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two former figures, indicate the position of the peri-gee and apogee respectively. In the case of fig. 36,as the moon is moving from p to b, the outward actionof the radial force causes the perigee to recede (seefig. 30), while, as the moon is moving over the arca V , the outward action of the radial force causesthe perigee to advance. The advance exceeds the re-cession. Again, as the moon is moving over tiearc b a, the action of the radial force (chiefly inward)causes the perigee to recede (see fig. 30) ; while, asthe moon is moving over the arc b' p, the chieflyinward action of the radial force causes the perigee toadvance. The recession exceeds the advance. Thusthere is a balance of recession to be set against theformer balance of advance; and though it' is easilyseen that in the actual circumstances indicated infig. 36 the balance of advance is somewhat the greater,so that there remains a final balance of advance due tothe radial force; yet this balance is very small com-pared with the balances we had to deal with in thetwo preceding paragraphs. Again, as to the tangen-tial action. It is retardative over the arc H band there (see fig. 33) causes recession; accelerativeover the arc M» a Me, and causes (fig. 32) an advanceover M 2 a, almost exactly compensated by recessionover a M 3 ; retardative over M 3 b' M„ and there causesadvance almost exactly compensating the recessionover the arc b M 2 ; and, lastly, it is accelerativeover the arc M 4 p M 1; and causes a recession overM t p, almost exactly compensated by advance over