Page:Conservationofen00stew.djvu/65

Rh depending jointly upon the mass of the attracting and of the attracted particle, and varying inversely as the square of distance between the two. A little explanation will make this plain.

Suppose a particle or system of particles of which the mass is unity to be placed at a distance equal to unity from another particle or system of particles of which the mass is also unity—the two will attract each other. Let us agree to consider the mutual attraction between them equal to unity also.

Suppose, now, that we have on the one side two such systems with a mass represented by 2, and on the other side the same system as before, with a mass represented by unity, the distance, meanwhile, remaining unaltered. It is clear the double system will now attract the single system with a twofold force. Let us next suppose the mass of both systems to be doubled, the distance always remaining the same. It is clear that we shall now have a fourfold force, each unit of the one system attracting each unit of the other. In like manner, if the mass of the one system is 2, and that of the other 3, the force will be 6. We may, for instance, call the components of the one system $$A_1, A_2$$, and those of the other $$A_3, A_4, A_5$$, and we shall have $$A_1$$ pulled towards $$A_3, A_4$$, and $$A_5$$, with a threefold force, and $$A_2$$ pulled towards $$A_3, A_4$$, and $$A_5$$, with a threefold force, making altogether a force equal to 6.