;1 \ American Economic Association GONOMIC STUDIES Vol. II. No. 4. Published Bi-Monthly Price, $2.50 per Year AREA AND POPULATION OF THE UNITED STATES AT THE ELEVENTH CENSUS BY WALTER F. WILLCOX, Ph.D. AUGUST, 1897 published for the American Economic Association BY The MacmiIvI/AN Company NEW YORK LONDON : SWAN SQNNENSCHEIN & CO. LIBR/ I Chap... UNITEI ^RY OF CONGRESS. Copyright No. Shelf. > STATES OF AMERICA. PRICE FIFTY CENTS. AMERICAN ECONOMIC ASSOCIATION, Organized at Saratoga, September 9, 1885. OFPICBRS: Ex-Presidents, CharIvES F Dunbar, LL.D., John B. CIvARK, IvL.D. President, Henry C. Adams^ Ph.D. Vice-Presidents, FrANKWN H. GiDDINGS, M.A., K. R. L. G0UI.D, Ph.D., R01.AND P. FaIvKNER, Ph.D. Secretary, WAI.TER F. WllvIyCOX, Ph.D., Cornell University, Ithaca, N. Y. Treasurer, Chari.es H. Huii,, Ph.D., Cornell University, Ithaca, N. Y. Publication Committee, F. W. Taussig, Ph.D., Chairman, Hai-vard University, Cambridge, Mass. John Graham Brooks, Davis R. Dewey, Ph.D., H. H. 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JNO. 4* Price, $2.50 PER Year AREA AND POPULATION OF THE UNITED STATES AT THE ELEVENTH CENSUS BY WALTER F.'WILLCOX, Ph.D. AUGUST, 1897 PXXBLISHED FOR THE American Economic Association BY The Macmii^IvAN Company NKW yOrk LONDON : SWAN SONNENSCHEIN & CO. Copyrighted 1897 by The American Economic Association PRESS OF Andrus & Church, Ithaca, N. Y. AREA AND POPULATION OF THE UNITED STATES AT THE ELEVENTH CENSUS PREFACE. This Study is the first part of a projected Introduction to the Social Statistics of the United States. It will be followed shortly by another on the Density and Distri- bution of their population. From this standpoint the prefatory chapter should be judged. Both Studies are the outcome of lectures on Social Statistics offered to university undergraduates and are published primarily for their convenience, but may be suggestive to others en- gaged in teaching or studying the subject. The writer's conception of statistics is that it is a method of giving pre- cision to knowledge by making quantitative and verifiable statements possible in some fields where they have been precluded. The comparative insignificance for social science of the topics which the statistical method frees from the subjectivity of personal opinion or individual observation should not blind one to the important fact that this method contributes to make progress in knowl- edge possible by liberating certain aspects of it from the labyrinth of personal and unverifiable argument. WALTER F. WIIvLCOX. Cornell university, July, 1897. ,'\ CONTENTS. PAGB Introduction 2^- Chapte;r I.— Area of the United States and its Divisions 211 Chapter II.— Popui^ation of the United States and its Divisions 228 UST OF TABI^ES. I. Area of Countries Controlling over One Million Square Miles 214 II. Gross Area of the States and Proportion of Coast Water, Lake and River Surface 218 III. Comparison of Measured Land Surface of Certain Counties with Census Figures 224 IV. Population of States by Censuses Taken Since 1890 . . . . 243 V. Comparison Between Results of Eleventh Census and Esti- mates 246 VI. Population of the most Populous Countries According to Various Authorities 252 VII. Total Population of Each State and Percentage of Country . 255 INTRODUCTION TO SOCIAI. STATISTICS. The meaning of the word statistics is still a subject of some dispute. In such a case the ultimate authority is not its etymology, but current usage. This author- ity is often vague in its utterances, and offers only an uncertain or ambiguous meaning which persons wish- ing to employ the word with scientific precision, may make more exact, though they may not overrule usage. Judged by this standard, the word statistics refers to the direct or indirect results of counting in the real world about the observer, and no further definite content can be assigned it. The counting may have occurred in any portion of the world. The estimate of the number of stars from enumeration of those in a certain field and multiplication results in statistics. The figures express- ing the annual production of iron, lumber or beef, or the average daily attendance at a fair are statistics. When- ever the word is used, the thought is suspended until the subject to which the figures refer is made known. Statistics of «, ^, or c is always the rounded notion. Nor is this an error of popular speech, which is avoided by exact writers, for experts give it the same meaning. During the meetings of the International Statistical In- stitute at Chicago in 1893, papers were offered upon agri- culture, railways, education, anthropometry, marriage and divorce and crime, and they were all welcomed as statistical.