the accumulation of water will continue to rise, and
    thereby carry on a constant motion, provided the load at xy be
    sufficient to overcome the friction on the rollers ABC.

    "Now to ascertain the quantity of this load in any particular
    machine, it must be stated that it is found by experiment that the
    water will rise in a fine sponge about an inch above its level; if,
    therefore, the band and sponge be one foot thick and six feet broad,
    the area of its horizontal section in contact with the water would
    be 864 square inches, and the weight of the accumulation of water
    raised by the capillary attraction being one inch rise upon 864
    square inches, would be 30 lb., which, it is conceived, would be
    much more than equivalent to the friction of the rollers."

The article, inspired no doubt by Sir William, then goes on to give
elaborate reasons for the success of the device, but all these are met
by the damning fact that the machine never worked. Some time afterwards
Sir William, at considerable expense, published a pamphlet in which he
explained and defended his views. If he had only had a working model
made and the thing had continued in motion for a few hours, he would
have silenced all objectors far more quickly and forcibly than he ever
could have done by any amount of argument.

And in his case there could have been no excuse for his not making a
small machine after the plans that he published and even patented. He
was wealthy and could have commanded the services of the best mechanics
in London, but no working model was ever made. Many inventors of
perpetual-motion machines offer their poverty as an excuse for not
making a model or working machine. Thus Dircks, in his "Perpetuum
Mobile" gives an account of "a mechanic, a model maker, who had a neat
brass model of a time-piece, in which were two steel balls A and B;--B
to fall into a semicircular gallery C, and be carried to the end D of a
straight trough DE; while A in its turn rolls to E, and so on
continuously; only the gallery C not being screwed in its place, we are
desired to take the will for the deed, until twenty shillings be raised
to complete this part of the work!"

And Mr. Dircks also quotes from the "Builder" of June, 1847: "This vain
delusion, if not still in force, is at least as standing a fallacy as
ever. Joseph Hutt, a frame-work knitter, in the neighborhood of the
enlightened town of Hinckley, professes to have discovered it [perpetual
motion] and only wants twenty pounds, as usual, to set it agoing."

The following rather curious arrangement was described in "The
Mechanic's Magazine" for 1825.

"I beg leave to offer the prefixed device. The point at which, like all
the rest, it fails, I confess I did not (as I do now) plainly perceive
at once, although it is certainly very obvious. The original idea was
this--to enable a body which would float in a heavy medium and sink in
a lighter one, to pass successively through the one to the other, the
continuation of which would be the end in view. To say that valves
cannot be made to act as proposed will not be to show the _rationale_
(if I may so say) upon which the idea is fallacious."

The figure is supposed to be tubular, and made of glass, for the purpose
of seeing the action of the balls inside, which float or fall as they
travel from air through water and from water through air. The foot is
supposed to be placed in water, but it would answer the same purpose if
the bottom were closed.

DESCRIPTION OF THE ENGRAVING, FIG. 13. No. 1, the left leg, filled with
water from B to A. 2 and 3, valves, having in their centers very small
projecting valves; they all open upwards. 4, the right leg, containing
air from A to F. 5 and 6, valves, having very small ones in their
centers; they all open downwards. The whole apparatus is supposed to be
air and water-tight. The round figures represent hollow balls, which
will sink one-fourth of their bulk in water (of course will fall in
air); the weight therefore of three balls resting upon one ball in
water, as at E, will just bring its top even with the water's edge; the
weight of four balls will sink it under the surface until the ball
immediately over it is one-fourth its bulk in water, when the under ball
will escape round the corner at C, and begin to ascend.

"The machine is supposed (in the figure) to be in action, and No. 8 (one
of the balls) to have just escaped round the corner at C, and to be, by
its buoyancy, rising up to valve No. 3, striking first the small
projecting valve in the center, which when opened, the large one will
be raised by the buoyancy of the ball; because the moment the small
valve in the center is opened (although only the size of a pin's head),
No. 2 valve will have taken upon itself to sustain the whole column of
water from A to B. The said ball (No. 8) having passed through the valve
No. 3, will, by appropriate weights or springs, close; the ball will
proceed upwards to the next valve (No. 2), and perform the same
operation there. Having arrived at A, it will float upon the surface
three-fourths of its bulk out of water. Upon another ball in due course
arriving under it, it will be lifted quite out of the water, and fall
over the point D, pass into the right leg (containing air), and fall to
valve No. 5, strike and open the small valve in its center, then open
the large one, and pass through; this valve will then, by appropriate
weights or springs, close; the ball will roll on through the bent tube
(which is made in that form to gain time as well as to exhibit motion)
to the next valve (No. 6), where it will perform the same operation, and
then, falling upon the four balls at E, force the bottom one round the
corner at C. This ball will proceed as did No. 8, and the rest in the
same manner successively."

[Illustration: Fig. 13.]

That an ordinary amateur mechanic should be misled by such arguments is
perhaps not so surprising, when we remember that the famous John
Bernoulli claimed to have invented a perpetual motion based on the
difference between the specific gravities of two liquids. A translation
of the original Latin may be found in the Encyclopædia Britannica, Vol.
XVIII, page 555. Some of the premises on which he depends are, however,
impossibilities, and Professor Chrystal concludes his notice of the
invention thus: "One really is at a loss with Bernoulli's wonderful
theory, whether to admire most the conscientious statement of the
hypothesis, the prim logic of the demonstration--so carefully cut
according to the pattern of the ancients--or the weighty superstructure
built on so frail a foundation. Most of our perpetual motions were
clearly the result of too little learning; surely this one was the
product of too much."

A more simple device was suggested recently by a correspondent of
"Power." He describes it thus:

The J-shaped tube A, Fig. 14, is open at both ends, but tapers at the
lower end, as shown. A well-greased cotton rope C passes over the wheel
B and through the small opening of the tube with practically little or
no friction, and also without leakage. The tube is then filled with
water. The rope above the line WX balances over the pulley, and so does
that below the line YZ. The rope in the tube between these lines is
lifted by the water, while the rope on the other side of the pulley
between these lines is pulled downward by gravity.

[Illustration: Fig. 14.]

The inventor offers the above suggestion rather as a kind of puzzle than
as a sober attempt to solve the famous problem, and he concludes by
asking why it will not work?

In addition to the usual resistance or friction offered by the air to
all motion, there are four drawbacks:

1. The friction in its bearings of the axle of the wheel B.

2. The power required to bend and unbend the rope.

3. The friction of the rope in passing through the water from z to x and
its tendency to raise a portion of the water above the level of the
water at x.

4. The friction at the point y, this last being the most serious of all.
An "opening of the tube with practically little or no friction, and also
without leakage" is a mechanical impossibility. In order to have the
joint water-tight, the tube must hug the rope very tightly and this
would make friction enough to prevent any motion. And the longer the
column of water xz, the greater will be the tendency to leak, and
consequently the tighter must be the joint and the greater the friction
thereby created.

A favorite idea with perpetual-motion seekers is the utilization of the
force of magnetism. Some time prior to the year 1579, Joannes Taisnierus
wrote a book which is now in the British Museum and in which
considerable space is devoted to "Continual Motions" and to the solving
of this problem by magnetism. Bishop Wilkins in his "Mathematical
Magick" describes one of the many devices which have been invented with
this end in view. He says: "But amongst all these kinds of invention,
that is most likely, wherein a loadstone is so disposed that it shall
draw unto it on a reclined plane a bullet of steel, which steel as it
ascends near to the loadstone, may be contrived to fall down through
some hole in the plane, and so to return unto the place from whence at
first it began to move; and, being there, the loadstone will again
attract it upwards till coming to this hole, it will fall down again;
and so the motion shall be perpetual, as may be more easily conceivable
by this figure (Fig. 15):

"Suppose the loadstone to be represented at AB, which, though it have
not strength enough to attract the bullet C directly from the ground,
yet may do it by the help of the plane EF. Now, when the bullet is come
to the top of this plane, its own gravity (which is supposed to exceed
the strength of the loadstone) will make it fall into that hole at E;
and the force it receives in this fall will carry it with such a
violence unto the other end of this arch, that it will open the passage
which is there made for it, and by its return will again shut it: so
that the bullet (as at the first) is in the same place whence it was
attracted, and, consequently must move perpetually."

[Illustration: Fig. 15.]

Notwithstanding the positiveness of the "must" at the close of his
description, it is very obvious to any practical mechanic that the
machine will not move at all, far less move perpetually, and the bishop
himself, after carefully and conscientiously discussing the objections,
comes to the same conclusion. He ends by saying: "So that none of all
these magnetical experiments, which have been as yet discovered, are
sufficient for the effecting of a perpetual motion, though these kind of
qualities seem most conducible unto it, and perhaps hereafter it may be
contrived from them."

It has occurred to several would-be inventors of perpetual motion that
if some substance could be found which would prevent the passage of the
magnetic force, then by interposing a plate of this material at the
proper moment, between the magnet and the piece of iron to be
attracted, a perpetual motion might be obtained. Several inventors have
claimed that they had discovered such a non-conducting substance, but it
is needless to say that their claims had no foundation in fact, and if
they had discovered anything of the kind, it would have required just as
much force to interpose it as would have been gained by the
interposition. It has been fully proved that in every case where a
machine was made to work apparently by the interposition of such a
material, a fraud was perpetrated and the machine was really made to
move by means of some concealed springs or weights.

A correspondent of the "Mechanic's Magazine" (Vol. xii, London, 1829),
gives the following curious design for a "Self-moving Railway Carriage."
He describes it as a machine which, were it possible to make its parts
hold together unimpaired by rotation or the ravages of time, and to give
it a path encircling the earth, would assuredly continue to roll along
in one undeviating course until time shall be no more.

A series of inclined planes are to be erected in such a manner that a
cone will ascend one (its sides forming an acute angle), and being
raised to the summit, descend on the next (having parallel sides), at
the foot of which it must rise on a third and fall on a fourth, and so
continue to do alternately throughout.

The diagram, Fig. 16, is the section of a carriage A, with broad conical
wheels _a_, _a_, resting on the inclined plane _b_. The entrance to the
carriage is from above, and there are ample accommodations for goods and
passengers. "The most singular property of this contrivance is, that its
speed increases the more it is laden; and when checked on any part of
the road, it will, when the cause of stoppage is removed, proceed on its
journey by mere power of gravity. Its path may be a circular road formed
of the inclined planes. But to avoid a circuitous route, a double road
ought to be made. The carriage not having a retrograde motion on the
inclined planes, a road to set out upon, and another to return by, are
indispensable."

[Illustration: Fig. 16.]

How any one could ever imagine that such a contrivance would ever
continue in motion for even a short time, except, perhaps, on the famous
_descensus averni_, must be a puzzle to every sane mechanic. I therefore
give it as a climax to the absurdities which have been proposed in sober
earnest. As a fitting close, however, to this chapter of human folly, I
give the following joke from the "Penny Magazine," published by the
Society for the Diffusion of Useful Knowledge.

    "'Father, I have invented a perpetual motion!' said a little fellow
    of eight years old. 'It is thus: I would make a great wheel, and fix
    it up like a water-wheel; at the top I would hang a great weight,
    and at the bottom I would hang a number of little weights; then the
    great weight would turn the wheel half round and sink to the
    bottom, because it is so heavy: and when the little weights reach
    the top they would sink down, because they are so many; and thus the
    wheel would turn round for ever.'"

The child's fallacy is a type of all the blunders which are made on this
subject. Follow a projector in his description, and if it be not
perfectly unintelligible, which it often is, it always proves that he
expects to find certain of his movements alternately strong and
weak--not according to the laws of nature--but according to the wants of
his mechanism.


2. FALLACIES

Fallacies are distinguished from absurdities on the one hand and from
frauds on the other, by the fact that without any intentionally
fraudulent contrivances on the part of the inventor, they seem to
produce results which have a tendency to afford to certain enthusiasts a
basis of hope in the direction of perpetual motion, although usually not
under that name, for that is always explicitly disclaimed by the
promoters.

The most notable instance of this class in recent times was the
application of liquid air as a source of power, the claim having been
actually made by some of the advocates of this fallacy that a steamship
starting from New York with 1000 gallons of liquid air, could not only
cross the Atlantic at full speed but could reach the other side with
more than 1000 gallons of liquid air on board--the power required to
drive the vessel and to liquefy the surplus air being all obtained
during the passage by utilizing the original quantity of liquid air that
had been furnished in the first place.

That this was equivalent to perpetual motion, pure and simple, was
obvious even to those who were least familiar with such subjects, though
the idea of calling it perpetual motion was sternly repudiated by all
concerned--the term "perpetual motion" having become thoroughly
offensive to the ears of common-sense people, and consequently tending
to cast doubt over any enterprise to which it might be applied.

That liquid air is a real and wonderful discovery, and that for a
certain small range of purposes it will prove highly useful, cannot be
doubted by those who have seen and handled it and are familiar with its
properties, but that it will ever be successfully used as an economical
source of mechanical power is, to say the least, very improbable. That a
small quantity of the liquid is capable of doing an enormous amount of
work, and that under some conditions there is _apparently_ more power
developed than was originally required to liquefy the air, is
undoubtedly true, but when a careful quantitative examination is made of
the outgo and the income of energy, it will be found in this, as in
every similar case, that instead of a gain there is a very decided and
serious loss. The correct explanation of the fallacy was published in
the "Scientific American," by the late Dr. Henry Morton, president of
the Stevens Institute, and the same explanation and exposure were made
by the writer, nearly fifty years ago, in the case of a very similar
enterprise. The form of the fallacy in both cases is so similar and so
interesting that I shall make no apology for giving the details.

About the year 1853 or 1854, two ingenious mechanics of Rochester, N.
Y., conceived the idea that by using some liquid more volatile than
water, a great saving might be effected in the cost of running an
engine. At that time gasolene and benzine were unknown in commerce, and
the same was true in regard to bisulphide of carbon, but as the process
of manufacturing the latter was simple and the sources of supply were
cheap and apparently unlimited, they adopted that liquid. The name of
one of these inventors was Hughes and that of the other was Hill, and it
would seem that each had made the invention independently of the other.
They had a fierce conflict over the patent, but this does not concern us
except to this extent, that the records of the case may therefore be
found in the archives of the Patent Office at Washington, D.C. Hughes
was backed by the wealth of a well-known lawyer of Rochester, whose son
subsequently occupied a high office in the state of New York, and he
constructed a beautiful little steam-engine and boiler, made of the very
finest materials and with such skill and accuracy that it gave out a
very considerable amount of power in proportion to its size. The source
of heat was a series of lamps, fed, I think, with lard oil (this was
before the days of kerosene), and the exhibition test consisted in first
filling the boiler with water, and noting the time that it took to get
up a certain steam pressure as shown by the gage. After this test,
bisulphide of carbon was added to the water, and the time and pressure
were noted. The difference was of course remarkable, and altogether in
favor of the new liquid. The exhaust was carried into a vessel of cold
water and as bisulphide of carbon is very easily condensed and very
heavy, almost the entire quantity used was recovered and used over and
over again.

But to the uninstructed onlooker, the most remarkable part of the
exhibition was when the steam pressure was so far lowered that the
engine revolved very slowly, and then, on a little bisulphide being
injected into the boiler, the pressure would at once rise, and the
engine would work with great rapidity. This seemed almost like magic.

The same experiment was tried on an engine of twelve horse-power, and
with a like result. When the steam pressure had fallen so far that the
engine began to move quite slowly, a quantity of the bisulphide would be
injected into the boiler and the pressure would at once rise, the engine
would move with renewed vigor, and the fly-wheel would revolve with
startling velocity. All this was seen over and over again by myself and
others. At that time the writer, then quite a young man, had just
recovered from a very severe illness and was making a living by teaching
mechanical drawing and making drawings for inventors and others, and in
the course of business he was brought into contact with some parties who
thought of investing in the new and apparently wonderful invention. They
employed him to examine it and give an opinion as to its value. After
careful consideration and as thorough a calculation as the data then at
command would allow, he showed his clients that the tests which had been
exhibited to them proved nothing, and that if a clear proof of the value
of the invention was to be given, it must be after a run of many hours
and not of a few minutes, and against a properly adjusted load, the
amount of which had been carefully ascertained. This test was never
made, or if made the results were not communicated to the prospective
purchasers; the negotiations fell through, and the invention which was
to have revolutionized our mechanical industries fell into "innocuous
desuetude."

That the inventors were honest I have no doubt. They were themselves
deceived when they saw the engine start off with tremendous velocity as
soon as a little bisulphide of carbon was injected into the boiler, and
they failed to see that this spurt, if I may use the expression, was
simply due to a draft upon capital previously stored up. The capacity of
bisulphide of carbon for heat is quite low, when compared with that of
water; its vaporizing point is also much lower and consequently, an
ordinary boiler full of hot water contains enough heat to vaporize a
considerable quantity of bisulphide of carbon at a pretty high pressure.

In even a still greater measure the same is true of liquid air, and this
was the underlying fallacy in the case of the tests made with liquid-air
motors.


3. FRAUDS

But while the inventors of these schemes may have been honest, there is
another class who deliberately set out to perpetrate a fraud. Their
machines work, and work well, but there is always some concealed source
of power, which causes them to move. As a general rule, such inventors
form a company or corporation of unlimited "lie-ability," as De Morgan
phrases it, and then they proceed by means of flaring prospectuses and
liberal advertising, to gather in the dupes who are attracted by their
seductive promises of enormous returns for a very small outlay. Perhaps
the most widely known of these fraudulent schemes of recent years was
the notorious Keeley motor, the originator of which managed to hoodwink
a respectable old lady, and to draw from her enormous supplies of cash.
At his death, however, the absolutely fraudulent nature of his
contrivances was fully disclosed, and nothing more has been heard of
his alleged discovery. But, while he lived and was able to put forward
claims based upon some apparent results, he found plenty of fools who
accepted the idea that there is nothing impossible to science.

It is true that the Keeley motor was examined by several committees and
some very respectable gentlemen acted in such a way as to give a seeming
endorsement of the scheme, but it must not be supposed for an instant
that any well-educated engineers and scientific men were deceived by Mr.
Keeley's nonsense. The very fact that he refused to allow a complete
examination of his machine by intelligent practical men, ought to have
been enough to condemn his scheme, for if he had really made the
discovery which he claimed there would have been no difficulty in
proving it practically and thoroughly, and then he might have formed
company after company that would have rewarded him with "wealth beyond
the dreams of avarice."

