FIGURE AND STABILITY OF A LIQUID SATELLITE. 
181 
Hence the potential of M/X is 
For the object immediately in view we only need the terms involving x, y, z, and 
may therefore drop the first and last terms. 
The expressions for q s 2 and for 1&. 2 S in terms of k 2 have been given above; by means 
of these I find that 
q 0 ' 2 (K 2 -q 0 2 ) _ 9 qj q 2 ' 2 ( K 2 -q 2 2 ) _ _ 9 q 2 
2To 4:Dk 2 ’ ~ & 2 2 4 Dk 2 
(note the interchange in the suffixes of the qs). 
2 /y 2 
A common factor - 4 - may be taken from all the coefficients of x 2 , y 2 , z 2 , and 
since q 2 q 2 2 — ^ k 2 this common factor is equal to 15/4 D. Hence the terms in x 2 , y 2 , z 2 
inside { } become 
15 x 2 
ww 
+ 
15 y 2 
Id¥ 
o ' 2 
15 z 2 
WW 
On substituting for the several coefficients their values in terms of k, I find that 
the potential of M/X may be written in the following form : — 
