ASTRONOMY: H. SHAPLEY 
483 
5%, an accuracy as yet quite unattainable by direct measurement for 
any stellar object except the nearest stars. 
The derivation of a probable value of the absolute luminosity of 
cluster- type variables will be given in the extended paper. Provision- 
ally we observe that the absolute median magnitude is probably within 
the limits —0.5 and +1.5 (unit of distance, tt = 0".01), and on that 
basis the absolute parallax of four of the above clusters is as follows: 
Messier 3 tt between 0*00006 and 0*! 00016 
Messier 5 tt between 0.00007 and 0.00018 
Messier 15 tt between 0.00006 and 0.00015 
CO Centauri tt between 0.00015 and 0.00038 
Only a small number of the globular clusters are known to contain 
short-period variables. The relative distances of the others can be 
estimated, however, on the basis of a relation, found in the clusters 
that contain variables, of the median magnitude to the average magni- 
tude of the brightest stars. To derive this relation the photographic 
magnitudes of all the brighter stars in each cluster were determined, 
excluding stars more distant from the center than 10' as possibly not 
members, and also these within 2' as too liable to uncertainty of meas- 
urement. Of those remaining, the first five in order of brightness were 
discarded as superposed stars, or as non-typical in luminosity. The 
mean magnitude of the next 25 stars, a homogeneous group of highly 
luminous objects, was formed. Thus were obtained the results of 
table 3, which seem as remarkable and as significant for stellar theories 
as the phenomenon of constant median magnitude. 
CLUSTER 
MEDIAN 
MAGNI- 
TUDE 
AVERAGE 
DEVIATION 
NUMBER 
OF VARI- 
ABLES 
MEAN 
MAGNI- 
TUDE 
BRIGHTEST 
25 STARS 
AVERAGE 
DEVIATION 
MEDIAN 
MINUS 
BRIGHTEST 
WEIGHT 
Messier 3 
15.50 
±0.08 
110 
14.14 
±0.16 
1.35 
4 
15.26 
±0.075 
61 
13.92 
±0.15 
1.34 
2 
15.59 
49 
14.28 
±0.18 
1.31 
2 
Messier 2 
8 
±0.22 
1.40 
1 
1.35 
In view of these results it is reasonable to believe that, if short-period 
variables did exist in one of the many globular clusters in which they 
have not been found, their median magnitudes would average about 
1.35 fainter than the average magnitude of the 25 selected brightest 