The Keeley motor was not put forward as a perpetual motion; in these
days none of these schemes is admitted to be a perpetual motion, for
that term has now become exceedingly offensive and would condemn any
invention; but the result is the same in the end, and the whole history
of perpetual motion is permeated with frauds of this kind, some of them
having been so simple that they were obvious to even the most unskilled
observer, while others were exceedingly complicated and most ingeniously
concealed. Many years ago a number of these fraudulent perpetual-motion
machines were manufactured in America and sent over to Great Britain for
exhibition, and quite a lucrative business was done by showing them in
various towns. But the fraud was soon detected and the British police
then made it too warm for these swindlers.

Mr. Dircks, in his "Perpetuum Mobile," has given accounts of quite a
number of these impostures. The following are some of the most notable:

M. Poppe of Tübingen tells of a clock made by M. Geiser, which was an
admirable piece of mechanism and seemed to have solved this great
problem in an ingenious and simple manner, but it deceived only for a
time. When thoroughly examined inwardly and outwardly, some time after
his death, it was found that the center props supporting its cylinders
contained cleverly constructed, hidden clock-work, wound up by inserting
a key in a small hole under the second-hand.

Another case was that of a man named Adams who exhibited, for eight or
nine days, his pretended perpetual motion in a town in England and took
in the natives for fifty or sixty pounds. Accident, however, led to a
discovery of the imposture. A gentleman, viewing the machine took hold
of the wheel or trundle and lifted it up a little, which probably
disengaged the wheels that connected the hidden machinery in the plinth,
and immediately he heard a sound similar to that of a watch when the
spring is running down. The owner was in great anger and directly put
the wheel into its proper position, and the machine again went around as
before. The circumstance was mentioned to an intelligent person who
determined to find out and expose the imposture. He took with him a
friend to view the machine and they seated themselves one on each side
of the table upon which the machine was placed. They then took hold of
the wheel and trundle and lifted them up, there being some play in the
pivots. Immediately the hidden spring began to run down and they
continued to hold the machine in spite of the endeavors of the owner to
prevent them. When the spring had run down, they placed the machine
again on the table and offered the owner fifty pounds if it could then
set itself going, but notwithstanding his fingering and pushing, it
remained motionless. A constable was sent for, the impostor went before
a magistrate and there signed a paper confessing his perpetual motion to
be a cheat.

In the "Mechanic's Magazine," Vol. 46, is an account of a perpetual
motion, constructed by one Redhoeffer of Pennsylvania, which obtained
sufficient notoriety to induce the Legislature to appoint a committee to
enquire into its merits. The attention of Mr. Lukens was turned to the
subject, and although the actual moving cause was not discovered, yet
the deception was so ingeniously imitated in a machine of similar
appearance made by him and moved by a spring so well concealed, that the
deceiver himself was deceived and Redhoeffer was induced to believe that
Mr. Lukens had been successful in obtaining a moving power in some way
in which he himself had failed, when he had produced a machine so
plausible in appearance as to deceive the public.

Instances of a similar kind might be multiplied indefinitely.

The experienced mechanic who reads the descriptions here given of the
various devices which have been proposed for the construction of a
perpetual-motion machine must be struck with the childish simplicity of
the plans which have been offered; and those who will search the pages
of the mechanical journals of the last century or who will examine the
two closely printed volumes in which Mr. Dircks has collected almost
everything of the kind, will be astonished at the sameness which
prevails amongst the offerings of these would-be inventors. Amongst the
hundreds, or, perhaps, thousands, of contrivances which have been
described, there is probably not more than a dozen kinds which differ
radically from each other; the same arrangement having been invented and
re-invented over and over again. And one of the strange features of the
case is that successive inventors seem to take no note of the failure of
those predecessors who have brought forward precisely the same
combination of parts under a very slightly different form.

It is true that we occasionally find a very elaborate and apparently
complicated machine, but in such cases it will be found, on close
examination, to owe its apparent complexity to a mere multiplication of
parts; no real inventive ingenuity is exhibited in any case.

Another singular characteristic of almost all those who have devoted
themselves to the search for a perpetual motion is their absolute
confidence in the success of the plans which they have brought forth. So
confident are they in the soundness of their views and so sure of the
success of their schemes that they do not even take the trouble to test
their plans but announce them as accomplished facts, and publish their
sketches and descriptions as if the machine was already working without
a hitch. Indeed, so far was one inventor carried away with this feeling
of confidence in the success of his machine that he no longer allowed
himself to be troubled with any doubts as to the machine's _going_ but
was greatly puzzled as to what means he should take to _stop_ it after
it had been set in motion!

These facts, which are well known to all who have been brought into
contact with this class of minds, explain many otherwise puzzling
circumstances and enable us to place a proper value on assertions
which, if not made so positively and by such apparently good authority,
would be at once condemned as deliberate falsehoods. That falsehood,
pure and simple, has formed the basis of a good many claims of this
kind, there can be no doubt, but at the same time, it is probable that
some of the claimants really deceived themselves and attributed to
causes other than radical errors of theory, the fact that their machines
would not continue to move.

While many have claimed the actual invention of a perpetual motion it is
very certain that not one has ever succeeded. How, then, are we to
explain the statements which have been made in regard to Orffyreus and
the claims of the Marquis of Worcester? For both of these men it is
claimed that they constructed wheels which were capable of moving
perpetually and apparently strong testimony is offered in support of
these assertions.

In the famous "Century of Inventions," published by the Marquis in 1663,
four years before his death, the celebrated 56th article reads as
follows (_verbatim et literatim_):

    "To provide and make that all the Weights of the descending side of
    a Wheel shall be perpetually further from the Centre, then those of
    the mounting side, and yet equal in number and heft to the one side
    as the other. A most incredible thing, if not seen, but tried before
    the late king (of blessed memory) in the _Tower_, by my directions,
    two Extraordinary Embassadors accompanying His Majesty, and the Duke
    of _Richmond_ and Duke _Hamilton_, with most of the Court, attending
    Him. The Wheel was 14. Foot over, and 40. Weights of 50. pounds
    apiece. Sir _William Balfore_, then Lieutenant of the _Tower_, can
    justifie it, with several others. They all saw, that no sooner these
    great Weights passed the Diameter-line of the lower side, but they
    hung a foot further from the Centre, nor no sooner passed the
    Diameter-line of the upper side, but they hung a foot nearer. Be
    pleased to judge the consequence."

Such is the account given by the Marquis himself, and that he exhibited
such a wheel at the time and place which he names, I have not the least
doubt. And that some of the weights on one side hung a foot further from
the center than did weights on the other side is also no doubt true,
but, as the judging of the "consequence" is left to ourselves we know
that after the first impulse given to it had been expended, the wheel
would simply stand still unless kept in motion by some external force.

[Illustration: Fig. 17.]

Mr. Dircks in his "Life, Times and Scientific Labours of the Second
Marquis of Worcester," gives an engraving of a wheel which complies with
all the conditions laid down by the Marquis and which is thus described:

    "Let the annexed diagram, Fig. 17, represent a wheel of 14 feet in
    diameter, having 40 spokes, seven feet each, and with an inner rim
    coinciding with the periphery, at one foot distance all round. Next
    provide 40 balls or weights, hanging in the center of cords or
    chains two feet long. Now, fasten one end of this cord at the top of
    the center spoke C, and the other end of the cord to the next
    right-hand spoke one foot below the upper end, or on the inner ring;
    proceed in like manner with every other spoke in succession; and it
    will be found that, at A, the cord will have the position shown
    outside the wheel; while at B, C, and D, it will also take the
    respective positions, as shown on the outside. The result in this
    case will be, that all the weights on the side A, C, D, hang to the
    great or outer circle, while on the side B, C, D, all the weights
    are suspended from the lesser or inner circle. And if we reverse the
    motion of the wheel, turning it from the right to the left hand, we
    shall reverse these positions also (the lower end of the cord
    sliding in a groove towards a left-hand spoke), but without the
    wheel having any tendency to move of itself."

But it is quite as likely that the wheel constructed by the Marquis was
like one of the "overbalancing" wheels described at the beginning of
this article.

It is upon this "scantling" that has been based the claim that the
Marquis really invented a perpetual motion, but to those who have seen
much of inventors of this kind, the discrepancy between the suggested
claim made by the Marquis and what we know must have been the actual
results, is easily explained. The Marquis felt sure that the thing
_ought to work_, and the excuse for its not doing so was probably the
imperfect manner in which the wheel was made. Only put a little better
work on it, says the inventor, and it will go.

Caspar Kaltoff, mechanician to the Marquis, probably got the wheel up in
a hurry so as to exhibit it on the occasion of the king's visit to the
tower. If he only had had a little more time he would have made a
machine that would have worked. (?) I have heard the same excuse under
almost the same circumstances, scores of times.

The case of Orffyreus was very different. The real name of this
inventor was Jean Ernest Elie-Bessler, and he is said to have
manufactured the name Orffyreus by placing his own name between two
lines of letters, and picking out alternate letters above and below. He
was educated for the church, but turned his attention to mechanics and
became an expert clock maker. His character, as given by his
contemporaries was fickle, tricky, and irascible. Having devised a
scheme for perpetual motion he constructed several wheels which he
claimed to be self-moving. The last one which he made was 12 feet in
diameter and 14 inches deep, the material being light pine boards,
covered with waxed cloth to conceal the mechanism. The axle was 8 inches
thick, thus affording abundant space for concealed machinery.

This wheel was submitted to the Landgrave of Hesse who had it placed in
a room which was then locked, and the lock secured with the Landgrave's
own seal. At the end of forty days it was found to be still running.

Professor Gravesande having been employed by the Landgrave to make an
examination and pronounce upon its merits, he endeavored to perform his
work thoroughly; this so irritated Orffyreus that the latter broke the
machine in pieces, and left on the wall a writing stating that he had
been driven to do this by the impertinent curiosity of the Professor!

I have no doubt that this was a clear case of fraud, and that the wheel
was driven by some mechanism concealed in the huge axle. As already
stated, Orffyreus was at one time a clock maker; now clocks have been
made to go for a whole year without having to be rewound, so that forty
days was not a very long time for the apparatus to keep in motion.

Professor Gravesande seems to have had some faith in the invention, but
then we must remember that it would not have been very difficult to
deceive an honest old professor whose confidence in humanity was
probably unbounded. The crowning argument against the genuineness of the
motion was the fact that the inventor refused to allow a thorough
examination, although a wealthy patron stood ready with a large reward
if the machine could be proved to be what was claimed.

And now comes up the question which has arisen in regard to other
problems, and will recur again and again to the end of the chapter: Is a
perpetual motion machine one of the scientific impossibilities?

The answer to this question lies in the fact that there is no principle
more thoroughly established than that no combination of machinery can
create energy. So far as our present knowledge of nature goes we might
as well try to create matter as to create energy, and the creation of
energy is essential to the successful working of a perpetual-motion
machine because some power must always be lost through friction and
other resistances and must be supplied from some source if the machine
is to keep on moving. And since the law of the conservation of energy
makes it positive that no more power can be given out by a machine than
was originally supplied to it, it seems as certain as anything can be
that the construction of a perpetual-motion machine is one of the
impossibilities.




V

TRANSMUTATION OF THE METALS


The "accursed thirst for gold" has existed from the earliest ages and,
as the apostle says, "is the root of all evil." Those who have a greed
for power, a craving for luxury, or a fever for lust, all think that
their wildest dreams might be realized if they could only command
sufficient gold. Never was there a more lurid picture of a mind inflamed
with all these evil passions than that set forth by Ben Jonson in the
Second Act of "The Alchemist," and who can doubt but that such desires
and dreams spurred on many, either to engage in an actual search for the
philosopher's stone, or to become the dupes of what Van Helmont calls "a
diabolical crew of gold and silver sucking flies and leeches."

As we might naturally expect, the early history of alchemy is shrouded
in myths and fables. Zosimos the Panopolite tells us that the art of
Alchemy was first taught to mankind by demons, who fell in love with the
daughters of men, and, as a reward for their favors, taught them all the
works and mysteries of nature. On this Boerhaave remarks:

    "This ancient fiction took its rise from a mistaken interpretation
    of the words of Moses, 'That the sons of God saw the daughters of
    men that they were fair, and they took them wives of all which they
    chose.'[2] From whence it was inferred that the sons of God were
    dæmons, consisting of a soul, and a visible but impalpable body,
    like the image in a looking-glass (to which notion we find several
    allusions in the evangelists); that they know all things, appeared
    to men and conversed with them, fell in love with women, had
    intrigues with them and revealed secrets. From the same fable
    probably arose that of the Sibyl, who is said to have obtained of
    Apollo the gift of prophecy, and revealing the will of heaven in
    return for a like favor. So prone is the roving mind of man to
    figments, which it can at first idly amuse itself with, and at
    length fall down and worship."

This idea of the supernatural origin of the arts permeates the ancient
mythology which everywhere teaches that men were taught the sacred arts
of medicine and chemistry by gods and demigods.

Modern science discards all these mythological accounts. Whatever
knowledge the ancients acquired of medicine and chemistry was, no doubt,
reached along two lines--pharmacy and metallurgy. That the pharmacist or
apothecary exercised his calling at a very early period we have positive
knowledge; thus in the Book of Ecclesiastes we are told that "dead flies
cause the ointment of the apothecary to send forth a stinking savor,"
and that men at a very early day found out the means of working iron,
copper, gold, silver, etc., is evident from the accounts given of Vulcan
and Tubalcain, as well as from the remains of old tools and weapons. And
that Alchemy, as it is generally understood, is a comparatively modern
outgrowth of these two arts, is pretty certain. No mention of the art of
converting the baser metals into gold, and no account of a universal
medicine or elixir of life is to be found in any of the authentic
writings of the ancients. Homer, Aristotle, and even Pliny are all
silent on the subject, and those writings which treat of the art, and
which claim an ancient origin, such as the books of Hermes Trismegistus,
are now regarded by the best authorities as spurious--the evidence that
they were the work of a far later age being irrefragable.

Several writers have taken the ground that the alchemical treatises
which have come down to us from the early writers on the subject, are
purely allegorical and do not relate to material things, but to the
principles of a higher religion which, in those days, it was dangerous
to expound in plain language. One or two elaborate works and several
articles supporting this view have been published, but the common-sense
reader who will glance through the immense collection of alchemical
tracts gathered together by Mangetus in two folio volumes of a thousand
pages each, will rise from such examination, very thoroughly convinced
that it was the actual metal gold, and the fabled universal medicine
that these writers had in view.

There can be little doubt that Geber, Roger Bacon, Albertus Magnus,
Raymond Lully, Helvetius, Van Helmont, Basil Valentine, and others,
describe very substantial things with a minuteness of detail which
leaves no room for doubt as to their materiality though we cannot always
be sure of their identity.

Some confusion of thought has been caused by the difference which has
been made between the terms alchemy and chemistry and their
applications. The word _alchemy_ is simply the word chemistry with the
Arabic word _al_, which signifies _the_, prefixed, and the history of
alchemy is really the history of chemistry--wild and erratic in its
beginnings, and giving rise to strange hopes and still stranger
theories, but ever working along the line of discovery and progress.
And, although many of the professional chemists or alchemists of the
middle ages were undoubted charlatans and quacks, yet did we not have
many of the same kind in the nineteenth century? We may use the word
alchemist as a term of reproach, and apply it to these early workers
because their theories appear to us to be absurd, but how do we know
that the chemists of the twenty-second century will not regard us in a
similar light, and set at naught the theories we so fondly cherish?

Only seven out of the large number of metals now catalogued by us were
known to the ancients; these were gold, silver, mercury, copper, tin,
lead, and iron. And as it happened that the list of so-called planets
also numbered exactly seven, it was thought that there must be a
connection between the two, and, consequently, in the alchemical
writings, each metal was called by the name of that one of the heavenly
bodies which was supposed to be connected with it in influence and
quality.

In the astronomy of the ancients, as is generally known, the earth
occupied the center of the universe, and the list of planets included
the sun and moon. After them came Mercury, Venus, Mars, Jupiter, and
Saturn. To the metal gold was given the name of Sol, or the sun, on
account of its brightness and its power of resisting corroding agents;
hence the compounds of gold were known as solar compounds and solar
medicines. As might have been expected, silver was assigned to Luna or
the moon, and in the modern pharmacop[oe]ia such terms as lunar caustic
and lunar salts still have a place. Mercury was, of course, appropriated
to the planet of that name. Copper was named after Venus, and cupreous
salts were known as venereal salts. Iron, probably from its being the
metal chiefly used for making arms and armor, was dedicated to Mars, and
we still speak of martial salts. Tin was named after Jupiter from his
brilliancy, the compounds of tin being called jovial salts. The dull,
leaden color of Saturn, with his apparently heavy and slow motion,
seemed to fit him for association with lead, and we still have the
saturnine ointment as a reminder of old alchemical times.

Of these metals gold was supposed to be the only one that was perfect,
and the belief was general that if the others could be purified and
perfected they would be changed to gold. Many of the old chemists worked
faithfully and honestly to accomplish this, but the path to wealth
seemed so direct and the means for deception were so ready and simple,
that large numbers of quacks and charlatans entered the field and held
out the most alluring inducements to dupes who furnished them liberally
with money and other necessaries in the hope that when the discovery was
made they would be put in possession of unbounded wealth. These dupes
were easily deceived and led astray by simple frauds, which scarcely
rose to the level of amateur legerdemain. In the "Memoirs of the Academy
of Sciences" for 1772, M. Geoffroy gives an account of the various modes
in which the frauds of these swindlers were carried on. The following
are a few of their tricks: Instead of the mineral substances which they
pretended to transmute they put a salt of gold or silver at the bottom
of the crucible, the mixture being covered with some powdered crucible
and gum water or wax so that it might look like the bottom of the
crucible. Another method was to bore a hole in a piece of charcoal, fill
the hole with fine filings of gold or silver, stopping it with powered
charcoal, mixed with some agglutinant so that the whole might look
natural. Then when the charcoal burned away, the silver or gold was
found in the bottom of the crucible. Or they soaked charcoal in a
solution of these metals and threw the charcoal, when powdered, upon the
material to be transmuted. Sometimes they whitened gold with mercury and
made it pass for silver or tin, and the gold when melted was exhibited
as the result of transmutation. A common exhibition was to dip nails in
a liquid and to take them out apparently half converted into gold; these
nails consisted of one-half iron neatly soldered to the other half,
which was gold, and covered with something to conceal the color. The
paint or covering was removed by the liquid. A very common trick was the
use of a hollow, iron stirring rod; the hollow was filled with gold or
silver filings, and neatly stopped with wax. When used to stir the
contents of the crucible the wax melted and allowed the gold or silver
to fall out.

