182 



Mr. Challis on the Distances 



Empirical Distances. 



4 



4 + 1 



4 + 1x2 



4 + 1x2' 

 4 + 1x2^ 

 4 + 1 X 2^ X 3 



= 4. 

 = 5. 

 = 6. 



= 8. 

 = 12. 



= 28. 



True Distances. 



4... 



5.13... 



6.30... 



, 8.14... 



DifTerences. 

 .0 

 ..- .13 

 ..- .3 

 ..- .14 



4 + 1 X 2^x3" = 76. 



.11.44 + .56 



.26.36 + 1.64 



.76.85 - .85 



For the satellites of Uranus a=i283, 6 = 437, -=7^ = 5 nearly. 



Suppose the distance of \he fourth satellite = 3 + 1 x (ii)^ = 5^, for 

 a similar reason to that before mentioned in treating of Jupiter's 

 satellites. 



True Distances. 

 • *•••• o ,yjo ■ • • • • 



Empirical Distances. 

 3 =3.. 



3 + 1 = 4.. 



3 + 1 X ll =41. 

 3 + 1 X {\\)- = 5i., 

 3 + 1 x(ll)^= 10|.. 

 3 + 1 X (11)' = 20^1. 



■ 3.97- 



. 4.58. 



, 5.25. 

 10.50. 

 21.00. 



For the planets = 4091396, 6 = 2912316, - 

 the Earth's distance = 4 + 2.3 = 10. Hence 



3 



4 



True Distances. 

 , .. 3.87.. 

 . .. 7.23.. 



..10. .. 

 . .. 15.24.. 

 , .. 27.39.. 



52 52.03 



4 + 2^3 = 100 95.39 



4 + 2'.3 = 196 191.83 



We have in each instance made use of the value of a and b 

 obtained by the process of combining equations, and in all the 



Diiferences. 



- .03 

 + .03 



- .08 



.0 



+ .091 

 -.916 



nearly. Suppose 



Differences. 



, + .13 



. - .23 



.0 



. + .^e 

 .+ .61 



. - .03 

 4.61 

 4.17 



