Astronomy. — "The Distribution of the Absolute Magnitudes among 

 the Stars in and about the Mi/kg Wag". (Second Communi- 

 cation). By Dr. W. J. A. Schouten. (Commiinicaled by Prof. 

 J. C. Kapteyn). 



(Communicated in the meeting of November 30, 1918). 



In a foimer communication we have communicated the results of 

 a re8earcii in wliich we determined according to Kapteyn's method tlie 

 mean luminosity curve for the whole sky and the corresponding- 

 curves for zones of different galactic latitude. We intend to communicate 

 in this essay the results that were found by treating the same data 

 according a method first proposed and used by Schwarzschild. 



1. * Schwarzschild's method and his results. 



ScHWARZSCHiLD Starts from the integral formulae that were first 

 framed by Sket-iger. Seeliger made use of the total number of stars 

 from the brightest star to those of determined magnitude. Schwarz- 

 SCHILD, however, uses the number of stars of each magnitude. This 

 is already a great simplification. Besides his work is characterized 

 by a severe nialhematical treatment. His merit consists chiefly in 

 giving an elegant general solution that is applicable to all funda- 

 mental problems of statistical astronomy '). 



Let ISfhdh be the number of stars with an apparent brightness 

 between h and h -|- dh and jr/, their mean parallax, then — if we 

 indicate the density once more by D{r) and the frequency curve of 

 the absolute magnitudes by (p{i) — the following relations are true: 



Nh = 4.n \D{r)(p{hr*)r* dr (1) 







CO 



and iVA ^/. = 4 .-r \D{r) ff (hr') r* dr . . . . . . (2) 







1) His articles have appeared in Astrmi. Nachr. Nos. 4422, 4557 and 4740. 



