Reflexion and Refraction of Light. 417 



for energy given in Thomson and Tait's i Natural Philosophy/ 

 § 693 (7). 



6. To find the total work required to alter the given portion 

 of solid from unstrained equilibrium to the strained condition 

 (u, v, w) we must take ^udxdydzW throughout the rigid 

 containing vessel. Taking first the last line of (1) ; integra- 

 ting the three terms each twice successively by parts in the 

 well-known manner, subject to the condition w = 0, vj = 0, 

 ic = Q at the boundary; we transform the factor within the last 

 vinculum to 



CCC 7 7 7 /dv dio dw du dudv\ 



Adding this with its factor — 4B to the other terms of (1) 

 under N^dxdydz, we find finally 



-nf/dw dv\ 2 (du dw\ 2 (dv du\ 2 l \ /a 

 + \\l^-di) + \dz-di) + \d- X -dy)\i -W- 



This shows that positive work is needed to bring the solid to 

 the condition (w, v, w) from its unstrained equilibrium and 

 therefore its unstrained equilibrium is stable, if A and B are 

 both positive, however small be either of them. 



7. If A = 0, as we are going to suppose it for our optical 

 problem, no work is required to give the medium any infi- 

 nitely small irrotational displacement ; and thus we see the 

 explanation of the zero-velocity of the condensational and 

 rare factional wave which Green notices as corresponding to 

 the case of A = 0. But for present convenience, and until the 

 Aberration of Light, or, generally, the motion of ponderable 

 bodies through ether and related questions of electrostatics, 

 electric currents, and magnetism, come to be considered in 

 connexion with conceivable qualities of the luminiferous ether, 

 we shall suppose forces proportional to cubes of strains to act 

 in such a manner as to render stable the equilibrium which is 

 neutral or "labile"* with no other forces acting than those 

 taken into account in (1) and (2) above. Accordingly, as a 



* This word, very well chosen as it seems to me, has I believe been, by 

 some French writers, employed to signify such equilibrium as that of a 

 rigid body on a perfectly smooth horizontal plane, or of water in a rigid 

 closed vessel entirely filled by it. 



