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Some Results of Gravitation . 699 
The total attraction of the central particle will decrease in 
proportion. A particle in the centre of the sun is surrounded 
by dense contiguous matter, one in open space by rare conti- 
guous matter, while the more distant matter of the universe 
does not greatly differ in its relations of distance to the two 
particles. Therefore the first is subject to a much greater 
total attraction than the second, and its reverse energy of 
attraction is much greater. The attractive energy of a par- 
ticle, then, is far from being a constant quantity, but varies 
with every variation in the relations of distance of surround- 
ing matter. 
These variations in attractive energy appear to make 
themselves instantaneously felt by all matter, there being 
no indication that time is necessary for the movement of 
this energy. We may not be able to comprehend the cause 
of this instantaneous aCtion, but we may draw a certain de- 
duction concerning it. For if the central particle has an 
equal attraction upon every possible shell of surrounding 
matter of equal density, it follows that it has an attraction 
upon every existing shell in proportion to its density, and 
upon every segment of such a shell in proportion to the 
density of this segment. Thus the attraction of a central 
upon an exterior particle is governed by the following rule : 
— Supposing that the attraction of the central particle upon 
the whole surface of a shell of unit density be taken as a 
unit of attraction, — if, then, any exterior particle be reduced 
to unit density and thickness, — it will form a certain fraction 
of the whole area of a unit shell, and will be attracted by 
that fraction of the unit attraction. 
Let us suppose lines to be drawn from the central particle 
to every portion of the edge of the exterior particle thus re- 
duced. These lines will compose a solid angle. If now the 
exterior particle be moved so as to form part of the surface 
of a shell of half the diameter of the preceding, and a solid 
angle again formed, this angle will be four times greater than 
the preceding one. Instead of saying that the attraction is 
increased fourfold, we may say that the angle or the leverage 
of attraction is so increased. 
We may then affirm that the vigour of attraction depends 
upon the degree of leverage exercised, masses of unit thick- 
ness and density, which form the same solid angle at an 
attracting centre, being equally attracted, whatever their 
distance from that centre, or their relative sizes. If any 
mass approach the centre the angle increases, if it recedes 
from the centre the angle decreases, and the leverage of 
attraction increases or decreases in accordance. If a particle 
2 Z 2 , 
