CERTAIN HARMONIES OP THE SOLAR SYSTEM 



15 



but the right order of their grouping must also be measurably maintained, to bring 

 about the coincidences in their appropriate places. Then, afterward, from Dione 

 downward, every limit has its corresponding satellite or ring, with the bare excep- 

 tion of that between the satellites and the rings. Then the discrepancy between 

 Law and Fact is, in most cases, all but insensible. The most conspicuous deviation is 

 that in the instance of the more recently discovered satellite Hyperion, the distance 

 of which is not yet well determined. Another fact seems also not without its sig- 

 nificance; viz., that the two ratios in the region of the rings have the same value, r'.y- 

 The somewhat abnormal deviation from Law in the instance oi Hyperion, presents 

 a case like those of Uranus (especially) and, also. Mars, in the planetary system f 

 the resemblance being all the more accurate because the difference from Law is, in 

 all these instances, negative. These, and other peculiarities, will be reviewed in 

 the aspect of theory, in Section III. 



Other Relations. 

 (19) The centre of gyration of the whole system of Bright Rings is at the dis- 

 tance from Saturn's centre = 1.9090; being just within the outer edge of the 

 inner Bright Ring (or Rings) which is at the distance 1.9276. 



In the subordinate system of the two outer Bright Rings the ratio of their dis- 

 tances (2.1825 - and 2.0522 -) = 1.06438; while ri = 1.06423. 



Manifestly, then, the arrangement of the Outer System of Bright Rings is 



Fact. 

 Exterior Ring 1 . . m vt, f 2.1825- ) , 



Interior Ring \ '"^^ ^S'^^^^"^ ^^^^ ^^^^^ \ 2.0522 - | 





System of Jupiter. 







Table (D). 





(20). Definite Arrangement of the System. 



Satellites. 



Law. Ratio. 



Fact. 



L.— F. 



ly. 

 III. 



15.35202] 



26.99835 

 15.35024 



0.000 

 + 0.002 — 



II. 



9.62347 



— 0.002 



I. 



6.04934 j r'= 1.5905 



6.04853 



+ 0.001 — 



Here r = r'{ 



-, or r'= rf ; and the value of r' regularly diminishes by 0.0051. 



^ The accepted values in the column of Fact agree very closely with the very careful deductions 

 of Capt. Jacob, from his own observations (Memoirs of the Boyal Astronoviical Society, vol. xxviii. 

 p. 108). These are referred to Titan's distance as the standard ; and when measured by Saturn's 

 eq. radius give for 



Rhea 9.5562 instead of 9.5528. 



Dione 6.8445 " " 6.8398. 



Tethys .'.... 5.3410 " " 5.3396. 

 Enceladus .... 4.320Y " " 4.3125. 

 = See Note 1 to (14). 

 ' Of these relations, and what else is connected with them, more hereafter in Section III. 



