MR. J. H. JEANS ON THE CONFIGURATIONS 
166 
Clearly, when q — 0, the value of X is oo, while when q — 1, X has some value X 7 
which is the root of 
x 
-g—.■+ TT— + -r—+0(l) = 1.(26) 
« 2 + X b +\ c“ + X T 
The value of E 0 is obtained by integrating over the area shaded in fig. 1. 
Changing the order of integration, we find 
in which the lower limit q is the root of equation (25), while the lower limit is the 
root of equation (26). 
'Idle value of E, is obtained by a double integration in the same plane over an area 
such as that shaded in fig. 2, the different directions of shading distinguishing the 
areas covered by the two separate integrals in equation (24). 
order of integration, we obtain 
7 rClbc 
2 
<1 
dx 
A ’ 
Again changing the 
(28) 
in which the lower limit q is again the root of equation (25). 
This completes the solution of the potential problem ; we now attack the main 
problem of determining configurations of equilibrium. 
General Equations of Equilibrium, 
10. We can only find configurations of equilibrium by assuming a definite law to 
connect pressure with density. We shall accordingly assume the relation 
(29) 
p — Kp y — cons, 
