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XVI. On the Reflexion and Refraction of Light at the Surface 

 of a Crystal on the Quasi-labile JEther Theory, By R. 

 t. Glazebrook, M.A., F.R.S* 



IN his comparison of the Electric Theory of Light and the 

 theory of a Quasi-labile iEther, in the Philosophical 

 Magazine for March 1889, Prof. Willard Gibbs has shown 

 that the conditions to be satisfied at the common surface of 

 two media, whether crystalline or not, are the same for the 

 Electromagnetic Theory of Light and for the new Labile 

 iEther theory of Sir William Thomson. The formulse which 

 give the intensities and azimuths of the planes of polarization 

 for the new theory may therefore be deduced from those 

 for the electromagnetic theory ; they may, however, be 

 obtained in a fairly simple manner from the new theory itself, 

 and it seems desirable to have them expressed and so to 

 bring out more clearly the connexion between the two 

 theories!. 



The pressural wave in the new theory disappears from the 

 equations of motion within the medium ; it has, however, its 

 effect in the conditions at the surface. Let us call u , v the 

 components of the displacement in this wave, and let the 

 axis of x be normal to the surface, and the axis of z the in- 

 tersection of the surface and the plane of the waves. Then 



for an isotropic medium u — -r~, v Q = -j- , where 

 2_. 

 ^r = Csin — (7 # +m y— Y i). 



A 



Also, if V, I, on, X are the corresponding quantities for the 

 transverse wave, we have the relations 



Y/X = V /A- , m/X = m /X ; 

 .-. yjr = Csm^^x + 7ny-Yt j. . . . (1) 



Now Sir William Thomson has shown that when A — 0, and 

 therefore V = 0, we must have C— -0, but at the same time 

 A is zero. Thus, if we put 2ttG1 = DX , we have 



* Communicated, by the Author. 



t Since much of the above was written, a paper on somewhat the same 

 subject has been read before the Mathematical Society by Mr. A. B. 

 Basset. Some of the results of his paper, which is not yet printed, have 

 been communicated to me in a letter from Mr. Basset, and. agree with 

 those of the present investigation. — June 18, 1889. 



