Elastic Solid JEther. 559 



conditions are that H is continuous and c -1 VyH is tangentially 

 continuous. It was sought to identify H with the velocity y 

 o£ a usual 21-constant elastic solid. Four quite definite steps 

 were thence taken. 



First step. In order that for an elastic solid with moduli 

 unvarying from point to point, the evoked volume force /3 

 may, with arbitrary displacement 77, satisfy the incompressible 

 condition SV/3 = 0, the twenty-one constants must reduce to 

 six in the following definite manner. When the density is 

 unity the potential energy iv per unit volume must be of the 

 form 



»=s(vr,? 2 )/<(vtri^)> 



where ^ is the pure strain Unity and h is a constant self- 

 conjugate Unity. 



Second step. In order that with h varying from point to 

 point the same condition Sy/3 = may hold (a condition 

 imposed in the hope of attaining the boundary condition 

 that AVy? is continuous) It must have the definite form 



Ao)= — S&>V • V#? 



where g is a scalar function of position. 



Third step. We may add to the volume potential energy 

 now attained, the hydrostatic quadratic term -J£(Sf\^£)- 3 

 because it is found that this generalized form, and this form 

 alone, produces an equation of motion in which curl and 

 convergence are propagated independently. [This step is 

 essentially a step of Green's, but it was actually taken without 

 reference to Green's work.] 



Fourth step. We naturally seek a simple description of 

 the volume energy attained. The very suggestive form of h 

 in terms of <j readily leads to the specification of § 1 above. 



I think it may be claimed that the theory finally reached 

 reconciles Green andMacCullagh, and especially that it pro- 

 vides what has been so persistently sought, an easily conceived 

 dynamical explanation of MacCullagh's foundation. Taken 

 in connexion with some such elaborate superstructure as 

 Dr. Larmor's 'iEther and Matter/ I think we may further say 

 that the theory furnishes the fundamental dynamical expla- 

 nation of modern electromagnetic theory. 



The following modification of the details of the specification 

 of § 1 seems worth considering. Suppose a large crystal to 

 be built up of component crystals whose linear dimensions are 

 small, in a sense, but are large compared with the wave- 

 length of light. We can then make D as small as 10 -8 gm. 

 per cub. cm. 



