519 



in course of preparation at the Astronomical Laboratory at Gronin- 

 gen for a long time already. 



In this prepai'ation are included the countings of stars of deter- 

 mined magnitude which are published in Publ. Groningen N"^^ 18 

 and 27, and the mean parallaxes of stars of determined magnitude 

 and galactic latitude, which will soon be pul)lished and have been 

 kindlj lent us for our use by Prof. Kaptkyn and Dr. Van Rhijn. 



It is a matter of course that the preliminary results obtained by 

 us, should be replaced by those of the dellnitive solution as soon 

 as these are available. Yet we thought we might publish our results 

 as they are pai-tly based on other data, because they give a notion 

 of the exactness that is to be obtained now already, and our preli- 

 minary results might be of some service perhaps until the time 

 that the definitive shall have appeared. 



In this communication we mention the results that we found, 

 when we tried to determine the luminosity law according to Kapteyn's 

 method for the whole sky and for five zones of different galactic 

 latitude. 



We intend to publish in a second communication the results that 

 are found, when Schwarzschild's method is applied to the same 

 data. At the same time we hope to compare oui- results with those 

 of other investigators. 



In this article we also gratefully tender our sincere thanks to 

 Prof. Kapteyn for his kind help, which favoured our investigation. 



2. Tlie Data of Observation. 



In applying Kapteyn's method we have to take from the obser- 

 vations the following data : 



1. the numbers iV,»,^. i.e. the numbers of stars of determined 

 apparent magnitude and proper motion, 



2. the mean parallaxes n-,„„ of stars of determined magnitude and 

 proper motion, 



3. the value of q, the probable error ol" the erroi' curve log. '^/tto 

 in which .-r is the real and -t, the probable parallax. 



In our investigation we divided the sky into 5 zones. The galactic 

 latitude we shall indicate by h. 



Zone 1 = part of the sky between h = — 10"^ and b = + 10°. 



Zone 11 = , , , , with /> from — 10^ to — 30° and + 10° to + 30°. 



Zone III- , . , , „ ft , _30° , -50° , + 80° . -}- 50°. 



Zone IV = . , . , , ft , -50° , -70° , + 50° , + 70°. 



Zone V = ft , -70° , -90° , -f- 70° , + 90°. 



