482 
ASTRONOMY: H. SHAPLEY 
taken from Bailey's tabulation with only slight modifications and addi- 
tions.® Subclass a, as the range of variation suggests, is the type that 
prevails in Messier 3 and 5. Although the stars of the three groups 
differ from each other in maximum and in range, as well as in period, 
the median magnitude is the same. The distribution of deviations 
again follows closely the probability curve. As before the short period 
variables are restricted to a small interval of brightness which can be 
represented with high accuracy by a mean median magnitude. The 
whole interval observed in co Centauri is six or seven magnitudes, but 
no fainter variables are found, and the two or three brighter ones are 
long-period Cepheids. The magnitudes used for this cluster are not 
referred to the Mount Wilson system, and, therefore, are not strictly 
comparable with those of the other clusters. They are probably about 
right, although the uncertainty may be as much as half a magnitude. 
4. Ten stars In Messier 2 have been suspected of variation.^ Eight 
have been verified on Mount Wilson plates, but as no comparisons with 
the Pole have been made, only provisional results are available. Meas- 
ures on three plates give the extreme variation as one and a third mag- 
nitudes, agreeing with all that precedes in showing that the short period 
variables are confined to a definite limit of magnitude. 
These results for the variables in five clusters have an obvious appli- 
cation in the determination of relative parallaxes. We need only the 
hypothesis, apparently reasonable in the light of the foregoing discussion, 
that the absolute median magnitudes, which appear so constant in 
each cluster, are actually identical in all systems. The observed dif- 
ferences in the mean values then become sensitive criteria of distance, 
and the relative parallaxes of these remote systems can be known with 
an accuracy which will depend only on the precision with which the 
photographic magnitudes can be determined. 
For instance, we find above that the median magnitude for Messier, 
3 is 15.49=^0.01, and the corresponding value for Messier 5, 15.25=^0.01. 
Possibly there are small systematic errors due to choice of variables, 
to errors in the maxima, or to remaining errors of zero point, which 
are not eliminated in taking the difference. But certainly we know 
the difference in the two median magnitudes within a tenth of a magni- 
tude, and consequently the difference in distance of these remote and 
nearly equidistant clusters within 40% of its value; while the difference 
in distance can be known within 7% of its value, if either cluster is com- 
pared with CO Centauri. And once we find the absolute median magni- 
tude of such variables — by no means a hopeless task — the actual dis- 
tances of all clusters with typical variables can be determined within 
