484 
ASTRONOMY: H. SHAPLEY 
stars. In other words, it is proposed to estimate the distances of clusters 
lacking typical variables on the basis of their bright stars. 
Finally it may be noted that our assumption of the identical lumi- 
nosity of these variables in the various clusters tacitly implies that the 
corresponding variables in the galactic system are all of the same abso- 
lute magnitude. That leads immediately, and without further hypothe- 
sis, to the derivation of highly precise relative parallaxes of the 40 
scattered stars of this type, and as some of these variables are extremely 
faint, the results bear directly on the extent of the general stellar 
system. 
Summary. — (1) The median magnitude of the short-period variables 
apparently has a rigorously constant value in each globular cluster. 
(2) These stars also possess essentially identical spectra and color vari- 
ations. (3) Such phenomena, implying remarkably similar physical 
conditions for all cluster-type variables, must play an important part 
in theories of Cepheid variation. (4) The present use of the photo- 
graphic magnitude observations, however, is to derive accurate relative 
distances of globular clusters on the basis of the differences, from system 
to system, of the mean median magnitude. (5) The method extends nat- 
urally to all isolated cluster- type variables in the galactic system. (6) 
By means of a relation between the median magnitude and the magni- 
tudes of the brightest stars in a cluster, the relative parallaxes of the 
many clusters lacking variables may be estimated with considerable 
assurance when the magnitudes have been measured. (7) The deter- 
mination of the absolute luminosity of some of these variables will give 
immediately absolute individual distances of the clusters and of the 
forty isolated cluster-type variables of known magnitude and period. 
(8) A preliminary value of this absolute median magnitude indicates 
that with one or two exceptions no globular cluster is nearer than thirty 
thousand Hght-years (tt = 0".00012). 
1 Bailey, S. I., Ann. Ohs. Harvard Coll., Cambridge, 38, 1902, (1-252), page 2. 
2 Shapley, H., Mt. Wilson Contrih., No. 91; Astroph. /., Chicago, 40, 1914, (443-447). 
3 Bailey, S. I., Ann. Ohs. Harvard Coll., Cambridge, 78, Part I, 1913, (1-98). 
4 Shapley, H., Mt. Wilson Contrib., No. 115, 1915, (1-92), pages 8 to 22. 
6 Bailey, S. I., Ann. Obs. Harvard Coll., Cambridge, 78, Part II, 1917, (103-192). 
^Ihid., 38, 1902, (1-253). 
