CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 213 
difference, and in the twelve remaining cases the second is the greatest, although, 
as a matter of fact, the two stress-differences, for these twelve cases, do not* diverge 
very much. 
Diagram 13.—Distribution of Principal Stretch, inside the Cylinder (case of Compression between 
Rough Rigid Planes). 
The number corresponding to each line = the value of .s%/.s for that line. 
-^ critical line. s\/s = '91.5. 
The actual greatest stress-difference is given in the following table :— 
Table of (Maximum Stress-difference)/Q. 
r. 
z = 0. 
II 1 
i 
z = 2c/0. 
z = 3e/6. 
= 4c/6. 
= 5c/6. 
= c. 
0 
1-13108 
1-12022 
1-08188 
•99730 
•82675 
•55221 
- -21092 
«/3 
1-10270 
1-09320 
1-05892 
•98861 
•85786 
•66217 
•71287 
2«/3 
1-02486 
1-01915 
-99853 
•97223 
• 93034 
•91798 
1-21101 
a 
-92695 
-91821 
-89246 
• 85845 
•88177 
1-04077 
1 • 686.35 
Here again jjlastic deformation will first occur round the perimeter of the ends 
when Q = of the value it should have, on the same theory of ripdure, in 
order to produce failure of elasticity in a uniformly compressed cylinder. 
So far, then, this theory leads to the same results as the maximum stress theory. 
Diagram 14 shows the distribution of maximum stress-difference. The lines of 
ecjual maximum stress-difference present very similar characteristics to those of ecpial 
maximum stretch. The critical line corresponds to a maximum stress-difference = 
•933 Q. 
Kemarks similar to those used in the last case apply in this. 
