2 SEE— DETERMINATION OF THE [Januarys. 



Of late years astronomers have given greatly increased attention to 

 "the question of the distances of the stars, and systematic campaigns 

 of the most laborious kind have been carried on by Gill ; Elkin and 

 Chase, of Yale; Kapteyn, of Groningen ; and Schlesinger, at the 

 Yerkes Observatory, Chicago. Some 350 stars have now been 

 studied by the standard method of parallaxes, and for most of these 

 objects, perhaps about 200 in number, fairly satisfactory data have 

 been deduced ; but the method can be extended only to stars within 

 less than 100 light-years of our sun, and is therefore very limited in 

 its applicability, owing to the small diameter of the earth's orbit, 

 and the insensible effects of the annual displacements resulting from 

 the orbital motion of our planet. As nature herself has fixed the 

 limits of this method, astronomers have naturally cast about for 

 other methods of greater generality and have finally developed 

 processes of surprising power, of which an account will be given in 

 the present paper. 



§ I. Outline of the Methods Adopted. 



Among previous investigators who have occupied themselves 

 with the difficult problem of the profundity of the Milky Way the 

 first place will be universally assigned to the incomparable Sir Wil- 

 liam Herschel, who extended his researches over many years, and 

 reached results which were for a time accepted, but have been 

 rejected for three quarters of a century, and yet are now proved to 

 be essentially correct. It is very remarkable and exceedingly unfor- 

 tunate that Herschel's conclusions have been generally rejected by 

 his son, Sir John Herschel, and other astronomers during the past 

 seventy-five years. But before discussing the circumstances which 

 led to this outcome I shall recall the modern attempts at the solution 

 of the problem of determining distances in the Milky Way. 



After the spectroscope came into use and Huggins had applied 

 Doeppler's principle to the motion in the line of sight (1868) it 

 was pointed out by Fox Talbot in 1871 (Brit. Assoc. Report, 1871, 

 p. 34, Pt. II.) that the possibility existed of determining the absolute 

 dimensions of the orbit of a pair of binary stars which had a known 



