OP ASPECT, POTATION , LIBRATION, ETC. 167

respect to the nodes is very variable. As shown in thepreceding chapter, the apses are sometimes advancingrapidly—and they advance on the whole or regredeon thewhole for several successive months—while at othersthey are almost as rapidlyregreding, and the node itself,though on the whole regreding in every lunation, yetsometimes advances slowly for several successive days.Thus the perigee and rising node are sometimes movingthe same way, at others in opposite ways; they maybe both advancing or both receding, or the perigeemay be advancing and the apogee receding, or theperigee receding and the apogee advancing. Wecan see from figs. 42 and 45 (Plate XI.) how variablethese relations are even when no account is taken ofthe advance and recession taking place during thecourse of individual lunations. However, so far asthe mean advance of the perigee from the node isconcerned, the case is sufficiently simple; for theperigee advances so as to complete a revolution onthe average in 3282'575 days, or 8'8505 years, whilethe node recedes so as to complete a revolution onthe average in 18‘5997 days. Thus the mean annualadvance of the perigee is of a revolution, whilethe mean annual regression of the perigee isof a revolution. Adding these together we find themean motion of the perigee with respect to the nodeequal to ~ of a revolution.* In other w’ords, the

* The agreement of the figures in the denominator of this fractionwith the last four in the fraction representing the motion of thenode is of course a merely accidentat coincidence.