570 RUSSELL— RELATIONS BETWEEN SPECTRA [Ap"1 20, 



contained in a given region of space, we would find the disparity to 

 be 100 to I the other way. 



It is therefore a fortunate circumstance that the stars whose 

 distances have been measured have for the most part been chosen, 

 not on account of apparent brightness, but because of relatively 

 rapid proper-motion — which is found by experience to be a fairly 

 good indication of actual nearness to our system. These stars, 

 therefore, represent mainly the sun's nearer neighbors, without 

 such an egregious discrimination in favor of stars of great actual 

 brightness as we have seen must occur if we choose our stars by 

 apparent brightness alone. Some traces of this discrimination will 

 still be unavoidable, for our knowledge of the proper-motions of the 

 fainter stars is still imperfect, and stops short at a little below the 

 ninth magnitude. 



In addition to the stars whose parallax has been directly ob- 

 served, we have data for many more, which belong to clusters 

 whose distances have been found by combining data regarding their 

 proper-motions and radial velocities. In this case too the absence 

 of proper-motion data (which decide whether or not a star really 

 belongs to the cluster) prevents us from obtaining information 

 about stars fainter than a certain limit; but otherwise our knowl- 

 edge is probably fairly complete. 



In the present discussion of the relation between the spectral 

 type and the real brightness of the stars, those directly measured 

 parallaxes have been employed which are confirmed by the work 

 of two or more observers, and also a few results obtained by single 

 observers whose work is known to be of high accuracy, and free 

 from sensible systematic errors. To these have been added the 

 members of the Hyades, the Ursa Major group, the "61 Cygni 

 group" and the moving cluster in Scorpius discovered independ- 

 ently by Kapteyn, Eddington, and Benjamin Boss. The spectra of 

 a very large number of these stars have been determined at Har- 

 vard especially for this investigation, and the writer takes pleasure 

 in expressing his most hearty thanks to Professor Pickering and 

 Miss Cannon for this generous and invaluable aid. 



The actual brightness of the stars may best be expressed by 



