3. The great expense of census enumeration, as well as the time necessary for the analysis of the vast bulk of data secured prevent the performance of annual enumerations. Conse quently where a population basis is required for the data of the intercensal years, estimates must be employed. For this two methods are available, the arithmetical and the geometrical.
(a) Arithmetical estimation: This method infers that a constant yearly increase in the number of the inhabitants has taken place between the censal years and that the same increase will occur for some years following the last census. For employ ment, divide the difference between the population returns of the censuses by the number of years between them. Multiply the quotient by the number of desired years following the census and add the result to the proper census population. Thus supposing the population of an area was 64,4r0 in 1890 and 82,624 in 190o and we desire to estimate the population in 1898 and 1904. Thus Pop. two 82,624 Pop. 1890 64,410 Increase ro years-18,214 divided by io equals 1821.4 per year. For 1898 the population estimated would be 1821.4 times 8, equals 14,571 plus 64,410 equals 78,981. For 1904, the population estimates would be 1821.4 times 4 equals 7285 plus 82,624 equals 89,909. This of course assumes that no census figures for igio were available.
(b) The geometrical estimation assumes a constant rate of increase. For application the following formula is commonly used: Pn equals Pc(r plus r)n Pn equals Pc(r plus r)n Pc For speed, logarithms are commonly employed for the solu tion of the second equation as follows: log. Pn — log Pc equals n log (1 plus r) Supposing that the 1900 census gave an area a population of 70,00o and the 1910 census ioo,000 and we desire an estimate of the 1904 population. Thus according to our formula Pn equals ioo,000, whose log is 5.000 Pc equals 70,000, whose log is 4.851 5.000 — 4.8451 equals o.1549 0.1549 divided by BD equals 0.01549, the log. of 1.036 or (1 plus r) of our formula.
0.01549 times 4 equals o.o62.
log. o.o62 plus log. 4.8451 equals 4.9071, which is the log of 80,75o, the 1904 population.
Each of these methods is best adapted to populations pre senting certain characteristics. The geometrical is best adapted to populations whose increase is due to the excess of births over deaths, while the arithmetical is best adapted to areas where growth is largely due to immigration. The latter is considered
best adapted for use in the United States. It is to be noted with these two methods, that in intercensal years the geometrical method will give results less than the arithmetical, but for postcensal years its results will be greater.
Where long time estimates are required, such as are required for planning the scope of public improvement for a long term of years, neither of these are reliable. It is better to compare the area with the development of other similar areas but of larger population, subsequent to the time when their popula tions were the same as that of the area under investigation.
These methods are not always applicable, as for example, where a population shows stationary indications or has even declined at the last census. Less accurate methods of estima tion only are available and these unfortunately are of no value in vital statistics. Thus we may estimate the population from the ratio of persons per dwelling, if the number of the latter are known. For the United States as a whole this is 5.2. A dwelling is defined as any building or set of rooms housing a family. Or the number of school children or trolley passengers may furnish a rough guide.
4. The commonest data tabulated from census returns rela tive to the composition of the population relates to sex, age, race (Fig. 125) nationality and conjugal condition. Of these age, sex and race are the most important for use in vital statistics. Male births are in excess of female in proportion of 21: 20, but male deaths are in excess of female deaths. The greater migra tory habits of males leads to a diminution in the relative pro portion of the sexes in older communities, so that females are in excess. Conversely in newly settled areas males will predom inate (Fig. 124).
5. Another population distinction of importance from our standpoint relates to the distinction between urban and rural populations. Distinction is upon a purely arbitrary basis. Thus in the 187o census towns of 8000 population or less were considered rural, in 188o, 4000 or less and in 1910, 2500 or less. Thus it can be seen that these distinctions have not been made on a constant basis. In the 187o census 32.90 per cent. of the country's population was urban and in the 188o census 37.3 per cent.