In a precisely similar manner two systems of sonorous waves can be caused to interfere and mutually to destroy each other: thus, by adding sound to sound, silence may be produced. Two beams of light also may be caused to interfere and effect their mutual extinction: thus, by adding light to light, we can produce darkness. Here indeed we have a critical analogy between sound and light—the one, in fact, which compels the most profound thinkers of the present day to assume that light, like sound, is a case of undulatory motion.
We see here the vision of the intellect prolonged beyond the boundaries of sense into the region of what might be considered mere imagination. But, unlike other imaginations, we can bring ours to the test of experiment; indeed, so great a mastery have we obtained over these waves, which eye has not seen, nor ear heard, that we can with mathematical certainty cause them to coincide or to interfere, to help each other or to destroy each other, at pleasure. It is perhaps possible to be a little more precise here. Let two stones—with a small distance between them—be dropped into water at the same moment; a system of circular waves will be formed round each stone. Let the distance from one little crest to the next following one be called the length of the wave, and now let us inquire what will take place at a point equally distant from the places where the two stones were dropped in. Fixing our attention upon the ridge of the first wave in each case, it is manifest that, as the water propagates both systems with the same velocity, the two foremost ridges will reach the point in question at the same moment; the ridge of one would therefore coincide with the ridge of the other, and the water at this point would be lifted to a height greater than that of either of the previous ridges.
COINCIDENCE AND INTERFERENCE.
Again, supposing that by any means we had it in our power to retard one system of waves so as to cause the first ridge of the one to be exactly one wave length behind the first ridge of the other, when they arrive at the point referred to. It is plain that the first ridge of the retarded system now falls in with the second ridge of the unretarded system, and we have another case of coincidence. A little reflection will show the same to be true when one system is retarded any number of whole wave-lengths; the first ridge of the retarded system will always, at the point referred to, coincide with a ridge of the unretarded system.
But now suppose the one system to be retarded only half a wave-length; it is perfectly clear that, in this case the first ridge of the retarded system would fall in with the first furrow of the unretarded system, and instead of coincidence we should have interference. One system, in fact, would tend to make a hollow at the point referred to, the other would tend to make a hill, and thus the two systems would oppose and neutralize each other, so that neither the hollow nor the hill would be produced; the water would maintain its ordinary level. What is here said of a single half-wave-length of retardation, is also true if the retardation amount to any odd number of half-wave-lengths. In all such cases we should have the ridge of the one system falling in with the furrow of the other; a mutual destruction of the waves of both systems being the consequence. The same remarks apply when the point, instead of being equally distant from both stones, is an even or an odd number of semi-undulations farther from the one than from the other. In the former case we should have coincidence, and in the latter case interference, at the point in question.
LIQUID WAVES.
To the eye of a person who understands these things, nothing can be more interesting than the rippling of water under certain circumstances. By the action of interference its surface is sometimes shivered into the most beautiful mosaic, shifting and trembling as if with a kind of visible music. When the tide advances over a sea-beach on a calm and sunny day, and its tiny ripples enter, at various points, the clear shallow pools which the preceding tide had left behind, the little wavelets run and climb and cross each other, and thus form a lovely chasing, which has its counterpart in the lines of light converged by the ripples upon the sand underneath. When waves are skilfully generated in a vessel of mercury, and a strong light reflected from the surface of the metal is received upon a screen, the most beautiful effects may be observed. The shape of the vessel determines, in part, the character of the figures produced; in a circular dish of mercury, for example, a disturbance at the centre propagates itself in circular waves, which after reflection again encircle the centre. If the point of disturbance be a little removed from the centre, the intersections of the direct and reflected waves produce the magnificent chasing shown in the annexed figure ([16]), which I have borrowed from the excellent work on Waves by the Messrs. Weber. The luminous figure reflected from such a surface is exceedingly beautiful. When the mercury is lightly struck by a glass point, in a direction concentric with the circumference of the vessel, the lines of light run round the vessel in mazy coils, interlacing and unravelling themselves in the most wonderful manner. If the vessel be square, a splendid mosaic is produced by the crossing of the direct and reflected waves. Description, however, can give but a feeble idea of these exquisite effects;—
"Thou canst not wave thy staff in the air,
Or dip thy paddle in the lake,
But it carves the brow of beauty there,
And the ripples in rhymes the oar forsake."
CHASING PRODUCED BY WAVES.
