7] THEORY OF JUPITER'S SATELLITES. 141 



3 33 /3 7 



25c 2 = c 2 + - OA + ^ 2 + T a, 2 + 5/c 2 - c, + - a, 



L t t \* O 



or 



3 33 /3 7 



24c 2 = -aA + ^ + ^ + S/c 2 -, + -(0 ............ (4). 



Z Z 4 \4 o 



From (l) neglecting terms of the second order 



Substitute this in (3), still neglecting the second order 



Substitute these values of a,, o, in the terms of the second order 

 in (1) ; 



A / Q 1 / i . J-W / OO /,., , L /,., , 



3Hl= -2-^ + 6 /C + / " C '-12 / " C + 8' / ' C 

 1 13 ,. . 21 , J 



-g>8 l + T /w- T /v i 



or 



Substitute the same values in (2), 



Now substitute the above found values of a^ and a. 2 in (3) and also 

 the approximate values of a, , c 1 in terms of the second order ; 



j / v + j / - + -i /'<=' + r| A' =/c J - ' 6 - /'' + 



1 19 , , 61 , 4 



