THE MOON’S MOTIONS.

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while the reduction of the radial force over the apogealarc 0 2 a O s results in an advance of the perigee. It isobvious also that the inward action of the radial forceover the arcs 0 1 0 2 and 0 3 0 4 will have opposite andexactly counterbalancing effects. We have only toinquire then whether the regression just mentioned isless or greater than the advance. It is obvious thatthe outward action over the arc 0 4 p is less thanthe outward action over the arc 0 2 a 0 8 ; more-over, the moon, moving more swiftly in perigee thanin apogee, is exposed for a shorter time to the formersmaller action than to the latter larger action. Ac-cordingly, on both accounts, the perigeal regressionis less than the perigeal advance, so far as the radialforce is concerned. There is therefore a balance ofadvance due to the radial action in a complete lunarevolution, when fhe perigee is as in fig. 34.

Next as to the tangential action. In moving from b' toP, the moon is accelerated. Hence, from fig. 32 we seethat the perigee recedes. In moving from p to b themoon is retarded; hence, from fig. 33 we see that theperigee still recedes. In like manner, in moving fro 1 ®b to a the moon is accelerated ; hence, from fig. 32 theperigee advances. And in moving from a to V themoon is retarded ; hence, from fig. 33 the perigeestill advances. Now, in order to ascertain whether

little practice the student will he able to deduce such results in aninstant; and with a little more he will have no occasion to refer tothe figures 30. 31. 32. and 33.