525 



Gro7iingen N». 8 hy a factor _VA^^R^'iN . The parallaxes, which may 



KAPTEYN 



be applied to the whole sky, are given in table 2. 



We ourselves have not tried to determine once more the probable 

 deviation of. the error curve log. Vrm- Moreover we have supposed 

 that (> does not vary with the galactic latitude. We made use of 

 the value 0.19, found by Kapteyn both in ouv solution for the whole 

 sky and in that foi- the 5 galactic zones. It has, however, been 

 proved in l^uhl. Gronuigen N". 11 that the value of (> has only 

 little influence on the result. 



3. Applying Kapteyn's Method. 



We have applied Kapteyn's method without any modification. For 

 a description in detail of this method we refer to his treatise iu 

 PuhL (rroniiu/en N". 11, which we cited already above. We shall 

 limit ourselves lo a short discussion of the hypotheses that have 

 been made and an explanation of the tables mentioned, in this essay. 



The hypotheses, made in Kapteyn's investigations, are three iu 

 number : 



l^fiy the density is only a function of r; 



2"f^'.^ the luminosity curve is independent of the distance from 

 the sun and there is no absorption of light in space; 



3^1^ the quantities z — log. "'^o are distributed according to the 

 law of errors. 



The first hypothesis is necessary if we want to derive frequency- 

 funclions that may be applied to the whole sky. We seek for mean 

 values for the unknown quantities and so we cannot take into 

 account the variations in the values with the galactic latitude and 

 longitude. Kapteyn's method may, however, be used just as well, 

 if we want to reckon with the influejice of the galactic latitude by 

 making separate solutions for the different galactic zones. 



The second hypothesis can hardly l)e dispensed with. If we have 

 certainty thai the frequency-function of absolute magnitudes is 

 everywheie the 8ame in space, Kapteyn's method offers the means 

 to examine, whether there is a perceptible extinction of light and, 

 on the other hand, when we know that there is nx) absorption we 

 can examine if the luminosity curve varies with the distance from 

 the sun. As neither one thing nor the other, however, is certain, 

 we are obliged for the time being to make the supposition in 

 question. 



If we establish the frequency- function for the different galactic 



