CIKCUI.AR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 193 
Hence 
[ d6 [ zzrdr = 7 r«^( 2 \i^Q+ (X + 2ix)iVq) 
' 0 JO 
+ (JlE X 27T 
f cd 
( 27 — 1 ) , 
^ / -7 I O o 
.*) 0 
i(27 + 1) 
+ iGa(2y+ ])S(- I)" 
f P^oip)dp 
TL'TTZ 
COS 
II («) 
J 
+ 2 A [ [r I, (^) - p\ (p) { - 2 } ] dp cos 
TITTZ 
e 
But 
P'Ti ip) ~ pTo (p) 
2 ^L 
0 _ o 
L n 
1 (dp = a~Io (a) — al| (a) | T^' — = 0 by (67), 
J ' I b J 
and 
f P^oip)^^P = «Ti («). 
so tliat we liave to make 
2\iip^ + (X + 2/x) 1(\ 
*^ry - 
“ / ■*- .■) I O O 
- 9 « ■ + 
y* 2 7 — 1 ^ (^7 + 1) 
G 4 
..1 
® — 1 Y* 'jITTZ 
+ 16 ( 2 y + 1 ) S - - cos — 
^ ^ n^TT^ c 
J 
Q. 
Now it is easy to show that 
^ (— 1 )" nriTZ 
N-, cos — 
1 n* c 
Z^TT* 
ITT* 
48c't 24(" 720 ’ 
whence finally 
2Xwq + (X + 2/x) Wq + 2^E I ^ + \cdc^ — - 4 - 5 - (2y + l) +| = — Q . . (93). 
(90) and (93) thus give us already two equations for Uq^ ?(-q, and E. We require a 
third equation. 
This is obtained from the condition that 
— A. 
2 C 
VOL. cxcvrii. 
