76 STATEMENT AND EXPOSITION OF 



But even this negative result seems almost like a shadowing forth of tlie catas- 

 trophe, which happened when the material of the half-planet interior to Uranus 

 [(43) etc.] passed over to Saturn ; which has so often asserted itself in our preced- 

 ing investigations. 



With the half-planet restored to its place [its distance as in Table (B), in (14), 

 and its mass, as in (41)], we shall have, by a comparison of Uranus, with that and 

 with Neptune, and the application of the formula, 



= 31.883 hours; 

 agreeing nearly with the former result.^ 



But if we combine Uranus and the restored interior half-planet, in a whole- 

 planet arrangement at the whole-planet limit (U) in Table (B), in (14); we shall 

 have (by a comparison with Neptune and the ancient Saturn i^, and the applica- 

 tion of the formula) for the time of rotation of whole-planet (U), 



e = 16.451 hours. 

 Was there, then, in the collection of material adapted to form a whole-planet at 

 limit (U), the origination of a moment of rotation of the remaining half-planet 

 Uranus, which was not all destroyed when the interior half-planet mass passed 

 over to Saturn n 



All this is not for a moment to be insisted upon ; but there seems to be a pos- 

 sibility that the failure of the Analogy in question, may, in this case, be due to these 

 special conditions here also appearing as if in question; as they ha-ve been heretofore. 



Approximate Result in the Case of Mars. 



(108) In the application to the case of Mars, we may make use of the relative 

 asteroid-mass as made out in (46); viz., 0.58929 of the mass of Mars. 



Then, as in (60) the indications were in favor of a half-planet arrangement of 

 the asteroid-mass, we have— distributing the mass [Note to (51)] in accordance 

 with that— the wi^en'or half-asteroid mass =0.33745 of the mass of Mars; and 

 the distances withal [in accordance with the Latvs foimd in (10) ] being derived 

 from those in the region in question (viz., Sattmi to Mars inclusive), as exhibited 

 in (12). 



From these and the masses, on the one side, and the mass and distance of the 

 Earth on the other, we may then obtain D, the diameter of Mars's sphere of attrac- 

 tion ; and then, .Mr. Walker's formula. 



e = ( 



a Y 



\2D/ 



will give for Mars's time of rotation 21h. 34»i.8.' Observation gives 2U. 37m.4. 

 The coincidence is as close as could be expected ; the masses being more or less 

 uncertain, and the formula confessedly " approximate." 



' For the interior half-planet ^i, if it ever had the planetary form and state, the time of rotation 



would be 337). 982. • m 1 1 Tt\ • 



= Deriving the distances from the more extended series in the column of Law in Table (J3), in 

 (14), we have 21hA&m.d, for the time of rotation. 



