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}, A₂, 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 A₂ pulled towards A_{3}, A_{4}, and A_{5}, with a threefold force, making altogether a force equal to 6. In the next place, let the masses remain unaltered, but let the distance between them be doubled, then the force will be reduced fourfold. Let the distance be tripled, then the force will be reduced ninefold, and so on. 66. Gravitation may be described as a very weak force, capable of acting at a distance, or at least of appearing to do so. It takes the mass of the whole earth to produce the force with which we are so familiar at its surface, and the presence of a large mass of rock or mountain does not produce any appreciable difference in the weight of any substance. It is the gravitation of the earth, lessened of course by distance, which acts upon the moon 240,000 miles away, and the gravitation of the sun influences in like manner the earth and the various other planets of our system. _Elastic Forces._ 67. Elastic forces, although in their mode of action very different from gravity, are yet due to visible arrangements of matter; thus, when a cross-bow is bent, there is a visible change produced in the bow, which, as a whole, resists this bending, and tends to resume its previous position. It therefore requires energy to bend a bow, just as truly and visibly as it does to raise a weight above the earth, and elasticity is, therefore, as truly a species of force as gravity is. We shall not here attempt to discuss the various ways in which this force may act, or in which a solid elastic substance will resist all attempts to deform it; but in all cases it is clearly manifest that work must be spent upon the body, and the force of elasticity must be encountered and overcome throughout a certain space before any sensible deformation can take place. _Force of Cohesion._