of the Axes of Elasticity, in Biaxal Crystals. 223 



light ; they are inconsistent with all received notions, and con- 

 tradict every theory that has been hitherto proposed. No 

 person, as far as I am aware, has even attempted to explain 

 them. 



But in the theory which I have constructed to represent the 

 laws of the action of crystallized bodies upon light, and which 

 has already brought so much within its grasp, the phenomena 

 in question do not offer any difficulty whatever: on the con- 

 trary, they are of a kind that would naturally be looked for, 

 antecedently to experiment. For, in this theory, I make no 

 hypothesis as to the constitution of the ether, or the arrange- 

 ment of its molecules ; nor any hypothesis, like that of Fresnel, 

 respecting the mechanical signification of the axes of elasticity. 

 The existence of three rectangular axes possessing peculiar pro- 

 perties is not a principle, but a result, of theory : their direc- 

 tions are determined by conditions perfectly analogous to those 

 which determine the principal axes of an ellipsoid from its ge- 

 neral equation ; and these directions are functions of certain 

 quantities which are constant when differentials of the second 

 and subsequent orders are neglected, but which vary when these 

 are taken into account. The differentials of higher orders in- 

 troduce terms depending on the wave-length ; and thus the 

 directions, as well as the lengths, of the principal lines depend on 

 the colour of the light, or, to speak more accurately, on the 

 length of the wave. 



All this will be easily understood if we recur to the first 

 principles of the theory. According to these, everything de- 

 pends on the form assigned to the function Y in the general 

 dynamical equation 



JJJ dxdydz 8$ + &, + dt = f dxdydzW, 



from which the motion of the ether is deduced. In my first 

 memoir on the subject (read to the Academy on the 9th of De- 

 cember, 1839), I showed that when differentials of the first 

 order only are preserved, the function Y which may perhaps 



