1112 



stars; bilt at the same time that the spread of the K stars is much 

 larger than that of the B stars. In consequence of this ciicumstance 

 there is a compcCratively large number of intrinsic bright K stars 

 and therefore it is possible that for a certain bright M the K stars 

 outnumber the B stars. For such absolute brightness the average 

 colour-index will be larg.3 and it maj be larger yet than for a 

 fainter absolute magnitude. 



In order to work out this |)roblem still further, Prof. Kapteyn 

 has deduced from Contrib. Mt. Wilson Observ. N'. 82, Fubl. Gron. 

 N'. 11 and from an article of Kohlschutter on the luminosity- 

 curve of the /'T stars, unpublished as yet, the number of, stars per 

 unit of volume near the sun, of each spectral type between the 

 abs. magn. — 0.5 and -J- 0.5. 



If we assume the luminosity-curve to be of the form 



h 



Prof. Kaptp:yn found that the curves of each type are determined 

 by the following values, of the constants K and h. 



We shall suppose as a first approximation that there are only 

 A stars and K stars and in concurrence with Seares, that their 

 mean colour-indices are respectively -|- 0.2 and -|- 1.3 '). From the 

 data, mentioned above, we now calculate the relati\e frequencies 

 of each spectrum (in the present instance A and K) for every 

 absolute magnitude and fioin these we deduct for every M the 

 mean colour-index in the mixture of A and K stars. 



These calculations have been performed by Prof. Kapteyn and 

 the results have been compared with Shapley's results for J/<e,s-.«Vr 13. 

 In order to be able to do this, he assumed that the parallax of this 



1) According to the above investigation of Schwarzschild the A stars are, if 

 M=0.0, 377,) and the K stars 31" „ of the total number. 



