468 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
We must now obtain We have 
= p J J J Su' -j- v' Sv' + w' Biv) (l + li jay dli cZS ; 
also 
y u- &U' (I + h'jaf dW = 27i (l + ^) M 8« + I A* + I AS 
\ dr“ dr~ 
, 4Jd [ • • dhu , du » 
= 2 A(i + a;;8« + g(A-;;)(f-8. 
. A^E/--rZSK \ 4dd\"(dZw » \ , (ddo 
+ & V‘ -Te + Je + tw - “> 
by (2) and (3). Treating the other terms in a similar way, we obtain 
SC = 2^/8 (1 -|- ^ Idled) I {u Su -j- V Sv + w Siv) cIS 
1 fdw r>"\/dSlO » \ 1 / 1 dw r,"\ f ^ 
Id \d£ ~ \lw ~ ^^7 ^ ~ \sin^ ^ 
+ E(^EK - ~)SKj fZS 
+ 1 /)A3E I U - ^ _ y'^; (S\ + 8/r) + - ~ Sw + ^-A vl 
^ ' ' ' a d6 a sin 0 d(p ' ^ a dd a sin 0 d(j> 
- (\ -h /x) Si'll 1 (IS 
Apid r r r 1 /dio 
u ) Su + - f ^ 8r + EK Sir ^ dS 
' a \sin 0 def) / 
• • m 
We must next find Sli. 
We have 
SU = II" (P' Sii + U' Sh) [a + h') sin 9 clh' + |f (Q' + U' Sid) {a + h') dli dO 
+ I NgU sin 6 Siv + I NjU Sir dd . (18), 
whence 
