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50 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.

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 soUd elastic substance will resist