that is, the force _f_ divided by the square of the number D. If one of the bodies, instead of weighing 1 lb., weigh the number of pounds expressed by A, their mutual attraction will be increased A times, and will therefore be expressed by (A × _f_)/D^2 In fine, if the other be also the number of pounds expressed by B, their mutual attraction will be (A × B × _f_)/D^2 (110.) Having explained the law of gravitation, we shall now proceed to show how the existence of this force is proved, and its law discovered. The earth is known to be a globular mass of matter, incomparably greater than any of the detached bodies which are found upon its surface. If one of these bodies suspended at any proposed height above the surface of the earth be disengaged, it will be observed to descend perpendicularly to the earth, that is, in the direction of the earth’s centre. The force with which it descends will also be found to be in proportion to the mass, without any regard to the species of the body. These circumstances are consistent with the account which we have given of gravitation. But by that account we should expect, that as the falling body is attracted with a certain force towards the earth, the earth itself should be attracted towards it by the same force; and instead of the falling body moving towards the earth, which is the phenomenon observed, the earth and it should move towards each other, and meet at some intermediate point. This, in fact, is the case, although it is impossible to render the motion of the earth observable, for reasons which will easily be understood. Since all the bodies around us participate in this motion, it would not be directly observable, even though its quantity were sufficiently great to be perceived under other circumstances. But setting aside this consideration, the space through which the earth moves in such a case is too minute to be the subject of sensible observation. It has been stated (107), that when two bodies attract each other, the space through which the greater approaches the lesser, bears to that through which the lesser approaches the greater, the same proportion as the mass of the lesser bears to the mass of the greater. Now the mass of the earth is more than 1000,000,000,000,000 times the mass of any body which is observed to fall on its surface; and therefore if even the largest body which can come under observation were to fall through an height of 500 feet, the corresponding motion of the earth would be through a space less than the 1000,000,000,000,000th part of 500 feet, which is less than the 100,000,000,000th part of an inch. The attraction between the earth and detached bodies on its surface is not only exhibited by the descent of these bodies when unsupported, but by their pressure when supported. This pressure is what is called _weight_. The phenomena of weight, and the descent of heavy bodies, will be fully investigated in the next chapter.