474 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
Ti = + ~ {?£ - E (Is + d?)} + i nim' +^E (aEiC - w + z) 
OCt OG/ 
2nli^ 
Mg = 2nhzs H—3 ^ + F 
OCt 
AnlP r d 
No = . , 
Basing l_(/0 
Gg = f n¥ (IS + ^ja) 
Hj — — -|- trr/a) 
(IS sin ^) — .dF cos ^ — 2?^ -|- X 
d(f>j 3a \d0 
J. (33) 
which give the values of the sectional stresses across a parallel of latitude ; and 
P \ nli^p 
OCl' 
T, =4«AB + ^(dr-E(E + df)l +f«ASdf' + ^h(aEK-w + Z) 
'1 
Ni 
_ _A,^ ld§ 
3a sin 6 \ dcf) 
Gj = -|n/(3(dF +B/a) 
Hg = f nh^ {p + vj/a) 
+ _/3cos 6^+ -|sin6>~) + 
dp\ 2pJP i 1 dto 
3a \sin 6 
— 27; + Y 
:> (34) 
j 
which give the values of the sectional stresses across a meridian. 
In these equations we may, if we please, substitute the approximate values of 
u, V, IV from (23), and by means of these values it can be shown that the values of 
Nj, Ng agree with the values which are obtained by substituting the values of the 
couples in the fourth and fifth of (5). 
Picking out the coefficients of Zu, Sv, Sw, in the surface integrals, we obtain the 
equations of motion, which are 
{d/ + |)“ + 
/dE dK _ ^ chv 
3a d6 3a^ dd 
sme 
= 471 ^ (^ sin d) cos 0 + 1 
4-7? fl 
+ {iS ^ + 3<, 
Yq (!£' sin 0 ) — HF' cos 0 + 
2ph 
d(j) J 
dy 
a sin ^ ^ sin 6 — y cos 
0\l35), 
