THE MOON'S MOTIONS.

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exceeds the radius of the moon's orbit, it is neverthe-less not so great but that there is an appreciablerelative difference between the moon's distance fromthe sun when in conjunction with him (or at the timeof new moon), and when in opposition (or at the timeof full moon). When the earth is at her mean dis-tance from the sun (or 91,500,000 miles from him),the moon’s distance from him when she is new is91,738,800 miles, and when she is full it is only91,261,200 miles,—so that these extreme distancesare proportioned as the numbers 917,388 and 912,612,or, nearly enough for our purposes, they are as thenumbers 201 and 200. Hence, by what has beenalready shown, the perturbing forces on the moon inthese two positions are as the numbers 203 and 200.Thus the difference, though slight, is perceptible.Yet again, the points where lines drawn from thesun touch the moon's orbit are not quite coincidentwith the points M 2 and M 4 (fig. 19), but are slightlydisplaced from these positions towards M x . Here,again, the amount of either displacement, thoughslight, is appreciable. It amounts, in fact, to an arcof about 8f minutes; so that the points in questiondivide the moon's orbit into two unequal arcs, whereofone, the farthest from the sun, exceeds a semicircle17j minutes, the other falling short of a semicircleby the same amount,—the larger thus exceeding thesmaller by 35', or more than half a degree.

It necessarily follows that the direct effect of thetangential force in increasing or diminishing the