These frauds were rendered all the more easy because of certain
statements which were current in regard to successful attempts to
convert lead and other metals into gold. These accounts were vouched for
by well-known chemists and others of high standing. Perhaps the most
famous of these is that given by Helvetius in his "Brief of the Golden
Calf; Discovering the Rarest Miracle in Nature; how by the smallest
portion of the Philosopher's Stone, a great piece of common lead was
totally transmuted into the purest transplendent gold, at the Hague in
1666." The following is Brande's abridgment of this singular account.

    "The 27th day of December, 1666, in the afternoon, came a stranger
    to my house at the Hague, in a plebeick habit, of honest gravity and
    serious authority, of a mean stature and a little long face, black
    hair not at all curled, a beardless chin, and about forty-four years
    (as I guess) of age and born in North Holland. After salutation, he
    beseeched me with great reverence to pardon his rude accesses, for
    he was a lover of the Pyrotechnian art, and having read my treatise
    against the sympathetic powder of Sir Kenelm Digby, and observed my
    doubt about the philosophic mystery, induced him to ask me if I
    really was a disbeliever as to the existence of an universal
    medicine which would cure all diseases, unless the principal parts
    were perished, or the predestinated time of death come. I replied, I
    never met with an adept, or saw such a medicine, though I had
    fervently prayed for it. Then I said, 'Surely you are a learned
    physician.' 'No,' said he, 'I am a brass-founder, and a lover of
    chemistry.' He then took from his bosom-pouch a neat ivory box, and
    out of it three ponderous lumps of stone, each about the bigness of
    a walnut. I greedily saw and handled for a quarter of an hour this
    most noble substance, the value of which might be somewhere about
    twenty tons of gold; and having drawn from the owner many rare
    secrets of its admirable effects, I returned him this treasure of
    treasures with a most sorrowful mind, humbly beseeching him to
    bestow a fragment of it upon me in perpetual memory of him, though
    but the size of a coriander seed. 'No, no,' said he, 'that is not
    lawful, though thou wouldest give me as many golden ducats as would
    fill this room; for it would have particular consequences, and if
    fire could be burned of fire, I would at this instant rather cast it
    all into the fiercest flames.' He then asked if I had a private
    chamber whose prospect was from the public street; so I presently
    conducted him to my best furnished room backwards, which he entered,
    says Helvetius (in the true spirit of Dutch cleanliness), without
    wiping his shoes, which were full of snow and dirt. I now expected
    he would bestow some great secret upon me; but in vain. He asked for
    a piece of gold, and opening his doublet showed me five pieces of
    that precious metal which he wore upon a green riband, and which
    very much excelled mine in flexibility and color, each being the
    size of a small trencher. I now earnestly again craved a crumb of
    the stone, and at last, out of his philosophical commiseration, he
    gave me a morsel as large as a rapeseed; but I said, 'This scanty
    portion will scarcely transmute four grains of lead.' 'Then,' said
    he, 'Deliver it me back:' which I did, in hopes of a greater parcel;
    but he, cutting off half with his nail, said: 'Even this is
    sufficient for thee.' 'Sir,' said I, with a dejected countenance,
    'what means this?' And he said, 'Even that will transmute half an
    ounce of lead.' So I gave him great thanks, and said I would try it,
    and reveal it to no one. He then took his leave, and said he would
    call again next morning at nine. I then confessed, that while the
    mass of his medicine was in my hand the day before, I had secretly
    scraped off a bit with my nail, which I projected on lead, but it
    caused no transmutation, for the whole flew away in fumes. 'Friend,'
    said he, 'thou art more dexterous in committing theft than in
    applying medicine; hadst thou wrapt up thy stolen prey in yellow
    wax, it would have penetrated and transmuted the lead into gold.' I
    then asked if the philosophic work cost much or required long time,
    for philosophers say that nine or ten months are required for it. He
    answered, 'Their writings are only to be understood by the adepts,
    without whom no student can prepare this magistery. Fling not away,
    therefore, thy money and goods in hunting out this art, for thou
    shalt never find it.' To which I replied, 'As thy master showed it
    thee so mayest thou perchance discover something thereof to me who
    know the rudiments, and therefore, it may be easier to add to a
    foundation than begin anew.' 'In this art,' said he, 'it is quite
    otherwise, for unless thou knowest the thing from head to heel, thou
    canst not break open the glassy seal of Hermes. But enough; tomorrow
    at the ninth hour I will show thee the manner of projection.' But
    Elias never came again; so my wife, who was curious in the art
    whereof the worthy man had discoursed, teazed me to make the
    experiment with the little spark of bounty the artist had left me;
    so I melted half an ounce of lead, upon which my wife put in the
    said medicine; it hissed and bubbled, and in a quarter of an hour
    the mass of lead was transmuted into fine gold, at which we were
    exceedingly amazed. I took it to the goldsmith, who judged it most
    excellent, and willingly offered fifty florins for each ounce."

Such is the celebrated history of Elias the artist and Dr. Helvetius.

Helvetius stood very high as a man and chemist, but in connection with
this and some other narratives of the same kind, it may be well to
remember that something over a hundred years before that time the
celebrated Paracelsus had introduced laudanum.

The following is another history of transmutation, given by Mangetus, on
the authority of M. Gros, a clergyman of Geneva, "of the most
unexceptionable character, and at the same time a skilful physician and
expert chemist."

    "About the year 1650 an unknown Italian came to Geneva and took
    lodgings at the sign of the Green Cross. After remaining there a day
    or two, he requested De Luc, the landlord, to procure him a man
    acquainted with Italian, to accompany him through the town and point
    out those things which deserved to be examined. De Luc was
    acquainted with M. Gros, at that time about twenty years of age, and
    a student in Geneva, and knowing his proficiency in the Italian
    language, requested him to accompany the stranger. To this
    proposition he willingly acceded, and attended the Italian
    everywhere for the space of a fortnight. The stranger now began to
    complain of want of money, which alarmed M. Gros not a little, for
    at that time he was very poor, and he became apprehensive, from the
    tenor of the stranger's conversation, that he intended to ask the
    loan of money from him. But instead of this, the Italian asked him
    if he was acquainted with any goldsmith, whose bellows and other
    utensils they might be permitted to use, and who would not refuse to
    supply them with the different articles requisite for a particular
    process which he wanted to perform. M. Gros named a M. Bureau, to
    whom the Italian immediately repaired. He readily furnished
    crucibles, pure tin, quicksilver, and the other things required by
    the Italian. The goldsmith left his workshop, that the Italian might
    be under the less restraint, leaving M. Gros, with one of his own
    workmen as an attendant. The Italian put a quantity of tin into one
    crucible, and a quantity of quicksilver into another. The tin was
    melted in the fire and the mercury heated. It was then poured into
    the melted tin, and at the same time a red powder enclosed in wax
    was projected into the amalgam. An agitation took place and a great
    deal of smoke was exhaled from the crucible; but this speedily
    subsided, and the whole being poured out, formed six heavy ingots,
    having the color of gold. The goldsmith was called in by the Italian
    and requested to make a rigid examination of the smallest of these
    ingots. The goldsmith not content with the touch-stone and the
    application of aquafortis, exposed the metal on the cupel with lead
    and fused it with antimony, but it sustained no loss. He found it
    possessed of the ductility and specific gravity of gold; and full of
    admiration, he exclaimed that he had never worked before upon gold
    so perfectly pure. The Italian made him a present of the smallest
    ingot as a recompense and then, accompanied by M. Gros, he repaired
    to the mint, where he received from M. Bacuet, the mint-master, a
    quantity of Spanish gold coin, equal in weight to the ingots which
    he had brought. To M. Gros he made a present of twenty pieces on
    account of the attention that he had paid to him and after paying
    his bill at the inn, he added fifteen pieces more, to serve to
    entertain M. Gros and M. Bureau for some days, and in the meantime
    he ordered a supper, that he might, on his return, have the pleasure
    of supping with these two gentlemen. He went out, but never
    returned, leaving behind him the greatest regret and admiration. It
    is needless to add that M. Gros and M. Bureau continued to enjoy
    themselves at the inn till the fifteen pieces which the stranger had
    left, were exhausted."

Narratives such as these led even Bergman, a very able chemist of the
period, to take the ground that "although most of these relations are
deceptive and many uncertain, some bear such character and testimony
that, unless we reject all historical evidence, we must allow them
entitled to confidence."

A much more probable explanation is that the relators were either
dreaming or deceived by clever legerdemain.

Of the possibility or impossibility of converting the more common metals
into gold or silver, it would be rash to give a positive opinion. To say
that gold, silver, lead, copper, etc., are elements and cannot be
changed, is merely to say that we have not been able to decompose them.
Water, potash, soda, and other substances, were at one time considered
elements, and resisted all the efforts of the older chemists to resolve
them into their components, but with the advent of more powerful means
of analysis they were shown to be compounds, and it is not impossible
that the so-called elements into which they were resolved may themselves
be found to be compounds. This has happened in regard to some substances
which were at one time announced as elements, and it is not impossible
that it may happen in regard to others. The ablest chemists of the
present day recognize this fully and are prepared for radical changes in
our knowledge of the nature and constitution of matter. Amongst the new
views is the hypothesis of Rutherford and Soddy, which, as given by Sir
William Ramsay, in a recent article contributed by him to "Harper's
Magazine," is that,

    "atoms of elements of high atomic weight, such as radium, uranium,
    thorium, and the suspected elements polonium and actinium, are
    unstable; that they undergo spontaneous change into other forms of
    matter, themselves radioactive and themselves unstable; and that
    finally elements are produced, which, on account of their
    non-radioactivity, are as a rule, impossible to recognize, for their
    minute amount precludes the application of any ordinary test with
    success. The recognition of helium however, which is comparatively
    easy of detection, lends great support to this hypothesis."

At the same time we must not lose sight of the fact that the substances
which we now recognize as elements have not only resisted the most
powerful analytical agencies and dissociating forces, but have
maintained their elemental character in spectrum analysis, and shown
their presence as distinct elements in the sun and other heavenly bodies
where they must have been subjected to the action of the most energetic
decomposing forces. So that in the present state of our knowledge the
near prospect of successful transmutation does not seem to be very
bright, although we cannot regard it as impossible. In the article from
which we have already quoted, Sir William Ramsay, after discussing the
bearing of certain experiments in regard to the parting with and
absorbing of energy by certain elements, says: "If these hypotheses are
just, then the transmutation of the elements no longer appears an idle
dream. The philosopher's stone will have been discovered, and it is not
beyond the bounds of possibility that it may lead to that other goal of
the philosophers of the dark ages--the _elixir vitæ_. For the action of
living cells is also dependent on the nature and direction of the energy
which they contain; and who can say that it will be impossible to
control their action, when the means of imparting and controlling energy
shall have been investigated!"

In the event of the discovery of a cheap method of producing gold, the
change which would certainly occur in our financial or currency system
would be important, if not revolutionary. It has become the fashion at
present with certain writers to scout the so-called "quantitative
theory" of money as if it were an exposed fallacy. Now the quantitative
theory of money rests on one of the most well-grounded and firmly
established principles in political economy: the trouble is that the
writers in question do not understand it or even know what it is. At
present, the production of gold barely keeps pace with the increasing
demand for the metal as currency and in the arts, but if that
production were increased ten-fold, the value of gold would decline and
prices would go up astonishingly.

One of the objects which the better class of alchemists had in view was
the making of gold to such an extent that it might become quite common
and cease to be sought after by mankind. One alchemical writer says:
"Would to God that all men might become adepts in our art, for then
gold, the common idol of mankind, would lose its value and we should
prize it only for its scientific teaching."


FOOTNOTES:

[2] Genesis vi, 2.




VI

THE FIXATION OF MERCURY


This is really one of the processes supposed to be involved in the
transmutation of the metals and might, therefore, perhaps, with
propriety, be included under that head. But as it has received special
attention in the apocryphal works of Hermes Trismegistus, who is
generally regarded as the Father of Alchemy, it is frequently mentioned
as one of the old scientific problems. Readers of Scott's novel,
"Kenilworth," may remember that Wayland Smith, in his account of his
former master, Demetrius Doboobius, describes him as a profound chemist
who had "made several efforts to fix mercury, and judged himself to have
made a fair hit at the philosopher's stone." Hermes, or, rather, those
who wrote over his name, speaks in the jargon of the adepts, about
"catching the flying bird," by which is meant mercury, and "drowning it
so that it may fly no more." The usual means for effecting this was
amalgamation with gold, or some other metal or solution in some acid.

To the ancient chemists mercury must have been one of the most
interesting of objects. Its great heaviness, its metallic brilliancy,
and its wonderful mobility, must all have combined to render it a
subject for deep thought and an attractive object for experiment and
investigation.

Living in a warm climate, as they did, there was no means at their
command by which its fluidity could be impaired. This subtle substance
seemed to defy the usual attempts to grasp it; it rolled about like a
solid sphere, but offered no resistance to the touch, and when pressed
it split up into innumerable smaller globules so that the problem of
"fixing" it must have had a strange fascination for the thoughtful
alchemist, especially when he found that, on subjection to a
comparatively moderate degree of heat, this heavy metal disappeared in
vapor and left not a trace behind.

I have often wondered what the old alchemists would have said if they
had seen fluid mercury immersed in a clear liquid and brought out in the
form of a lump of solid, bright metal. For, although this is not in any
sense a solution of the problem, yet it is a most curious sight and one
which was rarely seen before the discovery of the liquefaction of the
gases. To Geber, Basil Valentine, Van Helmont, Helvetius, and men of
their day, living in their climate, this startling phenomenon would have
seemed nothing short of a miracle.

In modern times the solidification of mercury had been frequently
witnessed by these who dwelt in northern climates and by the skilful use
of certain freezing mixtures made up of ordinary salts, it is not
difficult to exhibit this metal in the solid state at any time. But it
was not until the discovery of the liquefaction of carbonic acid,
nitrous oxide, and other gases by Faraday, about 1823, that the freezing
of mercury became a common lecture-room experiment.

In the year 1862 the writer delivered a course of lectures on chemistry,
in the city of Rochester, N. Y., and during the progress of these
lectures he reduced carbonic acid first to the liquid, and then to the
solid state, in the form of a white snow. The temperature of this snow
was about -80° Cent. (-176° Fahr.) and when it was mixed with ether and
laid on a quantity of mercury, the latter was quickly frozen. In this
way it was easy to make a hammer-head of frozen mercury and drive a nail
with it.

Another very interesting experiment was the freezing of a slender
triangular bar of mercury which might be twisted, bent, and tied in a
knot. This was done by folding a long strip of very stiff paper so as to
make an angular trough into which the mercury was poured. This trough
was then carefully leveled and a mixture of solid carbonic acid and
ether was placed over the metal in the usual way. In a few seconds the
mercury was frozen quite solid so that it could be lifted out by means
of two pairs of wooden forceps and bent and knotted at will. But the
most striking part of the experiment was the melting of this bar of
mercury by means of a piece of ice. The moment the ice touched the
mercury, the latter melted and fell down in drops in the same way that a
bar of lead or solder melts when it is touched with a red-hot iron.

The melted mercury was allowed to fall into a tall ale-glass of water,
the temperature of which had been reduced as nearly as possible to the
freezing point. When the mercury came in contact with the cold water,
the latter began to freeze and by careful manipulation it was possible
to freeze a tube of ice through the center of the column of water. The
effect of this under proper illumination was very striking.

Owing to the fact that the specific heat or thermal capacity of mercury
is only about one-thirtieth of that of water, it requires a considerable
amount of melted mercury to produce the desired result.

But these processes do not enable us to fix mercury in the alchemical
sense; the accomplishment of that still remains an unsolved problem, and
it is more than likely that it will remain so.




VII

THE UNIVERSAL MEDICINE AND THE ELIXIR OF LIFE


Love of life is a characteristic of all animals, man included, and
notwithstanding the fact that an occasional individual becomes so
dissatisfied with his environment that he commits suicide, and also in
the face of the poet's assertion that

    "protracted life is but protracted woe"

most men and women are of the same way of thinking as Charmian, the
attendant on Cleopatra, and "love long life better than figs." And the
force of this general feeling is appealed to in the only one of the
Mosaic commandments to which a promise is attached, the inducement for
honoring father and mother being "that thy days may be long in the land
that the Lord thy God giveth thee."

No wonder then that the old alchemists dreamed of a universal medicine
that would not only prevent or cure sickness but that would renew the
youth of the aged and the feeble, for in this, as in most other attempts
at discovery, the wish was father to the thought. That the renewal of
youth in the aged was supposed to be within the ability of the magicians
and gods of old, we gather from the stories of Medea and Aeson and the
ivory shoulder of Pelops, as referred to in Shakespeare, and explained
in the "Shakespeare Cyclopedia."

Of the form of this supposed elixir we know very little for the
language of the alchemists was so vague and mystical that it is often
very difficult to ascertain their meaning with any approach to
certainty. The following, which is a fair sample of their metaphorical
modes of expressing themselves, is found in the works of Geber. In one
of his writings, he exclaims: "Bring me the six lepers that I may
cleanse them." Modern commentators explain this as being his mode of
telling his readers that he would convert into gold the six inferior or,
as they were called by the alchemists, the six imperfect metals. No
wonder that Dr. Johnson adopted the idea that the word _gibberish_
(anciently written _geberish_) owed its origin to an epithet applied to
the language of Geber and his tribe.

Some have claimed that the elixir and the philosopher's stone were one
and the same thing, and some of the writings of the old alchemists would
seem to confirm this view. Thus, at the close of a formula for preparing
the philosopher's stone, Carolus Musitanus gives the following
admonition:

    "Thus friend, you have a description of the universal medicine, not
    only for curing diseases and prolonging life, but also for
    transmuting all metals into gold. Give therefore thanks to Almighty
    God, who, taking pity on human calamities, has at last revealed this
    inestimable treasure, and made it known for the benefit of all."

And Brande tells us that "nearly all the alchemists attributed the power
of prolonging life either to the philosopher's stone or to certain
preparations of gold, imagining possibly that the permanence of that
metal might be transferred to the human system. The celebrated Descartes
is said to have supported such opinions; he told Sir Kenelm Digby that
although he would not venture to promise immortality, he was certain
that life might be lengthened to the period of that of the Patriarchs.
His plan, however, seems to have been the very rational one of limiting
all excess of diet and enjoining punctual and frugal meals."

