lOl 



3607 



102 



The agreement is satisfactory in view of the fact that 

 3nly four places of decimals have been used in the solution, 

 rhe reduction in the sum of the squares of the weighted 

 ■esiduals is from 



i349''3 to 54''o 

 Finally the defmitive elements were used to compute 



the undisturbed positions of the comet for the dates of the 

 normal places. To these the perturbations were applied and 

 the results compared with the observed positions. The out- 

 standing differences, in the sense obs. — comput,, resulting 

 from a six place calculation are tabulated below, together with 

 the residuals obtained by direct substitution of the definitive 

 corrections to the elements into the equations of condition. 



In order to determine the effect of small variations in 

 dfi upon the sum of the sijuares of the weighted residuals 

 the values of the increments to the other elements were 

 substituted into the weighted observation equations and the 

 numerical terms were summed. The resulting equations of 

 condition for dfi were found to be : 



-HO. 0100 -HO. 0020 — 0.0020 — O.OIOO 



were successively applied to this logarithm and the resulting 

 values were sub.stituted in the above series of ei]uations. 

 The residuals found by each substitution were sejuared and 

 added. The following table exhibits the relation between 

 the sums and the variations assumed for dfi . 



in which the coefficients are logarithmic, and the logarithm 

 of the unit of measurement is 1.2700. 



The definitive value for log dfi was found by the least 

 square solution to be 9.9284. The variations' 



1899 August. 



My acknowledgements f(-r information and assistance 

 are due to many — to Profes;ors de Ball, Bruns, Kortazzi, 

 Pickering and Searle for observations from the unpublished 

 zones of the Astronomische Gesellschaft Catalogue; to Pro- 

 fessors Barnard, Davis, Holdcn, Howe and Javelle for in- 

 formation concerning observations and star catalogue data; 

 to Prof Harkness for special meridian circle observations 

 of comparison stars ; and especially to Prof Leuschner for 

 much assistance and many valuable suggestions concerning 

 the arrangement and prosecution of the work. 



Frederick H. Scares. 



