14 



STATEMENT AND EXPOSITION OE 



System of Saturn. 



Table (C). 



(18) Definite Arrangement of the System. 



Names, etc. 



Law. 



Fact. 



Diff. L.— F 



Japetus, 



- r 



. }■'■' 





■ 64.3590 



64.3590 



0.00 



Hyperion, 

 Titan, 



- r 



- r' 





" 27.4069 

 ^ 22.1397 



26.7834 

 22.1450 



+ 0.62 + 

 — 0.01 — 





>- r 



- '■■ } •■■ 



- r" I ri 



- r" I ri 



r' I ?•' 



. .. } .. 



- r V r 



9.5972 



9.5528 



+ 0.04 + 



Rhea, 



Dione, 



6.8453 

 1 5.3365 

 i 4.3109 



6.8398 



+ 0.01 — 



Tethys, 



5.3396 



— 0.00 + 



Enceladus, 



4.3135 



— 0.00 + 



Mimas, 



1 



1 3.3607 



{ 



3.3607 



0.00 



Outer B. Ring, 



>- r > r 



1 2.1165 



2.1246 



— 0.01 — 



Inner B. Ring, 

 Dusky Ring, 



) 



• } - 

 ■ r y r 



1 1.7097 

 1 1.3811 



1.7323 



— 0.02 + 



f 1.3402 

 \ 1.3588 



+ 0.04 + ) 

 + 0.02 + 1 



In the instance of the Dusky Ring two vahies appear in the column of Fact ; 

 the first of these indicating the position of the centre of gyration, if the Duslcy 

 Ring have an interval between it and the inner Bright Ring (proportional, perhaps, 

 on a smaller scale, to that which exists between the two systems of Bright Rings). 

 The second value is that which obtains, if we suppose the Dusky Ring to extend 

 quite up to the Bright Ring. The difference between the results is but a small 

 fraction of the quantity to be compared. 



[In view of the very considerable number of limits in the upper region of the 

 system at which no satellite is found, and the ratios themselves being so small, it 

 might almost seem that the approximate coincidence between Law and Fact was a 

 forced one, brought about by a special arrangement and combination of terms. But 

 not merely the number of terms (or ratios, or their equivalent) is indispensable. 



