170 ME. L N. G. FILON OX THE ELASTIC EQUILIBRIUM OF 
I ABLE 
of 
^ sin 2n + lx 
7 (2n+iy- ■ 
V 
5C. 
V 
X. 
V 
1 0 :. 
1 
V 
-/40 
■16639 
Ott/TO 
■57475 
1177/40 
■78536 
1677/40 
■89109 
2-/40 
•27830 
777^0 
■62754 
1277/40 
•81379 
1777/40 
■90202 
3-/40 
■ 36959 
877/40 
■67442 
1377/40 
■83839 
1877/40 
•90978 
47-/40 
■44740 
977/40 
■71602 
1477/40 
■85938 
1977/40 
■91442 
577/40 
■51513 
1077/40 
■75288 
1577/40 
•87690 
2O77/4O 
■91596 
We have thus the means of evaluating all those joarts of the expressions vTiich 
give rise to the most slowly convergent of the series employed. 
1'aking y = 2/3, the values found for u/, w,/ are talndated below :— 
n. 
Un 
U'n. 
0 
- ■13933 
+ -03040 
1 
- -01331 
- -00634 
2 
+ -00192 
+ -00098 
3 
+ -00043 
+ -00022 
4 
- -00011 
- -00005 
5 
- -00002 
- -00001 
6 
- -00001 
- -00000 
7 
- -00001 
- -00001 
8 
+ -00001 
+ -00001 
9 
+ -00001 
+ -00000 
Using these and the expressions given above for the finite terms, we can find the 
values of .the displacements on the outer surface of the cylinder. 
§ 10. Numerical Values of the Stresses and Disiolacements. 
The numerical values obtained in this way are tabulated below ; I have given the 
stresses in tlie form of ratio (stress) /Q, where Q is the unifoim tension which would 
produce a pull equal to that due to the shear S. 
