180 Mr. Challis on the Distances 



small bodies, Vesta, Juno, Ceres, Pallas. It is impossible to say 

 what would be the effect of breaking up a single planet into 

 several parts, in the way in which these planets have been 

 imagined to originate from the dismemberment of a single body, 

 how the recomposition of the parts would influence the present 

 distances of the other planets, and at what distance the compound 

 body would revolve. Leaving then these bodies out of considera- 

 tion, and supposing r = 2, there will be seven equations, by which 

 twenty-one different values of a and b may be found. 



Let a = 3870981, a + b - 7233323, a + rb = 10000000, a + r'b 

 = 15236935, 'a + r''6 = 5202-9U, a + r'i = 95387705, a+r''6 = 19183050. 

 The mean value of ^ = 4091396, that of 6 = 2912316. 



Empirical Values. True Values. Differences. 



Hence a = 4091396 387098I + 220415 



a + b = 7003712 7233323 - 229611 



a + rb = 9916028 10000000 - 83972 



a + rb = 15740660 15236935 + 503725 



a + r'b= 27389924 27352910^ j«t^-ouu^5+ 37014 



a + r*b = 50688452 5202791 1 - 1339459 



a + r^b = 97285508 95387705 +I897803 



a + 7''^b = 190479620 191833050 —1353430 



Here the difference for the Earth is less than those for the ad- 

 joining bodies, and its mass -is greater than theirs. But the 

 differences for Jupiter, the largest body of the sy.stem, and for 

 Mars, are the most considerable. This circumstance may be 

 referable to the anomaly of the four contiguous small bodies, 

 revolving all nearly at the .same distance. It is easy to conceive 

 that such an irregularity may have an effect on the arrangement 

 of the adjoining planets ; and this account of the matter is made 

 more proVnible by the small difference between the distance which 

 the law assigns, and the mean between the distances of Juno, 

 Ceres, and Pallas. These three bodies revolve at distances which 



