CIRCULAK CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS UP LOAD. 103 
Table of Constants. 
/c,i Ai 
4S ■ 
/UTtA, 
4S ■ 
481- ■ 
- -272602 
+ -205790 
+ -159464 
- -142172 
- -0.359051 
+ -0.354223 
+ -0323529 
+ -0163035 
- -00534980 
+ -00492450 
+ -00308747 
- -000612345 
- -000534505 
- -000374718 
+ -0000532623 
- -0000285886 
- -0000214593 
+ -00000237642 
- -00000413531 
- -00000325082 
+ -000000294829 
- -00000162159 
- -00000131798 
+ -000000101204 
+ -000000315996 
+ -000000263390 
- -0000000175353 
+ -0000000448505 
+ -0000000381292 
- -00000000224045 
From these I have calculated the coefficients of the Fourier’s series for the 
stresses and strains for r = 0, r = •2a, r = ’To, and r = 'Ga, For higher values of r 
the convergence becomes slower and the expressions more difficult to handle. In tlie 
case of the stresses and strains at the boundary r = a, special methods of a})proxima- 
tion have to be resorted to. 
The expressions for the strains and stresses are : 
u — 
me 
ijiTT^ 
— -00482 cos + -00380 cos — '00230 cos 
Ic He He 
— '00U43 cos ~ *0U00b cos ~ -|" . . . 
He He 
(r= - Za ), 
u = 
8Sc 
ytiTT- 
tt: 
— '01075 cos ' + •01412 cos ^ — '00541 cos 
*'/• *C' 
ITT. 
>c 
'00130 cos + ‘00023 cos-^ + '00002 cos +. . . 
V/' He 
(r — ‘4a), 
2c 
u = 
•0 
•T 
1897 cos + '02014 cos ^ 
2c 2c 
- '00330 cos 
2 ( 
. , loTTZ , „ ^ _ lOTT 
+ '00004 cos - + 'OOOOo cos -- 
2c 2c 
- IOtt: 
— '0000 I cos —r— + . . . 
2c 
OTTZ ’'VrC 
-'0099 L COS - „ 
2c 2c 
IItt: 
-^’+'00084 cos -f '000II cos 
2c 2c 2c 
iOTr'J ^ ^ I /TT.. 
—'00002 cos - 
'Hj: He 
= 'Ga) 
and in like manner for tv and the stresses. 
4’u save space, the coefficients of the series uiay he exhiljiied in talada.r form as 
follows :— 
Y 
