( 670 ) 



indeed the difference between Sol. VIII and IX is much smaller 

 than between VI and VII, and now leaxes nothini^ to be desired. 



Value.'s of //o- 

 Sol. VT + 0^0388 =fc ^0044 Sol. VIII + 0^0454 d= °.0029 

 Sol. VII + .0490 ± 24 Sol. IX + .0473 ± 14. 



For the other unknowns the ditferences between the solutions VIII 

 and IX are entirely negligible. In addition to the improvement of 

 the masses, also the reduction to one and the same fundamental 

 plane, and the corrections applied by Cookson to the values for 1 901 

 and 1902 are largely responsible for this improvement in the agree- 

 ment of the two solutions. 



II. Equntions of tlie centre. The values of the own excentricities 

 and perijoves were derived by me from the heliometer observations of 

 1891, 1901 and 1902, in Groii. Pabl. 17, Art. 19. (See also these 

 Proceedings, June 1907). The discussion was there carried out for 

 two sets of coefficients Xy, the results agreeing within their probable 

 errors. It is therefore unnecessary to repeat it here with the coeffi- 

 cients corresponding to the masses (C), which are intermediate 

 between the two sets tliei"e used. The reasons why the photographic 

 results of 1902 must be rejected, have already been given above. 

 The finally adopted values are thus the same as in Gron. Fubl.^7, 

 with only a few unimportant alternations in the last decimal places, viz: 



6'i=:0°.0031 =t°.0080 (Ö, = 155°.5 ± oo + |0M4703 ±\()Ö\U \t 



e, = 0.0n2± 40 o5,= G2 .7 ±10^0 -f |0 .038955 ±;.000455| « 



^3=10. 0868 ± 65 W3 = 338.3 ±3.0 -f {0. 007032 ± .OOOlBOj < 



^, = 0.4264± 20 «5,:= 283 .15± .304- |0 .001896 ± .000021* « 



The probable errors depend on judgment, and are probably esti- 

 mated rather too large. The values of e^ and tOj were not derived 

 from the observed values of h^ and k,^ , but from the inequalities of 

 group II, as will appear below when we treat of the libration. The 

 adopted p. e. of e^ is the largest value which can still be considered 

 to be not improbable having regard to the observed values of It^ 

 and /tj . This p. e. being larger than the value of e^ itself, the p. e. 

 of <ój cannot be stated. 



The motions have been computed by the masses (C) and their 

 probable errors correspond to the probable errors of these masses. 



These values of e, and wi , and the values of r^ corresponding to 

 the masses (6') give the residuals contained in Table II, together 



