CIRCULAR CYLINDER,S UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 183 
The condition that there is to he no shear over the curved surface no^v gives 
(Y + A,) + f?^ = o 
(s"). 
(writing a = ha, p = hr as l^efore). 
From (56) and (57) 
A - - 4- i 
A„ 
(J /«!„ 1 
7 
. (58). 
In what follows, the argument of tlie I-fnnctions, when not written, will always l)e 
assumed to ])e a. 
We find 
f +f')i„(p) 
rr — 2 (X + /x) ?«|j -j- X?c,,4 S 
Putting in this p = a 
2pC 
h- 
\ 
«I() _l_ 1 \ Ii(» 
F 1J p 
+niO)} 
cos /•'' . (59). 
r>/\i \ |\ 1 ^ 2yU.C 7^^ L'~ — (I + 7«") Tj" J 
{'i'r)r^o= 2 (X + /x) + \% 0 q 4-S y -=- - cos hz 
/.■ 7«ii 
Now expand the given pressure in the form 
{rr),^a ='P a,-, + S cy, cos 
nirz 
Where «n, « 
0; 
. are determined, P remains a free constant. 
We have at once, comparing coefficieiits. 
(61). 
2/xC 
/. 
yalj 
~P4. . . . 
1 
■ • • ■ (r,2) 
Po, .... 
. . . . (G3). 
Next we have = 0 when r — a, : = c 
where 
Wo« = — P^ 
«Ip(- Ip 
CO f( 
^ -n,/' 
1 2/xC 7«M,~ — (1 + 7«-) I," 
(fi4), 
((■,5). 
