G. W. Colles, Jr. — Distance of the Stars. 263 



lar motions are accurately known, this result can be of little 

 practical value at the present stage of astronomy. As an 

 interesting example of the principle, however, it may be worth 

 while to apply it, making the best use of the material at hand. 

 As nearly all the stars, whose velocities in the line of sight 

 have been measured, are in the northern hemisphere, I will 

 find the mean distance ot stars in this hemisphere only. The 

 annexed table includes the available data, gathered from the 

 following sources : the right ascensions, north polar distances 

 and magnitudes are taken from the " Catalogue of Almanac 

 Stars" in Professor Pickering's Annals of Harvard College 

 Observatory, 1890, the positions being reduced to 1900 - 0. 

 The proper motions are computed from the Greenwich Ten 

 Year Catalogue of 1887, and where possible, also, from 

 JSTewcomb's list in Astronomical Papers for the American 

 Ephemeris and Nautical Almanac (1882), the latter measure- 

 ments being given the greater weight. The data of the last 

 two columns are taken partly from Schemer's new Spectral- 

 analyse and partly from the record of observations at Green- 

 wich and Potsdam given in the Monthly Notices of the Royal 

 Astronomical Society. From this table we find, neglecting 

 signs, 



2(a) = 18*670, in seconds of arc per year. 

 2(a) ■=. 1620 - 7, in miles per second. 



Before dividing the latter value by the former, we must reduce 

 them to the same units by constant factors. With this altera- 

 tion, our equation may be expressed as 



v ; 2 c 3 2(a) 2(a)' 

 in which, taking our unit of length as the mile, 



C x = 86400X365-256, 



80X3600 



7tC 



C = — '= 10,224,841,560,000 ; 



giving us as a mean distance 



M(fZ) = 887,595, 11 1,000,000 miles, 



equivalent to 9,59o,000 astronomical units, or about 150*9 

 light-years. 



Before going further, however, it is necessary to return to a 

 consideration of our values for line-of-sight motions, on 

 whose accuracy the result chiefly depends. A glance over the 

 table will show that they fall at once into two classes : Yogel's 



