84 The Hon. J. W. Strutt on the Reflection of 



who does not appear to have seen that a continuity of strain 

 implies necessarily a continuity of statical properties across the 

 surface of separation, as is evident in a moment from D'Alem- 

 bert's principle. So far there is absolute agreement between 

 Green and Cauchy, the only difference being that Green went 

 deeper into the matter and gave the interpretation, if not the 

 justification of the principle assumed straight off by Cauchy. 

 The divergence which exists between the results of the two theo- 

 ries takes its rise in their treatment of the longitudinal wave 

 produced when the vibrations are in the plane of incidence, 

 whose consideration cannot be dispensed with, although its di- 

 rect effect is confined to within a few wave-lengths of the sur- 

 face. Green merely supposes that the velocity of propagation of 

 disturbances depending on change of volume is infinite in both 

 media, and accordingly arrives at a result which contains only 

 one constant — the refractive index ; while Cauchy, on the other 

 hand, imagines a sort of opacity to longitudinal vibrations, in 

 virtue of which the waves are damped, and introduces a new 

 constant called the coefficient of extinction. Cauchy, I believe, 

 never published the proof of his formula? ; but the want has been 

 supplied by German physicists*. Whatever may be thought of 

 the processes by which they are obtained, there can be no doubt 

 that Cauchy's formula? agree very well with the observations of 

 Jamin ; while the same cannot be said of Green's as they stand in 

 his original memoir. A modified form of the latter, however, has 

 been given by Haughton f, to which I am inclined to adhere. He 

 thought that, by supposing the incompressibility, though great, 

 to be still finite, the second constant might be introduced, without 

 which an agreement with observation is impossible. Apart from 

 the difficulty of explaining what becomes of the longitudinal 

 wave when the incidence is nearly normal, in which case it 

 must be propagated in the ordinary way, his reasoning is en- 

 tirely vitiated by an oversight already remarked on by Eisen- 

 lohr. The difference between Cauchy's formulae and Green's, 

 as modified by Haughton, is barely sensible in the experiments 

 of Jamin, which are for the most part confined to the neigh- 

 hood of the polarizing angle; but according to KurzJ, whose 

 observations extended over a wider range, the latter has a decided 

 advantage as an empirical representation of the facts. 



Quite different from the foregoing is the theory of Mac- 

 Cullagh and Neumann, which is given in an accessible form in 

 Lloyd's ' Wave-Theory of Light.' The following principles are 

 laid down as the basis of investigation : — 



* Beer, Pogg. Ann. vols. xci. and xcii. Eisenlohr, Pogg. Ann. vol. civ. 

 p. 346. 



t Phil. Mag. S. 4. vol. vi. p. 81. X Pogg- Ann. vol. cviii. 



