(106.) These attractions exist either between bodies of particular kinds, or are developed by reducing the bodies which manifest them to a certain state by friction, or some other means. There is, however, an attraction, which is manifested between bodies of all species, and under all circumstances whatever; an attraction, the intensity of which is wholly independent of the nature of the bodies, and only depends on their masses and mutual distances. Thus, if a mass of metal and a mass of clay be placed in the vast abyss of space, at a mile asunder, they will instantly commence to approach each other with certain velocities. Again, if a mass of stone and of wood respectively equal to the former, be placed at a like distance, they will also commence to approach each other with the same velocities as the former. This universal attraction, which only depends on the quantity of the masses and their mutual distances, is called the “attraction of gravitation.” We shall first explain the “law” of this attraction, and shall then point out some of the principal phenomena by which its existence and its laws are known. (107.) The “law of gravitation” sometimes from its universality called the “law of nature,” may be explained as follows: Let us suppose two masses, A and B, placed beyond the influence or attraction of any other bodies, in a state of rest, and at any proposed distance from each other. By their mutual attraction they will approach each other, but not with the same velocity. The velocity of A will be greater than that of B, in the same proportion as its mass is less than that of B. Thus, if the mass of B be twice that of A, while A approaches B through a space of two feet, B will approach A through a space of one foot. Hence it follows, that the force with which A moves towards B is equal to the force with which B moves towards A (68). This is only a consequence of the property of inertia, and is an example of the equality of action and reaction, as explained in Chapter IV. The velocity with which A and B approach each other is estimated by the diminution of their distance, A B, by their mutual approach in a given time. Thus, if in one second A move towards B through a space of two feet, and in the same time B moves towards A through the space of one foot, they will approach each other through a space of three feet in a second, which will be their relative velocity (91). If the mass of B be doubled, it will attract A with double the former force, or, what is the same, will cause A to approach B with double the former velocity. If the mass of B be trebled, it will attract A with treble the first force, and, in general, while the distance A B remains the same, the attractive force of B upon A will increase or diminish in exactly the same proportion as the mass of B is increased or diminished.