522 Mr. R. T. Glazebrook on the Application of the 



of double refraction, I say : — " The question arises, Are these 

 equations incompatible with Fresnel's wave-surface ? Lord 

 Rayleigh has of course proved that they are if the equation 



du dv dw _ ~ 



dx dy dz ' 

 expresses an absolutely necessary condition ;" i. e. if the aether 

 is incompressible, u 9 v, w being the displacements; "but it is 

 not difficult to show that if, instead of the above equation, we 

 put 



1 du 1 dv 1 dw _~ 

 a 2 dx b 2 dy c 2 dz ~ 



(a, by c being the principal wave-velocities), then the wave- 

 surface will be Fresnel's, the direction of vibration will be 

 normal to the ray, and will be in a plane containing the ray, 

 the wave-normal, and an axis of the section of the ellipsoid 

 a 2 x 2 + b 2 y 2 + c 2 z 2 = 1 by the wave-front, while the velocity of 

 propagation will be inversely proportional to the length of 

 this axis.'" 



At the date at which this extract was written I believed 

 that the aether must necessarily be incompressible, and there- 

 fore that the suggestion there made was impossible. The 

 recent paper of Sir William Thomson's has shown that the 

 condition of incompressibility is not necessary, and I propose, 

 therefore, to develop the theory given in outline in the 

 Report. 



Before so doing I wish to refer to three points in Sir 

 William Thomson's paper. He shows there that, under the 

 conditions already stated, viz. no motion at infinity, the 

 expression 



-r, f (dw dv\ 2 /du dw\ 2 /dv du\ 2 \ 

 + B \\Ty + Tz) + \di + dx) + \dx + dj)) 



/i"R / ^ V ^ W ,dwdu du dv \ "l . . 



\ dy dz dz dx dx dy J J ' * ^ ' 



which is Green's value for the work required to strain the 

 solid, transforms into 



W(J- £H£-£HS- SO]- • » 



and then, for the optical problem, A is put equal to zero. 

 Now the term with B for a coefficient in this expression is 



