214 
MR. L. N. G. FILON ON THE ELASTIC EQUILIBRIUM OF 
Diagram 14.—Distribution of Principal Stress-difference inside the Cylinder (case of Compression between 
Rough Rigid Planes). 
The number corresponding to each line denotes the value of the ratio (maximum stress-difference : Q) 
for that line. 
__, critical line. Stress-difference = '933 Q. 
§ 24. Distorted Shape of the Curved Surface. 
If we work out tlie values of a wlieu r = a, we kud, after'soiue reductions, 
nirr: 
= Ea= li - C ...C - S';';!- 
12 ® 
(112), 
where 
('ly + 1 ) « -b - (87 + 1 ) I k" — 4101^(27 + 1 ) 
. . (113). 
- (1 + 7«-)lr 
Now in tlie i)artic\dar case we are dealing witli, if a be large, r„ («) approximates to 
Write tlien 
r„ 
7 49 ^ an 
2 — 4« 1G«2 + 4«'’ ■ 
w = i - s +’*« .(n4). 
^1 1 1 4.1 • 
and substitute in (112). We find, putting in for _ ^^j,cos ^ and - cos ^ their 
known values. 
