CIECULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 187 
itself, is of comparatively restricted application, but by combining the two we are 
enabled to deal with far more general problems. 
Assume therefore 
• “l' I 
u = VqV + - - + 
Drz^ Er%” F^’U 
T + ^2 + A +T" + 
, 'lo.z^ J)'r^ 
W = IVqZ + -Y + ' 5 “ + ^ 
Yrh 
+ ^”+ 4 - +W 
(72) , 
(73) . 
The above power series are the most general expressions of the fifth degree con¬ 
sistent with the conditions that u must be odd in r and even in 2 , and w must be odd 
in 2 and even in r. 
In the above we have, as before. 
Consider first of all the condition that w is to be constant when 
fixes k : 
k = njTjc . 
Further we have 
F' = 0 
± c. 
iD'c + = 0. 
Now remember that u and w have to satisfy the differential equations 
(^+v),C.,s(™)+CS+(^+f‘)x” 
drdz 
0 , 
This 
(76) . 
(77) . 
(78) . 
. 1 du . Id/ div\ , \ d~w 
nx ; , 7 ; <■ 7 ,: + ()^ + 2^^) 753 = 0- 
r dr dz ' ^rdr\' dr J ' dz 
The parts U and W we have seen already v^ill satisfy these equations, provided 
Aj — A 2 ~h 2C/y/i-'.— 0.(79)- 
Consider therefore only the algebraic terms. Of these and always 
satisfy the above equations. 
The third order terms require 
3 '^h (^ + 2p) p,T> + (A + p.) I)' — 0.(80), 
2 ( X “b P-) T) “h 2pl)^ -j- (X “b 2p) = 0.(81)' 
2 .B 2 
