86 STATEMENT AND EXPOSITION OP 



51st. The distribution of masses which Consistency 50th would indicate, and the 

 Laws of Distance in (10), together enable us to compute the mass and mean distance 

 of material (possibly planetary) immediately interior to Mercury. And the mass 

 thus indicated seems to be adequate to produce the perturbations of Mercury's 

 orbit to the extent reqtdred hy M. Le Verrier. [See discussion of all in (52)]. 



52d. With the arrangement of distances of Jupiter and Saturn either in the 

 column of Law or in the column of Fact, in Table (B), in (14), and with the ascer- 

 tained value of their masses, we find, (53), the vis viva or moment of (simultaneous) 

 rotation of the one very accurately equal to that of the other ; so that the masses 

 are inversely as the squares of the radii of gyration ; i. e. here inversely as the 

 squares of the mean distances from the sun. 



There is, at least, a rude approximation to the same, on a large scale, when the 

 masses and distances of Neptune and the next term of the series [U>^] in Table (F) 

 in (45) are, in like manner, made the subjects of a proportion in (104). 



It may be then that the great divisions of the nebulous solar atmosphere (ante- 

 cedent perhaps to other planet-forming developments) were made in conformity to 

 the proportion here in question. 



But in what seems like the subsequent subdivision of the [Ut^J mass, in its 

 special comparison with Neptune, the proportion, (104), of distances inversely as 

 the ^ power of the masses is very accurately justified; in which the whole-planet 

 mass (U) (consisting of the mass of Uranus and that due to its now-missing interior 

 gi) enter, as well as the ancient Saturn \^; though, as already intimated in Consist- 

 ency 47<7i, the existing Saturn enters in the comparison with Jupiter. 



The moments of (simultaneous) rotation of the outer and inner systems of bright 

 rings of Saturn exhibit, (53), an approximation to equality like that of the great 

 outer masses here spoken of. 



[Also if the expressions of the respective velocities of the existing ring sys- 

 tems, at their centres of gyration be made to enter, instead of the 2d powers of the 

 same, we have, (53), with m and m' for the masses, and a and a! for the distances 

 from the centre of the planet 



m X a oi inner rings 



m' X a' of outer rings ' ' ■ 



Incidental very possibly, but curious.] 



53fZ. From what is stated in Consistency 52d, it would seem to have been the 

 case, that the large masses of the system, in the series from without inward, 

 increased in a more rapid ratio than the respective distances diminished (in a more 

 rapid ratio, viz., than the inverse ratio of the distances); the increased density of 

 material more than counterbalancing the efi"ect of its diminished quantity. 



Accordingly, in (67), with scarcely an exception, we find a continual increase 

 of the masses, from Neptune to Jupiter inclusive ; the mass of Jupiter being tran- 

 scendently the greatest of all. 



The like, (58), is true (Hyperion being the exception there) in the system of 

 Saturn ; Titan being the Jupiter of the system ; as is, (59), the Sd satellite among 

 the four satellites of Jupiter; while, lastly, the Earth and Venus, (101), are, 



