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 11 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 11 of 12)
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It throws a good deal of light upon the facts connected
with vision.

Procure a paste-board tube about seven or eight inches

Fig. 33-

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 op-
posite 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 sym-
pathy which exists between the two eyes, from our habit of
blending the images formed in both eyes so as to give a
single image.


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. Look-

Fig. 34-

ing 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 accompany-
ing 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 en-
graving. As the mirrors and the lower connecting tube
are concealed, and the upright tubes supporting the pre-
tended telescope, though hollow, appear to be solid, it is
not very easy for those who are not in the secret to dis-
cover 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-ray s ; lately it has been
attributed to the mysterious effects of radium !

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



N Arabian author, Al Sephadi, relates the follow-
ing 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 liberal-
ity. 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 mathe-
matician, 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

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




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 sat-
isfy Sessa's demand will be


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 nec-
essary 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, in-
cluding 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.


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 gentle-
man, 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 i, 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.


HE 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 hundreth 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 num-
ber 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 harm-
less 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 pro-
tected in some localities that it threatens to destroy the
small fruit industry.


(ANY 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 accu-
mulated 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 enter-
prise 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 pos-
session 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 in-
sisted 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

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" (Jest 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 suprised at the result.


EVEN 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 pur-
chasers 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 in-
tellectual 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 1 899. 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 Shakesperian
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.


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 con-
sidered a "catch" question, while the other is an interest-
ing 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 fright-
ened 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 3ist and i6th places, they were the last that were
left, and in this way they escaped death.


EXT 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 dis-
covered 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, suppos-
ing his machine constructed and mathematically perfect ;
that is to say, without friction, without gravity, and in com-
plete 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 di-
ameter 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, arid 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 quo-
tient 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 quo-
tient, 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 cen-
tury 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 Ar-
chimedes 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

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 allegori-
cal 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 fit-
ting 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

peace on JEartb anD <5ooD TOU Howard flfcen.



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 1 36

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 dimen-
sion 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
Dangerous, fascination of the






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 sym-
pathy in

Dircks 56, 71, 75

Discoveries, valuable, not due to per-
petual-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

1 2 3 4 5 6 7 8 9 11

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 11 of 12)