Vol. 8, 1922 
STATISTICS: PEARL AND BURGER 
71 
the purpose at Arequipa. Further observation is necessary before de- 
finitive results can be given, but for the preceding variables provisional 
periods and median magnitudes have been obtaained. 
The numbers, except the last are those published by Miss Leavitt. 
Colons indicate periods not well determined. For stars marked with an 
asterisk a multiple of the period given above satisfies the observations 
nearly or quite as well. 
The light curves are in all cases of the typical cluster form. From the 
plates now available, the elements of variation could not be determined 
for some of the other faint stars, bat for none do the observations demand 
a long period. 
The median magnitudes are derived from published values of maximum 
and minimum, except that for No. 1741 which is a revised unpublished 
value derived by Miss Leavitt, and that for No. 3610 — a hitherto unan- 
nounced variable. The medians are based on a provisional and apparently 
homogeneous system of magnitudes for the comparison stars. The 
standardization of these magnitudes is under way and will permit a new 
evaluation of the medians for the variable stars and a redetermination 
of the distance of the Small Magellanic Cloud. 
The mean of the thirteen periods is 15.4 hours. The mean of the thirteen 
median magnitudes is 16.13 =t 0.05, in close agreement with the median 
magnitude, 16.2, predicted from the extended period-luminosity curve 
for variables of this period. We are led to the conclusion, even after 
making ample allowance for the provisional nature of the magnitude 
scale and for the uncertainties that affect some of the periods, that cluster 
type variables are giant stars in the Small Magellanic Cloud, as previously 
found for certain globular clusters. Naturally we infer that they are 
giants stars wherever they occur. 
THE VITAL INDEX OF THE POPULATION OF ENGLAND AND 
WALES, 1838-1920^ 
By Raymond PearIv and Magdai^en H. Burger 
Department of Biometry and Vital Statistics, Johns Hopkins University 
Communicated, February 14, 1922 
The senior author ^ has suggested the term "vital index" as a convenient 
designation of the function 
100 Births 
V = 
Deaths 
which measures more effectively than any other demographic function 
yet devised the essential biological fitness of a population, in the sense of 
organic evolution. For a population V is the direct measure of survival 
