The method of _graphical extension_. This is the quickest and most simple of all. In this method a curve is plotted on rectangular coordinates to any convenient scale, with population as ordinates and years as abscissas. The curve is extended into the future by judgment of its general tendency. An example is given of the determination of the population of Urbana, Illinois, in 1950. Table 4 contains the population statistics which have been plotted on line A in Fig. 8 and extended to 1950. The probable population in 1950 is shown by this line to be about 21,000.
The method of _geometrical progression_. In this method the rate of increase during the past few years or decades is assumed to be constant and this rate is applied to the present population to forecast the population in the future. For example the rate of increase of population in Urbana for the past 7 decades has varied widely, but indications are that for the next few decades it will be about 20 per cent. Applying this rate from 1920 to 1950 the population in 1950 is shown to be about 17,800. It is evident that this method may lead to serious error as insufficient information is given in the table to make possible the selection of the proper rate of increase.
────┬──────────────────────────── │ Urbana, Illinois ────┼──────────┬────────┬──────── Year│Population│Absolute│Per Cent │ │Increase│Increase │ │for Each│for Each │ │ Decade │ Decade ────┼──────────┼────────┼──────── 1850│ 210│ │ 1860│ 2,038│ 1828│ 85.6 1870│ 2,277│ 239│ 10.5 1880│ 2,942│ 665│ 22.6 1890│ 3,511│ 569│ 16.2 1900│ 5,728│ 2217│ 38.7 1910│ 8,245│ 2517│ 30.5 1920│ 10,230│ 1985│ 19.4 ────┴──────────┴────────┴────────
────┬─────────────────────────────────────────────────────────────── │ Population of ────┼───────┬────────┬─────────┬────────┬──────┬───────────┬──────── Year│Decatur│Danville│Champaign│Kankakee│Peoria│Bloomington│ Ann, │ │ │ │ │ │ │ Arbor │ │ │ │ │ │ │Michigan │ │ │ │ │ │ │ ────┼───────┼────────┼─────────┼────────┼──────┼───────────┼──────── 1850│ │ 736│ │ │ 5,095│ 1,594│ 1860│ 3,839│ 1,632│ 1,727│ 2,984│14,045│ 7,075│ 5,097 1870│ 7,161│ 4,751│ 4,625│ 5,189│22,849│ 14,590│ 7,368 1880│ 9,547│ 7,733│ 5,103│ 5,651│29,259│ 17,180│ 8,061 1890│ 16,841│ 11,491│ 5,839│ 9,025│41,024│ 20,484│ 9,431 1900│ 20,754│ 16,354│ 9,098│ 13,595│56,100│ 23,286│ 14,509 1910│ 31,140│ 27,871│ 12,421│ 13,986│66,950│ 25,786│ 14,817 1920│ 43,818│ 33,750│ 15,873│ 16,721│76,121│ 28,638│ 19,516 ────┴───────┴────────┴─────────┴────────┴──────┴───────────┴────────