872 



only vvitli great difficulty, how far the results are based on extra- 

 polafion ^). 



Another drawback of the method is that we cannot inquire into 

 the dependence of (f{i) or ip ( K) on r. Moreover we are obliged 

 to assume that there is no such thing as absorption of the light 

 in space. 



In Schwarzschild's application of his method it was not investi- 

 gated, how the density varies with the galactic latitude. This is, 

 however, possible, if we have sufTicient data at our disposal. 



Several objections that may be raised against Schwarzschild's 

 method do not exist with respect to Kapteyn's method, with which 

 we dealt in a formei' communication. 



Yet we have also derived from our data of observation the 

 frequency curve of absolute niagnitudes in Schwarzschild's manner. 

 None of the methods proposed till now is entirely unassailable. 

 By applying methods based on different hypotheses we can judge 

 of the correctness of the suppositions that have been ujade and find 

 more reliable results. 



A great advantage of Schwarzschild's method is that it distinctly 

 represents the connection of the different quantities and enables us 

 to judge, whether the values found for the unknown quantities 

 coi'respond to each other and form a consistent system. 



In Astron. Nachr. N'. 4422 Schwarzschild has solved the two 

 problems above mentioned and has also given Jiumerical results of 

 the unknown quantities. Use was made of the luminosity curve, 

 derived by Kapteyn in Astron. Journal N'. 566 and of the numbers 

 iV„, published by him in Fuhl Groningen N'. 18. For log. Nm 

 Schwarzschild found : 



log. i\,n — 0.596 + 0.5612 m — 0.0055 ;«' .... (3) 



From these data the density was derived and the mean parallaxes :rr„,. 



In his second article Schwarzschild investigated in which way 

 the chief stellar statistical quantities depend on the three principal 

 laws and gave formulae to calculate the different quantities. An 

 exact application of the method requires, when we use the general 

 form of the functions, a very comprehensive arithmetical labour. 

 This is only advisable if a very large amount of data of observation 

 are at our disposal. Therefore suppositions were made about the 

 form of the unknown functions. 



1) How one may obtain strange results by such unallowed extrapolation is seen, 

 for instance, when Gharlier (Meddelanden Observ. Lund, Serie II, N^. 8, p. 21) 

 derives from the formula of Kapteyn and Schwarzschild, which is cited in this 

 communication by (3), that the numbers Nm increase up to m — 51. 