It is an old saying that history repeats itself. About forty years ago
certain medical practitioners strongly urged the use of salts of gold in
the treatment of disease, and great hopes were entertained in regard to
their efficacy. And the Keeley gold cure for drunkards is strongly in
evidence, even at the present day.

On the other hand, some have held that the elixir was quite distinct
from the stone by which metals might be transmuted into gold. In the
second part of "King Henry IV," Falstaff (Act III, Scene 2, line 355),
says of Shallow: "it shall go hard but I will make him a philosopher's
two stones to me," and this saying of his has given considerable trouble
to the commentators.

Warburton's explanation of this expression is, that "there was two
stones, one of which was a universal medicine and the other a transmuter
of base metals into gold." And in Churchyard's "Discourse and
Commendation of those that can make Gold," we read of Remundus, who

    Wrate sundry workes, as well doth yet appeare
    Of stone for gold, and shewed plaine and cleare
    A stone for health.

Johnson and some others have objected to this explanation, but it seems
to be evident that Falstaff meant that he would get health and wealth
from Shallow. He got the wealth to the extent of a thousand pounds.

The intense desire which exists in the human bosom for an elixir that
will cure all diseases, and prolong life has made itself evident, even
in recent times, and has called forth serious efforts on the part of
men occupying prominent positions in the scientific world. Both in
Europe and in this country suggestions have been made of fluids which,
when injected into the veins of the old and the feeble, would renew
youth and impart fresh strength. But alas! the results thus far attained
have been anything but gratifying, and the probabilities against success
in this direction are very strong.

The latest gleam of light comes from discoveries in connection with the
radioactive elements, as the reader will find, on referring to Sir
William Ramsay's utterance, which is given at the close of the article
on the "Transmutation of the Metals," on a preceding page.




ADDITIONAL "FOLLIES"


In addition to the seven "Follies," of which an account has been given
in the preceding pages, there are a few which deserve to be classed with
them, although they do not find a place in the usual lists. These are
known as

    PERPETUAL LAMPS.
    THE ALKAHEST OR UNIVERSAL SOLVENT.
    PALINGENESY.
    THE POWDER OF SYMPATHY.




PERPETUAL OR EVER-BURNING LAMPS


Part of the sepulchral rites of the ancients consisted in placing
lighted lamps in the tombs or vaults in which the dead were laid, and,
in many cases, these lamps were carefully tended and kept continually
burning. Some authors have claimed, however, that these men of old were
able to construct lamps which burned perpetually and required no
attention. In number 379 of the "Spectator" there is an anecdote of some
one having opened the sepulcher of the famous Rosicrucius. There he
discovered a lamp burning which a statue of clock-work struck into
pieces. Hence, says the writer, the disciples of this visionary claimed
that he had made use of this method to show that he had re-invented the
ever-burning lamps of the ancients. And Fortunio Liceti wrote a book in
which he collected a large number of stories about lamps, said to have
been found burning in tombs or vaults. Ozanam fills eight closely
printed pages with a discussion of the subject.

Attempts have been made to explain many of the facts upon which is based
the claim that the ancients were able to construct perpetual lamps by
the suggestion that the light sometimes seen on the opening of ancient
tombs may have been due to the phosphorescence which is well known to
arise during the decomposition of animal and vegetable matter. Decaying
wood and dead fish are familiar objects which give out a light that is
sufficient to render dimly visible the outlines of surrounding objects,
and such a light, seen in the vicinity of an old lamp, might give rise
to the impression that the lamp had been actually burning and that it
had been blown out by sudden exposure to a draft of air.

Another supposition was that the flame, which was supposed to have been
seen, may have been caused by the ignition of gases arising from the
decomposition of dead bodies, and set on fire by the flambeaux or
candles of the investigators, and it is quite possible that the
occurrence of each of these phenomena may have given a certain degree of
confirmation to preconceived ideas.

After the discovery of phosphorus in 1669, by Brandt and Kunckel, it was
employed in the construction of luminous phials which could be carried
in the pocket, and which gave out sufficient light to enable the user to
see the hands of a watch on a dark night. Directions for making these
luminous phials are very simple, and may be found in most of the books
of experiments published prior to the introduction of the modern lucifer
match. They were also used for obtaining a light by means of the old
matches, which were tipped merely with a little sulphur, and which could
not be ignited by friction. Such a match, after being dipped into one of
these phosphorus bottles, would readily take fire by slight friction,
and some persons preferred this contrivance to the old flint and steel,
partly, no doubt, because it was a novelty. But these bottles were not
in any sense perpetual, the light being due to the slow oxidation of the
phosphorus so that, in a comparatively short time, the luminosity of the
materials ceased. Nevertheless, it has been suggested that some form of
these old luminous phials may have been the original perpetual lamp.

After the discovery of the phosphorescent qualities of barium sulphate
or Bolognian phosphorus, as it was called, it was thought that this
might be a re-discovery of the long-lost art of making perpetual lamps.
But it is well known that this substance loses its phosphorescent power
after being kept in the dark for some time, and that occasional exposure
to bright sun-light is one of the conditions absolutely essential to its
giving out any light at all. This condition does not exist in a dark
tomb.

A few years ago phosphorescent salts of barium and calcium were employed
in the manufacture of what was known as luminous paint. These materials
shine in the dark with brilliancy sufficient to enable the observer to
read words and numbers traced with them, but regular exposure to the
rays of the sun or some other bright light is absolutely necessary to
enable them to maintain their efficiency.

More recently it has been suggested that the ancients may have been
acquainted with some form of radioactive matter like radium, and that
this was the secret of the lamps in question. It is far more likely,
however, that the reports of their perpetual lamps were based upon mere
errors of observation.

The perpetual lamp is, in chemistry, the counterpart of perpetual motion
in mechanics--both violate the fundamental principle of the conservation
of energy. And just as suggestions of impossible movements have been
numerous in the case of perpetual motion, so impossible devices and
constructions have been suggested in regard to perpetual lamps. Prior to
the development, or even the suggestion of the law of the conservation
of energy, it was believed that it might be possible to find a liquid
which would burn without being consumed, and a wick which would feed
the liquid to the flame without being itself destroyed. Dr. Plott
suggested naphtha for the fluid and asbestos for the wick, but since
kerosene oil, naphtha, gasolene, and other liquids of the kind have
become common, every housewife knows that as her lamp burns, the oil, of
whatever kind it may be, disappears.

Under present conditions the construction of a perpetual lamp is not a
severely felt want; for constancy and brilliancy our present means of
illumination are sufficient for almost all our requirements. Whether or
not it would be possible to gather up those natural currents of
electricity, which are suspected to flow through and over the earth, and
utilize them for purposes of illumination, however feeble, it might be
difficult to decide. But such means of perpetual electric lighting would
be similar to a perpetual motion derived from a mountain stream. Such
natural means of illumination already exist, and have existed for ages
in the fire-giving wells of naphtha which are found on the shores of the
Caspian sea, and in other parts of the east, and which have long been
objects of adoration to the fire-worshippers.

As for the outcome of present researches into the properties of radium,
polonium, and similar substances, and their possible applications, it is
too early to form even a surmise.




THE ALKAHEST OR UNIVERSAL SOLVENT


The production of a universal solvent or alkahest was one of the special
problems of the alchemists in their general search for the philosopher's
stone and the means of transmuting the so-called inferior metals into
gold and silver. Their idea of the way in which it would aid them to
attain these ends does not seem to be very clearly stated in any work
that I have consulted; probably they thought that a universal solvent
would wash away all impurities from common materials and leave in
absolute purity the higher substance, which constituted the gold of the
adepts. But whatever their particular object may have been, it is well
known that much time and labor were expended in the fruitless search.

The futility of such attempts was very well exposed by the cynical
sceptic, who asked them what kind of vessel could they provide for
holding such a liquid? If its solvent powers are such that it dissolves
everything, it is very evident that it would dissolve the very material
of the vessel in which it must be placed.

When hydrofluoric acid became a subject of investigation it was thought
that its characteristics approached, more nearly than those of any other
substance known, to those of the universal solvent, and the very
difficulty above suggested, presented itself strongly to the chemists
who experimented with it. Not only common metals but glass and porcelain
were acted upon by this wonderfully energetic liquid and when attempts
were made to isolate the fluorine, even the platinum electrodes were
corroded and destroyed. Vessels of pure silver and of lead served
tolerably well, but Davy suggested that the most scientific method of
constructing a containing vessel would be to use a compound in which
fluorine was already present to the point of saturation. As there is a
limit to the amount of fluorine with which any base can combine, such a
vessel would be proof against its solvent action. I am not aware,
however, that the suggestion was ever carried into actual practice with
success.




PALINGENESY


This singular delusion may have been partly due to errors of
observation, the instruments and methods of former times having been
notably crude and unreliable. This fact, taken in connection with the
wild theories upon which the natural sciences of the middle ages were
based, is a sufficient explanation of some of the extraordinary
statements made by Kircher, Schott, Digby, and others.

By palingenesy these writers meant a certain chemical process by means
of which a plant or an animal might be revived from its ashes. In other
words a sort of material resurrection. Most of the accounts given by the
old authors go no further than to assert that by proper methods the
ashes of plants, when treated with water, produce small forests of ferns
and pines. Thus, an English chemist, named Coxe, asserts that having
extracted and dissolved the essential salts of fern, and then filtered
the liquor, he observed, after leaving it at rest for five or six weeks,
a vegetation of small ferns adhering to the bottom of the vessel. The
same chemist, having mixed northern potash with an equal quantity of sal
ammoniac, saw, some time after, a small forest of pines and other trees,
with which he was not acquainted, rising from the bottom of the vessel.

And Kircher tells us in his "Ars Magnetica" that he had a long-necked
phial, hermetically sealed, containing the ashes of a plant which he
could revive at pleasure by means of heat; and that he showed this
wonderful phenomenon to Christina, Queen of Sweden, who was highly
delighted with it. Unfortunately he left this valuable curiosity one
cold day in his window and it was entirely destroyed by the frost.
Father Schott also asserts that he saw this chemical wonder which,
according to his account, was a rose revived from its ashes. And he adds
that a certain prince having requested Kircher to make him one of the
same kind, he chose rather to give up his own than to repeat the
operation.

Even the celebrated Boyle, though not very favorable to palingenesy,
relates that having dissolved in water some verdigris, which, as is well
known, is produced by combining copper with the acid of vinegar, and
having caused this water to congeal, by means of artificial cold, he
observed, at the surface of the ice, small figures which had an exact
resemblance to vines.

In this connection it is well to bear in mind that in Boyle's time
almost all vinegar was really what its name implies--_sour wine_ (_vin
aigre_)--and verdigris or copper acetate was generally prepared by
exposing copper plates to the action of refuse grapes which had been
allowed to ferment and become sour. Therefore to him it might not have
seemed so very improbable that the green crystals which appeared on the
surface of the ice were, in reality, minute resuscitated grape-vines.

The explanation of these facts given by Father Kircher is worthy of the
science of the times. He tells us that the seminal virtue of each
mixture is contained in its salts and these salts, unalterable by their
nature, when put in motion by heat, rise in the vessel through the
liquor in which they are diffused. Being then at liberty to arrange
themselves at pleasure, they place themselves in that order in which
they would be placed by the effect of vegetation, or the same as they
occupied before the body to which they belonged had been decomposed by
the fire; in short, they form a plant, or the phantom of a plant, which
has a perfect resemblance to the one destroyed.

That the operators have here mistaken for true vegetable growth the
fern-like crystals of the salts which exist in the ashes of all plants
is very obvious. Their knowledge of plant structure was exceedingly
limited and their microscopes were so imperfect that imagination had
free scope. As seen under our modern microscopes, there are few prettier
sights than the crystallization of such salts as sal ammoniac, potassic
nitrate, barium chloride, etc. The crystals are actually seen to grow
and it would not require a very great stretch of the imagination to
convince one that the growth is due to a living organism. Indeed, this
view has actually been taken in an article which recently appeared in a
prominent magazine. The writer of that article sees no difference
between the mere aggregation of inorganic particles brought together by
voltaic action and the building up of vital structures under the
influence of organic forces. This is simply materialism run mad.

Perhaps the finest illustration of such crystallization is to be found
in the deposition of silver from a solution of the nitrate as seen under
the microscope. A drop of the solution is placed on a glass slide and
while the observer watches it through a low power, a piece of copper
wire or, preferably, a minute quantity of the amalgam of tin and
mercury, such as is used for "silvering" cheap looking glasses, is
brought into contact with it. Chemical decomposition at once sets in and
then the silver thus deposited forms one element of a very minute
voltaic couple and fresh crystals of silver are deposited upon the
silver already thrown down. When the illumination of this object under
the microscope is properly managed, the appearance, which resembles that
shown in Fig. 18, is exceedingly brilliant, and beautiful beyond
description.

[Illustration: Fig. 18.]

That imagination played strange pranks in the observations of the older
microscopists is shown by some of the engravings found in their books. I
have now before me a thick, dumpy quarto in which the so-called seminal
animalcules are depicted as little men and women, and I have no doubt
that, to the eye of this early observer, they had that appearance. But
the microscopists of to-day know better.

Sir Kenelm Digby, whose name is associated with the Sympathetic Powder,
tells us that he took the ashes of burnt crabs, dissolved them in water
and, after subjecting the whole to a tedious process, small crabs were
produced in the liquor. These were nourished with blood from the ox,
and, after a time, left to themselves in some stream where they throve
and grew large.

Now, although Evelyn, in his diary, declares that "Sir Kenelm was an
errant mountebank," it is quite possible that he was honest in his
account of his experiments and that he was merely led astray by the
imperfection of his instruments of observation. It is more than likely
that the creatures which Digby saw were entomostraca introduced in the
form of ova which, unless a good microscope be used, are quite
invisible. These would develop rapidly and might easily be mistaken for
some species of crab, though, when examined with proper instruments, all
resemblance vanishes. When let loose in a running stream it would
evidently be impossible to trace their identity and follow their growth.

But while some of these stories may have originated in errors of
observation this will hardly explain some of the statements made by
those who have advocated this strange doctrine. Father Schott, in his
"Physica Curiosa," gives an account of the resurrection of a sparrow and
actually gives an engraving in which the bird is shown in a bottle
revived!

Although the subject, of itself, is not worthy of a moment's
consideration, it deserves attention as an illustration of the
extraordinary vagaries into which the human mind is liable to fall.




THE POWDER OF SYMPATHY


This curious occult method of curing wounds is indissolubly associated
with the name of Sir Kenelm Digby (born 1603, died 1665), though it was
undoubtedly in use long before his time. He himself tells us that he
learned to make and apply the drug from a Carmelite, who had traveled in
the east, and whom he met in Florence, in 1622. The descendants of Digby
are still prominent in England, and O. W. Holmes, in his "One Hundred
Days in Europe," tells us that he had met a Sir Kenelm Digby, a
descendant of the famous Sir Kenelm of the seventeenth century, and that
he could hardly refrain from asking him if he had any of his ancestor's
famous powder in his pocket.

Digby was a student of chemistry, or at least of the chemistry of those
days, and wrote books of Recipes and the making of "Methington
[metheglin or mead?] Syder, etc." He was, as we have seen in the
previous article, a believer in palingenesy and made experiments with a
view to substantiate that strange doctrine. Evelyn calls him an "errant
quack," and he may have been given to quackery, but then the loose
scientific ideas of those days allowed a wide range in drawing
conclusions which, though they seem absurd to us, may have appeared to
be quite reasonable to the men of that time.

From his book on the subject,[3] we learn that the wound was never to
be brought into contact with the powder. A bandage was to be taken from
the wound, immersed in the powder, and kept there until the wound
healed.

This beats the absent treatment of Christian Science!

The powder was simply pulverized vitriol, that is, ferric sulphate, or
sulphate of iron.

There was another and probably an older method of using sympathetic
powders and salves; this was to apply the supposed curative to the
weapon which caused the wound, instead of the wound itself. In the "Lay
of the Last Minstrel," Scott gives an account of the way in which the
Lady of Buccleuch applied this occult surgery to the wound of William of
Deloraine:

      "She drew the splinter from the wound,
      And with a charm she stanched the blood.
      She bade the gash be cleansed and bound:
      No longer by his couch she stood;
    But she has ta'en the broken lance.
      And washed it from the clotted gore,
      And salved the splinter o'er and o'er.
    William of Deloraine, in trance,
    Whene'er she turned it round and round
    Twisted as if she galled his wound.
      Then to her maidens she did say,
    That he should be whole man and sound,
      Within the course of a night and day.
    Full long she toiled, for she did rue
      Mishap to friend so stout and true."[4]

That no direct benefit could have been derived from such a mode of
treatment must be obvious, but De Morgan very plausibly claims that in
the then state of surgical and medical knowledge, it was really the very
best that could have been adopted. His argument is as follows: "The
sympathetic powder was that which cured by anointing the weapon with its
salve instead of the wound. I have been long convinced that it was
efficacious. The directions were to keep the wound clean and cool, and
to take care of diet, rubbing the salve on the knife or sword. If we
remember the dreadful notions upon drugs which prevailed, both as to
quantity and quality, we shall readily see that any way of _not_
dressing the wound, would have been useful. If the physicians had taken
the hint, had been careful of diet, etc., and had poured the little
barrels of medicine down the throat of a practicable doll, _they_ would
have had their magical cures as well as the surgeons. Matters are much
improved now; the quantity of medicine given, even by orthodox
physicians, would have been called infinitesimal by their professional
ancestors. Accordingly, the College of Physicians has a right to abandon
its motto, which is, _Ars longa, vita brevis_, meaning, _Practice is
long, so life is short_."

As set forth by Digby and others, the use of the Powder of Sympathy is
free from all taint of witchcraft or magic, but, in another form, it was
wholly dependent upon incantations and other magical performances. This
idea of sympathetic action was even carried so far as to lead to
attempts to destroy or injure those whom the operator disliked. In some
cases this was done by moulding an image in wax which, when formed under
proper occult influences, was supposed to have the power of transferring
to the victim any injuries inflicted on the image. Into such images pins
and knives were thrust in the hope that the living original would suffer
the same pains and mutilations that would be inflicted if the knives or
pins were thrust into him, and sometimes the waxen form was held before
the fire and allowed to melt away slowly in the hope that the prototype
would also waste away, and ultimately die. Shakespeare alludes to this
in the play of King John. In Act v., Scene 4, line 24, Melun says:

                "A quantity of life
    Which bleeds away, even as a form of wax,
    Resolveth from his figure 'gainst the fire?"

