Astronomy. — ''The Disiribntion of the absolute Magnitudes among 

 the Stars in and about tlie Milky ITn?//." (First Communication). 

 By Dr. W. J. A. Schouten. (Communicated by Prof. J. C. 

 Kapteyn). 



(Communicated in the meeting of October 26, 1918). 



1. Introduction. 



One of the most itnpoi-tant problems of statistical astronomy is to 

 examine, how in each part of space the stars with bright and faint 

 absohite magnitudes are mixed and of which percentage of stars the 

 luminosity lies between definite limits. Luminosity means the apparent 

 brightness, which a star would have at (lie unit of distance, and for 

 this unit we will take, in imitation of Professor Kapteyn, the distance 

 corresponding to an ainiual parallax rr = 0".l.. 



The first determination of the luminosity law was performed by Pro- 

 fessor Kapteyn and published in l*ubl. (lyoningeii N". 11 '). After- 

 wards several astronomers, employing different methods, have repeated 

 this investigation. Besides the studies of Comstock and Walkey, who 

 availed themselves of measured parallaxes, and whose results therefore 

 are not much to be relied upon, unless great cautiousness is used, 

 the researches of Seeligrr and Schwarzschild are well-known. In 

 our dissertation ') we have discussed the three methods mentioned, 

 and we have compared the results that were found. It appeared that 

 serious objections may be raised against Seeliger's investigation, so 

 that we cannot attach much value to the frequency-function of abso- 

 lute magnitudes found by him. We think we have also demonstrated 

 in our work just cited that the method of Kapteyn is for various 

 reasons greatly to be preferred to that of Schwarzschild. 



After we had finished this inquiry an earnest wish arose in us to 

 establish the luminosity law according to the method which we think 

 the best. It was known to us, that such a determination had been 



1) Also in these Proceedings, Vol. Ill, p. 658. 



2) On the Determination of the Principal Laws of Statistical Astronomy. Am- 

 sterdam, Kirchner 1918. 



