84 PROCEEDINGS OF THE AMEEICAN ACADEMY 



He suggests the employment of rectangular co-ordinates of the 

 various stars, assuming their relative distances according to magnitude, 

 as estimated by W. Struve. In this way he obtained the following 

 positions of the point towards which the motion is directed : — 



' Z) = 39° 29' ) 



^^ , - r 5 ^'i*^h different modes of treatment: 

 , =:26 44 ) 



J=:25G°54',Z) = 39°29' 

 = 261 29 



and his assistant Dunkin, from more stars, the following : — 



^=:261°14'.0, ^ = 32°55'.0> •,..,, \ .. . 



y , with Airy s two modes oi treatment. 

 = 263 43.9, =25 0.5) 



The proper motions here employed are the Rev. R. Main's, derived 

 from a direct comparison of the positions of the 12 and 6 year Green- 

 wich Catalogues with Bessel's Bradley, and are consequently (upon 

 the whole) more accurate than Miidler's, though not including so many 

 stars. A good many of them are substantially equal to the similar 

 values used by Argelander or Lundahl, Airy employed 113 and 

 Dunkin 1,167 stars: the former set are those whose proper motions 

 are the largest. 



Kovalski has used a similar method, employing Miidler's proper 

 motions, and assuming all the stars to be equidistant from the sun. 

 His results were in general similar to tliose of previous investi- 

 gators. 



III. But unfortunately both Airy an-d Dunkin express still some 

 doubt about the reality of the result ; for the sum of squares of the 

 observed motions is diminished by only one twenty-fifth part on the 

 introduction of the solar motion ; so that, although the accordance of 

 the various positions of the pole of motion is gratifying, the suggestion 

 is made by Dunkin that some improvement in our knowledge both of 

 stellar proper motions and stellar distances is yet necessary. 



IV. INIeauvvhile Argelander has within a few years cqllected the 

 materials for discussing the proper motions of several hundred stars, 

 mostly of the smaller magnitudes, which on this account had. been 

 previously overlooked. As the matter now stands, there are between 

 fifty and sixty known stars whose annual proper motion is greater 

 than 1'': not much more than half of these are visible to the naked 

 eye. So that, it seems, magnitude is a very uncertain criterion of 

 proper motion ; and all the evidence shows that it is als>o an uncertain 

 test of distance from us. 



V. Some years ago I made the attempt to determine the solar 

 motion from the 250 stars investigated by Argelander in the first part 



