698 Some Results of Gravitation. [December, 
three times that of the smaller, then the attraction upon a 
unit portion of its surface would be reduced to one-ninth. 
But the area of its surface would be nine times that of the 
smaller. Consequently the attraction upon the whole sur- 
face of each must be the same. 
In faCt the areas of spherical surfaces increase under the 
same law as that by which the force of gravity diminishes. 
No matter, then, what the difference in diameter, the above 
principle holds good, and the attractions of a central particle 
upon every possible spherical shell of unit density must be 
equal. Of course the same principle will apply to all similar 
and proportional portions of such surfaces, though the one 
contain but a single molecule, and the other myriads of 
molecules. 
These surfaces must be infinitely thin for an exaCt appli- 
cation of the law, and the existing equality is that of pos- 
sible, not of aCtual, attractions. It could become actual 
only in the case of the two shells being exactly equal, and 
uniform in density. Gravitative attraction is not a positive, 
but a relative vigour. Each atom pulls upon every other 
atom with an energy dependent upon the distance and the 
reverse attractive energy of this atom. Here, as in every 
case, action and reaction must be equal, and the total at- 
tractive energy exerted by the atom must be just equal to 
the total attraction exerted upon it by all the other attracting 
atoms in the universe. Its total energy is, therefore, subject 
to extreme variations. If an atom be removed from the 
sun’s centre to a position in space midway between the Sun 
and Sirius, its total attractive energy would be greatly 
cl 0ci*Cci.S0ci • 
The principle of equal attraction on equal spherical shells 
of unit density will enable us better to appreciate this piin- 
ciple of loss and gain. The total attraction of a central 
particle must depend on the total number of such shells into 
which all other particles can be formed. The possible num- 
ber of these is largely influenced by the location of the 
particle. For the quantity of matter necessary to compose 
such a unit shell increases with distance in the ratio of the 
square of its radius. In contiguous space a very small 
quantity of matter would form a unit shell. In remote 
space a very great quantity of matter would be requisite. 
Consequently the possible number of such shells depends 
upon the greater or less contiguity of matter as a whole. If 
the average distance of all matter be greater in one case 
than in another, then each unit shell will consume more 
matter, and the possible number of such shells decrease. 
