The Aether as an Elastic Solid. 185 



before the electromagnetic hypothesis had attracted much 

 attention, an elastic-solid theory in many respects preferable 

 to its predecessors was presented to the French Academy* by 

 Joseph Boussinesq (b. 1842). Until this time, as we have 

 seen, investigators had been divided into two parties, according 

 as they attributed the optical properties of different bodies to 

 variations in the inertia of the luminiferous medium, or to 

 variations in its elastic properties. Boussinesq, taking up a 

 position apart from both these schools, assumed that the aether 

 is exactly the same in all material bodies as in interplanetary 

 space, in regard both to inertia and to rigidity, and that the 

 optical properties of matter are due to interaction between the 

 aether and the material particles, as had been imagined more or 

 less by Neumann and O'Brien. These material particles he 

 supposed to be disseminated in the aether, in much the same 

 way as dust-particles floating in the air. 



If e denote the displacement at the point (x, y, z) in the 

 aether, and e' the displacement of the ponderable particles 

 at the same place, the equation of motion of the aether is 



rfie ?P&' 



P *jp = ~ ( k + ^ l ) g 11 " 1 div e + ^V 2 e - p, jp, (1) 



where p and p l denote the densities of the aether and matter 

 respectively, and k and n denote as usual the elastic constants 

 of the aether. This differs from the ordinary Cauchy-Green 

 equation only in the presence of the term pi&*'/dP, which 

 represents the effect of the inertia of the matter. To this 

 equation we must adjoin another expressing the connexion 

 between the displacements of the matter and of the aether: 

 if we assume that these are simply proportional to each 

 other say, 



e' = Ae, (2) 



* Journal de Math. (2) xiii (1868), pp. 313, 425 : cf. also Comptes Rendus, 

 cxvii (1893), pp. 80, 139, 193. Equations kindred to some of those of Boussinesq 

 M-ere afterwards deduced by Karl Pearson, Proc. Lond. Math. Soc , xx (1889), 

 p. 297, from the hypothesis that the strain-energy involves the velocities. 



