Chapter VII: The Universal Medicine and the Elixir of Life (2)

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 encyclopaedists 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, a 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 x 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 Andre 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.

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:

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.

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.

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.

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.

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.

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.

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.

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.

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.