164 
MR. J. H. JEANS ON THE CONFIGURATIONS 
From the previous investigation* it now follows that the value of V 0 ( q) is 
v. (?) = -xj7/+ 
<p (q) \ _ q s abc dp _ 
q 2 I [( q 2 a 2 + p) (q 2 b 2 + p) (q 2 c 2 + m)] 4 ’ 
• (14) 
in which the lower limit of integration p is the root of equation (13) at the external 
point x, «/, z at which the potential is being evaluated. The same formula (14) 
with p put equal to zero will give the value of V { (q), the potential at an internal 
point. 
To transform these expressions into a form suitable for use in the present problem, 
introduce new variables X, £, £ to replace p, £', ?/, these being defined by 
X = p/q< 2 , £ = q 2 £ r = x/(a 2 + X), &c.(15) 
XVe now have 
■P = F(£*0, 
q 2 f = 
x“ y- z~ 
+ 
+ 
I) 
« 2 + X b 2 + X c 2 + X 
1 
-r> 
a 2 a + X / r> 
!l , (l 1 \ , (l _L\£l 
f 2 \b 2 b 2 + X] dr, 2 \c 2 r 2 + X / 0f ’ 
while formula (14) becomes 
Jy /I 
( 16 ) 
m w 
hich A stands for [(« 2 + X) (6 2 + X) (c 2 + X)]% and X' is the root of 
x 2 
y 2“ 
+ 7~— + ^r 
a 2 + X b 2 + X c 2 + X 
+<p(q) = <? z .(1?) 
The same formula (16) in which X' is put equal to zero will of course give the 
value of V { (q). 
9. Attacking equations (10) and (l l), we now have 
rpo ri 
V o{q)dp = (p 0 -<r) V 0 (q)dq 2 
Jo- Jo 
= (po — <r) 
so that equation (10) becomes 
V 0 = p 0 V 0 (1) — (p 0 — ( r ) E 0J 
. . . (18) 
* ‘ Phil. Trans.,’ A, vol. 215, p. 27. 
