64 Dr Ghree, The Equilibrium of Isotropic [Jan. 27, 



The surface equations over (2) are obtained from these by 

 writing e for e and p for p. 



The two equations (9) and (10) lead to such results as 



and are really tantamount to but a single equation 

 f(0,<f>) = O. 



To obtain the values of principal terms over the surface (1) we 

 must write a (1 + ear-i) for r and retain terms containing the first 

 power of e ; for instance the contribution to rr of the principal 

 terms is easily found from (4) to be 



In the subsidiary terms proceeding from (5), (6) and (7) it 



suffices to write a for r. In such an expression as — e ~ rd the 



contribution of the subsidiary terms would be of order e 2 and so 

 is negligible. 



Bearing these points in mind, and noticing that the terms 

 independent of e cut out, it is easy to verify that the surface 

 conditions take the form : 



(i 2 - i - 3) m + n . „ , . . . „ 



— ■£-. — -j. a % Yi + 2 (i — 1) na l 2 Z; 



2i + 'S 



(i 2 + Si — l)m + n _ i _ l „ 

 + - 2i _ 1 a *_,_, 



97,3 



-2(i + 2)na-i-*Z_ i _ 1 =- ajr - j3 e(p-p') (11), 



_^+|)m-n a , F 2(^-1) ,_ 2 



(i + l)(2i + S) i 



(i? -l)m-n ._ x 



i{2i-\) a J - J '" 1 



2 (i + 2) ;-- 3 b 3 , , N ,_ ON 



- (i2 - i -^ +n ¥Y i+ 2(i-l)nb^Z i 

 2l+ 6 



(i? + 3i-l)m + n ._ a 

 + - -^^ o *_;_> 



Q/Y3 



- 2 (i + 2) n&-^- ^ = -ZL- e'(p-p') (13), 



