Vol. 6, 1920 
STATISTICS: PEARL AND REED 
277 
worked out in the Biological Laboratory of the Maine Experiment 
Station, such diverse phenomena as change of size of egg with successive 
layings, change of milk production with age, etc. Donaldson and Hatai^ 
have demonstrated the applicability of this type of equation to bodily 
growth in the white rat and frog. 
While the increase in size of a population cannot on a priori grounds be 
regarded, except by rather loose analogy, as the same thing as the growth 
of an organism in size, nevertheless it is essentially a growth phe- 
nomenon. It, therefore, seems entirely reasonable that this type of 
curve should give a more adequate representation of population increase 
than a simple third-order parabola. The actual event justifies this 
assumption, as will presently appear. 
Table 1 shows the counted population as determined by the Census 
Bureau on the dates mentioned from 1790 to 1910. The exact dates were 
furnished in a personal communication from the present Director of the 
Census. These figures embody some adjustments and corrections made 
by the Census Bureau since the original censuses were made. 
TABLE 1 
Showing the Dates of the Taking of the Census and the Recorded Populations 
FROM 1790 TO 1910 
DATS OF CENSUS 
RECORDED POPULATION 
(revised figures FROM 
STATISTICAL ABST., 1918) 
Year 
Month and Day- 
1790 
First Monday in August 
3,929,214 
1800 
First Monday in August 
5,308,483 
1810 
First Monday in August 
7,239,881 
1820 
First Monday in August 
9,638,453 
1830 
June 1 
12,866,020 
1840 
June 1 
17,069,453 
1850 
June 1 
23,191,876 
1860 
June 1 
31,443,321 
1870 
June 1 
38,558,371 
1880 
June 1 
50,155,783 
1890 
June 1 
62,947,714 
1900 
June 1 
75,994,575 
1910 
April 15 
91,972,266 
To the data of table 1 the following equation was fitted by the method 
of least squares, taking origin at 1780, and making due allowance in the 
abscissal intervals for the actual dates of the several censuses : 
y — a -{- hx -{- c%^ + d log % 
where y denotes population and x time. The actual equation deduced was 
y = 9,064,900- 6,281,430^ + 842,377a;2 + 19,829,500 log (iii) 
