(upon the moon and upon the stone), one second, because the experiment of the distance through which a stone falls in one second, and its result are the most familiar to our minds. If I had used one minute, I should have found for the space through which the earth draws the moon 0.0030452 of a mile; or if I had used one hour, I should have found 10.963 miles; and I should have had corresponding numbers for the space through which a stone would fall in the same time. These numbers it is to be observed, increase in the proportion of the squares of the times; and so do those for the fall of a stone (for a stone falls in two seconds four times as far as in one second; in three seconds it falls nine times as far as in one second; and so on).
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Fig. 57.
I will now compare the spaces through which the sun's attraction draws the planets in one hour, and as an instance I will take the earth and Jupiter. In Figure 57, let EF be the path described by the earth in one hour, Ee the path in a straight line which the earth would have described in one hour if nothing had disturbed it. JK the path described by Jupiter in one hour. Jj the path which Jupiter would have described in one hour if nothing had disturbed it. Then eF is the space through which the sun's attraction has drawn the earth in one hour, and jK is the space through which the sun's attraction has drawn Jupiter in one hour; and we shall proceed
