76 
STATISTICS: R. PEARL 
Proc. N. a. S. 
What seems to us of considerable interest biologically, is the extraordinary 
perfection, demonstrated in the figures here presented, of the self -regula- 
tion of population growth. Disturbances of the course of the birth rate 
have been compensated for, in the population and period under review, 
with the greatest nicety. It will be of interest to examine the facts for 
other populations, and this we hope later to do. 
^ Papers from the Department of Biometry and Vital Statistics, School of Hygiene 
and Public Health, Johns Hopkins University, No. 50. 
2 R. Pearl, "The Effect of the War on the Chief Factors of Population Change," 
Science (N. S.), 51, 1920 (553-556). 
3 Pearl, "The Vitality of the Peoples of America," A?ner. J. Hyg., 1, 1921, pp. 
592-674. 
* Pearl, "A Further Note on War and Population," Science (N. S.), 53, 1921, pp. 
120-121. 
^ Quarterly Return of Marriages, Births, and Deaths Registered in England and Wales, 
etc. Published by Authority of the Registrar-General. London. H. M. Stationery 
Office. Passim. Also corresponding Weekly Return, and Annual Reports. 
^ " For a Discussion of the Significance and Advantages of Plotting Trend Lines on a 
Logarithmic Scale," cf . Fisher, I. " The 'ratio' Chart for Plotting Statistics," Q. P. Am. 
Stat. Ass., 15, 1917, pp. 577-601, and Field, J. A., "Some Advantages of the Logarithmic 
Scale in Statistical Diagrams," J. Pol. Econ., 25, 1917, pp. 805-841. 
^ E. M. Elderlon, "Report on the English Birth Rate. Part I. England North of the 
Humber." Eugenics Lab. Mem., 19 and 20, Cambridge Univ. Press, 1914, pp. viii 
and 246. 
SEASONAL FLUCTUATIONS OF THE VITAL INDEX OF A POPU- 
LATION' 
By Raymond Pearl 
DSPARTM^NT OF BlOMBTRY AND VlTAI. STATISTICS, JOHNS HOPKINS UNIVERSITY 
Communicated, February 14, 1922 
In earlier papers the writer^ has discussed various aspects of the birth- 
death ratio, or vital index of a population, including age and sex specific 
vital indices, racial and secular fluctuations, etc. Table 1 of the preceding 
paper by Pearl and Burger^ gives the necessary data for finding, for one 
population, that of England and Wales, the course of the seasonal fluctua- 
tion of this important demographic constant. It is the purpose of this 
note to set forth biometrically the facts on this point, from the basic data 
mentioned. 
Table 1 gives the frequency distributions for variation in the value of 
the vital index of the population of England and Wales in each of the four 
quarters of the year, ending, respectively, on March 31, June 30, September 
30, and December 31, during the years 1838 to 1920, inclusive. The 
source of the data is given in Pearl and Burger already cited. 
The significant biometric constants from table 1 are presented in table 
2. It is apparent that there are a few highly aberrant observations in 
