176 Mr. Challis on the Distances 



in the corresponding bodies, which their known circumstances 

 and qualities may lead us to find out. The rationale of the 

 process is, that by combining the equations the mean values are 

 affected by the peculiarities of all the distances, and by those 

 most which are most predominant. 



Let us first take Jupiter's satellites. Here are four equations ; 

 a = 60485, a + i = 96235, a +rb = 153502, a + rb= 269983. Conse- 

 quently four difl^erent values of each of the quantities a, b, r, may 

 be obtained by combining the equations three and three. 



Equations. Values of a. Values of b. Values of r. 



1, 2,3 60485 , 35750 2.60 



1, 2,4 60485 35750 2.42 



1,3,4 60485 41782 2.25 , 



2,3,4 40850 55600 : 2.03 



4)222305 4)168882 4)9.30 



55576 42220 2.325 



Empirical Values. True Values. Differences. 



Hence a = 55576 60485 + 4909 



a+b = 97742 96235 - 1507 



a + r6 = 153683 153502 - 181 



a + rb= 283746 269983 - 13763 



The differences given by this method are, as was to be expected 

 more considerable than those before obtained. The circumstance 

 most worthy of remark is, that the difference corresponding to 

 the third satellite is much less than the others, some peculiarity 

 is therefore to be looked for in this satellite, and the most obvious 

 is its large size, and consequent superior attraction to that of the 

 others: — it is least disturbed and disturbs most. We are thus 

 presented with another argument tending to shew that the devia- 

 tions are connected with the gravitation and masses of the bodies. 



