TEANSACTIONS OF SECTION A. 677 



called by his ilhistrioua name. Men learnt from the ' Principia ' how to deal with 

 the motion of small particles under definite forces. The laws of wave motion were 

 obscure, and till the days of Young and Fresnel there was no second Newton to 

 explain them. There is truth in Whewell's words (' Inductive Sciences,' ii., chap, x.) : 

 ' That propositions existed in the " Principia " which proceeded on this hypothesis 

 was with many ground enough for adopting the doctrine.' Young's view, already 

 quoted, appears to me more just; and I see in Newton's hypothesis the first clear 

 indication of the undulatory theory of light, the first statement of its fundamental 

 laws. 



Three years later (1678) Huygens wrote his ' Traits de la Lumiere,' published 

 in 1690. He failed to meet the main difficulty of the theory, but in other respects 

 he developed its consequences to a most remarkable degree. For more than a cen- 

 tury after this there was no progress, until in 1801 the principle of interference 

 ■was discovered by Young, and again independently a few years later by Fresnel, 

 ■whose genius triumphed over the difficulties to which his predecessors had succumbed, 

 and, by combining the principles of interference and transverse vibrations, established 

 ^n undulatory theory as a fact, thus making Newton's theory a vera causa. 



There is, however, a great distinction between the emission theory as Newton 

 left it and Fresnel's undulatory theory. The former was dynamical, though it could 

 ■explain but little : the particles of light obeyed the laws of motion, like particles of 

 matter. The undulatory theory of Huygens and Fresnel was geometrical or kine- 

 matical : the structure of the ether was and is unknown ; all that was needed was 

 that light should be due to the rapid periodic changes of some vector property of a 

 medium capable of transmitting transverse waves. Fresnel, it is true, attempted to 

 give a dynamical account of double refraction, and of the reflexion and refraction 

 -of polarised light, but the attempt was a failure ; and not the least interesting part 

 of Mr. L. Fletcher's recent book on double refraction (' The Optical Indicatrix ') is 

 that in which he shows that Fresnel himself in the first instance arrived at his 

 theory by purely geometrical reasoning, and only attempted at a later date to give 

 it its dynamical form. ' If we reflect,' says Stokes,^ ' on the state of the subject as 

 Fresnel found it and as he left it, the wonder is, not that he failed to give a rigo- 

 rous dynamical theory, but that a single mind was capable of effecting so much,' 

 Every student of optics should read Fresnel's great memoirs. 



But the time was coming when the attempt to construct a dynamical theory of 

 light could be made. Navier, in 1821, gave the first mathematical theory of elas- 

 ticity. He limited himself to isotropic bodies, and worked on Boscovitch's hypo- 

 tihesis as to the constitution of matter. Poisson followed on the same lines, and 

 the next year (1822) Cauchy wrote his first memoir on elasticity. The phenomena 

 of light afforded a means of testing this theory of elasticity, and accordingly the 

 first mechanical conception of the ether was that of Cauchy and Neumann, who 

 ■conceived it to consist of distinct hard particles acting upon one another with forces 

 in the line joining them, which vary as some function of the distances between the 

 ■particles. It was now possible to work out a mechanical theory of light which 

 should be a necessary consequence of these hypotheses. Cauchy's and the earlier 

 theories do not represent the facts either in an elastic solid or in the ether. At 

 ipresent we are not concerned with the cause of this ; we must recognise them as the 

 first attempts to explain on a mechanical basis the phenomena observed. According 

 to this theory in its final form, there are, in an isotropic medium, two waves which 

 travel -with velocities V'A/p and \/B/p, A and B being constants and p the density. 

 Adopting Cauchy's molecular hypothesis, there must be a definite relation between 

 A and B. 



A truer ■view of the theory of elasticity is given by Green in his paper read 

 fcefore the Cambridge Philosophical Society in 1837. This theory involves the two 

 constants, but they are independent, and to account for certain optical effects A must 

 •either vanish or be infinite. The first supposition was, until a few years since, 

 thought to be inconsistent with stability ; the second leads to consequences which in 

 part agree with the results of optical experiment, but which differ fatally from those 



" ' Report on Double Refraction,' Srit. Assoc. Report, 1862, p. 254. 



