( ^73 ) 



altered within their probable errors. They would then be entirely 

 independent of eclipse observations. 



With the finally adopted elements we tind for Bessel the following 

 residuals. 



Bessel 1836.0 

 Observed Residual Observed Residual 



h^ _ o°.033 =b ".010 + °.008 /i, - 0°.704 ± °.007 + °.028 



k, — .188 ± 14 + .020 k, — .395 ± 9 + .026 



It thus appears that, although cö^ is well represented, h^ and k^ 

 leave large residuals. It is remarkable that all four residuals are 

 positive. This must probably be ascribed to systematic errors in the 

 observations, which have already been proved to exist by Schur's 

 discussion, and which probably are not entirely eliminated by the 

 empirical corrections applied by Schur.. 



The theoretical values of h^ and k^ are : 



i Ag = r^^e^ sin lo^ -\-r,,e^ sin w, + e^ sin to, + r,, e, sin <o, 

 i A-g = Tji (?j cos Wj + T32 é?2 ^os Ü), -{- <?3 cos («3 + T34 e^ cos w^. 



The two tirst terms are exceedingly small, but r^^ e^ is large, and 

 this term has been used by Laplace to determine rii^, with which 

 the coefficient t,^ is roughly proportional. An attempt to derive r^^ 

 from a comparison of the equations of the centre in 1836 and 1900 

 had to be given up, as will be easily understood by considering the 

 residuals and probable errors stated above. Also a comparison with 

 1750 is not possible, for Delambre and Damoiseau both state nothing 

 but the values of the coefficients and the arguments, and it is not 

 possible to derive from these the values of hi and ki as found 

 directly from the observations. I have thus been compelled to leave 

 m^ uncorrected. 



The values of oj^ and co^ for 1750, computed from the final values 

 for 1900.0 and the final motions, are : 



Delambre Damoiseau 



w, 313°.0 ± 10°3 309°4 315!o 



w, 179.3 ± 1.2 180.3 180.4 



The agreement is excellent, in fact better than could have been 

 expected. 



(To be continued). 

 46 



PioceeLlings Royal Acad. Amsterdam. Vol. X. 



