284 STATISTICS: PEARL AND REED Proc. N. A. S. 
TABLE 3 
P.ESULTS OF Fitting Population Data 1790 to 1910 by Equation (xviii) 
YEAR 
OBSERVED 
POPULATION 
CALCULATED POPULA- 
TION BY EQUATION 
(xviii) 
ERROR 
1790 
3,929.000 
3,929.000 
0 
1800 
5,308,000 
5.336.000 
+ 28,000 
1810 
7,240,000 
7.228.000 
— 12,000 
1820 
9,638,000 
9,757.000 
+ 119,000 
1830 
12,866,000 
13.109,000 
+243,000 
1840 
17,069,000 
17,506,000 
+437,000 
1850 
23,192,000 
23,192,000 
0 
1860 
31,443,000 
30,412,000 
—1,031,000 
1870 
38,558,000 
39,372,000 
+ 814,000 
1880 
50,156,000 
50,177,000 
+ 21,000 
1890 
62,948,000 
62,769,000 
— 179,000 
1900 
75,995,000 
76,870.000 
+ 875,000 
1910 
91,972,000 
91,972,000 
0 
equation (xviii) gives nearly or quite as good a fit to the observations 
as does the logarithmic parabola. If we properly graduated the data, 
by the method of moments, we should probably get a result measurably 
better than that from equation (iii) . 
The significance of the result lies in this consideration. A curve which 
on a priori grounds meets the conditions which must be satisfied by a true 
law of population growth, actually describes with a substantial degree of 
accuracy what is now known of the population history of this country. 
Let us examine some further consequences which flow from equation 
(xviii). The first question which interests one is this: when did or 
will the population curve of this country pass the point of inflection, and 
exhibit a progressively diminishing instead of increasing rate of growth? 
From (xii) it is easily determined that this point occurred about April i, 
1 91 4, on the assumption that the numerical values of (xviii) reliably 
represent the law of population growth in this country. In other words, 
so far as we may rely upon present numerical values, the United States 
has already passed its period of most rapid population growth, unless 
there comes into play some factor not now known and which has never 
operated during the past history of the country to make the rate of growth 
more rapid. This latter contingency is improbable. While prophecy is a 
dangerous pastime, we believe, from the fragmentary results already 
announced, that the 1920 census will confirm the result indicated by our 
cur^^e, that the period of most rapid population growth was passed some- 
where in the last decade. The population at the point of inflection works 
out to have been 98,637,000, which was in fact about the population 
of the .country in 19 14. 