^ By the concurrence of popular and scientific usage, then, the word statistics refers to the results ob- tained in any field of reality by methods of counting.^ 1 Bulletin de Iv'Institut International de Statistique, Tome VIII, Premiere Livraison. 1895. 2Riimeliu, Reden und Aufsatze, 1875, p. 226. 2o8 Economic Studies. The word statistics is derived from the same source as state, but the latter has two root meanings, a condition, as the state of one's health, and a political body, as the state of Portugal, and from which of the two statistics is a branch has been disputed/ Probably, however, statis- tics is derived from state in the sense of a political body and the word then means etymologically the science of states. Its history in brief, is as follows '? Early in the sixteenth century, and partly under the influence of Machiavelli,'^ the disinterested study of politics revived. Its practical aspects received in Italian the name of ragione di stato^ or in barbarous Latin the equivalent ratio status. In these phrases stato or status was the generic name for a political body, while the older and more usual terms, res publica^ civitas and iin- periiLwi.^ were restricted to specific kinds of political bodies. From stato in this sense was formed the Italian statista^ the German and English statist^ a statesman/ ' Some have claimed that both meanings of state were implicate in statistics. This notion apparently finds expression in the defini- tion of Webster, " a collection of facts respecting the condition of the people in a state." ^V. John, Der Name Statistik, in Zeitschrift fiir Schweizerische Statistik, 1883 ; Eng. trans, in J. Royal Stat. Soc, 46 : 656-679, (1883). V. John, G2schichte der Statistik, pp. 4-11. A. Gabaglio, Teoria Generale della Statistica, Vol. i, p. 59, Vol. 2, p. i. ' ** We find in him for the first time since Aristotle the pure passion- less curiosity of the man of science." — Pollock, History of the Science of Politics, p. 42. * Examples of the early use of statist in English, with the meaning of statesman are : 1602 : I once did hold it, as our statists do, A baseness to write fair and laboured much How to forget that learning . . . Shakspere, Hamlet, 5 : 2 : 33. Introduction to Social Statistics. 209 and from this the adjective siatisticiis^ relating to a statesman. The new studies in practical political science were called disciplina politicO'Statistica or in abbreviated form, statistics. That word thus became the name for the studies deemed of especial value to one aspiring to enter the service of a state. The difference between the present and the original meaning of statist and statistics is explained by the fact that the latter word was adopted nearly a century ago as the name of a study having a distinct origin, and pre- viously called ''political arithmetic." This study of society by the enumerating method had its origin in England, and its inspiration in the triumphs of mathe- matical and inductive methods gained in other fields by members of the embryonic Royal Society. It began 1609 : I do believe (Statist though I am none nor like to be) That this will prove a war.— Shakspere, Cymbeline, 2 :4 : 16. 1654 : {wfUten much earlier) To you the statists of long-flourishing Rome. — Webster, Appius and Virginia, i 14 1643: Among statists and lawyers. —Milton, Doctrine and Disci- pline of Divorce. 167 1 : Statists indeed and lovers of their country. — Milton, Paradise Regained, 4:354- As statist in this sense is obsolete the attempt to revive the word as a brief and euphonious substitute for statistician seems to deserve encouragement. A few illustrations of this use may be given. 1870: The keen statist reckons by tens and hundreds.— Emerson, Society and Solitude, (ed. 1876), p. 270. 1877 : The high rate of infant mortality continues to occupy the earnest attention of medical statists.— Farr, Vital Statis- tics, p. 190 1895 : How pleased I am to meet again such a body of statists. I like the old and short word. — W. W. Folwell, in Proceed- ings of Nat. Ass'u of Officials of Bureaus of Labor Statistics, P- 54. 2IO Eco7iomic Studies. with Captain Jolm Graunt, who published his Natural and Political Observations in 1662.