But how fast bodies fall near the surface of the earth may be known by the pendulum[182]; and by the exactest experiments they are found to descend the space of 16⅛ feet in a second of time; and the spaces described by falling bodies being in the duplicate proportion of the times of their fall[183], the number of feet, a body would describe in its fall near the surface of the earth in one minute of time, will be equal to 16⅛ twice multiplied by 60, the same as would be caused by the power which acts upon the moon. 5. IN this computation the earth is supposed to be at rest, whereas it would have been more exact to have supposed it to move, as well as the moon, about their common center of gravity; as will easily be understood, by what has been said in the preceding chapter, where it was shewn, that the sun is subjected to the like motion about the common center of gravity of it self and the planets. The action of the sun upon the moon, which is to be explain’d in what follows, is likewise here neglected: and Sir ISAAC NEWTON shews, if you take in both these considerations, the present computation will best agree to a somewhat greater distance of the moon and earth, viz. to 60½ semidiameters of the earth, which distance is more conformable to astronomical observations. 6. THESE computations afford an additional proof, that the action of the earth observes the same proportion to the distance, which is here contended for. Before I said, it was reasonable to conclude so by induction from the planets Jupiter and Saturn; because they act in that manner. But now the same thing will be evident by drawing no other consequence from what is seen in those planets, than that the power, by which the primary planets act on their secondary, is extended from the primary through the whole interval between, so that it would act in every part of the intermediate space. In Jupiter and Saturn this power is so far from being confined to a small extent of distance, that it not only reaches to several satellites at very different distances, but also from one planet to the other, nay even through the whole planetary system[184]. Consequently there is no appearance of reason, why this power should not act at all distances, even at the very surfaces of these planets as well as farther off. But from hence it follows, that the power, which retains the moon in her orbit, is the same, as causes bodies near the surface of the earth to gravitate. For since the power, by which the earth acts on the moon, will cause bodies near the surface of the earth to descend with all the velocity they are found to do, it is certain no other power can act upon them besides; because if it did, they must of necessity descend swifter. Now from all this it is at length very evident, that the power in the earth, which we call gravity, extends up to the moon, and decreases in the duplicate proportion of the increase of the distance from the earth.