126

THE MOON’S MOTIONS.

in 42 b) are equal. Another circuit would take theperigee to the position E 17 in one case, and E 19 inthe other. The arc of the advance between successiveconjunctions of the perigee with the sun, that is thearc corresponding to e x e 9 , fig. 42, is about 45° 51J', themean interval between such conjunctions being 411*767days. The perigee performs a complete circuit in amean interval of 3232'575 days.

Let it be particularly noticed that the point e 1 is nodefinite point of the earth’s orbit, but is taken torepresent the earth’s position at any epoch when theperigee is in conjunction with the sun. Again, it isto be noticed that the advance of the perigee does nottake place in reality after the comparatively simplemanner indicated in figs. 42 a and 42 b, since in eachlunation there are two periods of advance and two ofregression; whereas these figures take into accountonly the balance of advance or regression. Moreoverthe periods of advance and regression are of variouslengths in different lunations.

Fig. 42 aptly illustrates the circumstances mentionedwith respect to the lingering of the perigee in posi-tions favourable to advance. Let it be held so thatS is on the right and p x e a cq on the left (or upsidedown), then the perigee is in the position favourableto advance, or as in fig. 34. Now let it be held with S onthe right and p 2 e 2 a 2 on the left. Then, since the earthhas moved halfway of the way towards the position e s ,where the major axis is favourably placed for regres-sion, we should expect to have p 2 e 2 a 2 inclined half-