150 The Aether as an Elastic Solid. 



his theory, in the form to which it had then been brought, as a 

 final explanation of the properties of light. " If we are asked," 

 he wrote, " what reasons can be assigned for the hypotheses on 

 which the preceding theory is founded, we are far from being 

 able to give a satisfactory answer. We are obliged to confess 

 that, with the exception of the law of vis viva, the hypotheses 

 are nothing more than fortunate conjectures. These conjectures 

 are very probably right, since they have led to elegant laws 

 which are fully borne out by experiments ; but this is all we 

 can assert respecting them. We cannot attempt to deduce 

 them from first principles ; because, in the theory of light, 

 such principles are still to be sought for. It is certain, indeed, 

 that light is produced by undulations, propagated, with 

 transversal vibrations, through a highly elastic aether ; but the 

 constitution of this aether, and the laws of its connexion (if it 

 has any connexion) with the particles of bodies, are utterly 

 unknown/' 



The needful reformation of the elastic-solid theory of 

 reflexion was effected by Green, in a paper* read to the 

 Cambridge Philosophical Society in December, 1837. Green, 

 though inferior to Cauchy as an analyst, was his superior in 

 physical insight ; instead of designing boundary-equations for 

 the express purpose of yielding Fresnel's sine and tangent 

 formulae, he set to work to determine the conditions which are 

 actually satisfied at the interfaces of real elastic solids. 



These he obtained by means of general dynamical principles. 

 In an isotropic medium which is strained, the potential energy 

 per unit volume due to the state of stress is 



4 \te x de y 



+ (~- + ^} -4r-*~-4~~-4 



where e denotes the displacement, and k and n denote the two 



* Trans. Camb. Phil. Soc., 1838 ; Green's Math. Papers, p. 245. 



