ON THE PROPAGATION OF LIGHT IN CRYSTALLIZED 



MEDIA. 



IN a former paper* I endeavoured to determine in what way 

 a plane wave would be modified when transmitted from one 

 non-crystallized medium to another ; founding the investigation 

 on this principle: In whatever manner the elements of any 

 material system may act upon each other, if all the internal 

 forces be multiplied by the elements of their respective directions, 

 the total sums for any assigned portion of the mass will always 

 be the exact differential of some function. This principle re- 

 quires a slight limitation, and when the necessary limitation is 

 introduced, appears to possess very great generality. I shall 

 here endeavour to apply the same principle to crystallized bodies, 

 and shall likewise introduce the consideration of the effects of 

 extraneous pressures, which had been omitted in the former 

 communication. Our problem thus becomes very complicated, 

 as the function due to the internal forces, even when there are 

 no extraneous pressures, contains twenty-one coefficients. But 

 with these pressures we are obliged to introduce six additional 

 coefficients; so that without some limitation, it appears quite 

 hopeless thence to deduce any consequences which could have 

 the least chance of a physical application. The absolute neces- 

 sity of introducing some arbitrary restrictions, and the desire 

 that their number should be as small as possible, induced me 

 to examine how far our function would be limited by confining 

 ourselves to the consideration of those media only in which the 

 directions of the transverse vibrations shall always be accurately 

 in the front of the wave. This fundamental principle of 

 Fresnel's Theory gives fourteen relations between the twenty- 

 one constants originally entering into our function; and it seems 

 worthy of remark, that when there are no extraneous pressures, 

 the directions of polarization and the wave-velocities given by 

 our theory, when thus limited, are identical with those assigned 

 by Fresnel's general construction for biaxal crystals; provided 

 we suppose the actual direction of disturbance in the particles 



* Supra, p. 243. 



