FOOTNOTES:

[5] "History of Civilization in England." American edition, Vol. II, page 342.

[6] "The Natural History of h.e.l.l," by John Phillipson, page 37.

[7] "Flatland," by E. A. Abbott. London, 1884.

[8] "From Adam's Peak to Elephanta--" page 160.

HOW A s.p.a.cE MAY BE APPARENTLY ENLARGED BY CHANGING ITS SHAPE

The following is a curious ill.u.s.tration of the errors to which careless observers may be subject:

Draw a square, like Fig. 19, and divide the sides into 8 parts each.

Join the points of division in opposite sides so as to divide the whole square into 64 small squares. Then draw the lines shown in black and cut up the drawing into four pieces. The lines indicating the cuts have been made quite heavy so as to show up clearly, but on the actual card they may be made quite light. Now, put the four pieces together, so as to form the rectangle shown in Fig. 20. Unless the scale, to which the drawing is made is quite large and the work very accurate, it will seem that the rectangle contains 5 squares one way and 13 the other which, when multiplied together, give 65 for the number of small squares, being an apparent gain of one square by the simple process of cutting.

[Ill.u.s.tration: Fig. 19.]

[Ill.u.s.tration: Fig. 20.]

This paradox is very apt to puzzle those who are not familiar with accurate drawings. Of course, every person of common sense knows that the card or drawing is not made any larger by cutting it, but where does the 65th small square come from?

On careful examination it will be seen that the line AB, Fig. 20, is not quite straight and the three parts into which it is divided are thus enabled to gain enough to make one of the small squares. On a small scale this deviation from the straight line is not very obvious, but make a larger drawing, and make it carefully, and it will readily be seen how the trick is done.

CAN A MAN LIFT HIMSELF BY THE STRAPS OF HIS BOOTS?

I think it was the elder Stephenson, the famous engineer, who told a man who claimed the honor of having invented a perpetual motion, that when he could lift himself over a fence by taking hold of his waist-band, he might hope to accomplish his object. And the query which serves as a t.i.tle for this article has long been propounded as one of the physical impossibilities. And yet, perhaps, it might be possible to invent a waist-band or a boot-strap by which this apparently impossible feat might be accomplished!

Travelers in Mexico frequently bring home beans which jump about when laid on a table. They are well-known as "jumping beans" and have often been a puzzle to those who were not familiar with the facts in the case.

Each bean contains the larva of a species of beetle and this affords a clue to the secret. But the question at once comes up: "How is the insect able to move, not only itself, but its house as well, without some purchase or direct contact with the table?"

The explanation is simple. The hollow bean is elastic and the insect has strength enough to bend it slightly; when the insect suddenly relaxes its effort and allows the bean to spring back to its former shape, the reaction on the table moves the bean. A man placed in a perfectly rigid box could never move himself by pressing on the sides, but if the box were elastic and could be bent by the strength of the man inside, it might be made to move.

A somewhat a.n.a.logous result, but depending on different principles, is attained in certain curious boat races which are held at some English regattas and which is explained by Prof. W. W. Rouse Ball, in his "Mathematical Recreations and Problems." He says that it

"affords a somewhat curious ill.u.s.tration of the fact that commonly a boat is built so as to make the resistance to motion straight forward less than that to motion in the opposite direction.

"The only thing supplied to the crew is a coil of rope, and they have (without leaving the boat) to propel it from one point to another as rapidly as possible. The motion is given by tying one end of the rope to the afterthwart, and giving the other end a series of violent jerks in a direction parallel to the keel.

"The effect of each jerk is to compress the boat. Left to itself the boat tends to resume its original shape, but the resistance to the motion through the water of the stern is much greater than that of the bow, hence, on the whole, the motion is forwards. I am told that in still water a pace of two or three miles an hour can be thus attained."

HOW A SPIDER LIFTED A SNAKE

One of the most interesting books in natural history is a work on "Insect Architecture," by Rennie. But if the architecture of insect homes is wonderful, the engineering displayed by these creatures is equally marvellous. Long before man had thought of the saw, the saw-fly had used the same tool, made after the same fashion, and used in the same way for the purpose of making slits in the branches of trees so that she might have a secure place in which to deposit her eggs. The carpenter bee, with only the tools which nature has given her, cuts a round hole, the full diameter of her body, through thick boards, and so makes a tunnel by which she can have a safe retreat, in which to rear her young. The tumble-bug, without derrick or machinery, rolls over large ma.s.ses of dirt many times her own weight, and the s.e.xton beetle will, in a few hours, bury beneath the ground the carca.s.s of a comparatively large animal. All these feats require a degree of instinct which in a reasoning creature would be called engineering skill, but none of them are as wonderful as the feats performed by the spider. This extraordinary little animal has the faculty of propelling her threads directly against the wind, and by means of her slender cords she can haul up and suspend bodies which are many times her own weight.

Some years ago a paragraph went the rounds of the papers in which it was said that a spider had suspended an unfortunate mouse, raising it up from the ground, and leaving it to perish miserably between heaven and earth. Would-be philosophers made great fun of this statement, and ridiculed it unmercifully. I know not how true it _was_, but I know that it _might have been_ true.

Some years ago, in the village of Havana, in the State of New York, a spider entangled a milk-snake in her threads, and actually raised it some distance from the ground, and this, too, in spite of the struggles of the reptile, which was alive.

By what process of engineering did the comparatively small and feeble insect succeed in overcoming and lifting up by mechanical means, the mouse or the snake? The solution is easy enough if we only give the question a little thought.

The spider is furnished with one of the most efficient mechanical implements known to engineers, viz., a strong elastic thread. That the thread is strong is well known. Indeed, there are few substances that will support a greater strain than the silk of the silkworm, or the spider; careful experiment having shown that for equal sizes the strength of these fibers exceeds that of common iron. But notwithstanding its strength, the spider's thread alone would be useless as a mechanical power if it were not for its elasticity. The spider has no blocks or pulleys, and, therefore, it cannot cause the thread to divide up and run in different directions, but the elasticity of the thread more than makes up for this, and renders possible the lifting of an animal much heavier than a mouse or a snake. This may require a little explanation.

Let us suppose that a child can lift a six-pound weight one foot high and do this twenty times a minute. Furnish him with 350 rubber bands, each capable of pulling six pounds through one foot when stretched. Let these bands be attached to a wooden platform on which stand a pair of horses weighing 2,100 lbs., or rather more than a ton. If now the child will go to work and stretch these rubber bands, singly, hooking each one up, as it is stretched, in less than twenty minutes he will have raised the pair of horses one foot!

We thus see that the elasticity of the rubber bands enables the child to divide the weight of the horses into 350 pieces of six pounds each, and at the rate of a little less than one every three seconds, he lifts all these separate pieces one foot, so that the child easily lifts this enormous weight.

Each spider's thread acts like one of the elastic rubber bands. Let us suppose that the mouse or the snake weighed half an ounce and that each thread is capable of supporting a grain and a half. The spider would have to connect the mouse with the point from which it was to be suspended with 150 threads, and if the little quadruped was once swung off his feet, he would be powerless. By pulling successively on each thread and shortening it a little, the mouse or snake might be raised to any height within the capacity of the building or structure in which the work was done. So that to those who have ridiculed the story we may justly say: "There are more things in heaven and earth than are dreamed of in _your_ philosophy."

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 carca.s.s 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 lat.i.tude, 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 COMPa.s.s

Several years ago a correspondent of "Truth" (London) gave the following simple directions for finding the points of the compa.s.s 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 pa.s.sed 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 compa.s.s 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 compa.s.s. 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 compa.s.s.