vary among smaller areas, such as individual States, counties, and cities; but the sample was not large enough to yield reliable estimates for such areas. In interpreting the figures on erroneous omissions and erroneous inclusions, it should be recognized that these are defined with respect to the listings for a given census enumeration district. (See table B.) For example, some of the "omitted" cases represent the listing of a person in the wrong census enumeration district rather than his complete omission from the census. Such cases will be included in both the estimate of erroneous omissions and the estimate of erroneous inclusions (since such persons enumerated in the wrong census enumeration district are both omitted from the listing where their names should appear and included in a listing where their names should not appear). In the absence of duplicate enumeration these cases do not affect the net error. They do, however, affect the other values estimated in table B. report all addresses where they might have been enumerated. On the basis of a check against the listings for the census enumeration districts containing the reported addresses, it is estimated that about 400,000 persons were enumerated in the wrong enumeration district. This estimate is subject to some bias owing to incompleteness of address reports. Some persons were enumerated in the wrong enumeration district simply because the enumerator used the wrong boundary. The estimate of 400,000 may be subtracted from the estimates of erroneous omissions and erroneous inclusions if interest is restricted to those errors which affect the census tabulations for the United States as a whole. Actually all of the persons enumerated in the wrong enumeration district were enumerated in the correct region and most were enumerated in the correct State, so that this group of errors has practically no effect on either national or regional tabulations and an extremely small effect on State tabulations. Sampling variability of the Post-Enumeration Survey results.— The limitations of the Post-Enumeration Survey results have been discussed above. An additional limitation is, of course, the presence of sampling variability. Estimates of standard errors are presented in table C. In the interpretation of the Post-Enumeration Survey estimates, it should be remembered that the chances are about 2 out of 3 that the figures estimated from the sample (tables A and B) differ from those that would have been obtained from a post-enumeration survey of the entire population by amounts less than the standard error indicated in this table. The chances are about 19 out of 20 that the estimates are within twice the standard error of the figures which would result from a post-enumeration survey of the entire population. TABLE C.-STANDARD ERROrs of Coverage Error StATISTICS FOR PERSONS: 1950 Total [Range of 2 chances out of 3] 35 0.2 38 33 сл 5 Estimated standard error of specified types of coverage error 0.2 Persons who should have been Size of estimate of coverage error 99 0.1 91 0.1 5 In households properly in cluded. Population of the United States, Its Territories, The population of the United States, its Territories, possessions, etc., was about 154,230,000 on April 1, 1950 (table 1). If the population of the Philippine Islands is excluded from the 1940 total, the increase over the 10-year period was nearly 20,000,000, or 14.9 percent. Puerto Rico accounted for well over three-fifths of the population outside continental United States, and the Territories for more than one-sixth. The population abroad, principally members of the armed forces and members of their families, numbered close to 500,000. Population of Continental United States The population of continental United States on April 1, 1950, million, or 14.5 percent, over the corresponding figure for April 1, 1940 (table 2). In absolute numbers this increase is greater than the increase during any previous intercensal period. In relative terms, however, the increase between 1940 and 1950, although more than double that for the decade 1930 to 1940, is of roughly the same order of magnitude as the increases during the decades 1910 to 1920 and 1920 to 1930 and falls far short of the decennial rates of increase which occurred during the nineteenth century. An examination of the decennial rates of increase since 1790 indicates that during each of the seven decades up to 1860 the population increased by approximately one-third. On the basis of a correction made for the known underenumeration in 1870, the percentage increases for the decades 1860 to 1870 and 1870 to 1880 become, respectively, 26.6 and 26.0 rather than 22.6 and 30.1. (See footnote 3 of table 2.) On the basis of these revised were all in the neighborhood of 25 percent.2 The decennial rates of increase in the period 1890 to 1910 were about 20 percent and those for the period 1910 to 1930, about 15 percent. The percentage increase for the period 1930 to 1940, the decade of the depression, represents an all time low. Center of Population and Area The "center of population" is defined by the Bureau of the Census as that point which may be considered as the