^ His conclusions were mainly social rather than physical or biological, and the same is still true of the results obtained by the statistical method. There is, therefore, justification for giving political arithmetic the shorter name derived from the organized political life of man. Popular in- stinct and language were not entirely at fault. While the enumerating method has never been confined to the study of governmental phenomena, yet it is mainly used for the investigation of some aspect of man's social life. This fact is loosely expressed in both terms, political arithmetic and statistics. As the applications of the statistical method widen, it seems better to add some modifying word or phrase defining the subject. The work of which this Study is the opening part will be concerned with the applica- tions of the statistical method to man's social life ; it is therefore entitled Social Statistics. The primary aim, to interest students of society in an unfamiliar method, may be furthered by showing it at work and in connec- tion with its results better than by mere discussion of method. Statements of fact have been incorporated not primarily for their own sake but to elucidate the method. Only the simplest topics under the simplest division, viz., demography or the statistics of population, will be treated, because they best reveal and illustrate it, and in nearly every instance the illustrative facts will be drawn from some portion of the United States. ^ Natural and Political Observations mentioned in a following Index and made upon the Bills of Mortality by John Graunt, Citizen of Lon- don. Ivondon, 1662. CHAPTER I. AREA OF THE UNITED STATES AND ITS DIVISIONS. Area is usually treated in books on statistics as an un- questionable datum, but the imperfect condition of Am- erican surveys makes a brief criticism necessary. Other- wise the trustworthiness of subsequent determinations of the ratio between area and population, i. e.^ densit}^ of population, would be matter of faith rather than of reason. By area is meant the number of units of surface included within certain boundaries, on the assumption that the included surface is all at the level of the sea. In deter- minations of area the unit of reference is a square de- gree. Since its area varies v/ith its distance from the equator, the area for each degree of latitude, and so that between the equator and any two adjacent meridians may be requisite as units. From the measurements of a standard authority on the subject^ the area of the earth's surface, land and water together, is computed as 509,950,778 square kilometers or about 196,899,795 square miles. The area of any country is the sum of all the square degrees lying entirely within its bounds, and of such parts of the degrees cut by the boundary as He within the country. The former are found from BessePs tables or by a geodetic formula; the latter are measured by • F. W. Bessel and J. J. Bayer, Gradmessung in Ostpreussen, Berlin, 1838. Compare M. Levasseur in B. de L'lnst. Int. de Statistique, 1886, 2dme Livraison, p. 23. 212 Economic Studies, the polar planimeter on accurate maps. The maps of the United States, the theme of this Study, are of va- rying excellence and no accurate maps of the boundary of Alaska exist. Hence the official statement of its area " may easily be ten per cent, in error." ^ The boundary of the United States between the Lake of the Woods, Minnesota, and lake Superior, and between Schoodic lake, Maine, and the Atlantic ocean is also imperfectly mapped, but the possible error resulting from the un- certain location of these two fragments of our boundary is very slight. The standard measurement of the area of the United States was made by Mr. Henry Gannett and Mr. F. DeY. Carpenter in connection with the Tenth Census. ^ In defining the boundaries of the country, they excluded the sea within the three mile limit and the por- tions of the Great Lakes subject to the jurisdiction of the United States, but could state no rule with regard to the treatment of bays or gulfs. While Long Island sound was excluded, Delaware and Chesapeake bays were not. The area of the United States, within the limits thus de- fined, was measured as 3,025,600 square miles. To this should be added 531,000 square miles as the official es- timate of the area of Alaska^ and an undetermined amount as this country's share of the Great Lakes. The latter is estimated by M. Levasseur* as 133,000 square kilometers or about 51,350 square miles, and the total area of the United States excluding the sea within the • Mr. Henry Gannett in a personal letter to the author. 