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three lines joining the sun and moon, the sun andearth, and the earth and moon, as all lying in theplane of the moon’s orbit. We know, however, thatthe moon’s orbit is slightly inclined to the plane ofthe ecliptic; and although the inclination does notimportantly affect the value of the radial and tan-gential forces, it produces a very important andinteresting effect on the position of the lunar orbit.This effect we shall now proceed to examine.
In the first place, let us take the general case of abody moving on a path inclined to any plane. LetN M 1ST', fig. 43, be part of the path of the body aboutthe centre E, and let NmN'be the plane to which themotion is referred, so that NEN' is the line of nodes,and the angle PN« the inclination of the path.Then if, when at P, or passing from a node to itsgreatest distance from the plane of reference, thebody is disturbed by a force acting towards thatplane, it will proceed to move as along P h ,—the pro-longation of this new path (backwards) setting thenode as at n, or behind N, while the new inclination,or P n m, is obviously less than the former inclinationP N m. It is equally clear that if the body is at Qwhen it is deflected towards the plane of reference,the new path placed as Q n!, has its node n behindthe former position 1ST, but the inclination Q rim18 grater than the former inclination Q N' m.
Similarly if the disturbing force acts from the plane°f reference and the body is at P, or anywhere on thearc N M (fig. 44), the node advances as to n, and the
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