center of population gravity of the United States; in other words, the point upon which the United States would balance, if it were a rigid plane without weight and the population were distributed thereon with each individual being assumed to have equal weight and to exert an influence on a central point proportional to his distance from that point. The center of population of the United States moved westward from the State of Indiana into the State of Illinois between 1940 and 1950. The 1950 center of population is located in Denver township, Richland County, Ill., 8 miles north-northwest of Olney. This point is on a line between Cincinnati and St. Louis, about two-thirds of the distance to St. Louis. In terms of latitude and longitude, the 1950 center is located at latitude 38°50'21' North, longitude 88°9'33" West. During the decade from 1940 to 1950, the center of population moved 42 miles westward and 7.6 miles southward, reaching its most southerly point as well as its most westerly point. This westward movement of the center of population between 1940 and 1950 is the greatest during the present century and exceeds all movements westward since that for the decade of 1880 to 1890. The longest movement westward was during the decade from 1850 to 1860 when the center advanced 80.6 miles. The shortest movement westward was during the decade from 1910 to 1920 when it advanced only 9.8 miles. The point farthest north was the 1790 location, and the point farthest south, the 1950 location; but the difference is only 30.1 miles. The total westward movement from 1790 to 1940 was 644 miles. Table D and the accompanying map give the approximate location of the center of population at each census from 1790 to 1950. The position of the "center of area," that is, the point on which the surface of the United States would balance if it were a plane of uniform weight per unit of area, is located in Smith County, Kans. (approximate latitude 39°50′ North, longitude 98°35′ West). For a more extensive analysis of population growth in the United States during the nineteenth century, see U. S. Bureau of the Census, A Century of Population Growth, U 8. Government Printing Office, Washington, D. C., 1909, * In the actual calculation, the center of population is first assumed to be approxi mately at a certain point. Through this point a parallel and a meridian are drawn, each crossing the entire country. In the determination of the center of population in 1930 the point selected was the intersection of the parallel lat. 39° N. with the meridian af long. 85° W. I he product of the population of a given area by its distance from the assumed parallel is called a north or south moment, and the product of the population of the area by its distance from the assumed meridian is called an east or west moment. In the calculation of north and south moments, the distances are measured in minutes of latitude; in calculating cast and west moments, it is necessary to use miles because of the unequal length of the degrees and minutes of longitude in different latitudes. The population of the country is grouped by "square degrees"—that is, by areas included between consecutive parallels and meridians- as they are convenient units with which to work, The population of the incorporated and unincorporated places with 25,000 inhabitants or more is then deducted from that of the respective square degrees in which they he and treated separately. The center of population of each square degree is assumed to be at its geographical center, except where such an assumption is manifestly incorrect; In these cases the position of the center of population of the square degree is estimated as nearly as possible. The population of each square degree north or south of the asmed parallel is multiplied by the distance of its center from that parallel; a similar callation is made for the incorporated and unincorporated places with 25,000 inhabitants or more; and the sum of the north moments and the sum of the south moments are ascertained. The difference between these two sums, divided by the total populatom of the country, gives a correction to the latitude. In a similar manner the sums of the east and of the west moments are ascertained and from them the correction in Approximate location 85 32 53 8 miles north-northwest of Olney, Richland County, Ill. 2 miles southeast by east of Carlisle, Haddon township, Sullivan County, Ind. 3 miles northeast of Linton, Greene County, Ind. 8 miles south-southeast of Spencer, Owen County, Ind. In the city of Bloomington, Ind. 6 miles southeast of Columbus, Ind. 20 miles east of Columbus, Ind. 8 miles west by south of Cincinnati, Ohio (in Kentucky). 48 miles east by north of Cincinnati, Ohio. 20 miles south by east of Chillicothe, Ohio. 23 miles southeast of Parkersburg, W. Va.1 16 miles south of Clarksburg, W. Va.1 19 miles west-southwest of Moorefield, W. Va. 16 miles east of Moorefield, W. Va.! 40 miles northwest by west of Washington, D. C. (in Virginia). о " 1950... 38 50 21 88 9 33 1910... 1920. 1910. 1900. 39 10 21 39 10 12 9 36 38 56 54 87 22 35 3 45 87 8 6 86 43 15 86 32 20 85 48 54 1890. 1880. 