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. §§ 6S2, 683) 
dr 
— et\ P2 fts > 
- = -fh + et 2 -ft 3i 
d£ 
where 
dx 
B ~ 3n + 9k ’ 
: = ~Jk-fli+ et 3> 
f=-~- 
' 6/>, 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, 
U - = dr (/f >> J 
and the approximate assumption above gives 
^ = constant. 
dx 
From these five equations t 19 t 2 , t 3 , p , and £ are to be found. 
They show that t 3 is constant, and its value must therefore be 
-n 
u{ - al 
With the surface conditions, 
t 1 = - n when r = a 1 , 
l\ ~ ^ 5 ) T ~ ^0 "> 
we determine the arbitary constants, and it is easy to see that 
^=-n-/s( e -2 /+-&+/)) 
r a\-al\ r 2V V 
d£ 
dx 
= -11 
a\- a% 
(e-2/). 