And Hollinshed tells us that "it was alleged against Dame Eleanor Cobham
and her confederates that they had devised an image of wax, representing
the king, which, by their sorcerie, by little and little consumed,
intending thereby, in conclusion, to waste and destroy the king's
person."

In these cases, however, the operator always depended upon certain
occult or demoniacal influences, or, in other words, upon the art of
magic, and therefore examples of this kind do not come within the scope
of the present volume. In the case of the Powder of Sympathy the results
were supposed to be due entirely to natural causes.


FOOTNOTES:

[3] Touching the Cure of Wounds by the Powder of Sympathy. With
Instructions how to make the said Powder. Rendered faithfully out of
French into English by R. White, Gent. London, 1658.

[4] Canto III. Stanza 23.




A SMALL BUDGET OF PARADOXES, ILLUSIONS, AND MARVELS




THE FOURTH DIMENSION AND THE POSSIBILITY OF A NEW SENSE AND NEW
SENSE-ORGAN


This subject has now found its way not only into semi-scientific works
but into our general literature and magazines. Even our novel-writers
have used suggestions from this hypothesis as part of the machinery of
their plots so that it properly finds a place amongst the subjects
discussed in this volume.

Various attempts have been made to explain what is meant by "the fourth
dimension," but it would seem that thus far the explanations which have
been offered are, to most minds, vague and incomprehensible, this latter
condition arising from the fact that the ordinary mind is utterly unable
to conceive of any such thing as a dimension which cannot be defined in
terms of the three with which we are already familiar. And I confess at
the start that I labor under the superlative difficulty of not being
able to form any conception of a fourth dimension, and for this
incapacity my only consolation is, that in this respect I am not alone.
I have conversed upon the subject with many able mathematicians and
physicists, and in every case I found that they were in the same
predicament as myself, and where I have met men who professed to think
it easy to form a conception of a fourth dimension, I have found their
ideas, not only in regard to the new hypothesis, but to its
correlations with generally accepted physical facts, to be nebulous and
inaccurate.

It does not follow, however, that because myself and some others cannot
form such a clear conception of a fourth dimension as we can of the
third, that, therefore, the theory is erroneous and the alleged
conditions non-existent. Some minds of great power and acuteness have
been incapable of mastering certain branches of science. Thus Diderot,
who was associated with d'Alembert, the famous mathematician, in the
production of "L'Encyclopedie," and who was not only a man of
acknowledged ability, but who, at one time, taught mathematics and wrote
upon several mathematical subjects, seems to have been unable to master
the elements of algebra. The following anecdote regarding his deficiency
in this respect is given by Thiébault and indorsed by Professor De
Morgan: At the invitation of the Empress, Catherine II, Diderot paid a
visit to the Russian court. He was a brilliant conversationalist and
being quite free with his opinions, he gave the younger members of the
court circle a good deal of lively atheism. The Empress herself was very
much amused, but some of her councillors suggested that it might be
desirable to check these expositions of strange doctrines. As Catherine
did not like to put a direct muzzle on her guest's tongue, the following
plot was contrived. Diderot was informed that a learned mathematician
was in possession of an algebraical demonstration of the existence of
God and would give it to him before all the court if he desired to hear
it. Diderot gladly consented, and although the name of the mathematician
is not given, it is well known to have been Euler. He advanced toward
Diderot, and said in French, gravely, and in a tone of perfect
conviction: "_Monsieur, (a + b^n) / n = x, therefore, God exists;
reply!_" Diderot, to whom algebra was Hebrew, was embarrassed and
disconcerted, while peals of laughter rose on all sides. He asked
permission to return to France at once, which was granted.

Even such a mind as that of Buckle, who was generally acknowledged to be
a keen-sighted thinker, could not form any idea of a geometrical
line--that is, of a line without breadth or thickness, a conception
which has been grasped clearly and accurately by thousands of
school-boys. He therefore asserts, positively, that there are no lines
without breadth, and comes to the following extraordinary conclusions:

    "Since, however, the breadth of the faintest line is so slight as to
    be incapable of measurement, except by an instrument under the
    microscope, it follows that the assumption that there can be lines
    without breadth is so nearly true that our senses, when unassisted
    by art, can not detect the error. Formerly, and until the invention
    of the micrometer, in the seventeenth century, it was impossible to
    detect it at all. Hence, the conclusions of the geometrician
    approximate so closely to truth that we are justified in accepting
    them as true. The flaw is too minute to be perceived. But that there
    is a flaw appears to me certain. It appears certain that, whenever
    something is kept back in the premises, something must be wanting in
    the conclusion. In all such cases, the field of inquiry has not been
    entirely covered; and part of the preliminary facts being
    suppressed, it must, I think, be admitted that complete truth be
    unattainable, and that no problem in geometry has been exhaustively
    solved."[5]

The fallacy which underlies Mr. Buckle's contention is thus clearly
exposed by the author of "The Natural History of Hell."

    "If it be conceded that lines have breadth, then all we have to do
    is to assign some definite breadth to each line--say the
    one-thousandth of an inch--and allow for it. But the lines of the
    geometer have no breadth. All the micrometers of which Mr. Buckle
    speaks depend, either directly or indirectly, upon lines for their
    graduations, and the positions of these lines are indicated by
    rulings or scratches. Now, in even the finest of these rulings, as,
    for example, those of Nobert or Fasoldt, where the ruling or
    scratching, together with its accompanying space, amounts to no more
    than the one hundred and fifty thousandth part of an inch, the
    scratch has a perceptible breadth. But this broad scratch is not the
    line recognized by the microscopist, to say nothing of the geometer.
    The true line is a line which lies in the very center of this
    scratch and it is certain that this central line has absolutely no
    breadth at all."[6]

It must be very evident that if Mr. Buckle's contention that geometrical
lines have breadth were true, then some of the fundamental axioms of
geometry must be false. It could no longer hold true that "the whole is
equal to all its parts taken together," for if we divide a square or a
circle into two parts by means of a line which has breadth, the two
parts cannot be equal to the whole as it formerly was. As a matter of
fact, Mr. Buckle's lines are saw-cuts, not geometrical lines.
Geometrical points, lines, and surfaces, have no material existence and
can have none. An ideal conception and a material existence are two very
different things.

A very interesting book[7] has been written on the movements and
feelings of the inhabitants of a world of two dimensions. Nevertheless,
if we know anything at all, we know that such a world could not have any
actual existence and when we attempt to form any mental conception of
it and its inhabitants, we are compelled to adopt, to a certain extent,
the idea of the third dimension.

But at the same time we must remember that since the ordinary mechanic
and the school-boy who has studied geometry, find no difficulty in
conceiving of points without magnitude, lines without breadth, and
surfaces without thickness--conceptions which seem to have been
impossible to Buckle, a man of acknowledged ability--it may be possible
that minds constituted slightly differently from that of myself and some
others, might, perhaps, be able to form a conception of a fourth
dimension.

Leaving out of consideration the speculations of those who have woven
this idea into romances and day-dreams we find that the hypothesis of a
fourth dimension has been presented by two very different classes of
thinkers, and the discussion has been carried on from two very different
standpoints.

The first suggestion of this hypothesis seems to have come from Kant and
Gauss and to have had a purely metaphysical origin, for, although
attempts have been made to trace the idea back to the famous phantoms of
Plato, it is evident that the ideas then advanced had nothing in common
with the modern theory of the existence of a fourth dimension. The first
hint seems to have been a purely mathematical one and did not attract
any very general attention. It was, however, seized upon by a certain
branch of the transcendentalists, closely allied to the spiritualists,
and was exploited by them as a possible explanation of some curious and
mysterious phenomena and feats exhibited by certain Indian and European
devotees. This may have been done merely for the purpose of mystifying
and confounding their adversaries by bringing forward a striking
illustration of Hamlet's famous dictum--

    "There are more things in heaven and earth, Horatio,
    Than are dreamt of in your philosophy."

A very fair statement of this view is thus given by Edward Carpenter:[8]

    "There is another idea which modern science has been familiarizing
    us with, and which is bringing us towards the same conception--that,
    namely, of the fourth dimension. The supposition that the actual
    world has four space-dimensions instead of three makes many things
    conceivable which otherwise would be incredible. It makes it
    conceivable that apparently separate objects, e. g., distinct
    people, are really physically united; that things apparently
    sundered by enormous distances of space are really quite together;
    that a person or other object might pass in and out of a closed room
    without disturbance of walls, doors or windows, etc., and if this
    fourth dimension were to become a factor of our consciousness it is
    obvious that we should have means of knowledge which, to the
    ordinary sense, would appear simply miraculous. There is much,
    apparently, to suggest that the consciousness attained to by the
    Indian gñanis in their degree, and by hypnotic subjects in theirs,
    is of this fourth dimensional order.

    "As a solid is related to its own surface, so, it would appear, is
    the cosmic consciousness related to the ordinary consciousness. The
    phases of the personal consciousness are but different facets of the
    other consciousness; and experiences which seem remote from each
    other in the individual are perhaps all equally near in the
    universal. Space itself, as we know it, may be practically
    annihilated in the consciousness of a larger space, of which it is
    but the superficies; and a person living in London may not unlikely
    find that he has a back door opening quite simply and
    unceremoniously out in Bombay."

On the other hand, the mathematicians, looking at it as a purely
speculative idea, have endeavored to arrive at definite conclusions in
regard to what would be the condition of things if the universe really
exists in a fourth, or even in some higher dimension. Professor W. W. R.
Ball tells us that

    "the conception of a world of more than three dimensions is
    facilitated by the fact that there is no difficulty in imagining a
    world confined to only two dimensions--which we may take for
    simplicity to be plane--though equally well it might be a spherical
    or other surface. We may picture the inhabitants of flatland as
    moving either on the surface of a plane or between two parallel and
    adjacent planes. They could move in any direction along the plane,
    but they could not move perpendicularly to it, and would have no
    consciousness that such a motion was possible. We may suppose them
    to have no thickness, in which case they would be mere geometrical
    abstractions; or we may think of them as having a small but uniform
    thickness, in which case they would be realities."

                    ·       ·       ·       ·       ·

    "If an inhabitant of flatland was able to move in three dimensions,
    he would be credited with supernatural powers by those who were
    unable so to move; for he could appear or disappear at will; could
    (so far as they could tell) create matter or destroy it, and would
    be free from so many constraints to which the other inhabitants were
    subject that his actions would be inexplicable to them."

                    ·       ·       ·       ·       ·

    "Our conscious life is in three dimensions, and naturally the idea
    occurs whether there may not be a fourth dimension. No inhabitant of
    flatland could realize what life in three dimensions would mean,
    though, if he evolved an analytical geometry applicable to the world
    in which he lived, he might be able to extend it so as to obtain
    results true of that world in three dimensions which would be to him
    unknown and inconceivable. Similarly we cannot realize what life in
    four dimensions is like, though we can use analytical geometry to
    obtain results true of that world, or even of worlds of higher
    dimensions. Moreover, the analogy of our position to the inhabitants
    of flatland enables us to form some idea of how inhabitants of
    space of four dimensions would regard us."

                    ·       ·       ·       ·       ·

    "If a finite solid was passed slowly through flatland, the
    inhabitants would be conscious only of that part of it which was in
    their plane. Thus they would see the shape of the object gradually
    change and ultimately vanish. In the same way, if a body of four
    dimensions was passed through our space, we should be conscious of
    it only as a solid body (namely, the section of the body by our
    space) whose form and appearance gradually changed and perhaps
    ultimately vanished. It has been suggested that the birth, growth,
    life, and death of animals, may be explained thus as the passage of
    finite four-dimensional bodies through our three-dimensional space."

Attempts have been made to construct drawings and models showing a
four-dimensional body. The success of such attempts has not been very
encouraging.

Investigators of this class look upon the actuality of a fourth
dimension as an unsolved question, but they hold that, provided we could
see our way clear to adopt it, it would open up wondrous possibilities
in the way of explaining abstruse and hitherto inexplicable physical
conditions and phenomena.

There is obviously no limit to such speculations, provided we assume the
existence of such conditions as are needed for our purpose. Too often,
however, those who indulge in such day-dreams begin by assuming the
impossible, and end by imagining the absurd.

We have so little positive knowledge in regard to the ultimate
constitution of matter and even in regard to the actual character of the
objects around us, which are revealed to us through our senses, that the
field in which our imagination may revel is boundless. Perhaps some day
the humanity of the present will merge itself into a new race, endowed
with new senses, whose revelations are to us, for the present, at least,
utterly inconceivable.

The possibility of such a development may be rendered more clear if we
imagine the existence of a race devoid of the sense of hearing, and
without the organs necessary to that sense. They certainly could form no
idea of sound, far less could they enjoy music or oratory, such as
afford us so much delight. And, if one or more of our race should visit
these people, how very strange to them would appear those curious
appendages, called ears, which project from the sides of our heads, and
how inexplicable to them would be the movements and expressions of
intelligence which we show when we talk or sing? It is certain that no
development of the physical or mathematical sciences could give them any
idea whatever of the sensations which sound, in its various
modifications, imparts to us, and neither can any progress in that
direction enable us to acquire any idea of the revelations which a new
sense might open up to us. Nevertheless, it seems to me that the
development of new senses and new sense organs is not only more likely
to be possible, but that it is actually more probable, than any
revelation in regard to a fourth dimension.


FOOTNOTES:

[5] "History of Civilization in England." American edition, Vol. II,
page 342.

[6] "The Natural History of Hell," by John Phillipson, page 37.

[7] "Flatland," by E. A. Abbott. London, 1884.

[8] "From Adam's Peak to Elephanta--" page 160.




HOW A SPACE MAY BE APPARENTLY ENLARGED BY CHANGING ITS SHAPE


The following is a curious illustration of the errors to which careless
observers may be subject:

Draw a square, like Fig. 19, and divide the sides into 8 parts each.
Join the points of division in opposite sides so as to divide the whole
square into 64 small squares. Then draw the lines shown in black and cut
up the drawing into four pieces. The lines indicating the cuts have been
made quite heavy so as to show up clearly, but on the actual card they
may be made quite light. Now, put the four pieces together, so as to
form the rectangle shown in Fig. 20. Unless the scale, to which the
drawing is made is quite large and the work very accurate, it will seem
that the rectangle contains 5 squares one way and 13 the other which,
when multiplied together, give 65 for the number of small squares, being
an apparent gain of one square by the simple process of cutting.

[Illustration: Fig. 19.]

[Illustration: Fig. 20.]

This paradox is very apt to puzzle those who are not familiar with
accurate drawings. Of course, every person of common sense knows that
the card or drawing is not made any larger by cutting it, but where does
the 65th small square come from?

On careful examination it will be seen that the line AB, Fig. 20, is not
quite straight and the three parts into which it is divided are thus
enabled to gain enough to make one of the small squares. On a small
scale this deviation from the straight line is not very obvious, but
make a larger drawing, and make it carefully, and it will readily be
seen how the trick is done.




CAN A MAN LIFT HIMSELF BY THE STRAPS OF HIS BOOTS?


I think it was the elder Stephenson, the famous engineer, who told a man
who claimed the honor of having invented a perpetual motion, that when
he could lift himself over a fence by taking hold of his waist-band, he
might hope to accomplish his object. And the query which serves as a
title for this article has long been propounded as one of the physical
impossibilities. And yet, perhaps, it might be possible to invent a
waist-band or a boot-strap by which this apparently impossible feat
might be accomplished!

Travelers in Mexico frequently bring home beans which jump about when
laid on a table. They are well-known as "jumping beans" and have often
been a puzzle to those who were not familiar with the facts in the case.
Each bean contains the larva of a species of beetle and this affords a
clue to the secret. But the question at once comes up: "How is the
insect able to move, not only itself, but its house as well, without
some purchase or direct contact with the table?"

The explanation is simple. The hollow bean is elastic and the insect has
strength enough to bend it slightly; when the insect suddenly relaxes
its effort and allows the bean to spring back to its former shape, the
reaction on the table moves the bean. A man placed in a perfectly rigid
box could never move himself by pressing on the sides, but if the box
were elastic and could be bent by the strength of the man inside, it
might be made to move.

A somewhat analogous result, but depending on different principles, is
attained in certain curious boat races which are held at some English
regattas and which is explained by Prof. W. W. Rouse Ball, in his
"Mathematical Recreations and Problems." He says that it

    "affords a somewhat curious illustration of the fact that commonly a
    boat is built so as to make the resistance to motion straight
    forward less than that to motion in the opposite direction.

    "The only thing supplied to the crew is a coil of rope, and they
    have (without leaving the boat) to propel it from one point to
    another as rapidly as possible. The motion is given by tying one end
    of the rope to the afterthwart, and giving the other end a series of
    violent jerks in a direction parallel to the keel.

    "The effect of each jerk is to compress the boat. Left to itself the
    boat tends to resume its original shape, but the resistance to the
    motion through the water of the stern is much greater than that of
    the bow, hence, on the whole, the motion is forwards. I am told that
    in still water a pace of two or three miles an hour can be thus
    attained."




HOW A SPIDER LIFTED A SNAKE


One of the most interesting books in natural history is a work on
"Insect Architecture," by Rennie. But if the architecture of insect
homes is wonderful, the engineering displayed by these creatures is
equally marvellous. Long before man had thought of the saw, the saw-fly
had used the same tool, made after the same fashion, and used in the
same way for the purpose of making slits in the branches of trees so
that she might have a secure place in which to deposit her eggs. The
carpenter bee, with only the tools which nature has given her, cuts a
round hole, the full diameter of her body, through thick boards, and so
makes a tunnel by which she can have a safe retreat, in which to rear
her young. The tumble-bug, without derrick or machinery, rolls over
large masses of dirt many times her own weight, and the sexton beetle
will, in a few hours, bury beneath the ground the carcass of a
comparatively large animal. All these feats require a degree of instinct
which in a reasoning creature would be called engineering skill, but
none of them are as wonderful as the feats performed by the spider. This
extraordinary little animal has the faculty of propelling her threads
directly against the wind, and by means of her slender cords she can
haul up and suspend bodies which are many times her own weight.

Some years ago a paragraph went the rounds of the papers in which it was
said that a spider had suspended an unfortunate mouse, raising it up
from the ground, and leaving it to perish miserably between heaven and
earth. Would-be philosophers made great fun of this statement, and
ridiculed it unmercifully. I know not how true it _was_, but I know that
it _might have been_ true.

Some years ago, in the village of Havana, in the State of New York, a
spider entangled a milk-snake in her threads, and actually raised it
some distance from the ground, and this, too, in spite of the struggles
of the reptile, which was alive.

