1114 



Hertzsprung calculated the mean period and the theoretical parallax 

 of 13 (f Cepliei variable stars, mentioned in Boss' catalogue, and 

 therefore also their absolute magnitudes. With a period of ö'Vö, M 

 was found to be — 2,3 (visual magn.)- With these data we can find 

 for every (f Cephei variable star the parallax, if its period and 

 magnitude are known. 



In four cases in which such variable stars in the cluster are 

 known, we have indicated which result is found for the parallax 

 by this method. 



No great accuracy may be expected from Hkrtzsprung's method, 

 ingeniously devised though it may be. The scale of magnitudes on 

 which Miss Leavitt's researches are based, lias evidently not been 

 checked very accurately. Hertzsprung's determination of the mean 

 absolute magnitude of <f Cephei variable stars Wcis based on the 

 parallactic movement of only 13 stars. Therefore Shapley ') proposed 

 that we should cor'.fine ourselves to the variable stars in theelusters 

 that have a short period. As it is \ ery conspicuous that all variable 

 stars in Me.'isier 3 and }fes.üer 5 have all the same period, Shapley 

 presumes that all (S Cephei stars in the stellar clusters have the 

 same M everywhere. To a period of 0^154, according to Hertzsprung, 

 corresponds, in connection with the law found by Miss Leavitt, 

 il/=:-^l"\5 fphotogr.). Shapley begins by supposing 71/ to lie 

 between —0,5 and -|- 1.5 (photogr.). We tiien can determine the 

 parallax from the mean magnitude of the variable stars. 



Our results are made to agree perfectly with those of Shapley, if 

 we take for the absolute magnitudes of the variable stars: 



in Messier 3: i¥=-l-4.2 (photogr. magn.) 

 „ Messier 5 : = -1- 4.0 

 ,, Messier 13: = -}" ^-^ 

 in the Small Magellanic Cloud : zn -f~ ^-^ 



So there is an agreement between the determinations of parallaxes 

 from variable stars and those obtained by the aid of the luminosity- 

 curve, if the mean magnitude of the variable stars in the clusters 

 is fainter by a couple of magnitudes than is assumed by Hertzsprung 

 and Shapley. 



By way of example we shall determine in the above manner the 

 parallax of two clusters. For the application of this method to other 

 sidereal clusters we refer to a communication that will follow later on. 



1) H. Shapley, A Method for tlie Determination of the relative Distances of 

 globular Clusters. Proc. Nat. Acad. Vol. Ill, 479, July 1917. 



