174 Mr. Challis on the Distances 



in this instance to the action of the enormous ring of Saturn? 

 The arrangement wliich would have taken place but for the ring, 

 appears from the passage of the value of r from 2.03 to 1.79, to 

 be jjartially disordered, then entirely broken after the fifth satel- 

 lite : and it is worth observing how the remaining two, which 

 are considerably more distant from Saturn than the others, tend 

 to comply with the law. If our conjecture be admitted, and the 

 anomaly be rightly ascribed to an existing cause, it is natural to 

 suppose that the cause of the law itself is existing. 



4. Should the preceding instances be deemed insufficient to 

 establish the law of distances, no doubt I thiuk will be entertained 

 of its reality when the satellites of Uranus have been discussed. 

 Their mean distances are as 1312, 1720, 1984, 2275, 4551, 9101. 

 Subtracting from each of these the least mean distance, the results 

 are 408, 672, 963, 3239, 7789- The ratios of every two taken con- 

 secutively are 1.65, 1.43, 3.36, 2.41. Of these the first and 

 second differ by a quantity not greater than has happened in 

 other instances : the remaining two require particular considera- 

 tion. The cube root of 3.36 is l.50, and the .square root of 2.41 

 is 1.55. These quantities, being near each other and not very 

 different from the other two ratios, prove that the mean distances 

 diminished by the least mean distance ^are terms of a geometric 

 series nearly. The mean value of the common ratio is 1.53. 

 The great distance of Uranus, and the apparent smallness of his 

 satellites, which have never been seen but by the most jjowerful 

 telescopes, leave us at liberty to suspect that there are others 

 besides those already discovered. We know how the law of Bode 

 rendered probable the existence of a planet between Mars and 

 Jupiter. The same law, extending to the satellites of Uranus, 

 authorizes the conjecture that there are two between the "fourth 

 and fifth, and one between the fifth and sixth, making in all 

 nine. 



