120 JUPITER AND SATURN. 



The largest individual coefficient in the great inequahty is com- 

 posed of three terms, viz. : — 



Le Verrier. 

 -i545"-5i4 -1548" -66 



+ 25 -821 + 25 -88 



- I 728 - I 73 



-1521 -421 -1524 -51 



The other coefficients have been built up in the same way but 

 it is needless to present the details. 



The largest periodic perturbation of the mean longitude of Jupiter 

 which is independent of the excentricities, is given by the equatiori. 



U 



= B 1 t a -— sm2 (/— \ 



J'— i\v — I day ^ ' 



wherein 3 N ^N 



y — ^i da 



may be replaced by 



In this case the effect of the error in a is trifling, viz., 



hl = 66"-8go sin 2 (I'-X). (Le V. 66" -992.) 



The inequalities depending on the term 



— ^e (4 + D) bo I cos {2 1' — \ — w) 



compare as follows : — 



Le Verrier. 

 U -^ 67" -335 — 67" -436 



ce +133 -99 +134 -19 



cl -^128 -681 —128 -883 



In the case of Saturn disturbed by Jupiter, there is a great 

 inequality depending on the mutual elongation ; it compares as. 

 follows : — 



Le Verrier. 

 ^ai 6933"-286 6922"-i79 



^^1 534 -865 534 -487 



The part depending on /3- in c /' was also computed and found tO' 

 be — o"-52 agreeing with Le Verrier. 



The above comparisons are sufficient to show that the fourth 

 significant figure always and often the third significant figure 

 in Le Verrier's values of the periodical perturbances are incorrect. 

 As was to be expected, Le Verrier's values are invariably too large, 

 so that his theory, compared with observations, would necessarily 

 lead him to assign values of the masses which are too small. 



