( 221 ) 



XIX. 01$ THE DISPERSION OF THE OPTIC AXES, AND OF 

 THE AXES OF ELASTICITY, IN BIAXAL CEYSTALS. 



[From the Philosophical Magazine, VOL. xxi., October, 1842.] 



IN the last number of the Philosophical Magazine (p. 228), 

 there appeared an extract from the Proceedings of the Royal 

 Irish Academy, containing a notice of a memoir which I had 

 the honour of reading to that body on the 24th of May, 1841 ; 

 and in the concluding paragraph of the notice a brief allusion 

 is made to a "mathematical hypothesis" by which I had con- 

 nected the laws of dispersion and those of the elliptic polari- 

 zation of rock-crystal with the other laws that were there 

 announced. My present object is to indicate the development 

 of that hypothesis, with reference more particularly to the sub- 

 ject of dispersion in crystals, and to communicate a very simple 

 result which I have lately had occasion to obtain from it. The 

 result is remarkable as embracing and explaining a class of in- 

 tricate phenomena which hitherto have not been connected with 

 any theory, or rather have stood in opposition to all theories ; 

 I mean the phenomena of the dispersion of the optic axes, and 

 of the axes of elasticity (as they are called) in biaxal crystals. 



The name of axes of elasticity was given by Fresnel to 

 three rectangular directions, which, according to his theory, 

 exist in every crystallized medium, and which are distinguished 

 by the property, that if a particle of the medium be slightly 

 displaced in the direction of any one of them, the elastic force 

 thereby called into play will act precisely in the line of the dis- 



