THE MOON’S MOTIONS.

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with that indicated by the arrows on the moon’sorbit,—that is, in the direction of the moon’s advance.But when the earth has got to e 3 (somewhat morethan a quarter of a revolution) the position of themajor axis corresponds to that illustrated in fig. 35,and the recession is rapid: hence in passing to thisposition from e 2 , and away from this position to e 4 ,there is regression of the perigee, insomuch that theline p 4 e 4 er 4 is shifted back even beyond parallelism withPi e x a v In the next two stages, however, there is cor-responding advance; for at e 5 the earth is so placed thatthe major axis is directed towards the sun : and we seethat p 6 is very much advanced round the point e 6 . In thenext two stages there is regression, so that p s , thoughsomewhat advanced as compared with p lt is not somuch advanced as p 6 . Lastly, as the earth passes tothe position e 9 , there is advance. Matters are now asat first; and as the earth circles again round thesun, corresponding changes occur in the position ofthe perigee. The order of such changes is indicatedin fig. 42 a, where E 1 represents the position of theperigee when at p x : we see how it advances to 2 (cor-responding to p 2 ), recedes to 3 and 4, even behind 1;then advances to 5 and 6, recedes to 7 and 8, andlastly advances to 9. If we had begun with theposition p 3 e 3 a s , we should have had, in a completecircuit, the oscillatory progression indicated in fig. 42 b.It will be observed that the two figures agree per-fectly as respects the nature of the loops. Also thetotal angles of advance (1 E 9 in fig. 42 a, and 3 E 11