ACTING INVERSELY AS THE SQUARE OF THE DISTANCE. 157 
the line s intersects all the surfaces of equilibrium at right 
angles, a tangent to this line will everywhere represent the 
a. ON Per ; 
direction of the force, and hae will represent its intensity. 
The integral eo pcos @.ds, extended through a part of the 
line s, is evidently = « (V'—V°); V°, V' denoting the values of 
the potential for the limiting points. Thus if s be a closed line, 
the integral extended throughout the whole line will = 0. 
Ds 
It is evident that the potential must have an assignable value 
at every point of space lying without all the attracting or repel- 
ling particles; the same must also be true of all its differential 
coefficients, as well of the first as of the higher orders, as 
under the above supposition these must likewise assume the 
form of sums of assignable parts, or of integrals of differentials, 
of which the coefficients have throughout assignable values. 
Thus, 
dV a (a—2) p 
dx ry 
d?V 3(@=2)F 5/51 
d x = ( , a) M 
aV_5(b-9)¢ 
dy ‘haa 
@V_ 3 (3(b—y)? Z 
a et Taps to 
aV (c—zZ) 
dz S rhe) di 
WN = fa(ere eng ol 
Tat == Pagel Fey 
Thus the well-known equation 
OV EN ON 
an deta von 
holds good for all points of space situated outside the acting 
masses. 
6. 
Among the different cases in which the value of the poten- 
tial V, or of its differential coefficients, may be sought for a point 
not situated outside the acting masses, we will first consider the 
