THE 
JOURNAL OF SCIENCE. 
DECEMBER, 1881. 
I. SOME RESULTS OE GRAVITATION. 
By Charles Morris. 
t N considering the general results of the Newtonian law 
of gravitation we arrive at an interesting deduction, 
which it may be well to briefly describe. This is that, 
if we view the matter of the universe surrounding any cen- 
tral particle as made up of successive spherical shells, con- 
stantly increasing in diameter outwardly, then this particle 
must exert a precisely equal attraction upon each of these 
shells, no matter what its diameter, provided they be of 
equal density and of inappreciable thickness. 
Such a result necessarily flows from the law of diminution 
of attractive energy with distance. The force of gravity 
diminishes in the ratio of the inverse square of distance. 
At twice the distance the gravity is reduced to one-fourth. 
At three times the distance to one-ninth. But at twice the 
distance the surface area of such a hollow shell is increased 
fourfold ; at three times the distance ninefold. Thus, as the 
radii of these shells increase, their surface areas increase in 
the same proportion as the vigour of attraction diminishes, 
namely, in the ratio of the square of the radius. If we take 
two such shells, one with twice the radius of the other, then 
the attraction of the central particle upon every portion of 
the surface of the smaller shell will be four times as great 
as that upon an equal portion of the surface of the larger 
shell. But the whole surface area of the larger shell is four 
times that of the smaller. Therefore the vigour of attraction 
upon this whole surface must just equal that upon the whole 
surface of the smaller. If the radius of the larger were 
VOL. III. (THIRD SERIES.) 2 Z 
