878 



our deiermination as might perhaps be concluded from the values 

 of k and A; but that the two curves agree very well. 



No real significance can be ascribed to the maximum of the 

 luminosity curves, determined by us, as the numbers for the mag- 

 nitudes 5 and 6, etc. (notation of Kapteyn) are based on the numbers 

 which were found in the nearest vicinity of the sun. But our 

 countings are not complete here, because we excluded stars with 

 P.M. > 50". To this may be ascribed the decrease in the numbers 

 which we observed. 



Very remarkable is the way in which the values for k agree 

 that have been found for the different zones. It is true, there are 

 indications of a systematic difference in the values of k for higher 

 and less high galactic latitudes, but the differences between the 

 values of the numbers are not so great, if we take into consideration 

 the exactness of the data, that we can deduce from them with 

 certainty, that the luminosity curves of the various galactic zones 

 differ. How well the different curves agree, is most evident from 

 the figure which we inserted in our first communication. The six 

 lines in the upper part of the figure relate to the investigation now 

 discussed. 



We are of opinion that we may conclude with a tolerable degree 

 of probability from these results that the frequency curve of absolute 

 magnitudes does not vary with the galactic latitude. And if this 

 should not be entirely correct, then the variation is certainly very small. 



3. Comparison iviih the results of other investigators. 



If we wish to compare the luminosity curves determined or 

 assumed by different investigators in the course of time, then we 

 can perform this best graphically. We have drawn the principal 

 curves in the figure subjoined. 



The curve with the indication "Kaptkyn" represents the luminosity 

 law published in Puhl. Gronim/en N". 11. Our determination accord- 

 ing to the same method, which we marked by the figure II, gave 

 entirely the same result. They do not only agree in form, but the 

 numbers of stars of every absolute magnitude which were found 

 per unit of volume in the neighbourhood of the sun, are quite 

 the same. 



We added in order to make comparison possible a constant amount 



to each number log. N,„ for the other curves. 



Then we have drawn the luminosity curve, that Schwarzschild 

 deduced in A.stron. Nachr. N«. 4557 and also the frequency function, 



