212 Mr. Arry on the Figure of a Fluid Mass 
(18.) It will be observed that W (c) is now expressed by this 
form 
X10 204 x10 Bel" _ x'(0) 30 lee 
i ee 1.2° 5 a ae 
Pe ute pee AO Be ay SLC Lie ay 
i ©)-g sm to bapa sory. 9 
wekeee Ts (r° —c?) ash mead (c) ie; 
ad oe = 9 1 7 Oe + &e.} 
2 (7 16) Ga 1 
ss Wk an ()-7 941.13 7 od 
+ &e. 
(19.) Ifthe disturbing forces were not symmetrical about an 
axis, it would be necessary to assume for the equation to the 
surface a + y? + 2 =r? + y(a,y). The values of x, y, z, would 
be a—p sin. 0.cos. ¢, b- p sin. 0.sin. ¢, ¢—p cos. 6; a, b, c, being the 
co-ordinates of the attracted poimt. Substitutmmg these in the 
assumed equation, a value would be found for p, as in the case 
we have considered: and the integral dh S' to .sin. 8 would be taken 
C) 
in the same manner. And we should arrive at a similar equation 
2 : 
shy (a, b) +kw(a, b) + € (a, 6) = o kr?; and assuming a proper 
form for x(a, b), forming ¥ (4, 4), and eliminating ¢ by means of 
the equation c*=7*—a?—b*, the coefficients would be determined 
by the comparison of similar terms. As the applications of this 
theory are few, we shall content ourselves with thus pointing 
out the course to be pursued in any given case. 
(20.) Suppose «(c) to be of the form 4+ Bc’+ De'+Ec+Fe'. 
Then x (c) will evidently have the form P+Qc?+Re*+Sc&4+ Te'. 
From this, by the expression in (18), we find y (c) (neglecting the 
constant term) 
