of the Satellites from their Primaries. 173 



their mutual action must in time have brought about an accurate 

 conformity to it. The law before us would arrange them nearly 

 as they are arranged, and thus cause the mean motions to be 

 nearly such as they actually are. The conclusion of Laplace 

 therefore makes it probable that the deviations from the law of 

 distances are produced, in part at least, by the mutual actions of 

 the satellites, and so far connects the phenomenon w\\h gravita- 

 tion. 



3. Proceeding now to the satellites of Saturn and subtracting 

 from their mean distances the least mean distance, the remainders 

 will be found proportional to 95, 193, 347, 623, I873, 6101. The 

 ratios of every two taken consecutively are 2.03, 1.8O, 1.79, 3, 

 3.25. These ratios seem to indicate a twofold series: the three 

 first are not much different from each other, but different from 

 the two last, which again do not much differ from each other. 

 The mean of the three values 2.03, 1.80, 1.79, is 1.87; and the 

 mean of 3.oo, 3.25 is 3.12. Leta = 335, « + i/ = 430, r-=l.87, r' = 3.i2. 



Empirical Values. True Values. Differences. 



Hence a = 335 335 



a + b = 430 430 O 



a + rb = 513 528 +15 



a+r''b = 697 682 — 15 



a + b', ora+7-^b = 956 958 + 2 



a + r'b', or a + r'r'b = 2272 2208 -64 



a+r'^b', or a + r'r'-b = 6381 6436 +55 



It appears by this that the first, second, third, fourth, and fifth 

 are arranged according to one series; the first, fifth, sixth, and 

 seventh according to another. The recurrence of the first and 

 fifth in the two series is remarkable. 



If we have rightly inferred in the preceding Article that the 

 derangements of the law of distances are connected with gravi- 

 tation, may we not ascribe the singular interruption of the law 



