Vol. 6, 1920 STATISTICS: PEARL AND REED 
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to the right of the point of inflection is an exact reversal of the half lying 
to the left of that point. This implies that the forces which during the 
latter part of the population history of an area act to inhibit the rate of 
population growth are equal in magnitude, and exactly similarly dis- 
tributed in time, to the forces which in the first half of the history operate 
to accelerate growth. We do not believe that such rigid and inelastic 
postulates as these are, in fact, realized in population growth. 
The same objections apply to the use of the equation of an autocatalytic 
reaction to the representation of organic growth in the individual. This 
fact has been noted by Robertson^ ^ who was the first to discover that, in 
general, growth follows much the same curve as that of autocatalysis. 
What needs to be done is to generalize (ix) in some such form as will free 
it from the two restrictive features (location of point of inflection and 
symmetry) we have mentioned, and will at the same time retain its other 
essential features. We are working along this line now and hope presently 
to reach a satisfactory solution. 
We attach no particular significance to the numerical results of the 
preceding section. They obviously can give only the roughest approxima- 
tion to probable future values of the population of the United States. 
Our only purpose in presenting them at all at this time is to demonstrate 
that the hypothesis here advanced as to the law of population growth, 
even when fitted by a rough and inadequate method, so closely describes 
the known facts regarding the past history of that growth, as to make it 
potentially profitable to continue the mathematical development and re- 
finement of this hypothesis further. There is much that appeals to the 
reason in the hypothesis that growth of population is fundamentally a 
phenomenon like autocatalysis. In a new and thinly populated country the 
population already existing there, being impressed with the apparently 
boundless opportunities, tends to reproduce freely, to urge friends to come 
from older countries, and by the example of their well-being, actual or po- 
tential, to induce strangers to immigrate. As the population becomes 
more dense and passes into a phase where the still unutilized potentialties 
of subsistence, measured in terms of population, are measurably smaller 
than those which have already been utilized, all of these forces tending to 
the increase of population will become reduced. 
^ Papers from the Department of Biometry and Bital Statistics, School of Hygiene 
and Public Health, Johns Hopkins University, No. 13. 
2 Cf. for a discussion on the relation of curve fitting to true organic laws of change, 
Pearl, R. "Some Recent Studies on Growth," Amer. Nat., 43, 1909 (302-316). 
3 Perrin, K., "On Some Dangers of Extrapolation," Biometrika, 3, 1904 (99-103). 
^ Pritchett, A. S., "A Formula for Predicting the Population of the United States," 
Quart. Publ. Amer. Statistical Assoc., 2, 1891 (278-286). 
^ Pearl, R., "Variation and Differentiation in Ceratophyllum," Carnegie Inst. Wash- 
ington, Publ. 58, 1907 (136). 
^ Cf. the following papers: 
