12 KNUT LUNDMARK, GLOBULAR CLUSTERS AND SPIRAL NEBULiE. 



I g — 7( 2 (wJo — -£"+5+51ogjt) 2 



m = #_5_5l grc___£__^____ (3) 



e~**dz 



Here it is supposed, that the luminosity-law has the form given by Kapteyn: 



dM i/sTTTT^r: • w 



Concerning M 3 von Zeipel has found another form for the luminosity-law: 



tp(M)=B(m) (5) 



where B(m) means the number of stars brighter than ra 259 . 



From data that have been at my disposal, I have examined the form of the 

 luminosity-law in M 3, Mil, M 67 and N. G. C. 1647 85 , and found that they give a 

 law of the same form as the one von Zeipel has found 258 . However, these data 

 allow only a determination of the form of the luminosity-curve, but leave a constant 

 dependent on the unknown parallax undetermined, which causes that one cannot 

 enter this law into Kapteyn's integral equation without making special suppositions 

 about the distance or the absolute magnitude of any globular cluster. Hence I have 

 started from Kapteyn's luminosity-law for all spectral classes, given in Groningen 

 Publ. 102 and A. J. 24 103 , of the following form : 



dy{M) _ 0,2 48 ^ (A/ _,, i5)2 , 



dM V ^- e • W 



Just as these lihes were being written, van Schouten's work came under my 

 notice. In a great investigation he has by means of Kapteyn's method examined 

 the luminosity-law and discussed the investigations hitherto made in regard to this 

 question 179 . He finds as the main result a confirmation of the form given by Kap- 

 teyn in Groningen Publ. No. 11 for the dependence of the luminosity on the abso- 

 lute magnitude. In a more recent work 160 he uses this law reduced to the visual 

 Harvard scale and with the aid of calculations from various photometric catalogues 

 examines the parallaxes for a number of clusters, among which the globulars M 3, 

 5, 13 and 11. A slight uncertainty is brought into this investigation by the fact 

 that, at the reduction of the photographic measurements to visual ones, the author 

 has, I suppose, not been able to correct for the spectral types of the stars. The, 

 probably, too high mean value of the parallaxes obtained by van Schouten is, neverthe- 

 less, nearly 28 times lower than that of Charlier, but only 8 times higher than 

 that of Shapley, which speaks in favour of the 1 ätter parallax-system as being the 

 more correct one. 



By using Kapteyn's luminosity-law (6) and integral equation (3), the following 

 values are obtained for the parallaxes of M 3 and 13, if, for both of them, Shapley's 