By what process of engineering did the comparatively small and feeble
insect succeed in overcoming and lifting up by mechanical means, the
mouse or the snake? The solution is easy enough if we only give the
question a little thought.

The spider is furnished with one of the most efficient mechanical
implements known to engineers, viz., a strong elastic thread. That the
thread is strong is well known. Indeed, there are few substances that
will support a greater strain than the silk of the silkworm, or the
spider; careful experiment having shown that for equal sizes the
strength of these fibers exceeds that of common iron. But
notwithstanding its strength, the spider's thread alone would be useless
as a mechanical power if it were not for its elasticity. The spider has
no blocks or pulleys, and, therefore, it cannot cause the thread to
divide up and run in different directions, but the elasticity of the
thread more than makes up for this, and renders possible the lifting of
an animal much heavier than a mouse or a snake. This may require a
little explanation.

Let us suppose that a child can lift a six-pound weight one foot high
and do this twenty times a minute. Furnish him with 350 rubber bands,
each capable of pulling six pounds through one foot when stretched. Let
these bands be attached to a wooden platform on which stand a pair of
horses weighing 2,100 lbs., or rather more than a ton. If now the child
will go to work and stretch these rubber bands, singly, hooking each one
up, as it is stretched, in less than twenty minutes he will have raised
the pair of horses one foot!

We thus see that the elasticity of the rubber bands enables the child to
divide the weight of the horses into 350 pieces of six pounds each, and
at the rate of a little less than one every three seconds, he lifts all
these separate pieces one foot, so that the child easily lifts this
enormous weight.

Each spider's thread acts like one of the elastic rubber bands. Let us
suppose that the mouse or the snake weighed half an ounce and that each
thread is capable of supporting a grain and a half. The spider would
have to connect the mouse with the point from which it was to be
suspended with 150 threads, and if the little quadruped was once swung
off his feet, he would be powerless. By pulling successively on each
thread and shortening it a little, the mouse or snake might be raised to
any height within the capacity of the building or structure in which the
work was done. So that to those who have ridiculed the story we may
justly say: "There are more things in heaven and earth than are dreamed
of in _your_ philosophy."

What object the spider could have had in this work I am unable to see.
It may have been a dread of the harm which the mouse or snake might
work, or it may have been the hope that the decaying carcass would
attract flies which would furnish food for the engineer. I can vouch for
the truth of the snake story, however, and the object of this article is
to explain and render credible a very extraordinary feat of insect
engineering.




HOW THE SHADOW MAY BE MADE TO MOVE BACKWARD ON THE SUN-DIAL


In the twentieth chapter of II Kings, at the eleventh verse we read,
that "Isaiah the prophet cried unto the Lord, and he brought the shadow
ten degrees backward, by which it had gone down in the dial of Ahaz."

It is a curious fact, first pointed out by Nonez, the famous
cosmographer and mathematician of the sixteenth century, but not
generally known, that by tilting a sun-dial through the proper angle,
the shadow at certain periods of the year can be made, for a short time,
to move backwards on the dial. This was used by the French
encyclopædists as a rationalistic explanation of the miracle which is
related at the opening of this article.

The reader who is curious in such matters will find directions for
constructing "a dial, for any latitude, on which the shadow shall
retrograde or move backwards," in Ozanam's "Recreations in Science and
Natural Philosophy," Riddle's edition, page 529. Professor Ball in his
"Mathematical Recreations," page 214, gives a very clear explanation of
the phenomenon. The subject is somewhat too technical for these pages.




HOW A WATCH MAY BE USED AS A COMPASS


Several years ago a correspondent of "Truth" (London) gave the following
simple directions for finding the points of the compass by means of the
ordinary pocket watch: "Point the hour hand to the sun, and south is
exactly half way between the hour hand and twelve on the watch, counting
forward up to noon, but backward after the sun has passed the meridian."

Professor Ball, in his "Mathematical Recreations and Problems," gives
more complete directions and explanations. He says:

    "The position of the sun relative to the points of the compass
    determines the solar time. Conversely, if we take the time given by
    a watch as being the solar time (and it will differ from it only by
    a few minutes at the most), and we observe the position of the sun,
    we can find the points of the compass. To do this it is sufficient
    to point the hour-hand to the sun and then the direction which
    bisects the angle between the hour and the figure XII will point due
    south. For instance, if it is four o'clock in the afternoon, it is
    sufficient to point the hour-hand (which is then at the figure IIII)
    to the sun, and the figure II on the watch will indicate the
    direction of south. Again, if it is eight o'clock in the morning, we
    must point the hour-hand (which is then at the figure VIII) to the
    sun, and the figure X on the watch gives the south point of the
    compass.

    "Between the hours of six in the morning and six in the evening the
    angle between the hour and XII, which must be bisected is less than
    180 degrees, but at other times the angle to be bisected is greater
    than 180 degrees; or perhaps it is simpler to say that at other
    times the rule gives the north point and not the south point.

    "The reason is as follows: At noon the sun is due south, and it
    makes one complete circuit round the points of the compass in 24
    hours. The hour-hand of a watch also makes one complete circuit in
    12 hours. Hence, if the watch is held with its face in the plane of
    the ecliptic, and the figure XII on the dial is pointed to the
    south, both the hour-hand and the sun will be in that direction at
    noon. Both move round in the same direction, but the angular
    velocity of the hour-hand is twice as great as that of the sun.
    Hence the rule. The greatest error due to the neglect of the
    equation of time is less than 2 degrees. Of course, in practice,
    most people would hold the face of the watch horizontal, and in our
    latitude (that of London) no serious error would thus be introduced.

    "In the southern hemisphere, or in any tropical country where at
    noon the sun is due north, the rule will give the north point
    instead of the south."




MICROGRAPHY OR MINUTE WRITING AND MICROPHOTOGRAPHY


Minute works of art have always excited the curiosity and commanded the
admiration of the average man. Consequently Cicero thought it worth
while to record that the entire Iliad of Homer had been written upon
parchment in characters so fine that the copy could be enclosed in a
nutshell. This has always been regarded as a marvelous feat.

There is in the French Cabinet of Medals a seal, said to have belonged
to Michael Angelo, the fabrication of which must date from a very remote
epoch, and upon which fifteen figures have been engraved in a circular
space of fourteen millimeters (.55 inch) in diameter. These figures
cannot be distinguished by the naked eye.

The Ten Commandments have been engraved in characters so fine that they
could be stamped upon one side of a nickle five-cent piece, and on
several occasions the Lord's Prayer has been engraved on one side of a
gold dollar, the diameter of which is six-tenths of an inch. I have also
seen it written with a pen within a circle which measured four-tenths of
an inch in diameter.

In the Harleian manuscript, 530, there is an account of a "rare piece of
work, brought to pass by Peter Bales, an Englishman, and a clerk of the
chancery." D'Israeli tells us that it was "The whole Bible in an English
walnut, no bigger than a hen's egg. The nut holdeth the book: there are
as many leaves in his little book as in the great Bible, and he hath
written as much in one of his little leaves as a great leaf of the
Bible."

By most people, such achievements are considered marvels of skill, and
the newspaper accounts of them which are published always attract
special attention. And it must be acknowledged that such work requires
good eyes, steady nerves, and very delicate control of the muscles. But
with ordinary writing materials there are certain mechanical limitations
which must prevent even the most skilful from going very far in this
direction. These limitations are imposed by the fiber or grain of the
paper and the construction of the ordinary pen, neither of which can be
carried beyond a certain very moderate degree of fineness. Of course,
the paper that is chosen will be selected on account of its hard,
even-grained surface, and the pen will be chosen on account of the
quality of its material and its shape, and the point is always carefully
dressed on a whetstone so as to have both halves of the nib equal in
strength and length, and the ends smooth and delicate. When due
preparation has been made, and when the eyes and nerves of the writer
are in good condition, the smallness of the distinctly readable letters
that may be produced is wonderful. And in this connection it is an
interesting fact that in many mechanical operations, writing included,
the hand is far more delicate than the eye. That which the unaided eye
can see to write, the unaided eye can see to read, but the hand, without
the assistance or guidance of the eye, can produce writing so minute
that the best eyes cannot see to read it, and yet, when viewed under a
microscope, it is found to compare favorably with the best writing of
ordinary size. And those who are conversant with the more delicate
operations of practical mechanics, know that this is no exceptional
case. The only aid given by the eye in the case of such minute writing
is the arrangement of the lines, otherwise the writing could be done as
well with the eyes shut as open.

Since the mechanical limitations which we have noted prevent us from
going very far with the instruments and materials mentioned, the next
step is to adopt a finer surface and a sharper point. These conditions
may be found in the fine glazed cards and the metal pencils or styles
used by card writers. In these cards the surface is nearly homogeneous,
that is to say, free from fibers, and the point of the metal pencil may
be made as sharp as a needle, but to utilize these conditions to the
fullest extent, it is necessary to aid the eye, and a magnifier is,
therefore, brought into use. Under a powerful glass the hand may be so
guided by the eye that the writing produced cannot be read by the
unaided vision.

The specimens of fine writing thus far described have been produced
directly by the hand under the guidance either of a magnifier or the
simple sense of motion. Just how far it would be possible to go by these
means has never been determined, so far as I know, but those who have
examined the specimens of selected diatoms and insect scales in which
objects that are utterly invisible to the naked eye are arranged with
great accuracy so as to form the most beautiful figures, can readily
believe that a combination of microscopical dexterity and skill in
penmanship might easily go far beyond anything that has yet been
accomplished in this direction, either in ancient or modern times.

But by means of a very simple mechanical arrangement, the motion of the
hand in every direction may be accurately reduced or enlarged to almost
any extent, and it thus becomes possible to form letters which are
inconceivably small. The instrument by which this is accomplished is
known as a pantagraph, and it has, within a few years, become quite
popular as a means of reducing or enlarging pictures of various kinds,
including crayon reproductions of photographs. Its construction and use
are, therefore, very generally understood. It was by means of a very
finely-made instrument embodying the principles of the pantagraph that
the extraordinarily fine work which we are about to describe was
accomplished.

It is obvious, however, that in order to produce very fine writing we
must use a very fine pen or point and the finer the point the sooner
does it wear out, so that in a very short time the lines which go to
form the letters become thick and blurred and the work is rendered
illegible. As a consequence of this, when the finest specimens of
writing are required, it is necessary to abandon the use of ordinary
points and surfaces and to resort to the use of the diamond for a pen,
and glass for a surface upon which to write. One of the earliest
attempts in this direction was that of M. Froment, of Paris, who
engraved on glass, within a circle, the one-thirtieth of an inch in
diameter, the Coat of Arms of England--lion, unicorn, and crown--with
the following inscription, partly in Roman letters, partly in script:
"_Honi soit qui mal y pense_, Her Most Gracious Majesty, Queen Victoria,
and His Royal Highness, Prince Albert, _Dieu et mon droit_. Written on
occasion of the Great Exhibition, by Froment, à Paris, 1851."

The late Dr. Barnard, President of Columbia College, had in his
possession a copy of the device borne by the seal of Columbia College,
New York, executed for him by M. Dumoulin-Froment, within a circle less
than three one-hundredths of an inch in diameter, "in which are embraced
four human figures and various other objects, together with inscriptions
in Latin, Greek, and Hebrew, all clearly legible. In this device the
rising sun is represented in the horizon, the diameter of the disk being
about three one-thousandths of an inch. This disk has been cross-hatched
by the draughtsman in the original design from which the copy was made;
and the copy shows the marks of the cross-hatching with perfect
distinctness. When this beautiful and delicate drawing is brought
clearly out by a suitably adjusted illumination, the lines appear as if
traced by a smooth point in a surface of opaque ice."

Lardner, in his book on the "Microscope," published in 1856, gives a
wood cut which shows the first piece of engraving magnified 120
diameters, but he said that he was not at liberty to describe the method
by which it was done. As happens in almost all such cases, however, the
very secrecy with which the process was surrounded naturally stimulated
others to rival or surpass it, and Mr. N. Peters, a London banker,
turned his attention to the subject and soon invented a machine which
produced results far exceeding anything that M. Froment had
accomplished. On April 25, 1855, Mr. Farrants read before the
Microscopical Society of London a full account of the Peters machine,
with which the inventor had written the Lord's Prayer (in the ordinary
writing character, without abbreviation or contraction of any kind), in
a space not exceeding the one hundred and fifty-thousandth of a square
inch. Seven years later, Mr. Farrants, as President of the Microscopical
Society, described further improvements in the machine of Mr. Peters,
and made the following statement: "The Lord's Prayer has been written
and may be read in the one-three hundred and fifty-six thousandth of an
English square inch. The measurements of one of these specimens was
verified by Dr. Bowerbank, with a difference of not more than one
five-millionth of an inch, and that difference, small as it is, arose
from his not including the prolongation of the letter _f_ in the
sentence 'deliver us from evil'; so he made the area occupied by the
writing less than that stated above."

Some idea of the minuteness of the characters in these specimens may be
obtained from the statement that the whole Bible and Testament, in
writing of the same size, might be placed twenty-two times on the
surface of a square inch. The grounds for this startling assertion are
as follows: "The Bible and Testament together, in the English language,
are said to contain 3,566,480 letters. The number of letters in the
Lord's Prayer, as written, ending in the sentence, 'deliver us from
evil,' is 223, whence, as 3,566,480 divided by 223, is equal to 15,922,
it appears that the Bible and Testament together contain the same number
of letters as the Lord's Prayer written 16,000 times; if then the prayer
were written in 1-16,000 of an inch, the Bible and Testament in writing
of the same size would be contained by one square inch; but as
1-356,000th of an inch is one twenty-secondth part of 1-15,922 of an
inch, it follows that the Bible and Testament, in writing of that size,
would occupy less space than one twenty-secondth of a square inch."

It only now remains to be seen that, minute as are the letters written
by this machine, they are characterized by a clearness and precision of
form which proves that the moving parts of the machine, while possessing
the utmost delicacy of freedom, are absolutely destitute of shake, a
union of requisites very difficult of fulfilment, but quite
indispensable to the satisfactory performance of the apparatus.

I have no information in regard to the present whereabouts of any of the
specimens turned out by Mr. Peters, and inquiry in London, among persons
likely to know, has not supplied any information on the subject.

There was, however, another micrographer, Mr. William Webb, of London,
who succeeded in producing some marvellous results. Epigrams and also
the Lord's Prayer written in the one-thousandth part of a square inch
have been freely distributed. Mr. Webb also produced a few copies of the
second chapter of the Gospel, according to St. John, written on the
scale of the whole Bible, to a little more than three-quarters of a
square inch, and of the Lord's Prayer written on the scale of the whole
Bible eight times on a square inch. Mr. Webb died about fifteen years
ago, and I believe he has had no successor in the art. Specimens of his
work are quite scarce, most of them having found their way into the
cabinets of public Museums and Societies, who are unwilling to part with
them. The late Dr. Woodward, Director of the Army Medical Museum,
Washington, D.C., procured two of them on special order for the Museum.
Mr. Webb had brought out these fine writings as tests for certain
qualities of the microscope, and it was to "serve as tests for
high-power objectives" that Dr. Woodward procured the specimens now in
the microscopical department of the Museum. I am so fortunate as to have
in my possession two specimen's of Mr. Webb's work. One is an ordinary
microscopical glass slide, three inches by one, and in the center is a
square speck which measures 1-45th of an inch on the side. Upon this
square is written the whole of the second chapter of the Gospel
according to St. John--the chapter which contains the account of the
marriage in Cana of Galilee.

In order to estimate the space which the whole Bible would occupy if
written on the same scale as this chapter, I have made the following
calculation which, I think, will be more easily followed and checked by
my readers, than that of Mr. Farrants.

The text of the old version of the Bible, as published in minion by the
American Bible Society, contains 1272 pages, exclusive of title pages
and blanks. Each page contains two columns of 58 lines each, making 116
lines to the page. This includes the headings of the chapters and the
synopses of their contents, which are, therefore, thrown in to make good
measure. We have, therefore, 1272 pages of 116 lines each, making a
total of 147,552 lines.

The second chapter of St. John has 25 verses containing 95 lines, and is
written on the 1-2025th of an inch, or, in other words, it would go 2025
times on a square inch. A square inch would, therefore, contain 95 ×
2025 or 192,375 lines. This number (192,375), divided by the number of
lines in the Bible (147,552), gives 1.307, which is the number of times
the Bible might be written on a square inch in letters of the same size.
In other words, the whole Bible might be written on .77 inch, or very
little more than three-quarters of a square inch.

Perhaps the following gives a more impressive illustration: The United
States silver quarter of a dollar is .95 inch in diameter, so that the
surface of each side is .707 of a square inch. The whole Bible would,
therefore, very nearly go on one side of a quarter of a dollar. If the
blank spaces at the heads of the chapters and the synopses of contents
were left out, it would easily go on one side.

The second specimen, which I have of Mr. Webb's writing, is a copy of
the Lord's Prayer written on a scale of eight Bibles to the square inch.
According to a statement kindly sent me by the superintendent of the
United States Mint at Philadelphia, the diameter of the last issued gold
dollar, and also of the silver half-dime, is six-tenths of an inch. This
gives .2827+ of a square inch as the area of the surface of one side,
and, therefore, the whole Bible might be written more than two and a
quarter times on one side of either the gold dollar or the silver half
dime.

Such numerical and space relations are far beyond the power of any
ordinary mind to grasp. With the aid of a microscope we can see the
object and compare with other magnifications the rate at which it is
enlarged, and a person of even the most ordinary education can follow
the calculation and understand why the statements are true, but the
final result, like the duration of eternity or the immensity of space,
conveys no definite idea to our minds.

But at the same time we must carefully distinguish between our want of
power to grasp these ideas and our inability to form a conception of
some inconceivable subject, such as a fourth dimension or the mode of
action of a new sense.

Wonderful as these achievements are, there is another branch of the
microscopic art which, from the practical applications that have been
made of it, is even more interesting. This is the art of
microphotography.

