8] MASSES OF JUPITER'S SATELLITES ETC. 189 



value employed by Laplace ; hence the mass of II which is found thence 

 is the same as that which Laplace gives, or 



m' = 0-232355. 



We next take the great inequality of II which the actions of I and 

 III jointly produce. Damoiseau's coefficient (p. vi) is 



15 m 6 8 -331 = O d -01048995, 



or in angle 11 806" '03. Hence on the model of Laplace's equation (l), we 

 find 



i + m"l 7419336 = 1-6983516, 



and if we take Laplace's value of m" as an approximation, this equation 

 is satisfied by 



m = 0'1567892, w" = 0'884972, 

 with corrections to be presently determined 



*?=-*<. 9-832069. 



m m 



By p. ii, the annual sidereal motion of the perijove of IV is 41' 5l""57 

 or 7751 VV 759. We substitute this in the third and fourth equations for 

 g of Ch. vii., and thus form equations analogous to Laplace's (5) and (2) 

 of Ch. ix. The values of the ratios of the eccentricities which refer to 

 the perijove of IV are then evaluated thus : -Damoiseau gives the terms 



III l m 



IV - 55 m 37 8 '390 sin ( 4 - m t ). 



These are values at conjunction, and represent the sum of two terms 



15 M 



2h sin (u cr 4 ) - 'h sin (u 2w + w 4 ). 



4 1 



Hence we find 



A = 9"'28, A' = 78*'42, A" = 21<r-85, A'"=4644 W 74, 



and = [7-30059], , = [8-22747], L = [8'65700]. 