2 Tenth Census, Bulletin, The Areas of the United States, Washing- ton, i88r. ^ Eleventh Census, Alaska, p. 11. *0p. cit., 2^me I/ivraison, 1887, p. 204. Area of the United States and its Divisions. 213 three mile limit would thus be about 3,607,950 square miles. Ivight is thrown upon the territorial position of the United States by a comparison with that of other great powers. The land surface of the globe is stated by va- rious authorities as follows : A tttttorttv Date. I^and surface in Per cent. of total square kilo- meters. square miles. earth's surface. Levasseur^ Ravenstein^ .... Wagner and Supan^ . Juraschek* 1886 1890 1891 1893 136,100,000 135,490,765 135,454,265 52,160,000 51,250,800 52,330000 52,300,000 26.5 26.0 26.6 26.6 Probably between twenty-six and twenty-seven per cent, of the earth's surface is land. As inland water sur- faces are treated differently by different authorities, the divergencies shown in the table may be due in part to differences in definition of land surface and certainly are due in part to differences of measurement. A few great powers and many minor powers possess this land surface. The great powers, territorially con- sidered, may be held to include all owning over a mil- lion square miles of land. Since their boundaries are fluctuating and ill defined, especially in South America and Africa, any estimate of their areas must be merely approximate. Hence the following table^ does not claim ^ Op. cit., p. 237. 2 Statesman's Year-Book, 1892, p. xxv. 'Petermann's Mittheilungen, Krganzungsband, xxii, p xi. * Geographiscli-statistische Tabellen, 1893, p. 89. 5 Compiled from the Statesman's Year-Book, 1897. 214 Economic Studies. a high degree of accuracy but still it may serve to make clear the relative position of the United States : TABLE I. AR^A OF C0UNTRIE:S CONTROI^IvING OVER ONE MIIvI,ION SQUARE MII^ES. COUNTRY. Area in square miles, Per cent, of earth's surface. British Empire , . Russian Empire . . Chinese Empire . . United States . . . Brazil France^ Argentine Republic Ottoman Empire' . German Empire^ . Total 11,334,391 8,660,282 4,218,401 3,607,950 3,209,878 2,804,839 1,778,195 1,609,240 1,228,740 21 7 16.5 8.1 69 6.1 54 34 31 2.3 38,451,916 73 5 Among these nine great powers one is purely Asiatic, three purely American, and five inter-continental ; but in their origin seven are European and from present indi- cations the two non-Kuropean empires of China and Turkey are tottering. The table thus illustrates both the control of European civilization and governments over the world and the preeminent position territorially of a small number of states. Among these great powers the United States ranks fourth and exercises jurisdiction over between one-fifteenth and one-fourteenth of the earth's land surface. In the United States exclusive of Alaska, where no such measurements have been completed, there are about 17,200 square miles of coast waters, 14,500 square miles of rivers and 75,250 square miles of lakes.^ The Great ^ Including extensive African possessions. '^ Tenth Census, Bulletin, The Areas of the United States, etc., p. 5. Area of the United States and its Divisions. 215 lyakes include over two-thirds of the lake area of the country. As the land surface is 2,970,000 square miles, about -^yi per cent, of the entire area is water. On the average in each ten thousand square miles of total area there are 56 square miles of coast waters, 47 square miles of rivers, and 245, or excluding the Great I^akes, 79 square miles of lakes. A division conventional and temporary rather than natural, but important for the census, is that between Indian reservations and the rest of the country. Differ- ent agencies were employed to count their inhabitants, including the residents of Indian territory and Alaska. In 1890 there were 180,884 square miles of reservations, or 6 per cent, of the area of the country.^ Their extent, however, is rapidly decreasing. Between 1890 and 1896 they decreased to 130,320 square miles, or nearly 28 per cent.^ The United States, exclusive of purely national terri- tory, namely, the Great Lakes, Delaware, Raritan and lower New York bays, is divided into fifty-one political divisions, of which forty-four at the date of the last census were states.^ The Yellowstone National Park and No Man's I^and are apparently included for purposes of measurement within state bounds. Messrs. Gannett and Carpenter have measured the area of each state ex- ^ Eleventh Census, Indians, p. 91. - Report of the Commissioner of Indian Affairs, 1896. p. 495. ^ For the sake of brevity the word state or states will be applied henceforth, unless otherwise indicated, to all primarv divisions of the country including Alaska, Arizona, Indian, New Mexico, Oklahoma and Utah territories and the District of Columbia. 