ACTING INVERSELY AS THE SQUARE OF THE DISTANCE. 163 
extended through the whole surface, where & represents the 
density at the element ds. 
Upon the assumption of an infinitely small value of e, ae 
will further pass into the value of the partial differential quo- 
tient ei teats)" or sesh and the value of the integral (4.), or 
da da 
!—1 
into the integral 
dk 
fu .(a—2) dt 
LF aN 
extended through the whole space 7. 
Per !-l a—wN 
Lastly, for an infinitely small value of e, eal 5 oe 
3 is no other than the value of the partial differential coeffi- 
1 ames or Lis 
eda d x" 
ak (a—ax) dt 
move eX da’ Lipide) ge e288 
ae dz re re : 
where the first integration is to be extended through the whole 
space ¢, and the second over the whole of its surface. 
This result holds good, however near O may be to the surface, 
either on the inside or on the outside, providing it be not ac- 
We have consequently the simple result 
tually on the surface itself, where _ would have two differ- 
ent values. The first integral, it is true, varies continuously in 
passing through the surface; but according to a theorem which 
. : k (a — ds . 
will be demonstrated in the sequel, — He ee in 
passing from a point infinitely near the surface on the inside, 
to one on the outside, varies by the finite quantity 4 7k cos a, 
where k and « refer to the point of passage, and to this same 
quantity the difference between the two values of oe at this 
dx 
place will be equal. 
10. 
In like manner, if 8 and y have the same signification with 
relation to the second and third coordinate axes as « with rela- 
