208 
^lE. L. X. G. FILOX OX THE ELASTIC EQUILIBEIHM OF 
The values of tan 6 for the same points are given in the following table :— 
Table of Slope of Lines of Principal Stress (tan 6). 
,r = 0. 
Z = ry'G. 
= 2,2'/6. 
= 3c/6. 
~ = 4c/C. 1 
1 
' = 5c 6. 
j 
- . j 
0 
0 
0 
1 
0 
0 
0 ; 
0 
0 
«/3 
0 
•0064 
i - -00.38 
- -0204 
- -0690 ! 
- -2358 
- -8806 
2al3 
0 
•0044 
' - -0017 
- -0279 
- -09.36 , 
- -2.303 
- -43.31 
a 
\ 
0 
0 
: 0 
0 
0 I 
0 
0 
By the aid of the above, we may draw the lines of principal stress, which is done 
in Diagram 11, the slope being exaggerated in the ratio 10:1. In order to do so, 
we suppose the line of principal stress to remain always in the neighbourhood of the 
same generator, so that, in the above table, the values in any row apply to the same 
Diagram 11.—Lines of principal Stress for Cylinder compressed between Eough Planes (second example) 
line of principal stress. This of course is not correct near the ends, but it is sufficient 
for our purpose, the diagram being merely intended to show the general course of the 
lines of stress. These are sensibly parallel to the generators throughout the middle 
part of the cylinder, but slope outwards near the ends. 
Diagram 12"'' shows the distribution of the lines of equal principal stress ZZ 
* In Diagram 12, as in several others, a is represented as having the same value as c, so that the horizontal 
and vertical scales are not strictl}'^ the same, but differ in the ratio -n-jo. This has been done for con¬ 
venience in plotting. 
