6 KNUT LUNDMARK, GLOBULAR CLUSTERS AND SPIRAL NEBUL^. 



Charlier supposes, that the 800 bright Helium-stars, for which he has, by 

 the method employed by him, determined individual parallaxes 38 , form a skeleton to 

 the Galaxy. Partly by supposing that the centre of the system of globular clusters 

 is situated as far from the galactic plane as the centre of the Helium-star system, 

 and by supposing the dispersion a{z) in the same direction to be as great in both 

 systems, Charlier obtains two determinations of the scale-value. 



In order to get a synoptical comparison between Charlier's and Shapley's 

 investigations, I have put together their results in the adjoining table, where Char- 

 lier's distances are reduced to parallaxes and the ratio between Charlier's and 

 Shapley's parallaxes is given in the fourth column. As Charlier has employed 

 only Bailey\s diameter-values for obtaining the relativa parallaxes, I have in Col. 

 5—10 put together determinations based upon the photographic plates that were at 



0*zs 



H+O 0'aoaliO 



Fig. 1- Charlier's parallax- values considered as a function of Shai>i.ey's values. 



The values of ~ cA . 



The values of ~' c ; 4 . 



my disposal. In this table, B, M, P, Sh, D and Liz denote the estimations of the 

 diameter made by Bailey, Melotte, Perrine, Shapley, Davis and by the present 

 writer using the Wolf-Palisa charts, the Harvard Annals, Vol. 26 and 38, and, in 

 some cases, my own plates. Col. 12 contains the relative parallaxes calculated in 

 accordance with Charlier's formulse out of the mean given in Col. 11 and multiplied 

 with a constant e f , with the determination of which I am going to occupy myself 

 in the following. Col. 13 contains the ratio between Charlier's parallaxes, thus 

 reduced, and Siiapley's values. 



From the table it is evident that the ratio between tt^ and n gh (Col. 4) is 

 dependent on the value of the parallax. If the parallaxes are arranged aocording 

 to their numerical value, and if means are calculated, the above curve is obtained, 

 which gives the relation between the parallaxes in the two systems. 



We are now going to try to determine e' without employing any of the sup- 

 positions, made by Charlier and Shapley, in order to obtain, if possible, a de- 

 cision as to which of the two parallax-systems is nearer to truth. In the Populär 



