DISTANCE, SIZE, AND MASS. 25

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from it in such sort as to deduce tlie exact distance ofthe moon.*

In this process, however, the mass of the moonwould have to be taken into account. In fact, as willbe seen in the next chapter, we must add the moon’smass to the earth’s in considering the actual tendencyof the moon towards the earth; so that, if we knowthe moon’s mass, the earth’s size, and the moon’speriod, we can deduce the moon’s distance.f

Burckhardt applying this method, on the assumptionthat the moon’s mass is T V of the earth’s, deducedthe parallax^7' 0", corresponding to a distance of239,007 miles. Damoiseau, taking the moon’s massat ri of the earth’s, deduced a parallax of 57' 1",corresponding to a distance of 238,937 miles. Plana,

* The case may he compared to the following: In determiningthe rotation period of Mars (see Appendix A to my “ Essays onAstronomy”), I had certain dates, separated by long intervals, onwhich the planet presented a certain aspect. Now, knowing prettyaccurately the rotation period, I could divide one of these longintervals by this pretty accurate period, to get the total number ofrotations in the interval: I could be certain that I should not geta full rotation too many or too few, but only a small fraction ofa rotation, which could very well be neglected. Then, having thenumber of rotations, I could reverse the process, dividing theinterval by this number to obtain the rotation period more exactly,—to obtain, in fact, a period which, used as a divisor instead ofthe former rougher determination, would leave no small fractionover or above.

t The following is the treatment of the problem, on the assump-tion that the moon moves in a circle round the earth:—

Let P be the number of seconds in the moon’s periodic timeround the earth (the sidereal month) ; D, the distance of the moonm feet; g, the measure of the force of gravity at the earth’s surface