178 Mr. Challis on the Distances 



The differences compared with the corresponding distances are 

 upon the whole not greater in this case than in the preceding, 

 and the value 2^ is just as probably true as 2.325. The difference 

 corresponding to the third satellite is again the least, and is the 

 more to be observed because the other differences are consideiably 

 changed from whiit they were before. If r would have the value 

 2^ exactly in a particular case, from which the case of nature 

 is a deviation, and the third satellite, being a maximum cause 

 of the deviation, is itself caused to deviate least, then the result 

 of our calculation is such as should be expected, and affords a 

 probability that the value 2^ has foundation in nature. 



7. Let us now treat the satellites of .Saturn in a similar 

 manner, a = 335, a + 6 = 430, a4-ri = 528, a + 7-^6 = 682, aH-r^6 = 958, 

 a + r^'.r'.b = 2208, a + r^.r'\ h = 6436. Suppose r = 2, r' = 3. From 

 these seven equations twenty-one different values of a and b may 

 be, obtained. The mean value of a = 336, and that of i = 82. 



Empirical Values. True Values. Differences. 



Hence a = 336 335 - 1 



a+b = 418 430 + 12 



a + rb — 500 528 + 28 



n + rb = 664 682 + 18 



a + r'b ^ 992 958 - 34 



a + r^.r'.b =2304 2208 - 96 



a + r\r'\b = 6240 6436 + 196 



The differences are all considerable compared with that corres- 

 ponding to the first satellite, which is a very small body. One 

 peculiarity readily presenting itself in regard to this satellite, is 

 its proximity to the ring, the exterior radius of which is 233. 

 The ring may jjossibly have a deranging effect, similar to what 

 a large body would have, revolving at the distance of the .satellite ; 

 and at the .same time that it may have been the primary cause 

 of the two-fold series of distances, it may act as a disturbing 



