Letters on Natural Magic; Addressed to Sir Walter Scott, Bart.

by David Brewster

If, in place of a solid plate, we strew the sand over a stretched membrane, the sand will form itself into figures, even when the vibrations are communicated to the membrane through the air. In order to make these experiments, we must stretch a thin sheet of wet paper, such as vegetable paper, over the mouth of a tumbler-glass with a footstalk, and fix it to the edges with glue. When the paper is dry, a thin layer of dry sand is strewed upon its surface. If we place this membrane upon a table, and hold immediately above it, and parallel to the membrane, a plate of glass vibrating so as to give any of the figures shown in Fig. 47, the sand upon the membrane will imitate exactly the figure upon the glass. If the glass plate, in place of vibrating horizontally, is made to vibrate in an inclined position, the figures on the membrane will change with the inclination, and the sand will assume the most curious arrangements. The figures thus produced vary with the size of the membrane, with its material, its tension, and its shape. When the same figure occurs several times in succession, a breath upon the paper will change its degree of tension, and produce an entirely new figure, which, as the temporary moisture evaporates, will return to the original figure, through a number of intermediate ones. The pipe of an organ at the distance of a few feet, or the notes of a flute at the distance of half a foot, will arrange the sand on the membrane into figures which perpetually change with the sound that is produced.

The manner in which flat rulers and cylinders of glass perform their vibrations is very remarkable. If a glass plate about twenty-seven inches long, six-tenths of an inch broad, and six hundredths of an inch thick, is held by the edges between the finger and thumb, and has its lower surface, near either end, rubbed with a piece of wet cloth, sand laid upon its upper surface will arrange itself in parallel lines at right angles to the length of the plate. If the place of these lines is marked with a dot of ink, and the other side of the glass ruler is turned upwards, and the ruler made to vibrate as before, the sand will now accumulate in lines intermediate between the former lines, so that the motions of one-half the thickness of the glass ruler are precisely the reverse of those of the corresponding parts of the other half.

As these singular phenomena have not yet been made available by the scientific conjuror, we must be satisfied with this brief notice of them; but there is still one property of sound, which has its analogy also in light, too remarkable to be passed without notice. This property has more of the marvellous in it than any result within the wide range of the sciences. Two loud sounds may be made to produce silence, and two strong lights may be made to produce darkness!

If two equal and similar strings, or the columns of air in two equal and similar pipes, perform exactly 100 vibrations in a second, they will produce each equal waves of sound, and these waves will conspire in generating an uninterrupted sound, double of either of the sounds, heard separately. If the two strings or the two columns of air are not in unison, but nearly so, as in the case where the one vibrates 100 and the other 101 times in a second, then at the first vibration the two sounds will form one of double the strength of either; but the one will gradually gain upon the other, till at the fiftieth vibration it has gained half a vibration on the other. At this instant the two sounds will destroy one another, and an interval of perfect silence will take place. The sound will instantly commence, and gradually increase till it becomes loudest at the hundredth vibration, where the two vibrations conspire in producing a sound double of either. An interval of silence will again occur at the 150th, 250th, 350th vibration, or every second, while a sound of double the strength of either will be heard at the 200th, 300th, and 400th vibration. When the unison is very defective, or when there is a great difference between the number of vibrations which the two strings or columns of air perform in a second, the successive sounds and intervals of silence resemble a rattle. With a powerful organ, the effect of this experiment is very fine, the repetition of the sounds wow—wow—wow—representing the double sound and the interval of silence which arise from the total extinction of the two separate sounds.