2i6 Economic Studies. cept Alaska in the manner already explained^ and ad- justed the results to that obtained for the country. But as their boundaries have been surveyed and mapped less accurately than the national boundary and in cer- tain instances, e. g.^ between Virginia and West Virginia, are very ill ascertained, the area of a state may be deemed, in nearly every case, less accurate than that of the country. Colorado, Wyoming and Utah, being bounded entirely by parallels or meridians, are ex- ceptions. In the table on page 218, in which the states are arranged in order of size, it will be noticed that the numbers expressing the areas of the states all end in a cipher or a five. Hence they cannot be accurate to a square mile. In a personal letter from which I am per- mitted to quote, Mr. Gannett says : " The areas cannot be given with such accuracy as to make it worth while ^Sources. — The areas of the United States, of the states and territo- ries, and of the counties and parishes, at the date of the nth census, are stated in Census Bulletin 23, dated Jan. 21, 1891, and prepared "primarily for the use of the Census Office." The Bulletin gives the gross area, the land surface, and the water surface of the primary divisions of the country, and the land surface of each county and parish, except in the case of Oklahoma. It is apparently the standard authority for the area of the United States, its figures are repeated in standard English and Continental publications, and I am not ac- quainted with any independent determinations of area for the whole country with which its results may be compared. The area of each city of over 10,000 inhabitants was asked on the schedule of questions relating to the social statistics of cities, and the areas of fifty of these cities have been published in Census Bulletin 100, Social Statistics of Cities. The areas of the states of Massachusetts, Rhode Island, Connecticut and New Jersey, and of their counties and towns, townships or bor- oiughs, as they stood about 1890, have been published in recent bulle- tins of the United States Geological Survey, numbers 115-118. Area of the United States and its Divisions. 217 to give the unit figures exactly excepting in tlie case of two or three states, and rather than give an incorrect: impression of accuracy, I judged it best to round them; up to the nearest five or ten square miles." The water surface of each state except Alaska has- been approximately determined under the categories of lakes, rivers and coast waters/ From these measure-- ments the proportion of each kind of water surface to the whole area of the state has been computed and is also included in the table on the following page. On examining the second column two gaps in the series may be noticed between Georgia and Washington and between Maryland and West Virginia. All states above Missouri are larofer than the averag-e for the country, which is 69,723 square miles, and Missouri and, Washington are larger than the average for the country, exclusive of Alaska. The states then fall into three groups of large, medium and small. All states with more than 60,000 square miles lie west of the Mississippi, and including Alaska cover over nine- tenths of that region. All with less than 15,000 square miles except Vermont touch the Atlantic north of the Potomac. The medium sized states lie between the small and the large. The large states include 68 per cent, of the country's area, the medium states, 30.5 per cent, and the sttiall states about 1.5 per cent. The third column in Table II shows where the largest proportion of lake surface is found. The most extensive lake region is in the vicinity of the Great Lakes. From Minnesota to the Atlantic eveiy 'Tenth Census, Bulletin, The Areas of the United States, etc., p. 4, 2l8 Economic Studies. TABLE II. GROSS AR:eA OF THE) STATES AND PROPORTION OF COAST WATFR. I,AKF AND RIVER SURFACE. STATES. Alaska Texas . . California Montana New Mexico . . . Arizona Nevada Colorado Wyoming . . . . . Oregon Utah Idaho Minnesota .... Kansas South Dakota . . Nebraska .... North Dakota . . Missouri Washington . . . Georgia Michigan .... Florida Illinois Wisconsin .... low^a Arkansas .... Alabama .... North Carolina . New York .... Louisiana .... Mississippi . . . Pennsylvania . . Virginia Tennessee. . . . Ohio