THEORY OF JUPITER'S SATELLITES. 



167 



Here 



= 0-6285152. 



Let us first compute & and 

 geometric mean. 



1-6285152 

 0-3714848 

 2 ) 2-0000000 

 1-0000000 

 0-7777973 

 2 ) 1-7777973 

 0-8888986 

 0-8819282 

 2 ) 17708268 

 ' 0-8854134 

 0-8854065 

 2 ) 1-7708199 

 m iv 0-8854100 

 :n iv 0-8854100 



m 



n 



in 

 n' 



m 

 n" 



m 



W 



Hence 

 Again for v, 



= 2-2588406 



logX' 

 log TO' 



log X" 

 log m" 



log X" 2 

 logm'" 



log X'" 2 

 log m" 

 logX 1 ' 



9-1962558 

 Q-QOOOOOO 

 9-1962558 

 8-3925116 

 9-9488522 

 8-4436594 

 6-8873188 

 9-9471461 

 6-9401727 

 3-8803454 

 9-9471444 

 3-9332010 



by Gauss's method of the arithmetico- 



= 0'3538856. 



2X' 2 

 4X" 2 

 8X"' 2 



log 



logX 2 



log v = 9-5236624 



log p = 9-9471 444 



9-5765180 



0-04937892 



0-00308588 



0-00000607 



0-05247087 



8-7199182 



9-1962558 



Hence 



&! = 07543.069 log 6 1 = 9'3775480. 



Next compute b e and 6 10 for the same value of s from Legendre's 



formula. 



