189G.] Elastic Solid Shells of nearly Spherical form. 65 



_ i(i+2)m-n 2 (i- 1) 



(i+l)(2* + 3) J+ i ° Z * 



(t 2 - 1) m - n ,_,-_, v 

 i(2i-l) ° ^- ? "" 1 



These equations are identical with (38,) to (41^) if in the 

 latter we put 



R i = -2T i =3b s e(p-p')/(a 3 -b*), (15). 



RU = - 2T'i = 3a 3 e' (p -/)/(a 3 - 6 3 ) J 



The values of F$, ^, F_ z _!, i?_;_i in the present problem are 

 thus given by (68 A ) to (71^) when the substitutions (15) are made. 

 To obtain the subsidiary terms in the displacements for the 

 present problem, all we have to do is to take the results (92 A ), 

 (93 A ) and the corresponding expression for w, and in them replace 



R i hyWea i (p-p)l(a"-b% v 



B'i „ 3a*e'*i(p-p')/(a*-V), 



T'i „ -^a'eaiip-pyicP-V) 



A similar substitution in (94^) and (95^) gives the subsidiary 

 terms in the expressions for the stresses rr, rd. 



This substitution is perfectly straightforward, but the results 

 of it in general a little cumbrous; I propose giving them explicitly 

 only for the case when 



e =e, 



and hja = (a — b)/a 



is very small. 



In this case we make the substitutions (16) in (96 A ), (97J and 

 the corresponding expression for w, putting e = e. After effecting 

 the substitutions I have written h for a — b in the terms depending 

 on <Ti. Combining the subsidiary terms with the principal term 

 (3), it will be found that 



VOL. IX. PT. II. 5 



.(16). 



