230 
MR. L. N. G. FILON ON THE ELASTIC EQUILIBRIUM OF 
torsion over its whole length, the total couple applied being the same as in the 
present case. We find Tq = [xra = ttT and Vq = rca = ircTjix for the given example. 
Tables are given on page 229. 
Looking at these tables we see that, over the length free from external apj^lied 
shear, the strains and stresses inside the C}dinder are sensibly the same as what they 
would be on the hypothesis of a uniform torsion. (Outside zlc = '5 the torsion couple 
diminishes, and the stresses diminish in consequence. 
It is interesting to compare these results with those that we should have obtained 
if we had supposed the approximate results given on p. 223 to hold good in this 
case. Denoting Ijy v', r<j)', (f)z' the values of the displacement and stresses calculated 
on tins hypothesis, we have— 
Table of v'/vq. 
rja . 
zjc = 0 . 
• 1 . 
• 2 . 
.o 
u . 
• 4 . 
• 5 . 
• 6 . 
• 7 . 
• 8 . 
• 9 . 
1 . 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
* 2 
0 
•020 
•040 
•080 
•080 
•100 
•118 
•132 
•142 
•148 
•150 
•4 
0 
•040 
•080 
•120 
•160 
•200 
•236 
•264 
•284 
•296 
•300 
•6 
0 
•060 
•120 
•180 
•240 
•300 
•354 
•396 
•426 
•444 
•450 
1-0 
0 
•100 
•200 
•300 
•400 
•500 
•590 
•660 
•710 
•740 
•750 
Table of r^'/To- 
rja . 
zjc = 0 . 
• 1 . 
• 2 . 
• 3 . 
• 4 . 
• 5 . 
• 6 . 
• 7 . 
• 8 . 
• 9 . 
1 . 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
•2 
0 
0 
0 
0 
0 
\ -012732 
•012732 
•012732 
•012732 
•012732 
•012732 
•4 
0 
0 
0 
0 
0 
<f 0 
t -050930 
•050930 
•050930 
•050930 
•050930 
•050930 
: -6 
1 
0 
0 
0 
0 
0 
<f ® 
\ -114592 
•114592 
•114592 
•114592 
•114592 
•114592 
1 -0 
0 
0 
0 
0 
0 
<f ^ 
\ -318310 
•318310 
•318310 
•318310 
•318310 
•318310 
Table of 
rja . 
zjc = 0 . 
• 1 . 
• 2 . 
• 3 . 
- 4 . 
• 5 . 
• 6 . 
* 7 . 
• 8 . 
• 9 . 
1 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
• 2 
•20 
•20 
•20 
•20 
•20 
•20 
•16 
•12 
•08 
•04 
0 
•4 
•40 
•40 
•40 
•40 
•40 
•40 
•32 
•24 
•16 
•08 
0 
•6 
•60 
•60 
•60 
•60 
•60 
•60 
•48 
•36 
•24 
•12 
0 
1-0 
1-00 
1-00 
1-00 
1-00 
1-00 
1 -00 
•80 
•60 
•40 
•20 
0 
