(B). 



8 Mb GREEN, ON THE REFLEXION 



and thus we get 



under which form it may possibly be applied to uniaxal crystals. 



Lastly, if we suppose the function 2 symmetrical with respect to all 

 three axes, there results 



L = M= N, 

 P=Q =#; 



and consequently, 



^ [dy ' d% dx' dz dx' dy\' > 



or, by merely changing the two constants and restoring the values of 

 a, /3, and 7, 



, (du dv dw\- 

 ^ 2 \dx dy d»J 



(C). 

 7 i/du dv\~ (du dw\* (dv dwy .(dv dw du dw du dv\\ 

 \\dy dx] Was dx) \dx dy) \dy' dz dx' dz dx'dy))' 



This is the most general form that (p 2 can take for non-crystallized 

 bodies, in which it is perfectly indifferent in what directions the 

 rectangular axes are placed. The same result might be obtained from 

 the most general value of 2 , by the method before used to make <p 3 

 symmetrical all round the axes of z, applied also to the other two axes. 

 It was, indeed, thus I first obtained it. The method given in the text, 

 however, and which is very similar to one used by M. Cauchy, is not 

 only more simple, but has the advantage of furnishing two intermediate 

 results, which may possibly be of use on some future occasion. 



