250 ON THE REFLEXION AND REFRACTION OF LIGHT. 



the triple integrals extending over the whole volume of the 

 medium under consideration. 



But by the supposition, when u = 0, v = and w = 0, the 

 system is in equilibrium, and hence 



= [[(dx dy dz S<^ : 



seeing that <>, is a homogeneous function of s 1? s 2 , s a , a, /5, 7 

 of the first degree only. If therefore we neglect </> 3 , < 4 , &c. 

 which are exceedingly small compared with </> 2 , our equation 

 becomes 



\\\pdxdydz \-^% u + ^ 





the integrals extending over the whole volume under considera- 

 tion. The formula just found is true for any number of media 

 comprised in this volume, provided the whole system be perfectly 

 free from all extraneous forces, and subject only to its own mole- 

 cular actions. 



If now we can obtain the value of <> 2 , we shall only have to 

 apply the general methods given in the Mecanique, Analytique. 

 But < 2 being a homogeneous function of six quantities of the 

 second degree, will in its most general form contain 21 arbitrary 

 coefficients. The proper value to be assigned to each will of 

 course depend on the internal constitution of the medium. If, 

 however, the medium be a non-crystallized one, the form of </> a 

 will remain the same, whatever be the directions of the co-ordi- 

 nate axes in space. Applying this last consideration, we shall 

 find that the most general form of </> a for non-crystallized bodies 

 contains only two arbitrary coefficients. In fact, by neglecting 

 quantities of the higher orders, it is easy to perceive that 



