50 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
proach, at which point the equations become unexplainable. While 
Euler and La Place differ in their interpretations of the result, 
Boscovich sought to solve the apparent absurdity and inconceiva- 
bility by the invention of his ingenious and complex system of 
alternate spheres of attraction and repulsion, or change of sign, 
on a very near approach, with infinite repulsion at the focus, which 
so loaded down and vitiated his hypothesis as to cause its rejection. 
This result was similar to that of Le Sage’s speculations and those 
of the Ptolemaic astronomers, each thus working out the falsity of 
his respective scheme by superadded complications to readjust the 
theory to the progress of criticism or of observed fact. 
By attributing finite magnitude to the atomic mass, however, 
Boscovich’s difficulty disappears, as I had the honor of pointing 
out before this Society some ten years ago. This may be deemed a 
violent hypothesis in regard to a positive discrete simple absolute, 
as the atom is presumed to be, but parallel difficulties inhere in any 
other finite supposition, as, e. g., a sphere of repulsion. Under my 
provisional assumption, the way out follows from an elementary 
proposition of Newton’s, and it does not demand the gratuitous 
change of law or of continuity involved in the resort of Boscovich. 
The movement of a gravitating particle under stress of a center of 
gravitative force would be in all respects as the great 18th century 
mathematicians have demonstrated, until the margin of the par- 
ticle reached the attracting center, where, if we suppose the attrac- 
tive virtue to prevade the particle equally throughout a certain 
finite volume of mass, however minute, as gravity does the mass of 
a sphere, the maximum of attractive force would be attained ; for, 
as Newton has shown, homogeneous spheres are controlled under 
gravity by a law of force varying directly as the mass and inversely 
as the squares of the distance between their center of mass and the 
attracting center, at all points beyond the surface, and directly as 
the distance between the said centers within the surface; so that, 
after passing the surface, the attractive center must proceed on- 
wards to the gravitating center of mass (relatively), not by a force 
increasing to infinity, but by a force decreasing to zero, after pass- 
ing the maximum, since it is balanced at the center by opposing 
stresses.** 
* Let M be an exaggerated particle of mass and C'a fixed center of gravi- 
tation external thereto. Newton proved that for all positions outside of a 