About the middle of the last century Mr. J. B. Dancer, of Manchester,
England, produced certain minute photographs of well-known pictures and
statues which commanded the universal attention of the microscopists of
that day, and for a time formed the center of attraction at all
microscopical exhibitions. They have now, however, become so common that
they receive no special notice. Mr. Dancer and other artists also
produced copies of the Lord's Prayer, the Creed, the Declaration of
Independence, etc., on such a scale that the Lord's Prayer might be
covered with the head of a common pin, and yet, when viewed under a very
moderate magnifying power, every letter was clear and distinct. I have
now before me a slip of glass, three inches long and one inch wide, in
the center of which is an oval photograph which occupies less than the
1-200th of a square inch. This photograph contains the Declaration of
Independence with the signatures of all the signers, surrounded by
portraits of the Presidents and the seals of the original thirteen
States. Under a moderate power every line is clear and distinct. In the
same way copies of such famous pictures as Landseer's "Stag at Bay,"
although almost invisible to the naked eye, come out beautifully clear
and distinct under the microscope, so that it has been suggested that
one might have an extensive picture gallery in a small box, or pack away
copies of all the books in the Congressional Library in a small
hand-bag. With such means at our command, it would be a simple matter to
condense a bulky dispatch into a few little films, which might be
carried in a quill or concealed in ways which would have been impossible
with the original. If Major André had been able to avail himself of this
mode of reducing the bulk of the original papers, he might have carried,
without danger of discovery, those reports which caused his capture and
led to his death. And hereafter the ordinary methods of searching
suspected spies will have to be exchanged for one that is more
efficient.

The most interesting application of microphotography, of which we have
any record, occurred during the Franco-Prussian war in 1870-71.

[Illustration: Fig. 21.]

On September 21, 1870, the Germans so completely surrounded the French
capitol, that all communication by roads, railways, and telegraphs, was
cut off and the only way of escape from the city was through the air. On
April 23, the first balloon left Paris, and in a short time after that,
a regular balloon post was established, letters and packages being sent
out at intervals of three to seven days. In order to get news back to
the city, carrier pigeons were employed, and at first the letters were
simply written on very thin paper and enclosed in quills which were
fastened to the middle tail-feather of the bird, as shown in the
engraving, Fig. 21. It is, of course, needless to say, that the
ordinary pictures of doves with letters tied round their necks or
love-notes attached to their wings, are all mere romance. A bird loaded
in that way would soon fall a prey to its enemies. As it was, some of
the pigeons were shot by German gunners or captured by hawks trained by
the Germans for the purpose, but the great majority got safely through.

Written communications, however, were of necessity, bulky and heavy, and
therefore M. Dagron, a Parisian photographer, suggested that the news be
printed in large sheets of which microphotographs could be made and
transferred to collodion positives which might then be stripped from the
glass and would be very light. This was done; the collodion pellicles
measuring about ten centimeters (four inches) square and containing
about three thousand average messages. Eighteen of these pellicles
weighed less than one gramme (fifteen grains) and were easily carried by
a single pigeon. The pigeons having been bred in Paris and sent out by
balloons, always returned to their dove-cotes in that city.

M. Dagron left Paris by balloon on November 12, and after a most
adventurous voyage, being nearly captured by a German patrol, he reached
Tours and there established his headquarters, and organized a regular
system of communication with the capitol. The results were most
satisfactory, upwards of two and a half millions of messages having been
sent into the city. Even postal orders, and drafts were transmitted in
this way and duly honored.

And thus through the pigeon-post, aided by microphotography, Paris was
enabled to keep in touch with the outer world, and the anxiety of
thousands of families was relieved.

It is not likely, however, that the pigeon-post will ever again come
into use for this purpose; our interest in it is now merely historical,
for in the next great siege, if we ever have one, the wireless telegraph
will no doubt take its place and messages, which no hawks can capture
and no guns can destroy, will be sent directly over the heads of the
besiegers.

But let us hope and pray, that the savage and unnecessary war which is
now being waged in the east will be the last, and that in the near
future, two or more of the great nations of the globe will so police the
world, that peace on earth and good will toward men will everywhere
prevail.




ILLUSIONS OF THE SENSES


Our senses have been called the "Five Gateways of Knowledge" because all
that we know of the world in which we live reaches the mind, either
directly or indirectly, through these avenues. From the "ivory palace,"
in which she dwells apart, and which we call the skull, the mind sends
forth her scouts--sight, hearing, feeling, taste, and smell--bidding
them bring in reports of all that is going on around her, and if the
information which they furnish should be untrue or distorted, the most
dire results might follow. She, therefore, frequently compares the tale
that is told by one with the reports from the others, and in this way it
is found that under some conditions these reporters are anything but
reliable; the stories which they tell are often distorted and untrue,
and in some cases their tales have no foundation whatever in fact, but
are the "unsubstantial fabric of a vision."

It is, therefore, of the greatest importance to us, that we should find
out the points on which these information bearers are most likely to be
deceived so that we may guard against the errors into which they would
otherwise certainly lead us.

All the senses are liable to be imposed upon under certain conditions.
The senses of taste and of smell are frequently the subject of phantom
smells and tastes, which are as vivid as the sensations produced by
physical causes acting in the regular way. Even those comparatively new
senses[9] which have been differentiated from the sense of touch and
which, with the original five, make up the mystic number seven, are very
untrustworthy guides under certain circumstances. Thus we all know how
the sense of heat may be deceived by the old experiment of placing one
hand in a bowl of cold water and the other in a bowl of hot water, and
then, after a few minutes, placing both hands together in a bowl of
tepid water; the hand, which has been in the cold water will feel warm,
while that which has just been taken from the hot water, will feel quite
cold.

We have all experienced the deceptions to which the sense of hearing
exposes us. Who has not heard sounds which had no existence except in
our own sensations? And every one is familiar with the illusions to
which we are liable when under the influence of a skilful ventriloquist.

Even the sense of touch, which most of us regard as infallible, is
liable to gross deception. When we have "felt" anything we are always
confident as to its shape, number, hardness, etc., but the following
very simple experiment shows that this confidence may be misplaced:

[Illustration: Fig. 22.]

Take a large pea or a small marble or bullet and place it on the table
or in the palm of the left hand. Then cross the fingers of the right
hand as shown in the engraving, Fig. 22, the second finger crossing the
first, and place them on the ball, so that the latter may lie between
the fingers, as figured in the cut. If the pea or ball be now rolled
about, the sensation is apparently that given by two peas under the
fingers, and this illusion is so strong that it cannot be dispelled by
calling in any of the other senses (the sense of sight for example) as
is usually the case under similar circumstances. We may try and try, but
it will only be after considerable experience that we shall learn to
disregard the apparent impression that there are two balls.

The cause of this illusion is readily found. In the ordinary position of
the fingers the same ball cannot touch at the same time the exterior
sides of two adjoining fingers. When the two fingers are crossed, the
conditions are exceptionally changed, but the instinctive interpretation
remains the same, unless a frequent repetition of the experiment has
overcome the effect of our first education on this point. The
experiment, in fact has to be repeated a great number of times to make
the illusion become less and less appreciable.

But of all the senses, that of sight is the most liable to error and
illusion, as the following simple illustrations will show.

[Illustration: Fig. 23.]

[Illustration: Fig. 24.]

In Fig. 23 a black spot has been placed on a white ground, and in Fig.
24 a white spot is placed on a black ground; which is the larger, the
black spot or the white one? To every eye the white spot will appear to
be the largest, but as a matter of fact they are both the same size.
This curious effect is attributed by Helmholtz to what is called
irradiation. The eye may also be greatly deceived even in regard to the
length of lines placed side by side. Thus, in Fig. 25 a thin vertical
line stands upon a thick horizontal one; although the two lines are of
precisely the same length, the vertical one seems to be considerably
longer than the other.

[Illustration: Fig. 25.]

In Figs. 26 and 27 a series of vertical and horizontal lines are shown,
and in both forms the space that is covered seems to be longer one way
than the other. As a matter of fact the space in each case is a perfect
square, and the apparent difference in width and height depends upon
whether the lines are vertical or horizontal.

[Illustration: Fig. 26.]

[Illustration: Fig. 27.]

Advantage is taken of this curious illusion in decorating rooms and in
selecting dresses. Stout ladies of taste avoid dress goods having
horizontal stripes, and ladies of the opposite conformation avoid those
in which the stripes are vertical.

But the greatest discrepancy is seen in Figs. 28 and 29, the middle line
in Fig. 29 appearing to be much longer than in Fig. 28. Careful
measurement will show that they are both of precisely the same length,
the apparent difference being due to the arrangement of the divergent
lines at the ends.

[Illustration: Fig. 28.]

[Illustration: Fig. 29.]

[Illustration: Fig. 30.]

Converging lines have a curious effect upon apparent size. Thus in Fig.
30 we have a wall and three posts, and if asked which of the posts was
the highest, most persons would name C, but measurement will show that A
is the highest and that C is the shortest.

[Illustration: Fig. 31.]

A still more striking effect is produced in two parallel lines by
crossing them with a series of oblique lines as seen in Figs. 31 and 32.
In Fig. 31 the horizontal lines seem to be much closer at the right-hand
ends than at the left, but accurate measurement will show that they are
strictly parallel.

By changing the direction of the oblique lines, as shown in Fig. 32, the
horizontal lines appear to be crooked although they are perfectly
straight.

[Illustration: Fig. 32.]

All these curious illusions are, however, far surpassed by an experiment
which we will now proceed to describe.


FOOTNOTES:

[9] The old and generally recognized list of the senses is as follows:
Sight, Hearing, Smell, Taste, and Touch. This is the list enumerated by
John Bunyan in his famous work, "The Holie Warre." It has, however, been
pointed out that the sense which enables us to recognize heat is not
quite the same as that of touch and modern physiologists have therefore
set apart, as a distinct sense, the power by which we recognize heat.

The same had been previously done in the case of the sense of Muscular
Resistance but, as the author of "The Natural History of Hell" says,
"when we differentiate the 'Sense of Heat,' and the 'Sense of
Resistance' from the Sense of Touch, we may set up new signposts, but we
do not open up any new 'gateways', things still remain as they were of
old, and every messenger from the material world around us must enter
the ivory palace of the skull through one of the old and well-known
ways."




OBJECTS APPARENTLY SEEN THROUGH A HOLE IN THE HAND


The following curious experiment always excites surprise, and as I have
met with very few persons who have ever heard of it, I republish it from
"The Young Scientist," for November, 1880. It throws a good deal of
light upon the facts connected with vision.

[Illustration: Fig. 33.]

Procure a paste-board tube about seven or eight inches long and an inch
or so in diameter, or roll up a strip of any kind of stiff paper so as
to form a tube. Holding this tube in the left hand, look through it
with the left eye, the right eye also being kept open. Then bring the
right hand into the position shown in the engraving, Fig. 33, the edge
opposite the thumb being about in line with the right-hand side of the
tube. Or the right hand may rest against the right-hand side of the
tube, near the end farthest from the eye. This cuts off entirely the
view of the object by the right eye, yet strange to say the object will
still remain apparently visible to both eyes through a hole in the hand,
as shown by the dotted lines in the engraving! In other words, it will
appear to us as if there was actually a hole through the hand, the
object being seen through that hole. The result is startlingly
realistic, and forms one of the simplest and most interesting
experiments known.

This singular optical illusion is evidently due to the sympathy which
exists between the two eyes, from our habit of blending the images
formed in both eyes so as to give a single image.




LOOKING THROUGH A SOLID BRICK


A very common exhibition by street showmen, and one which never fails to
excite surprise and draw a crowd, is the apparatus by which a person is
apparently enabled to look through a brick. Mounted on a simple-looking
stand are a couple of tubes which look like a telescope cut in two in
the middle. Looking through what most people take for a telescope, we
are not surprised when we see clearly the people, buildings, trees,
etc., beyond it, but this natural expectation is turned into the most
startled surprise when it is found that the view of these objects is not
cut off by placing a common brick between the two parts of the telescope
and directly in the apparent line of vision, as shown in the
accompanying illustration, Fig. 34.

[Illustration: Fig. 34.]

In truth, however, the observer looks _round_ the brick instead of
through it, and this he is enabled to do by means of four mirrors
ingeniously arranged as shown in the engraving. As the mirrors and the
lower connecting tube are concealed, and the upright tubes supporting
the pretended telescope, though hollow, appear to be solid, it is not
very easy for those who are not in the secret to discover the trick.

Of course any number of "fake" explanations are given by the showman who
always manages to keep up with the times and exploit the latest mystery.
At one time it was psychic force, then Roentgen or X-rays; lately it has
been attributed to the mysterious effects of radium!

This illustration is more properly a delusion; there is no illusion
about it.




CURIOUS ARITHMETICAL PROBLEMS




THE CHESS-BOARD PROBLEM


An Arabian author, Al Sephadi, relates the following curious anecdote:

A mathematician named Sessa, the son of Dahar, the subject of an Indian
Prince, having invented the game of chess, his sovereign was highly
pleased with the invention, and wishing to confer on him some reward
worthy of his magnificence, desired him to ask whatever he thought
proper, assuring him that it should be granted. The mathematician,
however, only asked for a grain of wheat for the first square of the
chess-board, two for the second, four for the third, and so on to the
last, or sixty-fourth. The prince at first was almost incensed at this
demand, conceiving that it was ill-suited to his liberality. By the
advice of his courtiers, however, he ordered his vizier to comply with
Sessa's request, but the minister was much astonished when, having
caused the quantity of wheat necessary to fulfil the prince's order to
be calculated, he found that all the grain in the royal granaries, and
even all that in those of his subjects and in all Asia, would not be
sufficient.

He therefore informed the prince, who sent for the mathematician, and
candidly acknowledged that he was not rich enough to be able to comply
with his demand, the ingenuity of which astonished him still more than
the game he had invented.

It will be found by calculation that the sixty-fourth term of the double
progression, beginning with unity, is

    9,223,372,036,854,775,808,

and the sum of all the terms of this double progression, beginning with
unity, may be obtained by doubling the last term and subtracting the
first from the sum. The number, therefore, of the grains of wheat
required to satisfy Sessa's demand will be

    18,446,744,073,709,551,615.

Now, if a pint contains 9,216 grains of wheat, a gallon will contain
73,728, and a bushel (8 gallons) will contain 589,784. Dividing the
number of grains by this quantity, we get 31,274,997,412,295 for the
number of bushels necessary to discharge the promise of the Indian
prince. And if we suppose that one acre of land is capable of producing
in one year, thirty bushels of wheat, it would require 1,042,499,913,743
acres, which is more than eight times the entire surface of the globe;
for the diameter of the earth being taken at 7,930 miles, its whole
surface, including land and water, will amount to very little more than
126,437,889,177 square acres.

If the price of a bushel of wheat be estimated at one dollar, the value
of the above quantity probably exceeds that of all the riches on the
earth.




THE NAIL PROBLEM


A gentleman took a fancy to a horse, and the dealer, to induce him to
buy, offered the animal for the value of the twenty-fourth nail in his
shoe, reckoning one cent for the first nail, two for the second, four
for the third, and so on. The gentleman, thinking the price very low,
accepted the offer. What was the price of the horse?

On calculating, it will be found that the twenty-fourth term of the
progression 1, 2, 4, 8, 16, etc., is 8,388,608, or $83,886.08, a sum
which is more than any horse, even the best Arabian, was ever sold for.

Had the price of the horse been fixed at the value of all the nails, the
sum would have been double the above price less the first term, or
$167,772.15.




A QUESTION OF POPULATION


The following note on the result of unrestrained propagation for one
hundred generations is taken from "Familiar Lectures on Scientific
Subjects," by Sir John F. W. Herschel:

For the benefit of those who discuss the subjects of population, war,
pestilence, famine, etc., it may be as well to mention that the number
of human beings living at the end of the hundredth generation,
commencing from a single pair, doubling at each generation (say in
thirty years), and allowing for each man, woman, and child, an average
space of four feet in height and one foot square, would form a vertical
column, having for its base the whole surface of the earth and sea
spread out into a plane, and for its height 3,674 times the sun's
distance from the earth! The number of human strata thus piled, one on
the other, would amount to 460,790,000,000,000.

In this connection the following facts in regard to the present
population of the globe may be of interest:

The present population of the entire globe is estimated by the best
statisticians at between fourteen and fifteen hundred millions of
persons. This number would easily find standing-room on one half of Long
Island, in the State of New York. If this entire population were to be
brought to the United States, we could easily give every man, woman, and
child, one acre and a half each, or a nice little farm of seven acres
and a half to every family, consisting of a man, his wife, and three
children.

This question has also an important bearing on the preservation of
animals which, in limited numbers, are harmless and even desirable. In
Australia, where the restraints on increase are slight, the rabbit soon
becomes not only a nuisance but a menace, and in this country the
migratory thrush or robin, as it is generally called, has been so
protected in some localities that it threatens to destroy the small
fruit industry.




HOW TO BECOME A MILLIONAIRE


Many plans have been suggested for getting rich quickly, and some of
these are so plausible and alluring that multitudes have been induced to
invest in them the savings which had been accumulated by hard labor and
severe economy. It is needless to say that, except in the case of a few
stool-pigeons, who were allowed to make large profits so that their
success might deceive others and lead them into the net, all these
projects have led to disaster or ruin. It is a curious fact, however,
that some of those who invested in such "get-rich-quickly" schemes were
probably fully aware of their fraudulent character and went into the
speculation with their eyes open in the hope that _they_ might be
allowed to become the stool-pigeons, and in this way come out of the
enterprise with a large balance on the right side. No regret can be felt
when a bird of this kind gets plucked.

But by the following simple method every one may become his own promoter
and in a short time accumulate a respectable fortune. It would seem that
almost any one could save one cent for the first day of the month, two
cents for the second, four for the third, and so on. Now if you will do
this for thirty days we will guarantee you the possession of quite a
nice little fortune. See how easy it is to become a millionaire on
paper, and by the way, it is only on paper that such schemes ever
succeed.

If, however, you should have any doubt in regard to your ability to lay
aside the required amount each day, perhaps you can induce some
prosperous and avaricious employer to accept the following tempting
proposition:

Offer to work for him for a year, provided he pays you one cent for the
first week, two cents for the second, four for the third, and so on to
the end of the term. Surely your services would increase in value in a
corresponding ratio, and many business men would gladly accept your
terms. We ourselves have had such a proposition accepted over and over
again; the only difficulty was that when we insisted upon security for
the last instalment of our wages, our would-be employers could never
come to time. And we would strongly urge upon our readers that if they
ever make such a bargain, they get full security for the last payment
for they will find that when it becomes due there will not be money
enough in the whole world to satisfy the claim.

The entire amount of all the money in circulation among all the nations
of the world (not the _wealth_) is estimated at somewhat less than
$15,000,000,000, and the last payment would amount to fifteen hundred
times that immense sum.

The French have a proverb that "it is the first step that costs" (_c'est
le premier pas qui coute_) but in this case it is the last step that
costs and it costs with a vengeance.

