52 PROCEEDINGS OP THE AMERICAN ACADEMY 



II. 



ON THE SOLAR MOTION IN SPACE AND THE 

 STELLAR DISTANCES. 



(Second Paper.) 



By Truman Henry Safford. 



In a previous paper, I have examined some of the older known proper 

 motions, and sliovvn that they are favorable to the assumption that 

 the distances of the stars are, upon the average, inversely propor- 

 tional to their proper motions. We cannot expect that this will be 

 eqilally true in all regions of the heavens. It will be necessary, as mate- 

 rials accumulate for the study of this problem, and other collateral ones, 

 to pursue the investigation more into detail ; including more stars, and 

 examining their motions as related to their position on the celestial 

 sphere, and esi^ecially to the apex of solar motion. The present paper 

 contains such a detailed investigation for an important class of stars. 

 Those here investigated are the two hundred and fifty whose proper 

 motions Argelander has discussed in the seventh volume of the Bonn 

 Observations, Part I. ; I am myself preparing for another purpose a 

 similar discussion of about one hundred and fifty more, and other ma- 

 terial of the same kind is soon to be published in great quantities. So 

 that the present paper is also of use in fixing the form of the discussion. 

 From the formula3, — 



cos "^ = sin D sin d -{- cos D cos d cos (« — A) ; 



sin ^ cos 'ip' = — sin D cos 5 -\- cos D sin d cos (« — A); 



sin / sin \p' =. cos D sin (« — A) ; 



/i a cos 8 = /I g sin ip ; 



/J d = /] g cos xp ; 



where 



a, 8, the star's right ascension and declination, 



J a, /i d, its annual proper motion in these co-ordinates, 



A, D, the right ascension and declination of the apex of solar mo- 

 tion assumed known, 



;f, the star's angular distance from the apex, 



xp', the angle of position at the star of the arc of a great circle 

 directed away from the apex, 



xp, the angle of position of the star's apparent motion, 



are calculated the values of the followinji table. 



