19] CONTINUATION OF DAMOISEAU'S TABLES OF JUPITER'S SATELLITES. 115 



But if WD w 2 , 3 be derived for January 1, 1750, from the times given by 

 Damoiseau for the first mean conjunctions in 1750, we find that 



Hence the theoretical condition will be satisfied if we increase u t and u 3 

 and diminish w 2 by one-sixth of the quantity 0'01097 or by 0'00183. 



Therefore on the whole Damoiseau's values of u lt u.-,, u 3 , u t for January 

 1, 1750, are increased respectively by 



0'00583, 0'00217, 0'00583, and 0'00400. 



Hence the times of mean conjunction in January 1750 for the several Satel- 

 lites will be diminished by 



2 S> 48, T-85, 10 S '03, and 1G S> 09 respectively. 



Similarly on January 1, 1850, Le Verrier's value of the great inequality 

 of Jupiter exceeds Bouvard's value by 0'00435. 



At the same time the value of u, 3 u., + 2 u 3 derived from Damoiseau's 

 times for the first mean conjunctions in 1850 falls short of 180 by the 

 quantity 0'00834, so that the theoretical condition will be satisfied by 

 increasing u t and u a and diminishing n., by 0'00139. 



Therefore, on the whole, Damoiseau's values of u v u lt u 3 , and u t for January 

 1, 1850, are increased by 



0'00574, 0'00296, 0'00574, and 0'00435 respectively. 



Hence the times of mean conjunction in January 1850 for the several 

 Satellites will be diminished by 



2 8 '44, 2 S '52, 9 8 '87, and 17 S> 48 respectively. 



The corresponding corrections to Damoiseau's times of mean conjunction 

 in 1880 and 1890 will be as follows: 



Sat. I. Sat. II. Sat. III. Sat. IV. 



1880 -2-42 -272 -9-82 -17'89 

 1890 -2-42 -2-79 -9-80 -18'03 



The mean anomaly of Jupiter, which forms Arg' 1 for each Satellite, 

 has been found from Le Verrier's Tables of the planet. Corrections have 

 been applied to Damoiseau's values of the other arguments so as to make 

 them consistent with the data in p. iii of the Introduction. 



152 



