[Ill.u.s.tration: Fig. 22.]

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 circ.u.mstances. 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 b.a.l.l.s.

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 repet.i.tion 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 ill.u.s.trations will show.

[Ill.u.s.tration: Fig. 23.]

[Ill.u.s.tration: Fig. 24.]

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.

[Ill.u.s.tration: Fig. 25.]

In Figs. 26 and 27 a series of vertical and horizontal lines are shown, and in both forms the s.p.a.ce that is covered seems to be longer one way than the other. As a matter of fact the s.p.a.ce in each case is a perfect square, and the apparent difference in width and height depends upon whether the lines are vertical or horizontal.

[Ill.u.s.tration: Fig. 26.]

[Ill.u.s.tration: Fig. 27.]

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.

[Ill.u.s.tration: Fig. 28.]

[Ill.u.s.tration: Fig. 29.]

[Ill.u.s.tration: Fig. 30.]

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.

[Ill.u.s.tration: Fig. 31.]

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.

[Ill.u.s.tration: Fig. 32.]

All these curious illusions are, however, far surpa.s.sed 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 h.e.l.l" 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.

[Ill.u.s.tration: Fig. 33.]

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 ill.u.s.tration, Fig. 34.

[Ill.u.s.tration: 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 ill.u.s.tration 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, a.s.suring 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 quant.i.ty 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.