The Aether as an Elastic Solid. 179 



The quantities J and S are interpreted in the same way as 



in Fresnel's theory of total reflexion : that is, we take J to 

 mean the ratio of the intensities of the reflected and incident 

 light, while 3 measures the change of phase experienced by 

 the light in reflexion. 



The case of light polarized at right angles to the plane of 

 incidence may be treated in the same way. 



When the incidence is perpendicular, U evidently reduces 

 to v (1 + K 2 )*, and u reduces to - tan -1 K. For silver at perpen- 



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dicular incidence almost all the light is reflected, so J is nearly 

 unity : this requires cos v to be small, and K to be very large. 

 The extreme case in which K is indefinitely great but v indefinitely 

 small, so that the quasi- index of refraction is a pure imaginary, 

 is generally known as the case of ideal silver. 



The physical significance of the two constants v and K was 

 more or less distinctly indicated by Cauchy; in fact, as the 

 difference between metals and transparent bodies depends on 

 the constant K, it is evident that K must in some way measure 

 the opacity of the substance. This will be more clearly seen if 

 we inquire how the elastic-solid theory of light can be extended 

 so as to provide a physical basis for the formulae of MacCullagh 

 and Cauchy.* The sine-formula of Fresnel, which was the 

 starting-point of our investigation of metallic reflexion, is a 

 consequence of Green's elastic-solid theory : and the differences 

 between Green's results and those which we have derived arise 

 solely from the complex value which we have assumed for yu. 

 We have therefore to modify Green's theory in such a way as 

 to obtain a complex value for the index of refraction. 



Take the plane of incidence as plane of xy, and the metallic 

 surface as plane of yz. If the light is polarized in the plane of 

 incidence, so that the light- vector is parallel to the axis of z, 

 the incident light may be taken to be a function of the 

 argument 



ax + by + ct, 



* This was done by Lord Rayleigh, Phil. Mag. xliii (1872), p. 321. 



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