EPOCH OF YOUNG AND FRESNEL. 455 



able is, that it occurred when M. Arago had in his 

 possession the very letter of Young, in which he 

 proposed the same suggestion. 



Young's first published statement of the doc- 

 trine of transverse vibrations was given in the ex- 

 planation of the phenomena of dipolarization, of 

 which we shall have to speak in the next Section. 

 But the primary and immense value of this con- 

 ception, as a step in the progress of the undulatory 

 theory, was the connexion which it established be- 

 tween polarization and double refraction ; for it held 

 forth a promise of accounting for polarization, if any 

 conditions could be found, which might determine 

 what was the direction of the transverse vibrations. 

 The analysis of these conditions is, in a great mea- 

 sure, the work of Fresnel ; a task of profound phi- 

 losophical sagacity and mathematical skill. 



Since the double refraction of uniaxal crystals 

 could be explained by undulations of the form of a 

 spheroid, it was perhaps not difficult to conjecture 

 that the undulations of biaxal crystals would be 

 accounted for by undulations of the form of an 

 ellipsoid, which differs from the spheroid in having 

 its three axes unequal, instead of two only ; and 

 consequently has that very relation to the other, in 

 respect of symmetry, which the crystalline and 

 optical phenomena have. Or, again, instead of 

 supposing two different degrees of elasticity in 

 different directions, we may suppose three such dif- 

 ferent degrees in directions at right angles to each 



