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THE MOON’S CHANGES

Let Mj, fig. 59, Plate XIII., represent the middle ofthe disc when the moon shows the aspect indicated infigs. 61 and 63, Plate XIV.; M 2 the middle of thevisible half of the equator under the aspect shown infig. 62 ; and M 3 the same point under the aspect shownin fig. 64. Then if a circle, A M a B M s , be describedabout Mj as centre, and a point be supposed totraverse this circle at a uniform rate, in a nodicalmonth, starting from A when the moon is at a risingnode ; and if P be the position of this point at anypart of such a month, then P M drawn perpendicular toM 2 M s gives M, the position occupied by the middleof the visible half of the moon’s equator at thatmoment. Thus xve see that the middle point of themoon’s equator oscillates northwards and southwards(along the apparent projections of the moon’s polaraxis), moving very slowly near M 2 and M 3 , and mostquickly in crossing the point M 1} the middle of themoon’s disc.

It will be easily seen that, considering only theeffects due to the moon’s inclination, fig. 69, Plate XV.,represents the changes affecting points which, in themoon’s mean state (as in figs. 61 and 63, Plate XIV.),occupy the middle of the short vertical lines of thatfigure. Supposing the nodical month divided intotwelve equal parts (each, therefore, about days inlength), these points would travel upwards and down-wards along the vertical lines of fig. 69 (which linesare, of course, not really vertical on the moon’s discas we see it), traversing the points there marked irt