John Phin.

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 online

. (page 3 of 12)
Online LibraryJohn PhinThe 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 → online text (page 3 of 12)
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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



SQUARING THE CIRCLE 27

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 prac-
tical 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 accu-
rately determined to 1 5 2 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



28 THE SEVEN FOLLIES OF SCIENCE

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 pro-
fessor, set the well-sinker to thinking ; he studied mathe-
matics after a fashion, and announced that he had discovered
that the circumference was exactly 3! 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^ to I, 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 mathema-
tician, 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, accord-
ing to your proposition, -=.2604, and, therefore, the

1 2

chord is greater than its arc, which, you will allow, is
impossible."

This must seem, even to a school-boy, to be unanswer-
able, but it did not faze Mr. Smith, and I doubt if even the
method which I have suggested previously, viz., that of



SQUARING THE CIRCLE 29

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 an-
nounces 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 con-
siderable 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 !



THE DUPLICATION OF THE CUBE




HIS problem became famous because of the halo
of mythological romance with which it was sur-
rounded. 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 pre-
scribed 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

30



THE DUPLICATION OF THE CUBE 31

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 condi-
tions, and Apollo (the Sun) instead of causing disease by
the festering corruption of the usual filth of cities, especi-
ally 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 candi-
dates 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 Bram-
well, 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



32 THE SEVEN FOLLIES OF SCIENCE

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.



Ill

THE TRISECTION OF AN ANGLE




HIS problem is not so generally known as that of
squaring the circle, and consequently it has not
received so much attention from amateur mathe-
maticians, 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 un-
educated reader, whose mind has a mathematical turn, and
especially to a skilful mechanic, who has not studied theo-
retical geometry, it is apt to create a smile, because at first
sight most persons are impressed with an idea of its sim-
plicity, and the ease with which it may be solved. And
this is true, even of many persons who have had a fair gen-
eral 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 schoolboy who has played with a pair of com-
passes 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,

33



34



THE SEVEN FOLLIES OF SCIENCE



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




C



Fig. 4.



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 Euclidian construction. The ablest mathematicians
declare that the problem cannot be solved by such means,
and De Morgan gives the following reasons for this conclu-
sion : " The trisector of an angle, if he demand attention
from any mathematician, is bound to produce from his con-
struction, 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



THE TRISECTION OF AN ANGLE 3-5

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."

De Morgan gives an account of a " terrific " construc-
tion 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




T is probable that more time, effort, and money
have been wasted in the search for a perpetual-
motion machine than have been devoted to at-
tempts 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 sugges-
tions 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

36



PERPETUAL MOTION 37

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 seven-
teenth 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 prop-
erly entitled to the name of a perpetual-motion machine,
it must evolve more power than that which is merely re-
quired 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,



38 THE SEVEN FOLLIES OF SCIENCE

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 moun-
tain 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 wind-
ing, 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.



PERPETUAL MOTION 39

The changes which are constantly taking place in the .
temperature of all bodies, and the expansion and contrac-
tion 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 dis-
connecting 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 m$
of eight or nine degrees Fahrenheit was sufficient to wind v
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 differ-
ent 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 dis-
connects 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."



40 THE SEVEN FOLLIES OF SCIENCE

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 arrange-
ment which would obtain from that source much more
power than is required for that purpose. Indeed the prob-
ability 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 in-
vestments 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 sil-
ver 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



PERPETUAL MOTION 41

perpetually. Many years ago I made a pair of these col-
umns 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 unceas-
ingly." How much longer the columns would have con-
tinued 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 prac-
tical use except as embodied in Bohnenberger's electroscope.

Inventions of this kind might be multiplied indefi-
nitely, 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 : I. ABSURDITIES, 2. FAL-
LACIES, 3. FRAUDS. The following is a description of
the most characteristic machines and apparatus of which
accounts have been published.



42 THE SEVEN FOLLIES OF SCIENCE



I. 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 argu-
ments, which it drew forth. To require a working model
is a reasonable request and one for which the law duly pro-
vides, 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 informa-
tion in regard to the practicability of the invention.

The earliest mechanical device intended to produce per-
petual 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 reinvented hundreds of times. In its
simplest forms it is thus described and figured by Ozanam :



PERPETUAL MOTION 43

" 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


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Online LibraryJohn PhinThe 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 → online text (page 3 of 12)