172 Mr. Challis on the Distances 



observe a like law, I have met with success, the more surprising, 

 that, though easily attainable, it had not been anticipated. Before 

 I state the result of my enquiry, I will enunciate the law in 

 more express terms. It is this: — 



When several small bodies revolve round a much larger in 

 orbits nearly circular, their mean distances observe with more 

 or less accuracy, the following progression : 



a, a + b, a + rb, a + rb, &c. 



It is to be observed that the differences between the true 

 distances and those assigned by this progression, are in several 

 instances very considerable in the system of the planets, the only 

 one in which it has hitherto been recognized. 



2. The distances of Jupiter's satellites from his centre are 

 proportional to 6o485, 96235, 153502, 269983. These distances, 

 diminished by the least, leave remainders 35750, 93017, 209498. 

 The ratio of the second to the first is 2.60, of the third to the 

 second, 2.25. Half their sum = 2.42, which differs from either 

 about one-fourteenth of its own value. Let a = 60485, + 6 = 96235, 

 and r = 2 .42. 



Empirical Values. True Values. Difference-. 



Thea a = 6o485. 6o485 o 



a + b = 96235 96235 o 



a+rb = 147000 153502 6502 



a + r'b = 269851 269983 132 



The coincidence of the true and empirical values is as near as 

 happens with respect to the planets, and sufficiently exact to 

 warrant the assertion that the law of distances is true for the 

 satellites of Jupiter. 



It is well known that the mean motion, of the first satellite 

 + twice that of the third = three times that of the second. Now 

 Laplace has shewn, {Mec. Cel. htv. ii. cap. 8.) that if the primi- 

 tive mean motions of these satellites were near this propoition, 



