1109 



Laboratory at Groningen, was held out. Prof. Kapteyn had the 

 kindness to charge me with this task. For this and for man}- a 

 usefid hint during my investigation 1 tender my best thaid<s. 



In order to determine how nianj stars of every magnitude tiie 

 stellar cluster contains we diminish the number, given in the catalogue 

 by the nornial number for the surface under observation. The latter 

 is calculated with the aid of Publ. Gron. NV 27, Table IV, which 

 table we could consult, thanks to the kindness of Dr. Vam Rhun, 

 even before it had been published '). 



We take as unit the distance corres[)onding to jr = 0".l. The 

 I'elation between the absolute and the apparent magnitude is expressed 

 then by the formula: J\f := m -{- 5 -^ 5 log .t. As all stars of the 

 cluster are at the same distance, the distribution of the absolute 

 magnitudes is the same as that of the apparent. 



^4 „(-1-1 

 We now determine the numbers in which A,a represents the 



A,n 



number of stars of the magnitude m and see from the luminosity- 



Am-\-\ 



curve to which proportion these numbers correspond. Then we 



Am 



know to which M every m corresponds and we can determine jx. 

 We employ the luminosity-curve given by Kapteyn in Publ. Gron. 

 N". 11, Table 6. As we intend to express all magnitudes in the 

 visual Harvard scale the luminosity-curve is also reduced on this 

 scale. We shall find, if we apply a correction Potsdam-Harvard 

 _ _^0"\17: 



^) As we made u.se of visual magnitudes it would have been better to have 

 based our calculations on Table V of the work mentioned. That table was at that 

 time not yet at our disposal. We have ascertained tliat this inexactness can nowhere 

 have had any influence on the results obtained. 



77* 



