1 1 6 CA LIFOKNIA A CA DEMY OF SCIENCES. [ PROG. 3 D SER. 



absolute. The list of stars, given later, has been taken 

 from Professor Newcomb's "Catalogue of Fundamental 

 Stars for 1875 and 1900, reduced to an absolute System." 

 The apparent zenith distances, or the sums of the zenith 

 distances of the several pairs, are obtained from the 

 Meridian Circle observations; and the differences in the 

 refractions are found by computing the refractions from 

 some standard table. In this work the Pulkowa tables 

 have been used. The term ^(r s r n ) being of the nature 

 of a differential refraction, any error in the constant of 

 refraction of the table used will have practically no effect 

 upon this difference. The more nearly ideal conditions 

 (/. ., when r s =r n ) are approached, of course, the better the 

 determination of the refractions will be. 



This method has both its advantages and its disadvantages. 

 Among the former, the most important are: first, the total 

 elimination of the latitude and hence also of its variation ; 

 second, the elimination of the nadir, since (z' s +z' n ) is 

 nothing more nor less than the difference between the circle 

 readings, and is therefore independent of the zenith point; 

 third, there is no wait of twelve hours or of six months in 

 order to observe a star at both culminations, as is usually 

 done; and fourth, the simplicity of the reductions. 



The greatest disadvantage in this method lies in the fact 

 that the declinations of the stars have to be considered 

 known. But by taking fundamental stars, such as those 

 whose places are given by Professor Newcomb's new 

 Fundamental Catalogue, and by taking a large number of 

 these stars, this difficulty will be nearly completely eliminated. 



Having now the new refractions, the correction to the 

 constant of the table used (Pulkowa) is found from the 

 following equation [eq. (701) pg. 672, Vol. I, Chauvenet, 

 " Spherical and Practical Astronomy''] : 



dr=Ada + Bd, 

 where 



A=I 



a 



and ,,- ~ 



r> -a 2 /^dQ Q 



B = sm^z + - ( - - 

 \/3 W 2/3 



