CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OP LOAD. 191 
we 
find 
hQ — — 2(\ + i^)u^ — \Wq 
a- 
D' 
|(2X + 3/x)'Mj + — X. 
/6 a, + 10/i, \ 
“1-6- I"- 
+ /a) D + XiVi + 
a-^ 
(4 A + 6)ot)E + 3XE' 
A + /A 
F + 
/>„ — — ^ "jjU I"t" H” ,5 [ + 6^)E + 3XE ] 
8<X( 1). 1 + , 
•T 0 
li'Tr" 
n*Tr^ 
whence using equations (87) we find after long but otherwise straightforward 
reductions 
6o = - 2 (X + /r) Uq - \iVq 
0 O -I 
+ /xE|-lfcV-^(2y+l) + ~-^| 
4Ur/3 
- (- l)U^,/xE(2y+ 1) - l)*Ex.y. 
'/rTT' 
Hence, equating coefficients on both sides of equation (89) we obtain the relations 
2 (X + /r) Wy + XlCy — /xE j — T5 “ 1 (% + 1) + 
»'> o o 
• (90), 
—[(1 + y) ^1 + (1 — y) A- 2 ] Iq + 2 
« - /7 
= -(-l)-Exf?U2y+H-^A) . . 
n~7r \ a“)i~TT"j 
■ (ai). 
and it in (91) we substitute for A^, A 3 their values in terms of C//; deduced from (79) 
and ( 88 ), we have 
2gC Aylp^ - h^(l ^ Ay) 
k a-zE 
/ \ T-^ '^c~'c0^ 
- (- I >E X „ 
ifir- 
2 / + !+ 222 (^ 7 '^^) 
a-^n-TT" 
4(;h,(27 + 1)' 
(067rE 
