﻿Isotropic Spheres under Uniform Surface- Pressure. 173 

 In (c ,cc l . h) 



-^JnJM + in^-dkfa-nKct-e*))} 



(ce) 6 l J 



~ ^(^ + 4,1)6* + An (k l -k)(c*-e*))~j~\. * ' • ( 39) 

 In (b .a. a) 



_3y^(„ 1 _„)(i 1 (a* + 4n),»+4n(A,-A)( C 3 -, 3 ))} 

 + L.J { p - p '-)k{U + in) (3*! f 4/iJ 



+ 4/^V 1 -/l)(^3* + 4tt)c 3 -3*(» 1 -n)(cW))}].(40) 



\ce) 



These expressions may seem a little heavy, but it should be 

 remembered that in any specified individual case the some- 

 what lengthy constant coefficients are replaced by concise 

 numerical quantities. 



Two-layer Shell. 



§ 10. All the formula? established for the three-layer com- 

 pound shell (e.a.c.cn.b.a.a) may easily be modified so as 

 to apply to the simpler case of a two-layer compound shell. 

 Supposing this to be (e . a x . b . a . a) we put c = e in the previous 

 formula?, while if it were {e . a . c . «i . a) we should put b = a. 



Taking for example [e . «i . b . a . a), and regarding {e.* Y . b) 

 as the altered layer, we have by (17) 



Sp o =0, 



and by (16) 



^-SS5^5? (pi+ * ,) [ , * (% -" ) (^"' ) 



+WAi _ fc) 2^],. . . (41) 



