1110 



We assume that the liimiuositj-curve of Kapteyn shows the 

 frequencies of the different absolute magnitudes in the stellar clusters 

 observed, //the values that shall be found from the successive values 

 for the parallax, correspond, we may conclude that our hypothesis 

 is true. 



Most calculations, wanted for our investigation, had been performed 

 already, when Shapley began ro publish his interesting "Studies based 

 on the Colors and Moj^nitudes in Stellar Clusters' ^). In these he had 

 found i.a. remarkable results about the relations between colour and 

 magnitude. If from his researches it were to follow that the distribution 

 of colours in stellar clusters differs from that in the remaining part 

 of space, it is vei-y improbable thai we should find then the same 

 luminosity -curve. In order to examine how far this results from what 

 Shapley found, we must compare the distribution of colours found 

 by him with that among the stars of the same absolute magnitude 

 in a well-defined part of space. The latter is, however, only imperfectly 

 known. No great value can be put upon investigations about stars 

 with a measured parallax because of the selection of parallax stars. 

 One of the most impoitant contributions towards the solution of this 

 problem was given by Schwarzschild in his " Ueher die Hau/i(/keit 

 und Leuchtkraft der Sterne von verschiedenem Spektraltypus' "). He 

 made use of the component which is at right angles to the direction 

 towards the apex of the proper motions in Boss' Preliminary General 

 Catalogue. If we enlarge the table, occuriing on page 510 of' his 

 work, by interpolation and express the numbers in percentages of 



1) Gontrib. Mt Wilson Observatory Nos. 115, 116, 117 and 126; Proc. Nat. Acad, 

 of Sciences, Vol. I. page 483; Vol. 11, page 525; Vol. Ill, page 25, 267, 276 and 479. 



2) Sitzungsberichte Akademie Berlin 1914, p. 489-510. 



