All other predictions in optical science are, however, thrown into the shade by the theoretical discovery of conical refraction by the late Sir W. R. Hamilton, of Dublin. In investigating the passage of light through certain crystals, Hamilton found that Fresnel had slightly misinterpreted his own formulæ, and that, when rightly understood, they indicated a phenomenon of a kind never witnessed. A small ray of light sent into a crystal of arragonite in a particular direction, becomes spread out into an infinite number of rays, which form a hollow cone within the crystal, and a hollow cylinder when emerging from the opposite side. In another case, a different, but equally strange, effect is produced, a ray of light being spread out into a hollow cone at the point where it quits the crystal. These phenomena are peculiarly interesting, because cones and cylinders of light are not produced in any other cases. They are opposed to all analogy, and constitute singular exceptions, of a kind which we shall afterwards consider more fully. Their strangeness rendered them peculiarly fitted to test the truth of the theory by which they were discovered; and when Professor Lloyd, at Hamilton’s request, succeeded, after considerable difficulty, in witnessing the new appearances, no further doubt could remain of the validity of the wave theory which we owe to Huyghens, Young, and Fresnel.15
Predictions from the Theory of Undulations.
It is curious that the undulations of light, although inconceivably rapid and small, admit of more accurate measurement than waves of any other kind. But so far as we can carry out exact experiments on other kinds of waves, we find the phenomena of interference repeated, and analogy gives considerable power of prediction. Herschel was perhaps the first to suggest that two sounds might be made to destroy each other by interference.16 For if one-half of a wave travelling through a tube could be separated, and conducted by a longer passage, so as, on rejoining the other half, to be one-quarter of a vibration behind-hand, the two portions would exactly neutralise each other. This experiment has been performed with success. The interference arising between the waves from the two prongs of a tuning-fork was also predicted by theory, and proved to exist by Weber; indeed it may be observed by merely holding a vibrating fork close to the ear and turning it round.17
It is a result of the theory of sound that, if we move rapidly towards a sounding body, or if it move rapidly towards us, the pitch of the sound will be a little more acute; and, vice versâ, when the relative motion is in the opposite direction, the pitch will be more grave. This arises from the less or greater intervals of time elapsing between the successive strokes of waves upon the auditory nerve, according as the ear moves towards or from the source of sound relatively speaking. This effect was predicted by theory, and afterwards verified by the experiments of Buys Ballot, on Dutch railways, and of Scott Russell, in England. Whenever one railway train passes another, on the locomotive of which the whistle is being sounded, the drop in the acuteness of the sound may be noticed at the moment of passing. This change gives the sound a peculiar howling character, which many persons must have noticed. I have calculated that with two trains travelling thirty miles an hour, the effect would amount to rather more than half a tone, and with some express trains it would amount to a tone. A corresponding effect is produced in the case of light undulations, when the eye and the luminous body approach or recede from each other. It is shown by a slight change in the refrangibility of the rays of light, and a consequent change in the place of the lines of the spectrum, which has been made to give important and unexpected information concerning the relative approach or recession of stars.