6o Mr 0 Ivory on the Attractions of an 
<r 
&c. 
II. 
Investigation of the Attractions of Spheroids of a particular Kind, 
6. Instead of seeking immediately the attraction of a spheroid 
in any proposed direction, it will be more advantageous to 
investigate (as Laplace has done) the value of the expres- 
sion (to be henceforth denoted by V) which is the sum of 
the quotients produced by dividing all the molecules of the 
mass of the spheroid by their respective distances from the 
attracted point. For such is the nature of the analytical ex- 
pression now mentioned, that if it be first transformed into a 
function of three rectangular co-ordinates one of which is 
parallel to a line given by position, and the fluxion with re- 
gard to this co-ordinate be taken ; the coefficient of the partial 
fluxion after its sign is changed, will denote the attractive 
force which acts parallel to the given line. In order to de- 
monstrate this property of the function V, we shall suppose 
that x, y, % denote the co-ordinates of the molecule dM, and 
a, b, c , the co-ordinates of the attracted point : then 
| (&_y) 1 + (c — zf 
the fluent being understood to be extended to all the mole- 
cules of the mass of the spheroid : now if the fluxion of this 
