RAUIFIED OASES 



(10) Ttrmt of Two Dimensions. 



Put Qm(u + f)\ Since the resulting equation is true whatever be the values 

 of H. r, v, we may, after differentiation, put each of these quantities equal to 

 Nk We ahall thus obtain the same result which we might have obtained 

 by elimination between this and the former equations. We find 



or by ubatituting the mean values of these quantities from (29) 



I a 



with two other equations of similar form. 

 Similarly we obtain by putting Q = (i 



with two other equations of like form for /?y and 



(11) Terms of Three Dimensions. 



Putting @ =( + )* and in the final equation making u = v = iv = Q and 

 eliminating - by (41) we find 



