32 



STATEMENT AND EXPOSITION OF 



The conditions prevalent in this series (with a quasi double-planet arrange- 

 ment for every alternate term), require that the mean ratio ^i should nearly = ?•!, r 

 being the mean leading ratio for the whole-planet arrangement in Table (B), in 

 (14).^ Accordingly we find that, with the mean value of r, in Table (B), [which, 

 (13), =1.8253], that rt =2.4:660 + , while the mean value of R^ prevalent in this 

 new series, is 2.4021 



(45) The whole arrangement, in accordance with what has now been stated, is 

 exhibited in the following table; the symbols of mode of connexion, and depend- 

 ence, etc., being similar to those in Table (B), in (14). 



Table (F). 

 More Ancient State and Arrangements of the Planetary System. 



Names, etc. 



Symbols. 



Law. 



Fact and 

 Derivations. 



Diff. 

 L.— F. 



Diff. in 



terms of 



^quantity 



measured. 



Neptune 



11 



[09] 

 5 



30.06039 



12.44316 



5.165T4 



(2.15051) 



0.897801 

 0.37589 



30.05733 



12.40099 



5.20280 



(2.16051) 



0.88665 

 0.38710 



+ 0.003-1- 

 + 0.043 

 —0.037 



+ 0.011 

 —0.011 



+ 0.000 + 

 + 0.003 

 —0.007 



-^0.013 

 —0.030 



Whole-planet >^ ) 

 Jupiter 



Asteroid mass (A) | 

 Mars i ■ ■ 



Earth [ 



Venus ) 



Mercury 





The values of the ratio R^, which determine the numbers in the column of 

 Law, are — 



q? to [(U)i^] 2.4157 



[(U)l^] to H 2.4089 



^ to [^(A)] 2.4021 



[S(A)] to [©5] 2.3953 



[0 9] to 5 . . . ■ -• • •■ 2.3885 



Diff. 



0.0068 

 0.0068 

 0.0068 

 0.0068 



y Mean 2.4021. 



The mean value of R^ is, then, very nearly 2.4^ which =||== V?, so that every 



' It being among those conditions that the centre of gyration of the component masses should 

 very closely correspond in its position with that due to the intermediate term in the quasi dovhle- 

 planet series; a fact which itself seems to indicate, that the law of apportionment of the masses is 

 not independent of that of the distances, but that the one (in the mathematical sense of the term) is 

 & function of the other. 



