456 HISTORY OF OPTICS. 



other. This kind of generalization was tolerably 

 obvious to a practised mathematician. 



But what shall call into play all these elasticities 

 at once, and produce waves governed by each of 

 them? And what shall explain the different po- 

 larization of the rays which these separate waves 

 carry with them? These were difficult questions, 

 to the solution of which mathematical calculation 

 had hitherto been unable to offer any aid. 



It was here that the conception of transverse 

 vibrations came in, like a beam of sunlight, to dis- 

 close the possibility of a mechanical connexion of 

 all these facts. If transverse vibrations, travelling 

 through a uniform medium, come to a medium not 

 uniform, but constituted so that the elasticity shall 

 be different in different directions, in the manner 

 we have described, what will be the course and con- 

 dition of the waves in the second medium? Will 

 the effects of such waves agree with the phenomena 

 of doubly-refracted light in biaxal crystals? Here 

 was a problem, striking to the mathematician for 

 its generality and difficulty, and of deep interest 

 to the physical philosopher, because the fate of a 

 great theory depended upon its solution. 



The solution, obtained by great mathematical 

 skill, was laid before the French Institute by Fres- 

 nel in November, 1821, and was carried further 

 in two Memoirs presented in 1822. Its import is 

 very curious. The undulations which, coming from 

 a distant center, fall upon such a medium as we 



