572 RUSSELL— RELATIONS BETWEEN SPECTRA [April 20, 



spending group (giving half weight to a few stars of relatively un- 

 certain parallax or spectrum) — except for the stars of spectrum B 

 with directly measured parallaxes. In this case the parallaxes are 

 so small that a reliable value could he obtained only by taking the 

 mean of the observed magnitudes and parallaxes for the whole 

 group. These stars are of much greater apparent brightness than 

 most of those of class B, and their actual brightness may be 

 greater than the average for the class. No similar error of samp- 

 ling need be suspected in other cases, except for the faintest stars 

 in the clusters, where it is obvious in going over the lists that only 

 a few of the brightest stars of class K5 are above the limit of mag- 

 nitude at which our catalogues of stars belonging to the clusters 

 stop, and probable that some of the fainter stars of class K are 

 also excluded. 



With the exceptions just explained, the results of the two inde- 

 pendent determinations from the measured parallaxes and the 

 clusters are in remarkably good arrangement, considering the small 

 numbers of stars in many of the groups. The absolute magni- 

 tudes of stars of the same spectral class in different clusters are 

 in equally good agreement. The relation between absolute magni- 

 tude and spectral type appears therefore to be independent of the 

 origin of the particular star or group of stars under consideration. 



This relation seems to be very nearly linear, as is shown by the 

 last column of Table I., which gives for each spectral type an 

 absolute magnitude computed by the formula 



Abs. Mag. = 0.5 + 2.2 (Sp. — A), 



in which spectrum B is to be counted as o, A as i, F as 2, etc. It 

 is of interest in this connection to remember that the difference of 

 the visual and photographic magnitudes of the stars is also nearly 

 a linear function of the spectral type. 



The individual stars of each spectral class are remarkably simi- 

 lar in real brightness. Excluding those for which the parallax or 

 spectrum is considerably uncertain, there remain in all 218 stars. 

 Of these only 11, or 5 per cent, of the whole, differ more than two 

 magnitudes in absolute brightness from the value given by the 



