acted on by small Forces. 211 
lee ha 1 te Srxeyor oe 
+ 54) () 579 1 “agit + eet 
+Peg ix (¢) «97113 
+ &e. , 
(15.) The whole integral of = sin. 9 is therefore 
Ba \ (c+ a’) + (ch. 
This forms part of the equation to the surface on the suppo- 
sition that the attraction of the matter in volume 1 (collected 
into a point) at distance 1, is represented by 1; if it be represented 
=e. 
by &, the part of the equation is 27.k {- (?+a@)+wy ()}. 
(16.) Suppose the part of U arising from the disturbing forces 
to be 27.c/(c), «(c) being a given function of c. Then the equation 
to the generating curve will be 
Qa F k(e+a)+hy(c)+e(}=C, or 5k (2 +a") thal (0) +c (c)=C: 
where the two last terms of the first side are small. 
(17.) This must coincide with the equation @+c?=r*+  (c). 
And, therefore, if by means of this equation we eliminate a from 
the former, the resulting equation must be identically true. The 
value of a to be substituted in the large terms is r*—c* + (c): 
in the small terms 7’—c*. Thus we get the equation 
= kx (0) + ky (e) + e()=C—g kr. 
Assuming then for x(c) a form with indeterminate coefficients, 
such as the given form of ¢(c) appears to require, and deter- 
mining ¥(c), and eliminating a by putting a=r°—c’, every term 
of the equation multiplying a power of ¢ must be made =0, and 
thus a number of equations will be obtained sufficient to deter- 
mine all the constants, except that independent of c. 
DD2 
