and Refraction of Light. 501 



which the matter within pulls the interface, 



(A'-fB').3e. 



And for the component displacements of the matter outside 

 the interface, we have 



a 3 x a?y a?z 



whence, by (7) of § 9, we find for the force with which the 

 matter without pushes the interface, 



4B.e. 



Hence the sum of iuward push from without and inward pull 

 from within, on the interface, is 



3[A'+f(B-B')>. 



Hence for stability, or at least lability, it is necessary that 

 A ; + |(B — B') be positive, or at least zero. Hence if A'=0, 

 we must have B>B'. And if A = 0, we find, similarly, by 

 considering a case in which a portion of (A, B) solid is 

 embedded in (A', B') solid, that B' ^ B is necessary for 

 stability or lability. Hence for stability or lability, if A = 

 and A' = 0, we must have B = B'. The question does this 

 suffice for stability, or at least lability, is not answered by mere 

 consideration of the preceding spherical example : but that it 

 does suffice follows from § § 4, 5 of the Article. 



Mr. Glazebrook also yesterday evening showed me that my 

 hypothesis of zero velocity for condensational-rarefactional 

 wave allows the Stokes-Rankine-Rayleigh hypothesis of aelo- 

 tropic effective inertia to become valid for the explanation of 

 double refraction with exactly Fresnel's wave-surface, and 

 with velocity of propagation depending properly on the direc- 

 tion of the vibration ; but with the direction of vibration 

 perpendicular to the ray-direction : instead of being in the 

 tangent-plane to the wave-surface as in Fresnel's theory, and 

 as it essentially is in any theory which supposes the ether to 

 be an incompressible solid. He promises a paper on this subject 

 for the December [Number of the Philosophical Magazine. 



W. T. 



Train, Cambridge to Glasgow, 

 Noyember 1, 1888. 



Phil Mag. S. 5. Vol. 26. No. 163. Dec. 1888. 2 M 



