CYLINDRICAL AND SPHERICAL THIN ELASTIC SHELLS. 
459 
We have 
Y — ~ g sin (j), Ta = g cos (f >; 
whence, if W = 2gpah, the equations of equilibrium are 
(IT, 
d(j) 
-[- = W sin (j), 
= - Wcos(/>, 
a<p 
, AT TUT • J 
from which we obtain 
the integral of which is 
and, therefore, 
d </)2 
+ Tg = 2W cos (j), 
Tg = A cos ^ + B sin (j) W(j) sin </>, 
= A sin ^ — B cos (f) — W(f) cos (j). 
Since = 0 when ^ l tt, A = 0 ; also since Tg = -^ irW when 
whence 
Tg = sin (f), = — W(^ cos (f) . 
and, therefore. 
— 1 
— 2 
whence 
= Wa (6 cos (h — 7^ sin 6), 
a(p oa" 
Gj = Wa (<^ sin ^ + cos ^ ^ cos 
Since G^ = 0 when ^ 77, C = — :|W7ra; accordingly 
Gj = Wa j(/) sin (j) (l cos 0 — . 
3 N 2 
77, B = 0 ; 
(61), 
(62). 
