476 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
[IM/ 8u + N./ Sw + ( A ““ sin 9 d(f) 
j [ - ' ~ ygiii 0 0 ^ yj 
+ [jM/Sii + N/Sm; - - Sw)} add=0, 
M^hich shows that the work done by this system of stresses is zero. 
If, therefore, we suppose that the rectangle OADB, instead of being under the 
action of the remainder of the shell, is isolated, and that its state of strain is 
maintained by stresses applied to its edges, then it follows that if instead of the 
torsional couples Hj^, Hg, due to the action of contiguous portions of the shell, we 
apply torsional couples where 
= W .(38), 
= H, - H' .(39), 
the state of strain will remain unchanged, provided we apply in addition the stresses 
and 
^^3 — ^^3 + H /a 
. 
= + H'/al 
ja M . 
whence eliminating H' between (38) and (40), and between (39) and (41) respectively, 
we obtain 
and 
- Hi 
sin 9 — 
dcji 
i _ 
NoO sin 9 — 
dHi 
(42) 
(1(f) j 
M^a + H^ ] 
cm. !> 
— Nsu + 
(^9 
(43) 
in which we are to remember that = — |^ 2 > = — Hg. 
In these equations the Homan letters denote the stresses due to the action of 
contiguous portions of the shell, whilst the Old English letters denote the values of 
the actual stresses applied to the boundary. If, therefove, the shell consists of a 
