174 CARNEGIE INSTITUTION OF WASHINGTON. 



rediscussion, including more recent data, yields similar curves for Allegheny, 

 McCormick, and Mount Wilson, but the forms of the curves for Yerkes and 

 Sproul are considerably altered. 



PROPER-MOTIONS OF THE CEPHEID VARIABLES. 



From correlations of their parallactic and peculiar motions derived from 

 proper-motion and radial-velocity data, supplemented by the discovery that 

 in this class of stars the absolute magnitude is a function of the period, Shapley 

 found in 1918 that the Cepheid variables are exceptionally luminous stars 

 very distant from us, the distances of some of the individual stars being as 

 much as 20,000 light-years. Reasoning upon the assumption that the stars 

 of this class found in the globular clusters are of the same luminosity as those 

 outside of them, he was led to the startling conclusion that the diameter of 

 the stellar system must be about 300,000 light-years, ten times as large as 

 most of the earlier investigators had indicated it to be. One of the most 

 fundamental weaknesses in his deductions seemed to be in determining the 

 mean distance of the Cepheids from the proper-motions of but eleven of them. 



With these considerations in mind, Dr. Wilson made during the past 

 year a survey of all the positional data available for stars of this class, includ- 

 ing the San Luis and Albany unpublished observations. This survey resulted 

 in the determination of the proper-motions of 73 stars, to which were added 

 11 recently determined elsewhere. Investigation of the material showed 

 that for a discussion of the distances of stars with as small apparent motions 

 as those exhibited by the Cepheids, only the better material could be used, 

 as there appeared a marked dependence of the apparent motion upon the 

 errors of determination. In the final analysis the proper-motions of 55 stars 

 were used. The parallaxes derived from the correlation of the proper- 

 motion and radial-velocity data for different period groups closely paralleled 

 those derived by Shapley, It was shown that there is no evidence of an error 

 in Shapley's system of parallaxes exceeding 40 per cent, in contrast to the 

 seven or eight fold increase demanded by other investigators, and that the 

 most probable correction indicated by the material under discussion is in the 

 nature of an increase of approximately 30 per cent. If we accept the deduc- 

 tions based upon the relative magnitudes of the cluster and noncluster 

 Cepheids, we must conclude that the diameter of the stellar system is some- 

 where between 200,000 and 250,000 hght-years. 



PROPER-MOTIONS OF THE LONG-PERIOD VARIABLES. 

 In last year's report were given certain conclusions based upon an investi- 

 gation of the proper-motions of 154 red stars. Since that time a large 

 amount of additional material has become available, making possible a much 

 more thorough discussion of the motions, mean distances, and luminosities 

 of these stars. As the great majority of them are variables, the scope of 

 the investigation was enlarged to include all the long-period variables. The 

 proper-motions of about 400 of these stars have been determined by Dr. 

 Wilson during the year. An analysis of the motions by types shows that 

 the stars of Class N present in their motions peculiarities which may in part 

 be real but which are shown to be due in part, at least, to their peculiar dis- 

 tribution in the sky. Excluding those of Class N, the remaining 302 stars 

 give as the position of the apex of solar motion : 

 A = 275?5, D = -f31?7 



