26 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



(10) Rygiea. 

 Comparison, Observation — Computation, 1873, Sept. 20.4491, Ber. M. T. 



[Vol. XIV. 



Given a series of observations well distributed around the orbit and extending over as long 

 an interval as is available, the elements can be corrected by the method of least squares. 



For this purpose the formulae by Bauschinger ^ are convenient. The equations of condi- 

 tion are set up for the residuals in the plane of the orbit and perpendicular to the plane, as seen 

 from the earth. This resolution of the residuals is convenient because it keeps the same reso- 

 lution into components as is used in the theory of Hansen. 



It is to be noticed that the elements to be used in computing the differential coefficients 

 are the finally adopted constant elements referred to the equator by the proper transformation. 



The value of r to be used is 



r = r(l +y) 

 except in the equation 



sin/ (Hansen's notation) 



sm £ = 



ajVl- 



■Tafel lur Berechnun? der wahron .\nomalie, Vorodentlichun^en des Rechen-Instituts der Koius;licheii Sternwarte zu Berlin No. 1. 



' Ober das Problem der Bahnverbe-sserimg, Veroflentlichungen des Koniglichen Astronomischen Rechen-Instituts zu Berlin, No. 2!, Berlin, 



loai. 



