THE MOON’S CHANGES OP ASPECT, ETC. 139

books of astronomy have hitherto left these mattersalmost untouched.

In the first place, then, it is to be noticed that themoon completes the circuit of the heavens on theaverage in 27’322 days, that is in 27 a - 7^ 43 - 7 m - Ifwe watched her motion from the time when she wasin conjunction with any given star until the nextconjunction, and the next again, and so on, for manysuccessive conjunctions, we should find that the meaninterval is that just stated. This is called the siderealmonth.

If, however, instead of taking a star, we took thepoint on the heavens where the ecliptic crosses to thenorth of the equator, we should not find the intervalexactly the same as the sidereal month; because thispoint on the heavens is constantly, though slowly,moving backwards, or so as to meet the moon’s motion.This point—called, as all know, “ the first point ofAries”—makes the complete circuit of the heavensin 25,868 years; and therefore in a sidereal monthtravels over a very minute arc indeed, less in factthan 4". So that the difference between this newkind of month, called the tropical month, and thesidereal month, i3 very minute. The mean tropicalmonth is necessarily slightly less than the sidereal.The latter is, with great exactness, 27'32166 days,the tropical month is 27‘32156 days, or about 6£seconds shorter.

Now let us in the first instance consider this motionas though it took place in the ecliptic, and uniformly,