Kentucky .... Oklahoma .... Indiana Maine Indian territory South Carolina . West Virginia . . .Maryland .... Vermont .... New Hampshire Massachusetts . New Jersey . . . Connecticut . . . Delaware .... Rhode Island . . District of Columbia United States 1 Gross area. 531,000 ( 265,780 158,360 146,080 122,580 113,020 110,700 103,925 97,890 96,030 84,970 84,800 83,365 82,080 77,650 77,510 70,795 69,415 69,180 59,475 58,915 58,680 56,650 56,040 56,025 53,850 52,250 52,250 49,170 48,720 46,810 45,215 42,450 42,050 41,060 40,400 39,030 36,350 33,040 31,400 30,570 24, 780 12,210 9,565 9,305 8,315 7,815 4,990 2,050 1,250 70 3,076,950 Square Miles in 10,000 of area. Lake. River. 7 100 25 23 96 318 38 456 7 52 8 208 384 24 209 21 49 2 33 183 350 21 7 6 24 39 6 30 697 ? 398 237 108 45 80 160 245 30 15 28 9 7 3 26 9 52 9 24 43 46 7> 82 ? 51 44 67 91 75 73 100 61 III 73 44 123 48 34 93 ? 91 91 ? 59 55 410 52 86 72 154 160 291 80 1429 47 Coast •waters. 95 34 200 25 307 6 625 71 218 6 420 165 71 1515 151 262 50 146 1080 56 Total. 1 Excluding Alaska and the sea within the three mile limit but including Dela- ■ware, Raritan and lower New York bays and this country's portion of the Great J^akes. Area of the United States and its Divisions. 219 state on the northern boundary of the country except Ohio, and every New England state except Connecticut, has over one per cent, of its area in lakes. The same is true of Florida, Louisiana, California and Utah. From the fourth column it appears that the largest proportion of river surface is found along the Atlantic coast in Con- necticut, New Jersey, Delaware, Maryland and Virginia, and also in the lower Mississippi valley, in Arkansas and Louisiana, each of these states having over one per cent, of river surface. The states which had over five per cent, of their area in Indian reservations in 1890 were : Per cent, of States. area in ] ndian reservations. Indian territory 100 Oklahoma 48 South Dakota 47 New Mexico 13 Montana ii Washington 9 Minnesota 9 Arizona 9 Utah 8 North Dakota 7 Idaho 5 It will be seen that they lie mainly west of the Mississippi along the northern and southern boundaries of the country. In the census volumes ^ the fifty states of the Union excluding Alaska are divided into five geographical ^ See for example the Abstract of the Eleventh Census, second edi- tion, p. 10. The student should have this excellent hand-book at his side. References will be made to it, rather than to the large volumes, wherever possible. .- ***~^ 220 Economic Studies. groups, the north Atlantic, south Atlantic, north cen- tral, south central and western. The primary line of division is perhaps that between the Rocky Mountain and Pacific Coast states and those lying east of the great plateau. It follows the meridian of 104 degrees west, i. ^., the western boundary of the Dakotas, or the state boundary nearest thereto. It also coincides roughly with the line of 5,000 feet of altitude. Only a trifling part of the area to the east of it rises above that eleva- tion, while fully half of the land to the v/est is more than that height above the sea level. The states east of this line are divided upon geo- graphic, historic and economic grounds into north and south. The division is made by a line coinciding in the main with that separating the former slave states from the free states. It follows Mason and Dixon's line, the Ohio river, and the parallel of 36 degrees 30 minutes, or the state line nearest to that, until it intersects the division line between the central and western states. Missouri is thus classed with the north and Oklahoma with the south. Bach of the southern states as thus defined, except West Virginia and Oklahomia, has over ten per cent, of negroes in its population, while this is true of no northern state. The last division, that between the Atlantic and the central states, follows as nearly as the state lines allow the height of land separating the two drainage areas but is invariably somewhat to the west of this natural divi- sion. West Virginia is the only exception. While most! of the state sends its rainfall to the Ohio river it Area of the United States and its Divisions. 