464 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
whence 
also 
= ^2 H- 
a 
— _L ^ 
— + - 
a 
A 
m + n 
1 dvj 
a dd 
1 dw 
a sin 9 dcj) 
- EK 
^2 
a 
a 
1 , E ^ 
a {m + n) dO a d6 \ 
1 dA E ^ ' 
a {m + n) sin (fe d^ a sin 6 dcj^ ^ 
Ai 
m + n 
— E (\ 4- /x) 
J 
(2j, 
(3). 
16, We can now obtain the equations of motion in terms of the sectional stresses. 
If dS be an element of the middle surface whose coordinates are {a, 6, <f)), and 
dS' an element of a layer of the shell whose coordinates are (a + h', 0, (j)), then 
dS' = (1 + h'/ay dS; whence, if in the figure OA, OB respectively coincide with the 
meridians and circular sections, we obtain by resolving parallel to OA, 
^ (T^a sin 6 8^) S9 — T^a cos 6S6 S(}) (M^a S6) + NgCt sin 6 B6 S(f) 
= p dS f(u' - X) (1 + h'/af dll , , (4), 
But 
accordingly if we substitute the values of {dujdr) and (dhi/dr^) from (2) and (3), and 
recollect that all quantities which vanish with h may be omitted when multiplied by 
h^, the right hand side of (4) becomes 
pdS |2^ fi- 
, JdE dlt 
7 3a dd 
47d dio 
~de 
Resolving parallel to OB, 00, and then taking moments about OA, OB, 00 we 
shall obtain in a similar way five other equations, which, together with (4), may be 
written. 
