24 



STATEMENT AND EXPOSITION OF 



half-planet on that other side [as they are represented in Fig. 8], gathering around 

 C", C", the one on the one side, and the other on the other side of CD, the 

 dividing limit of neutrality, where the forces being equivalent and opposed would 

 be in equilibrio. It would seem then to be desirable to ascertain whether the 

 limit thus defined will agree with either, or nearly with both, of the other two 

 determinations already made. 



Fiff. 9. 



Now when two planets (Pand P') are in conjunction, as seen from the sun (at S), 

 the position of the point {N), at which their attractions would be equivalent and 

 opposite, and so neutralize one another, may be found, as is well known, by so 

 dividing the distance {PP') between those planets, that 



NP _ l/of mass of P' ^ 

 NP' ~ i/of mass ofP' 



Fig. 10. 



But, in the act of the rending described in the Note on p. 22, portions such as Q 

 and Q would act on one another directly (in the line QQ') very much as would two 

 small planets ; and so the neutral point (iV) be determined as before, viz. : — 



QN __V of mass of Q\ 

 QN y of mass of~^' 



And the local oblique action of neighboring portions would conform to very nearly 

 the same ratio ; so that the whole action within distances at which it would be 

 appreciable would have its neutral limit (N'NN") dividing the distance between 

 the points of reference of rupturing annular masses in a manner approximating to 

 that which obtains in the case of two planets. And what is here stated of them, 

 might also be asserted of the sections of shells, parallel to the equatorial rings, 

 with approximately the same result as to the dividing limit. 



Making use then, as heretofore, of the half-planets themselves, as accumulated 

 around what were their respective points of reference, while yet their masses were 



' The point N is one of the limits of Prof. Kirkwood's spheres of attraction, made use of in his 

 Analogy. 



