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the advance or recession is greater, we have only tonotice that,—(1) the moon moves more rapidly overthe arc V p b than over the arc b a V , so that any givenacceleration or retardation will produce a smallerproportionate increase or decrease of velocity in theformer than in the latter arc; (2) fig. 84 shows thatthe actual forces are less in the former than in thelatter arc; and (3) the forces act for a shorter timeover the former than over the latter arc, because themoon moves over the former arc more quickly. Onall three accounts the perigeal advance exceeds theperigeal recession. Thus there is a balance of advancedue to the tangential force. But there is also abalance of advance due to the radial force. Hence,there is a total balance of advance when the moon istraversing her orbit placed as shown in fig. 34.
It is perfectly obvious that precisely the same resultwould have followed if the apogee had been turneddirectly towards the sun instead of the perigee.
Next, let the major axis of the moon’s orbit beplaced at right angles to the line from the sun, as mfig. 35; and let similar constructions be employed mthis case as in the former. Now, here it is obviousthat the radial forces acting outwards on the moon asshe traverses the arcs 0 4 b 0, and 0 2 V 0 3 , produceopposite and exactly counterbalancing effects. Butthe radial forces acting inwards on the moon whentraversing her apogeal arc 0, a 0 2 produce a regres-sion of the perigee (see fig. 31), which exceeds theadvance of the perigee produced by the radial forces