As already noted, the great difficulty with most circle-squa_The Seven Follies of Science [2nd ed.] 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

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THE SEVEN FOLLIES

OF SCIENCE

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

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

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."

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 Athenaeum 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