Page:Popular Science Monthly Volume 76.djvu/390

386
THE POPULAR SCIENCE MONTHLY

 A. ${\displaystyle P=89.7}$ C. ${\displaystyle P=89.7}$ E. ${\displaystyle P=91.4}$ B. ${\displaystyle P=89.3}$ D. ${\displaystyle P=91.4}$ F. ${\displaystyle P=91.3}$

It will be observed that these forecasts fall into two classes, in one of which the numbers run between eighty-nine and ninety millions and the other a little over ninety-one millions. The former are based more strictly upon the formula as it stands, including the entire set of observations. In the latter, greater weight is given to more recent observations, as it is supposed that they represent more nearly the present rate of increase in the population. The last formula (F) is based upon three observations only, those for 1880, 1890, and 1900. It is probable that while the formulæ yielding the lower results conform more nearly to the population of our country in the past, the results which are yielded by the other set of formulæ are more correct for 1910. As an illustration of the closeness with which the formulæ conform to past conditions, we will determine the results for each census by means of formula:

${\displaystyle P=5.13+0.358X+0.666X^{2}.}$

 Year⁠ P (Census)⁠ P (By formula)⁠ Difference⁠ 1800 5.3 5.3 0.0 1810 7.2 6.2 1.0 1820 9.6 8.5 1.1 1830 12.9 12.2 0.7 1840 17.1 17.2 0.1 1850 23.2 23.6 0.4 1860 31.4 31.3 0.1 1870 38.6 40.3 1.7 1880 50.2 50.7 0.5 1890 62.6 62.4 0.2 1900 76.3 75.4 0.9 6.7

The formula published by Dr. H. S. Pritchett, in The Popular Science Monthly, of November, 1900, agreed more closely with the results of past censuses than the one used here. It will be noted that while the sum of the various deviations resulting from each application of the formula is 6.7 millions, that from Dr. Pritchett's formula is only about 4 millions. This formula, however, does not seem to fit the future conditions so well as the one employed here, for it gives a population of 77.5 millions for 1900, while the census returns show it to be 76.3 millions.

As a method of determining the population of the United States during the coming decades, the application of these formulæ is interesting. By the use of formula E—

${\displaystyle P=5.4+0.12X+0.7X^{2}}$