1912.] AND OTHER CHARACTERISTICS OF STARS. 577 



The mean absolute magnitudes agree almost perfectly with those 

 already derived for other groups of stars, showing that we have 

 come again upon just the same giant and dwarf stars in still a dif- 

 ferent way. The computed masses, although subject to errors 

 which may in some cases be as great as 50 per cent., show that the 

 brighter stars are more massive than the fainter, but that the dif- 

 ferences in mass are small compared with those in luminosity. 



We may go farther with the aid of the information regarding 

 stellar densities which can be obtained from the eclipsing variables, 

 which are mostly of classes B and A. The average density of the 

 eclipsing variables of class B is about one seventh of the Sun's 

 density. We may therefore estimate that a typical star of the class, 

 with seven times the sun's mass, is between three and four times the 

 sun's diameter, and has about 15 times his superficial area. But we 

 have already found that such a star, on the average, gives out more 

 than 200 times as much light as the sun. Hence its surface bright- 

 ness must be about 15 times as great as that of the sun. In the 

 same way it is found that stars of class A must exceed the sun 

 five-fold in surface intensity. On the other hand, the faint stars of 

 classes K5 and M give off on the average about i/ioo of the sun's 

 light, with masses exceeding half the sun's. Even if they were as 

 dense as platinum, their surface brightness could not exceed 1/15 

 that of the sun. 



This diminution of surface brightness with increasing redness, 

 which has been proved to exist among the dwarf stars, is in obvious 

 agreement with the hypothesis (now well established on spectro- 

 scopic grounds) that the principal cause of the differences between 

 the spectral classes is to be found in differences in the effective 

 surface temperatures of the stars ; and the numerical results here 

 obtained are in good agreement with those computed by Planck's 

 formula from the effective temperatures derived by Wilsing and 

 Scheiner from their study of the distribution of energy in the 

 visible spectrum. 



That the same law of diminution of the surface brightness with 

 increasing redness holds true among the giant stars is highly prob- 

 able, for giant and dwarf stars of the same spectral class are almost 



