studies in Stellar Statistics 



29 



The determinant of and being = — 1, these formulae give the values 

 of tn^ aud . 



All parameters of the functions and are in this manner unequivocally 

 determined. 



If the observations should not be represented by the formulae (61) but through 

 any other forms for a{m) and Mm(2'>), then we must have recourse to the general 

 solutions of Schwarzschild. 



Our working plan is now the following: 



1) Try to represent the observational result regarding the brightness aud the 

 mean motions of the stars through relations of the form (61); 



2) If that is possible, the density of the Milky Way and the frequency func- 

 tion for the absolute brightness (— luminosity) of the stars are given by (60), the 

 parameters , o^, and being found from (62) and (62*). 



3) We can add: if (61) are approximately satisfied the general forn:i of 

 and (fo may be found with the help of the general form of frequency curves of 

 type A). 



14. Finishing here, at least for the moment the theoretical treatment of the 

 subject I shall proceed to numerical applications. From the 48 squares, into 

 which we have divided the sky according to § 12, I take the squares aud 

 for which I shall here treat the problem as fully as possible. Tiie square 6'^ is 

 situated at the pole of the Milky Way and the square lies in the Milky Way 

 itself. The material that will here be treated is taken from two different sources : 

 1) the Bonner Durchmusterung (abbreviated BD] and 2) the Cartes du Ciel (abbr. C 

 du C) according to the Paris astrophotographic program. 



The numbers of stars from BD are given in the following table 



Tab. 1. Number of stars in BD. 



m 



c, 



C. 



1.0-1.9 



0 



2 



2.0—2.9 



0 



1 



3.0—3.9 



5 



7 



4.0—4.9 



8 



9 



5.0—5.9 



39 



37 



6.0—6.9 



117 



155 



7.0—7.9 



331 



605 



8.0-8.9 



1473 



3391 



9.0 



562 



1594 



9.1 



306 



854 



9.2 



448 



1525 



9.B 



862 



2409 



9.4 



521 



2254 



9.5 



2625 



8429 



var. 



1 



7 



neb. 



16 



1 



v 



7314 



21279 



