OF ASPECT, ROTATION, AND LIBRATION. 147

illuminated hemisphere, we have only to imagine apoint traversing the semicircle ABC uniformly in14| days. Prom whatever position as a, this movingpoint would have reached in so many days, we mustlet fall a perpendicular am on A C. Then m willobviously be the position of the advancing edge at thetime in question; for Am is obviously the projectedview of an arc exactly equal to A a. Hence thesemi-ellipse BmD indicates the concave outline ofthe illuminated portion at this epoch. Thus, in thefigure, A a is one-fourth of the semicircle ABC, and,therefore, ABmD is the shape of the moon’s crescentwhen she is an eighth of a lunation old, or nearly3, 7 o days old. In like manner, if b be midway betweenB and C, bn perpendicular to A C gives us B n D,the elliptical outline of the gibbous moon, at the timewhen she is gibbous, midway between first quarterand full; and A B n D is the phase of the moon atthis time, when she is about 11-^ days old. It is readilyseen that B C D m is the figure of the gibbous moonat a time midway between “full” and third quarter;while, lastly, BCDti is the figure of the waningmoon at a time midway between third quarter andnew.

Now, as the lunar month contains about 29 J days,P we divide A C into 14| equal parts, as shown bythe numbered division-lines, we obtain, by letting fallperpendiculars, the daily progress of the advancingri m of light from new to full, as shown by thenumbered division-marks on C A. We have only tol 2