12. 



EFFECT OF THE LONG INEQUALITY OF JUPITER AND SATURN 

 UPON THE MOTIONS OF JUPITER'S SATELLITES. 



[IN his "Continuation of Damoiseau's Tables" (Supplement to Nautical Almanac, 1881; 

 Works, vol. I. p. 113), Adams remarks: 



" The terms which involve sin (5u - 2w - 34'542) in Damoiseau's formulae for 

 Table III. of each Satellite are sufficiently accurate as they stand." 



These are the terms that express the effect of the long inequality of Jupiter and 

 Saturn upon the Satellites, and Damoiseau's values do not differ much from those of the 

 Mecanique Celeste, 1. xvi. ch. VH. 



In Oct. 1878, after the publication of the above, M. Souillart wrote to Adams to 

 remark that he believed Laplace's determinations to be vitiated by an error of theory, 

 and Adams re-examined them and detected the curious sequence of numerical errors 

 detailed below, whose removal produced a close accordance with the results of 

 M. Souillart ; subsequently, at the request of M. Puiseux, the corrections were com- 

 municated to him and are given in a note at the end of t. v. of the new edition 

 of the Mecanique Celeste, 1882. 



When it became necessary to continue the Tables from 1890 to 1900, Adams 

 derived values of these inequalities from Le Verrier's Tables of Jupiter, and Souillart's 

 theory, and used them for calculating the continuation of Table III. ; but no commu- 

 nication of the adopted expressions was made to the Nautical Almanac office, and 

 the approximate values given in vol. I. p. 124 are not Adams's own, but were derived 

 a posteriori.] 



In the Mecanique Celeste, 1. xvi. ch. vi. Laplace finds the effect of 

 the great inequality of Saturn and Jupiter upon the satellites of the latter, 

 but his numbers are in fault at several points and require substantial 

 corrections. 



In t. v. p. 462, line 6 from bottom, quoting from the new edition, the 

 number 44",334, being the coefficient of the inequality of the fourth 

 satellite, is not consistent with the formula preceding it, which gives 

 42", 863, and the coefficients of the inequalities of the first three satellites 

 should be diminished in the same ratio ; but in the formula itself a term is 



