Vol. 6, 1920 
STATISTICS: PEARL AND REED 
279 
to him, namely, the census counts of 1790, to 1860, inclusive, he would have 
got this result: 
y = 8,619,800 -5,680,540^^ + 822,709x^+ 16,987,200 log x (iv) 
If he had calculated from this equation the probable population in 
1910, the figure he would have obtained would have been 92,523,000, a 
result only approximately a half million, or 0.6%, in error, as subsequent 
events proved. A prophecy less than 1% in error of an event to happen 
50 years later is undeniably good predicting. 
POPULATION OF UNITED STATES 
/OO,OOO.000 
80,000,000 
9, 064, 90O - 6,281,- 1-30 x * 
342,37*^ x\ * I9j^d29,50(p log x 
(50,000000 
40,000000 
20,000,000 
o\ I I i I I I t I 1 I 1 i I i 
/BOO mio leto I630 mo • /eso laeo jsro leeo /eoo j9oo i9io 
YEAR 
FIG. 1 
Diagram showing observed and calculated populations (from logarithmic parabola) 
from 1790 to 1920. 
It is of interest to exhibit the equations and results in predicting the 
1910 population obtained by fitting our logarithmic parabola to the data 
available after the completion of each successive census from 1870 on. 
We have: 
Data for 1790 to 1870, inclusive: 
y = 8,287,700 -5,300,270:^ + 795,540^t:2 + 15,778,000 log x (v) 
Predicted population in 1910 = 91,201,000. 
Deviation of prediction from actual, 1910 = — 771,000. 
Percentage error = 0.8%. 
Data for 1790 to 1880 inclusive: 
y = 7,981,100 -4,971,040:r + 764,896:\;2 _^ 14,993,500 log x (vi) 
