CIECULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 215 
u,^a = Ea-" 
_11 , 
12 378 729 
49 TT* /s;- — c"\2 r 65 
180 81 
a- 
00 
96 2880 V«3 ) [ 
3f3\ 1 1 
j 7c® ® (— 1)" HTTZ 335 c®“ ( — 1)" ;i7r~' 
-:,--COS-— —T — A-^COS- 
77- 1 6‘ StT’ 1 77-'’ C 
— -IN (— 1)' — cos - 
nitZ 
c 
(115). 
where, putting in now ira ■=■ 3c, we have the following values for r,'. :— 
//. 
'n (iTl). 
I 
. . --42430 
.) 
. . --01807 
3 
. . --00223 
4 
. . --00063 
5 
. . --00024 
6 . 
. . —-00010 
Whence, using the methods of § 20, we find the following values for uju^, Avhere 
Uq = lateral expansion of a cylinder of the same dimensions under the same total 
pressure uniformly distributed : — 
7f/«0- 
0 . . 
. . . -97861 
c/6 . 
. . . -96325 
2c/6 . 
. . . -91118 
3c/6 . 
. . . -80402 
4 c/6 . 
. . . -61209 
5c/6 . 
. . . -30863 
c 
. . . -00000 
These results are exhibited in Diagram 15. We see that the cylinder lias a single 
bulge in the centre, and indeed it is easy to verify that (dh(/c/ 2 '-),j <0 liy difTerentiating 
ecpiation (115) and putting in the numerical values. 
I>iagr;im 15.—Showing Distortion of Curved Surface (second example). 
