( 665 ) 



discussion is carried out in (^apo XIT. 3, based on the masses ot 

 Souillart's theory. It must now be repeated vvitii the masses {A). 

 Further the following corrections must be applied. 



a. The observed values of pi and qi must be reduced to one and 

 the same fundamental plane for all epochs. At the time when the 

 discussion of Cape XI I. 3 was made, I had not at my disposal the 

 data for carrying out this reduction for the epochs 1901 and 1902. 



b. In the discussion of Cape XII. 3 I was compelled to reject the 

 observations of the satellites III and IV in 1901 and 1902. Cookson 

 had found in the latitude of IV an empirical term, which had also 

 influenced the results for III, and which could be demonstrated not 

 to exist in the observations of 1891, 1903 and 1904. Mr. Cookson 

 has since then found the true explanation of this apparent periodic 

 term, and has corrected his results accordingly. The corrected results 

 must now be introduced into the discussion. It appears that now not 

 only nothing must be rejected, but that also the representation of 

 the observations generally is much improved. 



c. The results of the photographs of 1902, which were not yet 

 known when the discussion of Cape XII. 3 was made, must be taken 

 into account. 



It seems unnecessary to mention here all the details of the dis- 

 cussion. It will be published in Cape XII. 1, Appe7idix, and it will 

 suffice here to state the results. 



It may be remembered that in Cape XII. 3 two final solutions 

 were made, of which Sol. VI was based exclusively on modern 

 observations, while in Sol. VII the motion of é^.^ was derived from 

 a comparison with Delambre (1750), and the motions of the other 

 nodes theoretically corresponding with this were adopted ^). Thus x' 

 was not introduced as an unknown in this solution. The agreement 

 of the solutions VI and VII was very good, with the exception of 

 n' and y^. The values {A) of x and r^- are chosen so that the 

 corresponding motions of the nodes are about the means of those 

 found in Sol. VI and Sol. VII. 



The corrections (a), [b) and (c) were now applied, the quantities 

 (Jy and lii, which are used in the solution were altered so as to 

 correspond with the masses (A), and a new solution was made 

 (Sol. VIII) in which, similarly to Sol. VI, the unknowns were 

 y/, Jlo, ^^0» yo ^"d da'. The method by which the solution was 

 effected is the same as in Cape XII. 3, and has also been described 



") The correspondence was only approximate, the expressions of the motions of 

 the nodes as functions of the masses (Gron. PuhL 17, art. 17), not yet being 

 computed at that time. 



