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THE MOON’S CHANGES

there will be such and such weather when the linejoining the cusps is seen (for instance) nearly hori-zontal, the moon being new, is the same as assertingthat there must be such and such weather at the timeof new moon in February and March, if the moon isthen nearly at her maximum distance from theecliptic. And so with all such cases. If there wereany value at all in such predictions, they wouldimply the strictly cyclic return of such and suchweather.

Secondly, as to the rate at which the moon changesin shape.

Let us suppose that AB C D, fig. 51, Plate XII.,represents the moon’s disc (dark in the first instance),and that when the illumination begins on the right, B Dis the line joining the cusps. Now, from what has justbeen shown, it is seen that the position of B D mustvary during the progress of the lunar month, unlesswe suppose the moon to be moving in the ecliptic.As, however, we may wish to know the rate at whichthe moon fills, we may make this assumption forconvenience. Now, the variation of phase, obviouslycorresponds exactly to the supposition that the semi-circle BAD, which separates on the right the darkfrom the illuminated hemispheres, rotates round theaxis B D, the point A travelling apparently straightacross to C, but in reality, of course, traversing asemicircle, which is seen projected into the straightline A 0. Now, to find what point of A C will havebeen reached by the advancing boundary of the