46 



STATEMENT AND EXPOSITION OF 



(Reckoning from Japetiis inward), sub- 



mulliples of peiiodic-time of Japetds, 



and corresponding distances. 



Distances in accordance with 



ratios of terms in 



Table (C). 



(Reckoning from Titan outward) mul- 

 tiples of the periodic-time of Titan, 

 and corresponding distances. 



p. TIME. 



DISTANCE. 



51.9925 



41.9986 ■ 



33.9271 



27.4069 (Ih/perion) 



p. TIME. 



DISTANCE. 



1 that of JAPETUS 



6 



3 " " 



7 



49.109 



40.544 

 34.939 

 27.919 



3^ that of TITAN 



2 



51.037 

 40.782 

 35.145 

 29.014 



In the Interval from Titan to Rhea. 



In accordance with Ratios of 

 Terms in Table (C.) 



(Reckoning from Titan inward) snbmultiples of the 

 periodic-time of Titan, and corresponding distances. 



DISTANCE. 



PEEIODIC TIME. 



DISTANCE. 



17.2598 



13.4556 



10.8696 



(Bhea) 9.5972 



1 that of TITAN 

 I ■' 



1 "' 

 3 



1 



16.894 



13.947 



10.644 



9.604 



In this region the coincidences, it will be perceived, are more perfect than in the 

 other region exterior to Titan. 



But it is here, again, worthy of remark, that Hyperion, outside of Titan, in a 

 place analogous to that of Uranus in the planetary system, has, like that planet, 

 seemingly fallen in someiohat from its true position in series ; as if influenced by 

 the great interior body, under stringent circumstances. [See, again, 6 of (43).] 



Exact Commensurahility of Periodic Times. — Explanation of this. 



(67) M. Laplace, in the course of his comments on his own hypothesis, espe- 

 cially notices and accounts for " the rigorous equality observed between the angular 

 motions of rotation and revolution of every satellite ;" all which will be considered 

 in another connexion. 



But, he adds, that " the first three satellites of Jupiter present a still more extra- 

 ordinary phenomenon ;" which consists in this, that " the mean longitude of the first 

 minus three times that of the second, plus twice that of the third, is always equal 

 to two right angles." 



Next, with respect to the existing satellites of Saturn, we have the statement of 

 Sir J. Herschel that " A remarkable relation subsists between the periodic times 

 of the two interior satellites and those of the two next in order of distance, viz., 

 that the period of the third (Tethys) is double that of the first (Mimas), and that 



