( 711 ) 



with their probable en-ors. The |)liotogra[)hi(* detei-niination of 1902 

 lias been rejected for the reason which has already been explained. 



From these values of .iv have been derived the equations of con- 

 dition, which will be given below. 



The arguments of these inequalities are /;+ r, where 



,, 3^ /.^ _ 2/, = h — 21, + 180^ 



Theii' periods are thus nearly the same as those of the equations of 

 the centre, and in a short series of obsei'vations, such as those used 

 here, the great inequalities are not well separated from the equations 

 of the centre. This is the reason of the bad agreement of the results 

 from the three series of obser\'ations. 



In the eclipses the period of the great inequalities is the same for 

 the three satellites, viz : 438 days ^). The periods of the equations 

 of the centre in the eclipses have between 10 and 19 times this 

 length, and the two classes of unknowns are thus well separable by 

 eclipse observations. Here however, there arises a new complication, 

 which did not exist in the case of extra-eclipse observations. The 

 periods of the inequalities of group II, wiiich are between 406 and 

 486 days, are nearly the same as the period of the great inequalities, 

 and therefore the reliability of the determination of ,*;/ from eclipse 

 observations will depend in a large measure on the accuracy of our 

 knowledge of the inequalities of group II. Thus (^ ^/. with the masses 

 (6') the coefficient of the inequality in the longitude of satellite II, 

 which has a period of 463 days, is .038. This inequality is entirely 

 neglected by Damoiskau (being proportional to e^), and it is probable 

 that his value of .i\ — which, according to the introduction to his 

 tables, was derived directly from the observations — will be more 

 or less affected by this circumstance. The same thing is true in a 

 somewhat lesser degree of the corresponding terms in the longitudes 

 of I and III. 



The uncertainty which still reigns supreme with regard to the 

 values of the great inequalities, is disappointing. We may hope that 

 the reduction of the j^hotometric eclipse observations of the Harvard 

 observatory will contribute to diminishing this uncertainty. 



IV. The Libration. 



The mean longitudes /j, /.,, 4, have been derived from the obser- 

 vations of 1891 (Gill, heliometer), 1892—93, 1893—94, 1894—95, 

 1895—96, 1897, 1898 (Helsingfors and Pulkowa, plates), 1901, 1902 



1) See Laplace. Mécanique Celeste, Tome IV, Livre VIII, Ghapitre II. 



