PROCEEDINGS 
OF THE 
NATIONAL ACADEMY OF SCIENCES 
Volume 6 JUNE 15. 1920 Number 6 
ON THE RATE OF GROWTH OF THE POPULATION OF THE 
UNITED STATES SINCE lygo AND ITS MATHEMATICAL 
REPRESENT A TION' 
By Raymond Peari^ and LowelIv J. Rekd 
Department of Biometry and Vital Statistics, Johns Hopkins University 
Read before the Academy, April 26, 1920 
It is obviously possible in any country or community of reasonable 
size to determine an empirical equation, by ordinary methods of curve 
fitting, which will describe the normal rate of population growth. Such 
a determination will not necessarily give any inkling whatever as to the 
underlying organic laws of population growth in a particular community. 
It will simply give a rather exact empirical statement of the nature of the 
changes which have occurred in the past. No process of empirically 
graduating raw data with a curve can in and of itself demonstrate the 
fundamental law which causes the occurring change. ^ In spite of the 
fact that such mathematical expressions of population growth are purely 
empirical, they have a distinct and considerable usefulness. This use- 
fulness arises out of the fact that actual counts of population by census 
methods are made at only relatively infrequent intervals, usually 10 
years and practically never oftener than 5 years. For many statistical 
purposes, it is necessary to have as accurate an estimate as possible of the 
population in inter-censal years. This applies not only to the years 
following that on which the last census was taken, but also to the inter- 
censal yearis lying between prior censuses. For purposes of practical 
statistics it is highly important to have these inter-censal estimates of 
population as accurate as possible, particularly for the use of the vital 
statistician, who must have these figures for the calculation of annual 
death rates, birth rates, and the like. 
The usual method followed by census offices in determining the popula- 
tion in inter-censal years is of one or the other of two sorts, namely, by 
arithmetic progression or geometric progression. These methods assume 
that for any given short period of time the population is increasing either 
in arithmetic or geometric ratio. Neither of these assumptions is ever 
absolutely accurate even for short intervals of time, and both are grossly 
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