486 
ASTRONOMY: SHAPLEY AND DAVIS 
Proc. N. a. S. 
as they are distributed in the layers and shells of the Lewis-Langmuir 
static atom. The ratio, vjv^, of the K critical absorption frequency 
for tungsten to the Rydberg fundamental frequency is 5118 according to 
the theory, which is exactly our experimental value (see table 1). The 
agreement to four figures between the two values must be regarded as a 
matter of chance, however, as the errors in both the experimental and cal- 
culated numbers amount to a fraction of 1%. 
^ See Sommerf eld's paper on the fine structure of the jS-line (Miinchener Akademie, 
June 1, 1918 (367)). 
2 Professor Siegbahn kindly communicated these results by letter. 
3 Physik. Zs., 19, 1918 (441, 465). 
4 Phil. Mag., June, 1919 (601). 
5 Comptes Rendus, May 25, 1920 (1245). 
« Sitz. Ber. Bayr. Akad. Wiss., June, 1918. 
^ Since this explanation was presented to the Physical Society in February, papers 
by W. Kossel and A. Sommerfeld (Zeitschrift fiir Physik, Jan., 1920) have reached us. 
In these papers the same explanation for the discrepancy is discussed as that here put 
forward. 
STUDIES OF MAGNITUDE IN STAR CLUSTERS, XIL SUM- 
MARY OF A PHOTOMETRIC INVESTIGATION OF THE 
GLOBULAR SYSTEM MESSIER 3"- 
By Hari^ow ShaplKy and Heji^En N. Davis 
Mount Wilson Observatory, Carnegie Institution of Washington 
Communicated by G. E. Hale, June 24, 1920 
1. The study at Mount Wilson of the distances and structure of stellar 
clusters is of necessity based upon observations extensive in number and 
considerably varied in character. When general and comprehensive 
results have been obtained for a few typical systems, it becomes possible 
to interpret more accurately the less detailed observations on other clusters, 
and to place greater confidence in the hypothesis of the galactic system 
that has developed from the investigations of cluster and variable stars. 
For two open clusters. Messier 67 and 11, and for two globular clusters, 
Messier 13 and 3, fairly complete surveys of the photographic and photo- 
visual magnitudes of the individual stars have now been carried through 
and published in some detail; for about forty other systems the photo- 
metric and spectral investigations have been of a special character, and, 
in publishing the results, the observational data have for the most part 
only been summarized. 
2. The catalogue of magnitudes and colors of 848 stars in Messier 3, 
which is appearing as Mount Wilson Contribution No. 176, ^ was begun in 
1915. Fourteen photographs, made at the primary focus of the 60- 
inch telescope, have been used for the ten thousand measures of magnitude 
involved in the investigation. Special care was taken to look into the 