While on this subject let me suggest to my readers to figure up the
amount of which they will be possessed if they will begin at fifteen
years of age and save ten cents per week for sixty years, depositing the
money in a savings bank as often as it reaches the amount required for a
deposit, and adding the interest every six months. Most persons will be
surprised at the result.




THE ACTUAL COST AND PRESENT VALUE OF THE FIRST FOLIO SHAKESPEARE


Seven years after the death of Shakespeare, his collected works were
published in a large folio volume, now known as "The First Folio
Shakespeare." This was in the year 1623. The price at which the volume
was originally sold was one pound, but perhaps we ought to take into
consideration the fact that at that time money had a value, or
purchasing power, at least eight times that which it has at present;
Halliwell-Phillips estimates it at from twelve to twenty times its
present value. For this circumstance, however, full allowance may be
made by multiplying the ultimate result by the proper number.

This folio is regarded as the most valuable printed book in the English
language--the last copy that was offered for sale in good condition
having brought the record price of nearly $9,000, so that it is safe to
assume that a perfect copy, in the condition in which it left the
publisher's hands, would readily command $10,000, and the question now
arises: What would be the comparative value of the present price,
$10,000, and of the original price (one pound) placed at interest and
compounded every year since 1623?

Over and over again I have heard it said that the purchasers of the
"First Folio" had made a splendid investment and the same remark is
frequently used in reference to the purchase of books in general,
irrespective of the present intellectual use that may be made of them.
Let us make the comparison.

Money placed at compound interest at six per cent, a little more than
doubles itself in twelve years. At the present time and for a few years
back, six per cent is a high rate, but it is a very low rate for the
average. During a large part of the time money brought eight, ten, and
twelve per cent per annum, and even within the half century just past it
brought seven per cent during a large portion of the time. Now, between
1623 and 1899, there are 23 periods, of 12 years each, and at double
progression the twenty-third term, beginning with unity, would be
8,388,608. This, therefore, would be the amount, in pounds, which the
volume had cost up to 1899. In dollars it would be $40,794,878.88. An
article which costs forty millions of dollars, and sells for ten
thousand dollars, cannot be called a very good financial investment.

From a literary or intellectual standpoint, however, the subject
presents an entirely different aspect.

Some time ago I asked one of the foremost Shakespearian scholars in the
world if he had a copy of the "First Folio." His reply was that he
could not afford it; that it would not be wise for him to lose $400 to
$500 per year for the mere sake of ownership, when for a very slight
expenditure for time and railway fare he could consult any one of
half-a-dozen copies whenever he required to do so.




ARITHMETICAL PUZZLES


A good-sized volume might be filled with the various arithmetical
puzzles which have been propounded. They range from a method of
discovering the number which any one may think of to a solution of the
"famous" question: "How old is Ann?" Of the following cases one may be
considered a "catch" question, while the other is an interesting
problem.

A country woman, carrying eggs to a garrison where she had three guards
to pass, sold at the first, half the number she had and half an egg
more; at the second, the half of what remained and half an egg more; at
the third the half of the remainder and half an egg more; when she
arrived at the market-place she had three dozen still to sell. How was
this possible without breaking any of the eggs?

At first view, this problem seems impossible, for how can half an egg be
sold without breaking any? But by taking the greater half of an odd
number we take the exact half and half an egg more. If she had 295 eggs
before she came to the first guard, she would there sell 148, leaving
her 147. At the next she sold 74, leaving her 73. At the next she sold
37, leaving her three dozen.

The second problem is as follows: After the Romans had captured Jotopat,
Josephus and forty other Jews sought shelter in a cave, but the refugees
were so frightened that, with the exception of Josephus himself and one
other, they resolved to kill themselves rather than fall into the hands
of their enemies. Failing to dissuade them from this horrid purpose,
Josephus used his authority as their chief to insist that they put each
other to death in an orderly manner. They were therefore arranged round
a circle, and every third man was killed until but two men remained, the
understanding being that they were to commit suicide. By placing himself
and the other man in the 31st and 16th places, they were the last that
were left, and in this way they escaped death.




ARCHIMEDES AND HIS FULCRUM


Next to that of Euclid, the name of Archimedes is probably that which is
the best known of all the mathematicians and mechanics of antiquity, and
this is in great part due to the two famous sayings which have been
attributed to him, one being "Eureka"--"I have found it," uttered when
he discovered the method now universally in use for finding the specific
gravity of bodies, and the other being the equally famous dictum which
he is said to have addressed to Hiero, King of Sicily,--"Give me a
fulcrum and I will raise the earth from its place."

That Archimedes, provided he had been immortal, could have carried out
his promise, is mathematically certain, but it occurred to Ozanam to
calculate the length of time which it would take him to move the earth
only one inch, supposing his machine constructed and mathematically
perfect; that is to say, without friction, without gravity, and in
complete equilibrium, and the following is the result:

For this purpose we shall suppose that the matter of which the earth
is composed weighs 300 pounds per cubic foot, this being about the
ascertained average. If the diameter of the earth be 7,930 miles,
the whole globe will be found to contain 261,107,411,765 cubic
miles, which make 1,423,499,120,882,544,640,000 cubic yards, or
38,434,476,263,828,705,280,000 cubic feet, and allowing 300 pounds to
each cubic foot, we shall have 11,530,342,879,148,611,584,000,000 for
the weight of the earth in pounds.

Now, we know, by the laws of mechanics, that, whatever be the
construction of a machine, the space passed over by the weight, is to
that passed over by the moving power, in the reciprocal ratio of the
latter to the former. It is known also, that a man can act with an
effort equal only to about 30 pounds for eight or ten hours, without
intermission, and with a velocity of about 10,000 feet per hour. If then
we suppose the machine of Archimedes to be put in motion by means of a
crank, and that the force continually applied to it is equal to 30
pounds, then with the velocity of 10,000 feet per hour, to raise the
earth one inch the moving power must pass over the space of
384,344,762,638,287,052,800,000 inches; and if this space be divided by
10,000 feet or 120,000 inches, we shall have for a quotient
3,202,873,021,985,725,440, which will be the number of hours required
for this motion. But as a year contains 8,766 hours, a century will
contain 876,600; and if we divide the above number of hours by the
latter, the quotient, 3,653,745,176,803, will be the number of
centuries during which it would be necessary to make the crank of the
machine continually turn in order to move the earth only one inch. We
have omitted the fraction of a century as being of little consequence in
a calculation of this kind. The machine is also supposed to be
constantly in action, but if it should be worked only eight hours each
day, the time required would be three times as long.

So that while it is true that Archimedes could move the world, the space
through which he could have moved it, during his whole life, from
infancy to old age, is so small that even if multiplied two hundred
million times it could not be measured by even the most delicate of our
modern measuring instruments.

There is a modern saying which has become almost as famous amongst
English-speaking peoples as is that of Archimedes to the world at large.
It is that which Bulwer Lytton puts into the mouth of Richelieu, in his
well-known play of that name:

    "Beneath the rule of men entirely great
    THE PEN IS MIGHTIER THAN THE SWORD."

About thirty years ago it occurred to the writer that these two
epigrammatic sayings--that of Archimedes and that of Bulwer Lytton,
might be symbolized in an allegorical drawing which would forcibly
express the ideas which they contain, and the question immediately
arose--Where will Archimedes get his fulcrum and what can he use as a
lever?

And the mental answer was: Let the pen be the lever and the printing
press the fulcrum, while the sword, used for the same purpose but
resting on glory, or in other words, having no substantial fulcrum,
breaks in the attempt. The little engraving which, with a new motto,
forms a fitting tail-piece to this volume, was the outcome.

It is true that the pen is mighty, and in the hands of philosophers and
diplomats it accomplishes much, but it is only when resting on the
printing press that it is provided with that fulcrum which enables it to
raise the world by diffusing knowledge, inculcating morality, and
providing pleasure and culture for humanity at large.

When assigned to such a task the sword breaks, and well it may. But we
have a well-grounded hope that through the influence of the pen and the
printing press there will soon come an era of universal

[Illustration: Peace on Earth and Good Will Toward Men.]




INDEX


 Absurdities in perpetual motion, 42

 Accuracy of modern methods of squaring the circle, 17

 Adams, perpetual motion, 71

 Ahaz, dial of, 133

 Air, liquid, 65

 Alkahest, or universal solvent, 104

 Altar of Apollo, 30

 Angelo, Michael, finely engraved seal, 136

 Angle, Trisection of, 33

 Apollo, Altar of, 30

 Approximations to ratio of diameter to circumference of circle, 17
   De Morgan's Illustration of, 18
   New Illustration of, 19

 Archimedean screw, 49

 Archimedes, area of circle, 13
   Ratio of circumference to diameter, 14

 Archimedes and his fulcrum, 171

 Arithmetic of the ancients, 15

 Arithmetical problems, 163
   Chess-board problem, 163
   Nail problem, 164
   A question of population, 165
   How to become a millionaire, 166
   Cost of first folio Shakespeare, 168
   Arithmetical puzzles, 170
   Archimedes and his fulcrum, 171

 Army Medical Museum, 142


 Ball, Prof. W. W. R., 39, 129, 133, 134

 Balloons for conveying letters, 147

 Balls--proportion of weight to diameter, 32

 Bean, jumping, 128

 Bells kept ringing for eight years, 41

 Bible in walnut shell, 136

 Bible, written at rate of 22 to square inch, 141

 Boat-race without oars, 129

 Bolognian phosphorus, 102

 Boots--lifting oneself by straps of, 128

 Boyle and palingenesy, 107

 Bramwell, Sir Frederick, 38

 Brick, to look through, 151

 Buckle and geometrical lines, 119

 "Budget of Paradoxes," De Morgan, 6, 18, 118


 Carbon bisulphide for perpetual motion, 67

 Capillary attraction, 53

 Carpenter, Edward--fourth dimension, 122

 Catherine II, 118

 "Century of Inventions," 74

 Chess-board problem, 163

 Child lifting two horses, 131
   Perpetual motion by a, 64

 Circle, squaring the, 9
   Supposed reward for squaring the, 9
   Resolution of Royal Academy of Sciences on, 10
   What the problem is, 12
   Approximation to, by Archimedes, 14
   Jews, ratio accepted by, 13
   Egyptians, ratio accepted by, 14
   Symbol for ratio introduced by Euler, 14
   Graphical approximations, 22

 Circumference of circle, to find, when diameter is given, 22

 Clock that requires no winding, 38

 Columbia College seal, 140

 Column of De Luc, 40

 Compass, watch used as a, 134

 Congreve, Sir William, 53

 Cube, duplication of, 38

 Crystallization seen by microscope, 108
   Mistaken for palingenesy, 100


 Dancer--microphotographs, 144

 Dangerous, fascination of the, 1

 Declaration of Independence, 145

 De Luc's column, 40

 De Morgan--Legend of Michael Scott, 6
   Ignorance _v._ learning, 8
   Illustration of accuracy of modern attempts to square the circle, 18
   "Budget of Paradoxes," 6, 18
   Trisection of angle, 34, 118
   On powder of sympathy, 112
   Anecdote of Diderot, 118

 Dial of Ahaz, 133

 Diderot, anecdote of, 118

 Digby, Sir Kenelm, and palingenesy, 109
   Sir Kenelm and powder of sympathy, 111

 Dircks, 56, 71, 75

 Discoveries, valuable, not due to perpetual-motion-mongers, 36

 Duplication of the cube, 30


 Elixir of life, 95

 Engineering, insect, 130

 Euler, 14, 118


 Fallacies in perpetual motion, 65

 Falstaff and the philosopher's stone, 97

 Faraday's discovery, 93

 Farrants, Prest. Royal Mic. Soc, 140

 Figure, a, enlarged by cutting, 126

 First folio Shakespeare, cost of, 168

 Fixation of mercury, 92

 Follies of Science, The Seven, 2
   D'Israeli's list, 2
   An inappropriate term, 3

 Fourth dimension--conception of, 117
   Flatland, 120
   Kant and Gauss, 121
   Spiritualists, 121
   Edward Carpenter on, 122
   Possibility of a new sense, 123

 Frauds in perpetual motion, 69

 Freezing of mercury, 93

 Froment, micrographs, 139


 Gases, liquefaction of, 93

 Geiser's clock, 71

 Geometrical quadrature impossible, 21

 Gibberish, origin of word, 96

 God, demonstration of existence of, 118


 Hammer made of solid mercury, 93

 Hand, to look through, 156

 Heat and cold, illusions, 150

 Hesse, Landgrave of, 77

 Hindoos, ratio accepted by, 16

 Holmes, O. W., and powder of sympathy, 111

 Homer's Iliad in nutshell, 136

 Honecourt, Wilars de, 42

 Horses lifted by child, 131

 Hydrofluoric acid, 104

 Hydrostatic paradox, 46


 Iliad of Homer in nutshell, 136

 Impossible, fascination of the, 1

 Insect engineering, 130

 Irradiation, 152


 Jews, ratio accepted by the, 13


 Keeley gold cure, 97

 Keeley motor, 69

 Kircher and palingenesy, 106


 Lacomme, on squaring circle, 27

 Lamps, ever-burning, 100

 Library, Congressional, in hand-bag, 145

 Light from electric earth-currents, 103

 Lines, geometrical, 119

 Lines, direction of, deceptive, 154
   Length of, deceptive, 153

 Liquid air, 65

 Lodge, Sir Oliver, on conservation of energy, 5

 Longitude, relation of squaring the circle to, 10


 McArthur, on arithmetic of ancients, 15

 Machin, 16

 Magnetism for perpetual motion, 61

 Man lifting himself, 128

 Mathematicians--how they go to heaven, 8

 Mercury, fixation of, 92
   Freezing of, 93

 Metals. See _Transmutation_.

 Metius, Peter, 16

 Micrography, or minute writing, 136
   Homer in a nutshell, 136
   Michael Angelo's seal, 136
   Ten Commandments, 136
   Bible in a nutshell, 136
   Earliest micrographic engraving, 139
   Micrographic copy of seal of Columbia College, 139
   Peters' machine, 141
   Lord's Prayer written at rate of 22 Bibles to square inch, 141
   Webb's fine writing, 142
   Calculation in regard to, 143
   Microphotographs by Dancer, 144
   Pigeon-post in Franco-Prussian War, 146

 Millionaire, to become a, 166

 Miracle--dial of Ahaz, 133

 Morgan. See _De Morgan_.

 Morton, President Henry, 66

 Motion, perpetual. See _Perpetual motion_.

 Muir, Prof. On Archimedes, 14

 Musitanus, Carolus, 96


 Nail problem, 164

 Nicomedean line, 29


 Orffyreus--his real name, 77
   His fraudulent machine, 77

 Overbalancing wheels, 43


 Paint, luminous, 102

 Palingenesy, 106

 Patent office U. S. and perpetual motion, 42

 Pen mightier than the sword, 173

 Perpetual lamps, 100

 Perpetual motion, 36
   What the problem is, 37
   Clock that requires no winding, 38
   Watch wound by walking, 39
   Clock wound by tides, 41
   By electricity, 41
   Absurdities, 42
   Overbalancing wheels, 43
   Dr. Young, on, 44
   Bellows action, 45
   Hydrostatic paradox, 46
   Bishop Wilkins, 48
   Archimedean screw, 49
   Archimedean screw, by mercury, 51
   Congreve's, by capillary attraction, 53
   Tube and balls, 56
   Tube and rope, 59
   Magnetism, 61
   Self-moving railway carriage, 63
   A child's perpetual motion, 64
   Fallacies, 65
   Liquid air, 65
   Bisulphide of carbon, 66
   Frauds, 69
   Keeley motor, 69
   Geiser's clock, 71
   Adams, 71
   Redhoeffer, 72
   Lukens, 72
   How to stop the machine, 73
   Marquis of Worcester, 74
   Dircks' model, 75
   Orffyreus, 77
   Possibility of, 78

 Peters' micrographs, 141

 Philosopher's stone, 97

 Phosphorus, discovery of, 101

 Pigeon-post, 146

 Population, a question of, 165

 Power, the, of the future, 40

 Ptolemy, on the circle, 15

 Puzzles, arithmetical, 170


 Railway carriage, self-moving, 63

 Ramsay, Sir William, 80, 98

 Ratio of diameter to circumference carried to 127 places, 17

 Redhoeffer's perpetual motion, 72

 Rosicrucius, 100

 Rutherford, 16


 Schott, Father, and palingenesy, 107

 Schweirs, Dr., 52

 Scott, Michael, and his slave demons, 6

 Scott, Sir Walter, legend of the great Wizard, 6
   Powder of sympathy, 112

 Self-moving railway carriage, 63

 Senses--illusions of, 148
   Taste and smell, 149
   Heat and cold, 150
   Hearing, 150
   Touch, 150
   Sight--size of spot, 152
     Length of lines, 153
     Direction of lines, 154
   Objects seen through hand, 156
   Looking through a brick, 158

 Sense, possibility of a new, 123

 Shadow going backward on dial, 133

 Shakespeare, cost of first folio, 168
   Philosopher's stone, 97
   Witchcraft, 114

 Shanks--value of ratio carried to 707 places, 16

 Sharp, Abraham, 16

 Sight, sense of, deceived, 152

 Smith, James, on squaring circle, 28

 Snake lifted by spider, 130

 Solvent, universal, 104

 Space enlarged by cutting, 126

 Spider lifting a snake, 130

 Sun-dial--shadow going backward, 133


 Taste and smell--illusions, 149

 Tides, clock moved by, 40
   Will be the great source of power of the future, 40

 Time it would take Archimedes to move the world, 171

 Touch, sense of, deceived, 150

 Transmutation of the metals, 79
   Ancient fables, 79
   Hermes Trismegistus, 80
   Treatises not allegorical, 81
   Seven metals, 82
   Metals named after planets, 82
   Methods of cheating, 83
   "Brief of the Golden Calf," 84
   Story of unknown Italian, 87
   Possibility of effecting, 88
   Sir William Ramsay, 89
   Effect of such discovery on our currency system, 90

 "Tribune," New York, 29

 Trisection of angle, 33

 Tube and balls, 56

 Tube and rope, 59


 Universal medicine. See _Elixir of Life_.


 Van Ceulen, Rudolph, 16


 Wallich, Dr., 35

 Watch that is wound by walking, 39
   Used as a compass, 134

 Webb micrographs, 142

 Whewell's refutation of 3-1/8 ratio, 28

 Wilkins, Bishop, 48

 Witchcraft or magic, 113

 Worcester, Marquis of, 74

 Writing, fine, 139


 Young, Dr. Thomas, 44