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

 The following corrections are special to each Satellite : 



SATELLITE I. 

 Add to the formula for Table III. 



- 4 9 '2 sin (H - A,,) + 8 '5 sin (II - A m ). 



SATELLITE II. 



Instead of the term -9 8 731 sin (II- A n ) in Table III., 

 Substitute the terms 



- 2 9 '5 sin (n - A n ) - 1 9 '5 sin (n - A ni ). 



SATELLITE III. 



Instead of the term -5 3 775 sin(n - A m ) in Table III., 

 Substitute the terms 



- 9 "4 sin (n - A n ) - 5 S 7 sin (n - A in ) + 9 '5 sin (n - A IT ). 



SATELLITE IV. 



In Table III. instead of the term 1G 3 '694 sin (n - A IV ), 

 Substitute the terms 



2 S '0 sin (n - A in ) + 16 9 '9 sin (n - A IV ). 



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

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



Damoiseau states that the values of J, <j>, </> i; SJE and Sr which he 

 employs in the formation of the several Tables III., are taken from Bouvard's 

 Tables of Jupiter. Mr Godward, however, has found that the numbers in 

 these Tables do not accurately repi'esent the results given by Damoiseau's 

 formula?. It may be remarked also that the value of Argument 1, or the 

 mean anomaly of Jupiter, employed by Damoiseau slightly differs from Bou- 

 vard's value, except at the Epoch 1750, when the two coincide. 



In order to be strictly accurate in forming the complete Arguments, 

 the values of J and of J+(f> corresponding to the actual time should be 

 employed; whereas Table I. only includes the values of those quantities 

 corresponding to the beginning of the year. 



