448 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
Let 
i£'= X' + E (X' + fx'), J?' = /a' + E (X' + /x') . . . . (37), 
then 
8W3 = f + 2 + ^SX' + + I TsSp) dS ; 
from this result, together with (24), it is seen that SWg and SW 4 each consist 
of two parts, which may be denoted by SW 3 ', SW 3 " and SW 4 ', SW/' resj)ectively. The 
values of SWg' and SW 4 ,' may at once be written down from (30), by changing iS, 
CT into i£', xf?', p' and IS, ^IF, p respectively, and by altering the coefficients from 4wA 
into fw/?® and Anld’jda respectively. With regard to SWg" we have 
8W3" = I ?zA 3 |j(m SV + B S/.t' + 1 t^tS/) c/S. 
Substituting the value of X' from (18) and integrating once by parts, we obtain 
[fa 8 xws = [[Ea~ds 
= E — Ell— 
Treating the other terms in a similar way, we shall finally obtain 
r/„ o-ri^ dSK nh^ cZ8K\ , {(2vM , 
8W, = j (1 ^ ^ ^) “# + J ^ + J ^ 
<76K\ 
-fn/i3 
111 ":!'#* 
1 Clr^\ rfSK , Y.fim , . cItz\ dSK EI3 ^ M 70 
+ + ■ .. 
If in the first surface integral in this equation, we substitute the approximate values 
of the coefficients of dSK/cfo, &c., from (32), which we may do, since this integral is 
multiplied by W, and then substitute the values of SWo", SC, SU, and SH in (25), it 
will be found that all the terms involving d^lLld,z, cZSK/d^, and SX + Sp, cut outwe 
are, therefore, no longer concerned with them, and the value of SWg" reduces to the 
last line. On this understanding we may, therefore, write 
SWg" + SW'' = 
Anld 1 
3a 
4 ^ 7 ^ ^ JirSp) dS 
4:nJdC{^dBw , m /dBw rv M i, 
’ r f r , 1 dcT /dBw O' M 70 
+ 
4nh' 
3 a 
■ (39). 
