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this part of the orbit the moon is also drawn towardsthe plane of the ecliptic. Throughout the whole ofher revolution, then, under the imagined condition,the moon is drawn towards the plane.
Thus the line of nodes regredes throughout. Theinclination diminishes while the moon is moving fromN to M, increases as she moves to N', decreases asshe moves to M', and increases as she moves to N.It is therefore, on the whole, very little affected duringthe complete revolution.
A like result obviously follows if the line of nodesis situated as in fig. 39, but the places of the nodesinterchanged.
Thirdly, let the line of nodes be supposed to remainthroughout a complete revolution of the moon in aposition intermediate to those just considered, as atN N' (figs. 40,41). First let the moon pass a node inmoving from Mj to M 2 , fig. 40. Then it will readily beseen (from considerations precisely like those in thepreceding cases) that over the arcs M 4 M, N' andM 2 M 3 N the moon is drawn towards the plane of theecliptic, whereas over the two shorter arcs, N' Mjand N M 4 , she is drawn from that plane. Hence, onthe whole, there is a balance of nodal regression inthe complete revolution. I do not trace out thechange of inclination, for the same reasons that I didnot trace out the change of eccentricity,—viz., first, toavoid prolixity, and secondly, because the change isan oscillatory one, producing no permanent effects.It will be found, however, that in the case indicated