574 
Proceedings of the Royal Society 
obvious that the principal tractions are along a radius, parallel to 
the axis, and in a direction perpendicular to each of these, we have 
at once (Thomson and Tait, Nat. Phil. §§ 682, 683) 
dp _ 
dr 
- et i ~ftt ~fta > 
d t 
dic = ~f tl ~ + et?J ’ 
where 
1 1 
e ~ 3n + 9* 
f«. 1 .. 1 
J 6 n 9 k 
1 . 
Here ^ is the compressibility, and n the rigidity. 
In addition we have for the equilibrium of an element bounded 
by concentric cylinders, planes through the axis, and planes per- 
pendicular to it, 
and the approximate assumption above gives 
d£ 
dx 
= constant. 
From these five equations t x , t 2 , t 3 , p , arid £ are to be found. 
They show that t% is constant, and its value must therefore be 
n 
f -«0 
With the surface conditions, 
- n when r = d 1 , 
*1= ^ » r==a o> 
we determine the arbitary constants^ and it is easy to see that 
p- = _ n -s_ 
r a\ - a\ 
v+% («+/)) 
T = - n T^( e “ 2 /)- 
dx a{- clq ' 
