4 KNUT LUNDMARK, GLOBULAR CLUSTERS AND SPIRAL NEBULJE. 



Sir W. Herschel 77-83 attempted with the aid of the magnification, which in his great 

 reflector was required in order to distinguish the stars in the particular globular 

 clusters, and the thereby calculated »space-penetrative power» of the instrument, to 

 determine the distribution in space of these objects. Afterwards many results have 

 been obtained, which throw some light upon the question of the real position in 

 space of the globular clusters and spiral nebulae, but no decision can yet be said to 

 have been made as to the latter. On the other hand, very remarkable results re- 

 garding the distribution in space of the globular clusters are given through the great 

 researches made by Shapley 188 - 207 and Charlier 37-39 . Although their results strike 

 us as very contradictory, there seems to exist some possibility of explaining — at 

 any råte partly — the origin of the comparatively small distances for globular 

 clusters, calculated by Charlier. 



In a series of extensive investigations Shapley has determined individual.pa- 

 rallaxes for 69 globular clusters, or all objects that have with certainty been identi- 

 fied as such. Almost at the same ti me, Charlier in an extensive treatise has sol ved 

 this problem by another method, and he, thereby, for his clusters gets distances, 

 which fall below the corresponding values found by Shapley by 40—290 times. 

 With regard to the great importance of this question I have therefore considered 

 it justifiable here to publish a few small calculations and deliberations, which may 

 possibly contribute to the knowledge of the relations of globular clusters and spiral 

 nebula? to the stellar system. 



The starting-point for Shapley's parallax-measures is the remarkable relation 

 between the length of period and the absolute magnitude of the S-Cephei variables, 

 which was first discovered by Miss Leavitt 117 . After having with great accurateness 

 established this connection anew from more recent data, Shapley, presuming that 

 the considerable number of cluster-variables (blink-variables, antalgol stars) found 

 in certain globular clusters are to be considered as ö-Cepheids with the same qualities 

 as the ones found in the Milky Way, deduces the absolute magnitude M for these, 

 from which the parallax tt comes forth, according to the well-known formula: 



M = m + 5 + 5 log ;:. (1) 



After having by this method obtained parallaxes for the globular clusters in which 

 cluster-variables have been observed, or N. G. C. 5272, 5904, 6205, 6656, 7078 

 and 5139, and the small Magellanic cloud, Shapley finds that the mean of the ab- 

 solute magnitude of the 25 brightest stars in a globular clusters has a constant 

 value of 



m m 



Jf = — 1,51 ±0,3. 



By means of this law empirically found, Shapley obtains the parallaxes of the 

 28 globular clusters, for which it has been possible to determine the apparent magni- 

 tude of the brightest stars. 