39 11 56 4 8 84 39 40 1 West Virginia was set off from Virginia Dec. 31, 1862, and admitted as State June 19, 1863. Area and Density The gross area, land and water, of the territory under the jurisdiction of the United States at the time of the 1950 Census was 3,628,130 square miles (table 1). The Territories, possessions, etc., had an area of 605,743 square miles and constituted 16.7 percent, or one-sixth, of the aggregate area. The area in 1790 was 892,135 square miles, or somewhat less than one-fourth of the present area, and embraced substantially all the territory between Canada and Florida and between the Atlantic Ocean and the Mississippi River, together with part of the drainage basin of the Red River of the North. This original territory and the successive major accessions of territory from 1790 to 1920 are shown on the map which appears on page 5. In 1803 the area of the country was nearly doubled by the Louisiana Purchase; and, between 1840 and 1850, three large accessions of territory resulted in further increases aggregating 1,204,896 square miles, equivalent to two-thirds of the former area. For continental United States, the population per square mile of land area in 1950 was 50.7 (table 2). Beginning with the Census of 1790 in which the population per square mile was 4.5, the figures at each subsequent census have shown an increase in density with the exception of those for the Censuses of 1810 and 1850. In each of these years, the density was lower than it had been in the immediately preceding census because of large accessions of sparsely populated territory in the preceding decade. Urban and Rural Areas According to the new definition that was adopted for use in the 1950 Census, the urban population comprises all persons living in (a) places of 2,500 inhabitants or more incorporated as cities, boroughs, and villages, (b) incorporated towns of 2,500 inhabitants or more except in New England, New York, and Wisconsin, where "towns" are simply minor civil divisions of counties, (c) the densely settled urban fringe, including both incorporated and unincorporated areas, around cities of 50,000 or more, and (d) unincorporated places of 2,500 inhabitants or more outside any urban fringe. The remaining population is classified as rural. According to the old definition, the urban population was limited to all persons living in incorporated places of 2,500 classified as urban under special rules relating to population size and density. In both definitions, the most important component of the urban territory is the group of incorporated places having 2,500 inhabitants or more. A definition of urban territory restricted to such places would exclude a number of equally large and densely settled places, merely because they were not incorporated places. Under the old definition, an effort was made to avoid some of the more obvious omissions by the inclusion of the places classified as urban under special rules. Even with these rules, however, many large and closely built-up places were excluded from the urban territory. To improve the situation in the 1950 Census, the Bureau of the Census set up, in advance of enumeration, boundaries for urban-fringe areas around cities of 50,000 or more and for unincorporated places outside urban fringes. All the population residing in urban-fringe areas and in unincorporated places of 2,500 or more is classified as urban according to the 1950 definition. (Of course, the incorporated places of 2,500 or more in these fringes are urban in their own right.) Consequently, the special rules of the old definition are no longer necessary. For the convenience of those who are interested in the trend of the urban and rural population, the 1950 population is shown in accordance with the old definition as well as in accordance with the 1950 definition. Although the Bureau of the Census has employed other definitions in the course of its history, the statistics on the population by urban and rural residence shown for years prior to 1940 are consistent for the most part with the 1940 definition. The count of urban places according to the new urban definition includes all incorporated places of 2,500 or more regardless of location and unincorporated places of 2,500 or more. Incorporated places of fewer than 2,500 inhabitants which lie in the urban fringe are not recognized as urban places even though their population is counted as urban. Under the old definition, all incorporated places of 2,500 inhabitants or more and all areas classified as urban under special rules were recognized as urban places. Thus, although the urban population under the old definition was exactly the population living in urban places, the urban population under the new definition includes persons living in territory outside urban places, that is, in incorporated places under 2,500 and unincorporated territory included in the urbanfringe areas. The rural population is by no means identical with the farm population, that is, the population living on farms. (The ruralnonfarm population of the United States exceeds the rural-farm population.) Practically all of the farm population, however, is rural. Statistics on the farm population