221 is classed for historic reasons among the Atlantic states, and while it has a smaller proportion of negroes than any other southern state, or than Missouri of the north- ern, it is classed for the same reason among the southern states. With the exception of the District of Columbia and Alaska, each of the fifty-one primary divisions of the country is subdivided territorially. In 1890 there were about twenty-eight hundred (2790) of these subdivisions, or counties as they are almost uniformly called. This includes the District of Columbia, the parishes of I^ouisi- ana, the six reservations of Indian territory, and two parcels of unorganized territory about the size of counties, one in North Dakota and one in Nebraska. For the sake of brevity all these secondary divisions will hence- forward be called counties. The average size of a county in the United States is rather more than one thou- sand (1085) square miles and the range is from Bristol county, Rhode Island, with only twenty-five square miles to Yavapai county, Arizona, over one thousand times as large (29,236 square miles). It is not generally true, however, that the smallest states have the smallest counties. On the contrary the smallest counties occur as a rule in the border states east of the Mississippi river where their average size is less than five hundred square miles, as a little computation will readily con- vince the reader. The areas of the country and of the states published in connection with the census of 1880 were not changed for the census of 1890. But the areas of the counties 222 Economic Studies. were " thoroughly revised " ^ involving a correction on the average of perhaps five per cent., a part of which may have been due to changes during the decade in the location of county boundaries, but more to increased accuracy of measurement. The method of measure- ment resembled that employed for the country and the states : that is, the area of each state was the starting point and the county areas, determined primarily by the polar planimeter, were corrected by a reference to the requisite total ; but as the mapping of county lines is generally less accurate than that of state boundaries, the probable error in county areas is greater. Mr. Gannett writes me : " Excepting where we have accurate maps of county boundaries, the areas given can be regarded only as very rough approximations and this is true in all the eastern states and especially so in those of the south where the location of county boundaries is not repre- sented alike upon any two maps." In Rhode Island, where the Geological Survey also has determined the land surface of the counties, the re- sults of the two are comparable, and show an average variation of six per cent.^ The results of the Geological Survey in New Jersey were the basis of the census figures, and in Massachusetts and Connecticut the former gives the gross area, not the land surface. If both were accurate in the latter states, the Geological Survey fig- ures would form a maximum limit not exceeded in any 1 Eleventh Census, Bulletin 23, p. i. Compare Tenth Census, Bul- letin, The Areas of the U. S., etc. 2 The land surface of the counties of Rhode Island is given as fol- lows in the two authorities : Area of the United States and its Divisions. 223 case by those of the census. In fact the land surface of eight of the twenty-two counties is stated by the census bulletin as greater than their gross area indicated by the Geological Survey, a proof of not a little inaccuracy in one or the other/ Such discrepancies have made it seem worth while to attempt a determination of the probable error in the official census statement of county areas. The simplest method to follow would be a repetition of planimetric measurements on our most accurate county maps, the United States post route maps. This method has al- ready been employed by a German critic and the results in three cases published,^ but it is obviously open to the objection that in those maps the county lines may have been inaccurately drawn. Far more accurate than those are the maps of the United States Coast and Geodetic Survey and of the United States Lake Survey, but these latter represent only natural not political divisions and COUNTIES. Geological Survey Bulletin. Census Bulletin 23- Per cent, of varia- tion. Bristol Kent Newport Providence 25 169 117 411 331 25 180 ICG 440 340 7 15 7 3 Washington Total 1,053 1,085 ^ For example the Survey bulletin gives the gross area of Berkshire county, Mass., as 942 and of Norfolk county, Mass., as 433 square miles, while the census gives the laud surface alone of the same counties as 959 and 494 square miles. ^ Cf. Petermann's Geographische Mittheilungen, Brganzungsbaude 17 -18, No. 84, p. 4, footnote. 