The phenomenon corresponding to this in the case of light is perhaps still more surprising. If a beam of red light issues from a luminous point, and falls upon the retina, we shall see distinctly the luminous object from which it proceeds; but if another pencil of red light issues from another luminous point, anyhow situated, provided the difference between its distance and that of the other luminous point from the point of the retina, on which the first beam fell, is the 258th thousandth part of an inch, or exactly twice, thrice, four times, &c., that distance; and if this second beam falls upon the same point of the retina, the one light will increase the intensity of the other, and the eye will see twice as much light as when it received only one of the beams separately. All this is nothing more than what might be expected from our ordinary experience. But if the difference in the distances of the two luminous points is only one-half of the 258th thousandth part of an inch, or 1½, 2½, 3½, 4½, times that distance, the one light will extinguish the other and produce absolute darkness. If the two luminous points are so situated, that the difference of their distances from the point of the retina is intermediate between 1 and 1½, or 2 and 2½, above the 258th thousandth part of an inch, the intensity of the effect which they produce will vary from absolute darkness to double the intensity of either light. At 1¼, 2¼, 3¼ times, &c., the 258th thousandth of an inch, the intensity of the two combined lights will be equal only to one of them acting singly. If the lights, in place of falling upon the retina, fall upon a sheet of white paper, the very same effect will be produced, a black spot being produced in the one case, and a bright white one in the other, and intermediate degrees of brightness in intermediate cases. If the two lights are violet, the difference of distances at which the preceding phenomena will be produced will be the 157th thousandth part of an inch, and it will be intermediate between the 258th and the 157th thousandth part of an inch for the intermediate colours. This curious phenomenon may be easily shown to the eye, by admitting the sun’s light into a dark room through a small hole about the 40th or 50th part of an inch in diameter, and receiving the light on a sheet of paper. If we hold a needle or piece of slender wire in this light, and examine its shadow, we shall find that the shadow consists of bright and dark stripes succeeding each other alternately, the stripe in the very middle or axis of the shadow being a bright one. The rays of light which are bent into the shadow, and which meet in the very middle of the shadow, have exactly the same length of path, so that they form a bright fringe of double the intensity of either; but the rays which fall upon a point of the shadow at a certain distance from the middle, have a difference in the length of their paths, corresponding to the difference at which the lights destroy each other, so that a black stripe is produced on each side of the middle bright one. At a greater distance from the middle, the difference becomes such as to produce a bright stripe, and so on, a bright and a dark stripe succeeding each other to the margin of the shadow.

The explanation which philosophers have given of these strange phenomena is very satisfactory, and may be easily understood. When a wave is made on the surface of a still pool of water, by plunging a stone into it, the wave advances along the surface, while the water itself is never carried forward, but merely rises into a height and falls into a hollow, each portion of the surface experiencing an elevation and a depression in its turn. If we suppose two waves equal and similar to be produced by two separate stones, and if they reach the same spot at the same time, that is, if the two elevations should exactly coincide, they would unite their effects, and produce a wave twice the size of either; but if the one wave should be just so far before the other, that the hollow of the one coincided with the elevation of the other, and the elevation of the one with the hollow of the other, the two waves would obliterate or destroy one another, the elevation as it were of the one filling up half the hollow of the other, and the hollow of the one taking away half the elevation of the other, so as to reduce the surface to a level. These effects will be actually exhibited by throwing two equal stones into a pool of water, and it will be seen that there are certain lines of a hyperbolic form where the water is quite smooth, in consequence of the equal waves obliterating one another, while, in other adjacent parts, the water is raised to a height corresponding to both the waves united.

In the tides of the ocean we have a fine example of the same principle. The two immense waves arising from the action of the sun and moon upon the ocean produce our spring-tides by their combination, or when the elevations of each coincide; and our neap-tides, when the elevation of the one wave coincides with the depression of the other. If the sun and moon had exerted exactly the same force upon the ocean, or produced tide waves of the same size, then our neap-tides would have disappeared altogether, and the spring-tide would have been a wave double of the wave produced by the sun and moon separately. An example of the effect of the equality of the two waves occurs in the port of Batsha, where the two waves arrive by channels of different lengths, and actually obliterate each other.

Now, as sound is produced by undulations or waves in the air, and as light is supposed to be produced by waves or undulations in an ethereal medium, filling all nature, and occupying the pores of transparent bodies, the successive production of sound and silence by two loud sounds, or of light and darkness by two bright lights, may be explained in the very same manner as we have explained the increase and the obliteration of waves formed on the surface of water. If this theory of light be correct, then the breadth of a wave of red light will be the 258th thousandth part of an inch, the breadth of a wave of green light the 207th thousandth part of an inch, and the breadth of a wave of violet light the 157th thousandth part of an inch.

Among the wonders of modern skill, we must enumerate those beautiful automata by which the motions and actions of man and other animals have been successfully imitated. I shall therefore describe at present some of the most remarkable acoustic automata, in which the production of musical and vocal sounds has been the principal object of the artist.

Many very ingenious pieces of acoustic mechanism have been from time to time exhibited in Europe. The celebrated Swiss mechanist, M. le Droz, constructed for the King of Spain the figure of a sheep, which imitated in the most perfect manner the bleating of that animal; and likewise the figure of a dog watching a basket of fruit, which, when any of the fruit was taken away, never ceased barking till it was replaced.