308 
DETERMINATION OF THE ATTRACTION OF AN 
[604 
12. Expressing il in terms of a, b, c, we have 
cvT« + 
b ' 2 + c 2 
il 2 (6 -h/ 2 ) 2 (d+gj (0+A 2 ) 2 ' 
0 2 
We have o- 2 = ^y 2 , = (7 2 il 2 , and 
whence 
or, since 
this is 
U= a (£-a) + ß ( v -b) + 7 (£-c), 
= -0(jf+f?+I?)> = ~ 0B - = BGil ‘ ; 
p' 2 O- 2 _ rr 1 _ C^il 2 25(7il 2 , 
^ = - 0 +2Z7-+l, =— 7r + —— + 1, 
y* * y* & y* y% & yV 
-<X»(° + ”) + 1 
4 + 2bI+cT=o, 
^--4CQ» + X = a»(T_4C) 
_«* if ±_J_ 
i2 2 ’ * E 2 ~il 2 
This last equation may also be written 
¿-¿<*+*+t')-c(£+£+£ 
or, what is the same thing, 
if for shortness 
a 2 
2 — Jh 
+ §1 
+ _T 2 
1 
1 
(7 
^2 _ 
il 2 
Z 2 ’ 
1 
1 
(7 
G*~ 
IT 2 
Z’ 
1 
1 
(7 
tf 2 ^ 
O 2 ” 
A 2 ’ 
viz. substituting herein for G its value — — , these equations give 
y _ Of Qj_ _ ^¿7 Qh 
Vd+/ 2 ’ ~ Vd+p 2 ’ “ V0 +A 2 ’ 
where il stands for its expression in terms of a, A, c.