1759, and though Halley did not live to enjoy the sight, it was actually detected on the night of Christmas-day, 1758. A second return of the comet was witnessed in 1835 nearly at the time anticipated.

In recent times the discovery of Neptune has been the most remarkable instance of prevision in astronomical science. A full account of this discovery may be found in several works, as for instance Herschel's Outlines of Astronomy' and 'Grant's History of Physical Astronomy,' Chapters XII and XIII.

Predictions in the Science of Light.

Next after astronomy the science of physical optics has furnished the most beautiful and early instances of the prophetic power of correct theory. These cases are the more striking because they proceed from the profound application of mathematical analysis, and show an insight into the mysterious workings of matter which is surprising to all, but especially to the great majority of men who are unable to comprehend the methods of research employed. By its power of prevision the truth of the undulatory theory of light has been conspicuously proved, and it is especially to be remarked that even Newton received no assistance from his Corpuscular theory in the detection of new experiments. To his followers who embraced that theory we owe little or nothing in the science of light, and even the lofty genius of Laplace did not derive from it a single discovery. As Fresnel himself remarks" :

'The assistance to be derived from a good theory is not to be confined to the calculation of the forces when the laws of the phenomena are known. There are certain laws so complicated and so singular, that observation Taylor's Scientific Memoirs,' vol. v. p. 241.

alone, aided by analogy, could never lead to their discovery. To divine these enigmas we must be guided by theoretical ideas founded on a true hypothesis. The theory of luminous vibrations presents this character, and these precious advantages; for to it we owe the discovery of optical laws the most complicated and most difficult to divine.'

Physicists who embraced the barren emission theory had nothing but their own native capacity and quickness of observation to rely upon. Fresnel having once seized the conditions of the true undulatory theory, as previously stated by Young, was enabled by the mere manipulation of his mathematical symbols to foresee many of the complicated phenomena of light. Who could possibly suppose, or even believe on the ground of mere common sense, that by stopping a large portion of the rays passing through a circular aperture, the illumination of a point upon a screen behind the aperture might be many times multiplied. Yet this paradoxical effect was predicted by Fresnel, and verified both by himself, and in a careful repetition of the experiment in later years, by Billet. Comparatively few persons even now are aware that in the very middle point of the shadow of an opaque circular disc is a point of light sensibly as bright as if no disc had been interposed. This startling fact was deduced from Fresnel's theory by Poisson, and was then verified experimentally by Arago. Airy, again, was led by pure theory to predict that Newton's rings would present a modified appearance if produced between a lens of glass and a plate of metal. This effect happened to have been observed fifteen years before by Arago, unknown to Airy; but another prediction of Airy, that there would be a further modification of the rings when made between two substances of very different refractive indices, was verified by subsequent trial with a diamond. A reversal of the rings takes place

when the space intervening between the plates is filled with a substance of intermediate refractive power, another phenomenon predicted by theory and verified by experiment as Sir John Herschel has described. There is hardly a limit to the number of other complicated effects of the interference of rays of light under different circumstances which might be deduced from the mathematical expressions, if it were worth while, or which, being previously observed can be explained, as in an interesting case observed by Sir John Herschel and explained by Airy P.

By a somewhat different effort of scientific foresight, Fresnel discovered that any solid transparent medium might be endowed with the power of double refraction by mere compression. For as he attributed the peculiar refracting power of crystals to the unequal elasticity in different directions, he inferred that unequal elasticity, if artificially produced, would give similar phenomena. With a powerful screw and a piece of glass, he then produced not only the colours due to double refraction, but the actual duplication of images. Thus, by a great scientific generalisation, are the apparently unique properties of Iceland spar shown to belong to all transparent substances under certain conditions".

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 Airy's, 'Mathematical Tracts,' 3rd edit. p. 312. a Young's Works,' vol. i. p. 412.

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 somewhat different, but equally strange, effect is produced. These phenomena are peculiarly interesting, because cones and cylinders of light are not produced in any other cases. They are, in fact, wholly opposed to all analogy, and constitute singular, or exceptional cases, of a kind which we shall afterwards have to consider more fully. Their very 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 great theory of waves, which we owe to Huyghens, Young, and Fresnel.

Predictions from the Theory of Undulations.

It is curious to reflect that the undulations of light, although so inconceivably rapid and small, admit of more accurate observation and measurement than the waves of any other medium. 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 powers of prediction. Sir John Herschel was perhaps the first to suggest that two sounds might be made to destroy each other by interferences. For if onehalf of a wave travelling through a tube could be separated, and conducted by a somewhat longer passage, so as, on rejoining the other half, to be one-quarter of a vibraLloyd's 'Wave Theory,' Part ii. pp. 52-58. Babbage, 'Ninth Bridgwater Treatise,' p. 104, quoting Lloyd, 'Trans. of the Royal Irish Academy,' vol. xvii. Clifton, 'Quarterly Journal of Pure and Applied Mathematics,' January, 1860.

r

S

Encyclopædia Metropolitana,' art. Sound, p. 753

tion behindhand, the two portions would exactly neutralise each other. This experiment has recently been performed with success by Quincke and Königt. 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 turning round a vibrating fork close to the ear".

It is a plain 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 versa, when the relative motion is in the opposite direction, the pitch will be more grave. It arises from the less or greater intervals of time 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 M. Buys Ballot, on Dutch railways, and of Mr. Scott Russell, in England. Whenever, indeed, 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 it would often amount to a tone. A corresponding effect is produced in the case of light undulations, when the eye and the luminous body rapidly 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 most important and unexpected information conTyndall's 'Sound,' p. 261. u Ibid. p. 273.

x Ibid. p. 78.