are presented in Chapter B of this volume. There were no urbanized areas delineated in the Territories or possessions. The urban population in Alaska, Hawaii, and Puerto Rico comprises all persons living in places of 2,500 inhabitants or more. Urban and Rural Population Under New and Old Definitions Under the new urban-rural definition, 96,467,686 persons, or 64.0 percent of the population of the United States, were classified as urban. The remaining 54,229,675 persons constituted the •The areas urban under special rules in 1940 were of 3 types. The first type was limited to the States of New Hampshire, Massachusetts, and Rhode Island, in which States it is not the practice to incorporate as municipalities places with fewer than 16,000 inhabitants. This type was made up of towns (townships) in which there was village or thickly settled area having 2,500 inhabitants or more, and which comprised, either by itself or when combined with other villages in the same town, more than 50 percent of the total population of the town. The second type of areas urban under special rule was made up of townships and other political subdivisions (not mcorporated as municipalities nor containing any areas so incorporated) with a total of 10,000 or more and a population density of 1,000 or more per square mile. The third type of area urban under special rule consisted of 7 places-1 in Vermont and 6 in Maine which had been classified as urban places in 1930 but about whose status as rural population. The urban population according to the old definition was 88,927,464, and the rural population was 61,769,897. The 1950 urban population according to the new urban definition consisted of the following: (a) The 86,550,941 inhabitants of the 3,883 incorporated places of 2,500 inhabitants or more; (b) the 1,994,727 inhabitants of the 401 unincorporated places of 2,500 inhabitants or more; and (c) the 7,922,018 persons living in the urban-fringe areas but outside the incorporated places of 2,500 or more. Under the old definition, the urban population consisted of the 86,550,941 inhabitants of the 3,883 incorporated places of 2,500 inhabitants or more and the 2,376,523 persons living in 140 of the areas classified as urban under special rules in 1940. (There were 141 such areas in 1940. One of the areas, Claremont town, Sullivan County, N. H., was incorporated as a city in 1948; and, consequently, was classified as urban because it was an incorporated place of 2,500 or more.) Table E presents a cross-classification of the population by urban and rural residence under the new and old urban-rural definitions. As shown in this table, 88,589,867 persons were living in territory classified as urban under both definitions and 53,892,078 were living in territory classified as rural under both definitions. Of the population classified as urban under both definitions, 86,550,941 were residents of incorporated places of 2,500 inhabitants or more. The remaining 2,038,926 of these persons were classified as urban under the old definition because of residence in areas urban under special rules; under the new definition 1,718,422 were classified as urban because of residence in unincorporated territory included in urban-fringe areas and 320,504 because of residence in unincorporated places of 2,500 inhabitants or more. An additional 7,877,819 persons were classified as urban under the new definition, 6,203,596 because of residence in urbanfringe areas (577,992 of whom were living in incorporated places under 2,500 inhabitants and 5,625,604 in unincorporated territory) and 1,674,223 because of residence in unincorporated places of 2,500 or more; these persons were included in the rural population under the old definition. On the other hand, 337,597 persons living in the areas urban under special rules according to the old definition were included in the rural population according to the new definition. To summarize, the urban population under the new definition included 6,203,596 persons living in urban-fringe areas and 1,674,223 persons living in unincorporated places of 2,500 inhabitants or more who would have been included in the rural population under the old definition. On the other hand, 337,597 persons living in areas urban under special rules according to the old definition were classified as rural according to the new definition. The net increase in the urban population which resulted from the change in definition, therefore, is 7,540,222, or 5.0 percent of the total population of the United States. In terms of the population classified by urban and rural residence in accordance with the old definition, the change in definition resulted in an increase of 8.5 percent in the urban population and a decrease of 12.2 percent in the rural population (table 14). The population of the incorporated places of 2,500 inhabitants or more constituted 89.7 percent of the urban population under the new definition and 97.3 percent of the urban population under the old definition. The population living in other territory in the urban-fringe areas accounted for 8.2 percent of the urban population under the new definition, and the population in unincorporated