( 664 ) 



Finally I add for the sake of conipleteness: 



V. The ratio of the two exeentricities of III, from which m^ must 

 be determined. It has not been possible to determine this ratio from 

 the data at my disposal, and I have therefore been compelled to 

 leave )n^ uncorrected. 



The investigation can thus be divided into the following parts, or 

 subordinate investigations: 



I. The determination of the inclinatiojis and nodes on the different 

 epoclis, and of the motions of the nodes. This discussion must at the 

 same time give the position of the mean equator, since the major 

 part of the motions of the nodes is due to the compression of the 

 planet, and consequently the plane of the equator is the one to which 

 the theoretical motions are referred, and on which the own inclina- 

 tions are constant. This discussion has been made with preliminary 

 values of j); and q; in Cape XI 1. 3, Chapters XV — .YAT. 



II. The determination of the equations of the centre and of their 

 secular variations. This was done in Gron. Fuhl. 17, Art. 19. 



III. The determination of the great inequalities. These have been 

 adopted unaltered from the heliometer observations of 1891, 1901 

 and 1902. 



IV. The determination of the libration. This was carried out in 

 Gron. PuhL 17. 



The determination of the masses from the equations of condition 

 furnished by these various subordinate investigations was effected in 

 Gron. Fuhl. 17, so far as it was possible with the data which were 

 then at my disposal. I there found the masses : 



x'= + 0.025 v^ — + 0.050. 



. . . . {A) 

 r^= — 0.360 1^3 = 4- 0.025^ 



The equations of condition from which corrections to these values 

 were derived, will be communicated below. I will now first describe 

 the various subordinate investigations I to IV, to which I add V : 

 the determination of the mean motions, and VI: the determination 

 of the mass of the system. 



I. Inclinations and Nodes. 



The data are the values of/?/ and qi for the live epochs 189J .75 

 1901.61, 1902.60, 1903.72, 1904.89. The unknowns are y/, rio , 

 ,i\, //„ and the motions of the nodes ^). These latter depend on yJ 

 and Vi, of which onlj^ y.' has been introduced as unknown. The 



'j hi this investigation we put for abbreviation H — \\\ — &^ 