224 Eco7ioinic Studies. include only our boundary districts. There are, however, six cases in which natural divisions between land and water coincide with county lines ; in other words along the boundary of the United States there are six islands or groups of islands which are also counties. They are Nantucket, Martha's Vineyard, Long island, Staten island. Isle Royale and Beaver, Pox and Manitou islands. Long island is divided into three counties, and is the only island containing more than one. The areas of these counties on the Coast Survey or Lake Survey charts have been twice measured carefully by Mr. J. F. Hay ford, C.B., formerly of the United States Coast Survey and now of Cornell university, and from his results I have prepared the following table : TABLE III. COMPARISON OF MEASURED I,AND SURFACE OF CERTAIN COUNTIES IN SQUARE MII.es WITH CENSUS FIGURES. 1 Per Cent. of varia- COUNTY Area by- Area by Area by- tion of ISLAND OR Meas- Census Census other census AND GROUP. ured Bulletin, Bulletin, an hori- 1890 area STATE. area. 1880. 1890. ties. from measure- ment. Martha's Dukes, Mass. Vineyard. 103.4 120 124 IIO^ 20 Nantucket, *' Nantucket. . 49-7 60 65 51* 3t Kings, Queens and Suffolk, New York . Long island . 1353-8 IIIO IC07 i682t 25 Ricbmonrl, New York. Staten island. 55-7 60 61 59t 10 Manitou, Beaver, Fox Mich. and Manitou 109.3 200 120 . . . . 10 Isle Royale, Mich. Isle Royale . 203.7 230 215 1 .... 5 *U. S. Geological Survey, Bulletin 116. t New York Census of 1875, p. 264. Area of the United States and its Divisions. 225 If these instances were typical, the county areas in Census Bulletin 23 were in error by an average amount of 17 per cent. But the north central and western states are probably better mapped and measured than these results would indicate. It should also be re- marked that in four of the six cases the changes made in 1890 resulted in greater inaccuracy than before. It has surprised me to find that the area of Long is- land, perhaps the largest and certainly the most impor- tant island in the country, has not been determined to within twenty-five per cent. The latest Federal author- ity, as appears from the preceding table, gives it as 1007 square miles, while what is I believe the latest state au- thority, the state census of 1875, basing itself directly upon Hough's Gazetteer and ultimately upon French's Gazetteer of i860, gives its area as 1682 square miles. The latter is the authority followed by such good second- ary sources as the last editions of the Encyclopaedia Britannica and Johnson's Cyclopaedia. It will be seen that the state and Federal authorities differ by over six hundred and fifty square miles and that each is over three hundred miles wide of the truth as first established by Mr. Hayford's measurements. ^ ^ To illustrate the care with which his v/ork has been done I append his report to nie on the measurement of the area of Long island. The map from which liis measurements vv^ere made was the Coast and Geodetic Survey Chart, No. 52, " Montauk Point to New York." It will be seen that his two determinations differ by less than a fourth of one per cent. He is confident that the errors of measurement as distinguished from the errors of the map are well within one per cent. LiNCOiwN Hai,!,, April 29, 1896. Prof. W. F. Willcox : D^AR Sir — By the use of the polar planimeter on the C. & G. S. 226 Eco7iomic Studies. The census makes no sfeneral effort to determine the area of divisions smaller than counties, except in the case of large cities. The areas of fifty of these are stated in one of the bulletins and assurance is given that they " have been either determined by actual measurements from latest obtainable maps or from re- cords in oihces of the several city engineers."^ The areas of nearly all the cities and towns of Massachusetts, Rhode Island, Connecticut and New Jersey are given in recent bulletins of the United States Geological Sur- vey. Eleven of the fifty cities included in Census Bul- letin loo are in these four states and six other cities are co- extensive v/itli counties of the same name. Hence for one-third of the fifty cities there are two independent and comparable determinations of area. The general result map which you furnished, I have obtained the following results. Long island was for convenience divided into seven sections, arbitra- rily, and the area of each section measured twice. Sq. stat. miles Sq. stat. miles No. of Section. ist measurement. 2d measurement. I 129 6 127,2 2 246.6 246.1 3 334- i 335.2 4 9-0 9-9 5 • * . . 287.1 2S6.4 6 253.9 256.2 7 95-1 9^-2 Total area 1355-4 1352.2 Mean of two measurnients = 1353.