"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 compa.s.s 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 lat.i.tude (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 nutsh.e.l.l. 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 s.p.a.ce 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 ma.n.u.script, 530, there is an account of a "rare piece of work, brought to pa.s.s 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 a.s.sistance 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 h.o.m.ogeneous, 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 gla.s.s 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 gla.s.s 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 gla.s.s, 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 surpa.s.s 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 s.p.a.ce 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 a.s.sertion 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 s.p.a.ce 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 dest.i.tute 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 gla.s.s 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 s.p.a.ce 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 t.i.tle pages and blanks. Each page contains two columns of 58 lines each, making 116 lines to the page. This includes the headings of the chapters and the synopses of their contents, which are, therefore, thrown in to make good measure. We have, therefore, 1272 pages of 116 lines each, making a total of 147,552 lines.

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

In other words, the whole Bible might be written on .77 inch, or very little more than three-quarters of a square inch.

Perhaps the following gives a more impressive ill.u.s.tration: 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 s.p.a.ces 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 s.p.a.ce 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 s.p.a.ce, 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 gla.s.s, 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.

[Ill.u.s.tration: Fig. 21.]

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

Written communications, however, were of necessity, bulky and heavy, and therefore M. Dagron, a Parisian photographer, suggested that the news be printed in large sheets of which microphotographs could be made and transferred to collodion positives which might then be stripped from the gla.s.s 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 circ.u.mstances. 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: