( 378 ) 



excentricity and the longitude of the i)erigee ojdy, and tlieir periodic 

 cliaracter fully confirms the existence of the inequality discovered 

 l)y Xkwc'O.mh. 



At a closer inspection, however, it aj)pears that Xewcomb's forniula 

 does not re|»resent satisfactorily my // and /•, and this need not 

 astonish us if \\e consider the great extrapolation involved in the 

 apjdication of Newcomb's formnla to my results. 



8. To correct Nkwcomb's formnla by successive approximations 

 I have proceeded in the following way : 



By comparing the // and /• now obtained with those in the table in 

 JnveMlgatlon p. 28, it may be easily seen that the |)eriod of the argu- 

 ment ^V, on which 1l and /• (lei)end through the formulae Ji = It,, — asinX 

 and l=:k^-]-acosX, niusi l)e greater than IGVs years — the period 

 assuuied i)y Kewcomb — and cannot differ much from 18 years. 

 This corresponds to an annual \ariation of 20" and it will be con- 

 venient to adopt this value as a first approximation. 



The special aim of my first operation was to find reliable values for 

 the constant ]»arts of the coefficients, //,. and /v. 1 tried to attain this- 

 by calculating values of h and /■ for each year of the 18 year-cycle 

 l)y means of the results of Xewcomb's two series and of those foujid 

 for 1895—1902. 



Assuming the argument for 1862.0 =t // X ^^ b) be 0, I derived 

 normal values for the arguments 0.5, 1.5 etc. to 17.5, assigning 

 the weights 1, 3 and 2 to the results of the 3 series. I had no 

 value for the argument 14.5 and therefore had to form it by 

 interpolation. 



In this wav I found : 



