CYLINDRICAL AND SPHERICAL THIN ELASTIC SHELLS. 
465 
^ (Ti sin 0) — T 3 cos 6 ' + + Ng sin 
L 
= i 2/i (1 + - J - —2 LAj - 2^ (1 + YTs) X \pa sm 
3a7 j' 
— + (M^ sin 0) + cos ^ sin 0 
d(f) do 
= D'MI +,5*’ + ; 
4A® (ZtC Wr I 
‘. ■ a ~ 02 • ~ ij "77 ~ 2A 1 + Y sm P, 
o(X sin 0 dc^ ocP sin d<f> \ 3a"' 1 
^ (N 3 sin 0 ) 4 - ^ — (Ti + To) sin 0 
= \ 2hl I + w-i ¥ E (X + p) - I' EK - 2A (1 + S Z \pa sin 0,\ 
dG^ 
d<^ 
d 
+ NjCt sin 0 4 - (H^ sin 0) — H 3 cos 0 
dd 
1 dtv 
sin 6 dO 
3?; 4 - 2 Y) sin 0, 
(Go sin 0) 4 " Gi cos 0 — Ngtt sin 0 4- 
dd 
= - I ph? (“I - 3m + 2 X) sin e, 
(Ml - MJa - Hi - H3= 0. 
17. We shall now (as in the case of a cylindrical shell) proceed to obtain the 
values of the couples and the stresses M 3 by direct calculation. 
We have 
whence 
a sin 0 S(p = { P' (a 4- h') sin 0 Bcf) dh '; 
J —h 
T. = 2AP + |43(|^) + |(A 
T, = 2AQ + iA3('P)+f(f 
Mi = M.= 2«/» + L*3(53) + |A(‘|3 
G3 = |/i» 
-U? 
dr a 
H, = -R,= -idhur^ 
dWr 
dr 
3 o 
(6). 
MDCCCXC.—A. 
