30 STATEMENT AND EXPOSITION OF 



For the mean distance from the sun of the (now missing) interior half-planet ^i, 

 and that of Saturn [as recorded in the column of Law in Table (B), in (14)] being, 

 respectively, 14.64275 and 9.44511, the application of Kepler's 3d Law will give 

 us the corresponding periodic times; and then the measurement of the greater of 

 these by the less, will show the periodic time due to the half-planet gi' to be to 

 the periodic time of the ancient Saturn i^ at its theoretical distance, in the ratio 

 of 1.9303 to 1; and a still more scrupulous determination of the data in question 

 than that exhibited in Table (B), might, perhaps, show the ratio to be very accu- 

 rately that of 2 to 1.^ 



But with this ratio existing, the perturbations of one of the masses by the other 

 at their nearest approach (intensified, it may be, by eccentricity of form or of 

 orbit; or otherwise) would recur after ei^ery two subsequent revolutions of the 

 ancient Saturn y^ ; and very possibly the effect of those perturbations become, in 

 this way, cuinulative ; and thus the passing over of the material of the half-planet 

 have been furthered and aided, until its mass was absorbed by the ancient Saturn >^.^ 



10. 



It is not inconsistent with all that has just now been stated, that the term for 

 the distance of Saturn reported in the column of Laio in Table (B) is less than the 

 corresponding term in the column of Fact; the ancient Saturn i^ having, as it 

 were, been draimi outward in the completion of the catastrophe of the absorption 

 of S^■; while Uranus, as indicated in Consistency 5 of this series, may, perhaps, 

 have somewhat fallen in. 



11. 



The (additional) 11th of these consistencies has much more extensive relations; 

 some of which will here be exhibited and explained ; they being especially such 

 as are comprehended under the following title: — 



The more Ancient Arranfjement of the Material of the Planetary System. 



For if — always adhering to the hypothesis that the material of the existing Saturn was 

 increased in the way so often already specified — we endeavor to show what was the 

 more ancient combination and arrangement of the material of the solar system (viz , 

 ere the rending and the rupture, of which we now seem to find traces, were, in all 

 their extent, accomplished), we shall find that, by regarding the masses in ques- 

 tion {half-planets. Asteroid mass or masses, etc.), as recombined about their respec- 

 tive centres of gyration, and then ascertaining \he positions of those centres, to serve 

 as our points of reference, we shall thus obtain a neio and fidly justified series of 

 terms, in which, very much as in the other instances of leading ratios in the plane- 

 tary, and also in the satellite systems, every term will have a ratio to the next 



" The distance of §i being, as stated, 14.642'75; then, to perfectly justify a ratio of the periodic 

 times of 2 to 1, would require the distance of the ancient Saturn 1^ to be 9.24562 instead" of 9.44511. 



' [For a further discussion and application of what is here intimated; as well as that of what 

 more the relation in question may be signilicant, see Articles (64) to (6T) inclusive.] 



