III. THEORETICAL STRESSES 



The Lame equations'-^' for the stresses in thick-walled spheres 



are: 



(T 



m 



0", 



Pob3(2R3 + a^) p^a^CZR^ + b^) 

 2R3(a3 - b3) " ZR3(a3 - b^) 



Pob3(R3 . a3) p.a3(b3 - r3) 



"" R3(a3 - b3) R3(a3 . b3) 



^h = <^m 



Since the internal pressure was zero, 



gm _ b3(2R3"+ a3) 

 Po 2R3(a3 - b3) 



^ _ b3(R3 - a3) 

 Po R3(a3 - b3) 



On the concave side of the head 



- 15. 9 psi/psi 

 Po 



= 



Po 



On the convex side of the head 



"~ = 15. 4 psi/psi 

 Pq 



'^r 



— = - 1 psi/psi 



Po 



