The Torsion Problem for Bodies of Revolution. 153 
as the boundary lines of the body of revolution in a meridian plane. The 
stress-components will then be given by 
(8) 
Since 
ri = 
1 
6^ = 
'lr = '- 
S<t> j 
= 
S(}> 
dz 
_ 1 
H] 
Vr = 
_ _^ 1 
^\ 
' Iz J 
(9) 
1 
. rB = 
r 
[X' 
1 
/X 
. = 
r 
fX ' 
1 
Sr 
1 
S(p 
Sz' 
Section 3. 
The Bisplacement ug. 
For Ug we have from 2 and 8 : 
Sue ^ Hd 
cr r 
hie 
Jri r) 
Sz \ r / 
Integrating, we have 
ne = (0 + c) - - - - (10) 
/X 
where c is a constant. 
fi is the " rigidity" of the material, and 
2(1 + .)' 
where E is "Young's modulus " and o- " Poisson's liatio." 
From equation 10 we see further that (p — constant will be the lines of 
constant angular displacement. 
Section 4, 
Polar Form of Equations. 
We make the transformation 
