PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 699 



the serial number of any satellite of this series, gives, for a quotient, 

 the square root of the mean distance of that satellite. The tables 

 of Saturn's serial relations are interesting on account of the 

 remarkable resemblance which they bear to those of the solar 

 system. 



Satellites' Serial Square roots of the Theoretical Actual k'n. 



names. numbers, mean distances. distances. distance. 



1,740 -f- 1 = 1740. 



1,740 '"^ 2 " 870. 



1,740 " 3 " 580. 



1,740 " 4 " 435. 



1,740 " 5 " 348. 



1,740 " 6 " 290. 



1,740 " 7 " 249. 



1,740 " 8 " 217. 



1,740 " 9 " 193. 



1,740 " 10 " 174. 



Japetus 1,740 " 11 " 158. 2,496,000 2,414,000 



1,740 " 12 " 145. 



1.740 " 13 " 134. 



1,740 " 14 " 124. 



1,740 " 15 " 116. 



1,740 " 16 " 109. 



Hyperion 1,740 " 17 " 102. 1,080,000 1,050,000 



1,740 " 18 " 97. 



Titau.-... 1,740 " 19 " 91.5 837,000 800,000 



Rhea 1,740 " 29 " 60. 360,000 358,000 



Dione 1,740 " 34 " 51. 260,000 256,000 



Tethys 1,740 " 30 " 44.6 200,000 200,000 



Enceladus 1,740 " 44 " 39.5 156,000 161,000 



Mimas 1,740 " ^9 " 35.5 126,000 126,000 



Serial Relations of the Satellites of Uranus. 

 Exj^lanation of Table 14. 

 The satellites of Uranus are yet the subjects of discussion and 

 doubt, and their elements are generally regarded by astronomers 

 as unsettled. In contrasting table 14, I have put down four of 

 the satellites according to Dr. Larduer. The two nearest satellites 

 to the primary are not mentioned by him, and have been but 

 lately discovered. I find their distances stated in Nichol's Cyclo- 

 pedia of the Physical Sciences; and from this datum I have calcu- 



