470 
MR. A. B. BASSET OE" THE EXTENSION AND FLEXURE OE 
These are the equations which have been obtained by Mr. Love,"' and which have 
been employed by him in discussing the extensional vibrations of a spherical shell. 
Again 
SWg = f nJi^ + dFSp- + \p^v) 
Substituting the values of X, fju, p from (8) we obtain 
IflcSXrfS= -|j E + Sw + e(^‘ + ^|? + S«cot 9+28®)} sin ecWd<l, 
= — j jEI£ sin 6hu — (12 sin 0) Sw -}- IE sin 0 — jEIESr d0 
+ fli 
Esin^^f 8ii + E^Sy 
cW d(j} 
cP 
also 
— \ — 2 (12 sin 6*) -j- (1 -f 2E) 12 sin 0 } hw 
IjdlFS/x c?S = — 
1 drho „ dSw ^ . . 
Ai 7A + ^ " 7A + ^ 
sin 6 d(f)-^ dB 
cW d(f) (24), 
+ E sin 0 + ~ d- Sfi cos 0 + 2Siv sin d0 d(f) 
= — I(E.dl?’ sin 0Bu + cos 0Siv) dcf) 
sin 6 d(f) 
- f(E#8i; - — Sw; + ^ d0 
J \ sin B a (h sm B dip j 
Esin^'^Sw + E'^Sv 
dB dcp 
~ {^0 7 ^ “ ^ 
In the last term^^Sp, we must treat the integral which involves d~Biv/d0 dcp exactly 
in the same way as in the corresponding case of a cylindrical shell, and we shall thus 
obtain 
dSw d^Bto 
[pSprfS=}|p(cot9^- 
d0 d(f) 
icp d0d(f) J 
i I Cl -P + {p “t» + i I) ««’ - H 
. 
* ‘ Phil. Trans.,’ A, 1888, p. 527. Equation (23) corresponds to Love’s equations (46), (47), and (48) 
and (22) to (72). 
