114 CONTINUATION OF DAMOISEAU'S TABLES OF JUPITER'S SATELLITES. [19 



A further small correction has been applied to Darnoiseau's epochs of 

 Mean Conjunction of the first three Satellites, so as to make them exactly 

 satisfy the theoretical relation known to exist between the mean longitudes 

 of these Satellites, viz. : 



The long inequalities of the Satellites depending on the quantities n A 

 which enter into Table III. have been re-computed, the values given by 

 Damoiseau being incorrect in consequence of his having omitted to take 

 into account the modification of these inequalities caused by the mutual 

 action of the first three Satellites. 



Damoiseau's formulae for the values of the mean arguments are not 

 quite correctly derived from the fundamental data in p. iii of the Intro- 

 duction. Small corrections have been accordingly applied to the arguments 

 in order to make them consistent with the data and with each other. 



These Tables have not been carried beyond the year 1890 as it is 

 probable that new Tables of Jupiter's Satellites, founded on more accurate 

 elements than those employed by Damoiseau, will appear before it becomes 

 necessary to make the computations for the Nautical Almanacs of subsequent 

 years. 



FORMATION AND USE OF THE TABLES. 



TABLE I. 

 Epochs of Mean Conjunction. 



Le Verrier's value of the great inequality of Jupiter on January 1, 1750, 

 exceeds Bouvard's value by 0'00400. Hence, in order that the times of 

 mean conjunction as affected by the great inequality may remain unaltered, 

 we must increase Damoiseau's value of the excess of the mean longitude 

 of each Satellite over the mean longitude of Jupiter by the above quantity. 



If u 2 , u 3 represent these excesses for the first three Satellites at 

 any time, we know by the theory that 



Uj 3 u<, + 2 u 3 = 180 exactly. 