places of 2,500 inhabitants or more accounted for the remaining 2.1 percent. Table 3 presents the 1950 and 1940 population of the 140 areas urban under special rules in 1940 (omitting Claremont) and the classification of their 1950 population by urban and rural residence in accordance with the new definition. Of the 140 areas, only 4 had all of their population classified as rural under the new definition, whereas 21 had all of their population classified as urban under the new definition. The 337,597 persons Trends in Urban and Rural Population, 1790 to 1950 Trends in the urban and rural population can be examined only on the basis of the old definition. On this basis, the urban population increased from 74,423,702 in 1940 to 88,927,464 in 1950, and the rural population from 57,245,573 in 1940 to 61,769,897 (table 15). The gains of 14,503,762 in the urban, and 4,524,324 in the rural, population represented increases of 19.5 and 7.9 percent, respectively. The numerical gain in the urban population was second only to the increase of 14,796,850 recorded in the decade 1920 to 1930 and marked the seventh consecutive decade in which the numerical increase in the urban population exceeded that in the rural population. The numerical increase in the rural population was the largest since the gain of 4,993,205 for the decade 1890 to 1900. In 1790, 1 out of every 20 of the 3,929,214 inhabitants of the United States was living in urban territory (table 15). In every decade thereafter, with the exception of that from 1810 to 1820, the rate of growth of the urban population exceeded that of the rural population. By 1860, one out of five persons was included in the urban population. The process of urbanization continued in the following decades, and by 1920 the urban population exceeded the rural population. In 1950 about three out of every five persons were living in urban territory. Places Classified According to Size There were 5 places of 1,000,000 or more in 1950; 101 places of 100,000 to 1,000,000; 378 places of 25,000 to 100,000; 3,800 places of 2,500 to 25,000; and 4,437 places of 1,000 to 2,500 (tables 5a, 5b, and K). On the other hand, the places of 1,000,000 or more contained 11.5 percent of the total population; those of 100,000 to 1,000,000, 17.9 percent; those of 25,000 to 100,000, 11.8 percent; those of 2,500 to 25,000, 17.6 percent; those of 1,000 to 2,500, 4.6 percent; and the remaining 36.6 percent lived in smaller places, the unincorporated parts of urban fringes, and the open country. If we regarded each urbanized area as only one "place," the distribution would be somewhat different. For example, "places" of 1,000,000 or more would then contain 25.1 percent of the population and areas outside places of 1,000 or more would account for only 31.7 percent (table 5a). Again, historical comparisons of groups of places according to size can be made only in terms of the old urban definition (table 5b). Population changes in the size-groups of largest places may be very great because the inclusion or exclusion of a single metropolis has a very marked effect. New York City first achieved a population of a million at the Census of 1880. At that time it included 2.4 percent of the national population total. By 1950, the five places of this size-class included 11.5 percent of the total. The number of places in all but two size-groups has tended to increase steadily up through the latest census. The number of places of 250,000 to 500,000 has been about the same since 1930, but here there are too few cases for the determination of the recent trend. The number of incorporated places of less than 1,000 has declined slightly since 1930. In terms of population, all size groups have a remarkably consistent history of growth, except, again, for the very smallest incorporated places. In terms of percentage of the total population accounted for, the picture is less consistent. In general, the larger size-classes have gained relative to the smaller ones, but there are several recent exceptions. The peak proportion of the United States total was reached in 1930 for both cities of 1,000,000 or more and cities of 250,000 to 500,000. Places of 5,000 to 10,000 represent the smallest class that has been increasing its share. Areas outside places of 1,000 or more, which included 60.9 percent of the population in 1890, included only 37.4 percent in 1950. APPORTIONMENT Apportionment Population The primary reason for the establishment of the decennial census of population, as set forth in the Constitution, was to provide a basis for the apportionment of members of the House of Representatives among the several States. Such an apportionment has been made on the basis of every census from 1790 to 1950, except that of 1920. Prior to 1870, the population basis for apportionment was the total free population of the States, omitting Indians not taxed, plus three-fifths of the number of slaves. After the apportionment of 1860 the fractional count of the number of slaves, of course, disappeared from the procedure; and in 1940 it was determined that there were no longer any Indians who should be classed as "not taxed" under the terms of |