THE PRIME RESULTANT 109 



Were the members of our system actuated only by their 

 mutual attractions, it is clear that they would speedily 

 precipitate themselves into the sun. On the other hand, 

 were they released from this bond and subjected solely 

 to the action of the Eesultant, they would necessarily fall 

 in sheer lines. Inasmuch, now, as they are acted upon 

 by both of these forces jointly, it follows that they can 

 do neither the one thing nor the other singly, but must 

 automatically effect a compromise between them. A little 

 reflection will show that the only permanent compromise 

 arrangement conceivable is, that the impetus of the cos- 

 mic fall of the planets, on the one hand, and their mutual 

 attractions on the other, shall reciprocally balance, or, in 

 other words, that the centrifugal force shall equal the 

 centripetal. The second consideration, as already ad- 

 verted to in Chap. II, is, that the Prime Eesultant is not 

 a mathematical line but a vast sheaf of rays of attraction 

 which, in combination, operate at torsion. Returning now 

 to our former (implied) equation (v. p. 78) : 

 M C+C'=M' 



we perceive that C and G are no longer mere nullities, 

 but immense real quantities, of a creative nature ; though 

 they cancel each other, indeed, in the shape of the work 

 done in whirling about the huge boulders we call planets. 

 If this conception of mine, namely, that the Prime 

 Resultant is the mother of the centrifugal forces, be 

 sound, then we do not need to search any further for the 

 explanation of those classical problems of celestial me- 

 chanics: the secular acceleration of the moon's mean mo- 

 tion, the rotations of the lines of apsides, and the 

 anomaly of Mercury's perihelion motion; for all of these 

 alike are soluble on the hypothesis that the source of the 

 centrifugal power is accelerative, in unison with the law 

 of falling bodies. The extreme importance which New- 

 tonians have been attaching to these enigmas, especially 

 to that concerning the moon, may be gleaned from the 

 fact that ever since the time of Newton, when Halley first 

 discovered the anomaly, scarcely one of the first rank of 

 mathematical astronomers has failed to give it preced- 



