140

THE MOON’S CHANGES

so that in fact we are supposing the moon to moveapparently in the same course among the stars as thesun, only that instead of taking about 365£ days incompleting the circuit she takes about 27J days.

Let E E', fig. 46, Plate XII., represent a part of theearth’s path round the sun S, and let M x M 2 M 3 M,be the path of the moon, and suppose that themoon is at Mj when the earth is at E. Then it is thetime of “ new moon; ” the moon lies towards thesun’s place, and if she could be seen, would be at thesame part of the ecliptic, or in conjunction with thesame star s. Let E E' be the arc traversed by theearth in 27'322 days, or in a sidereal month. Thenthe moon has gone once round, and is in conjunctionwith the same star,—in other words, the line II'mjSdirected towards the moon, is in the same directionas E s ,—that is, E'wq s' is parallel to E s. But themoon has not come up to the line E'M/S, joining thesun and earth. Some time has still to elapse, there-fore, before it is again new moon. In like manner, ifthe moon had been at M 2 when the earth was at E,it was the time of “first quarter,”—she would be at Wjwhen the earth is at E',—in other words, she wouldnot yet have reached M 2 ', the place of “ first quarter.”And similarly if it had been “ full moon,” “ thirdquarter,” or any other lunar epoch, when the earthwas at E, the corresponding epoch would not havearrived, when a sidereal month had elapsed.

We see then that the lunation, or the time in whichthe moon goes through her phases, is longer than the