OF ASFECT, ROTATION, LI 11 RATION, ETC. 103

cycle later, or about 13 - 95 years from its commence-ment, the moon’s orbit is in or near the positione M e'M', fig. 54, the rising node having shifted back-wards from E to near e ; and, lastly, at the end of thecomplete cycle of 18 - 6 years, the moon’s orbit is in ornear its original position.

It is obvious that since, on the whole, the lunarnodes thus regrede, or, as it were, meet the advancingmoon, she must cross her nodes at intervals some-what shorter than a sidereal month. In fact, sup-posing her to start from her rising node at the be-ginning of a sidereal month of 27‘322 days, then atthe end she has returned to the part of the eclipticshe had occupied at the beginning, while the node hasregreded on the average by that amount which is dueto a period of 27‘322 days. This amount is easilycalculated, since the node regredes through thecomplete circuit of the ecliptic in 6793’391 days: itis rather less than 1° 27'. So that, estimating hermotion with reference to her rising node, the mooncompletes a circuit and nearly a degree and a halfover, in 27'322 days ; hence she completes a nodalcircuit in a period less than 27'322 in the proportionvery nearly of 360 to 361 £.* This period, called the

* Or another and more exact way of viewing the matter is asfollows :—The moon advances at a mean rate of JJjjf degrees perday, the node regredes at a mean rate of degrees per day.

rm » ” oiw 89

Anus the diurnal advance of the moon with respect to the node isthe sum of these two quantities, and we have only to calculate howoften this sum is contained in 360 degrees to find the exact,numberH 2