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the perigee is due to the excess of a force which atits maximum is represented by a A', over a forcewhich at its maximum is represented by p A; whilein the case illustrated by fig. 35, the regression ofthe perigee is due to the excess of a force which atits maximum is represented by the line E a over aforce which at its maximum is represented by theline E p. Clearly the former excess must be doublethe latter, just as the former forces are double thelatter. It is easy also to see that the moon’s orbit inpassing from the position where maximum advanceprevails, to the position where maximum regressionprevails, will be longer in a position involving ad-vance than in a position involving regression,—simplybecause the degree of advance which is reduced tozero by such change of position, is greater than thedegree of regression which is afterwards acquired. Sothat not only is the absolute maximum of perigealadvance greater than the maximum rate of perigealregression, but advance continues during a longerperiod than regression.
Another circumstance causes the advance to hegreater than it would otherwise be. The balance ofadvance really depends on the excess of the disturbingaction at and near apogee over the action at andnear perigee. It will therefore be increased by anycause tending to increase the time during which theapogeal action takes place. Such a cause is to be foundin the fact that the moon’s motion round the earthdoes not exceed the sun’s apparent motion round the