154 [194 
194. 
NOTE ON THE THEORY OF ATTRACTION. 
[From the Quarterly Mathematical Journal, vol. II. (1858), pp. 338—339.] 
Imagine a closed surface, the equation of which contains the two parameters m, h, 
Call this the surface (m, h), and suppose also that for shortness the shell of uniform 
density included between the surfaces (m, h), (n, h) is called the shell (m, n, h). 
Suppose now that the surface is such : 
1°. That the infinitesimal shell (m, m + dm, h) exerts no attraction upon an 
internal point. 
2°. That the equipotential surfaces of the shell in question for external points 
are the surfaces (m, Jc), where k is arbitrary. 
Then, first, the attraction of the shell on a point of the equipotential surface 
(m, k) is proportional to the normal thickness at that point of the shell (m, m + 8m, k); 
or (more precisely) taking the density of the attracting shell as unity, the attraction is 
= 47r x mass of shell (m, m + dm, h) into normal thickness of shell (m, m + Sm, k) 
divided by mass of the last-mentioned shell. 
In fact the shell (m, m + 8m, k) exerts no attraction on an internal point, 
consequently if over the surface (m, k) we distribute the mass of the original shell 
(m, m + dm, h) in such manner that the density at any point is proportional to the 
normal thickness of the shell (m, m + 8m, k) the distribution will be such that the 
attraction on an internal point may vanish; but in order that this may be the case, 
the density must be equal to into the attraction upon that point of the shell 
(m, m + 8m, k). Hence the attraction is proportional to the normal thickness, and if 
the whole mass distributed over the surface (m, k) is precisely equal to the mass of 
the shell (m, m + dm, h), then the density at any point must be equal to the mass