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OUR CENTER OF POPULATION.

By FRANK D. Y. CARPENTER, C. E.

Written for VAN NOSTRAND'S ENGINEERING MAGAZINE.

If a man in San Francisco and another certain established units of weight and living in New York should wish to hold measurement. In the subject now under a conference, it requires no mathematical treatment the forces considered are the demonstration to prove that the proper individuals of our population; and since place for them to meet would be at a all people, rich and poor, large and point half-way between these two cities. small, ignorant and learned, infant and In this manner the burden of travel is adult, male and female, are of uniform shared equally between the two. But, importance in swelling the grand total if one man in San Francisco and two of an enumeration, these forces are taken men in New York should desire to come as of equal intensity, and their moments together, the subject becomes more in- vary directly with the lengths of their volved. It is evident that it would be lever-arms. In ordinary mechanical inunjust to require the solitary Californian vestigations the value of a moment is to perform the entire journey across the estimated in foot-pounds, the product Continent to meet his colleagues at their being named from its component factors; homes, and it would be equally unfair a corresponding and appropriate term to oblige the two New Yorkers to with which to measure the moments of travel half-way to San Francisco to con- this special discussion would be “milefer with one person from there. The men.' question is, how great a penalty should If, now, with the one Californian and the former pay for his isolation, and how the two New Yorkers aforesaid, we commuch benefit should the latter reap from bine groups of three from Chicago, four their association? from New Orleans, and, to make the An equitable compromise is effected problem still more complicated, five from by apportioning the distance in inverse the central city of Saint Louis, it is still ratio to the number of persons con- possible to find, by the appliance of wellcerned. The one from San Francisco known principles in mechanics, some travels two-thirds of the distance while point at which they could assemble with the two from New York come one-third. justice to all, and that would be the cenThus, it will be observed, the amount of ter of this population of fifteen souls. It travel on each side of the rendezvous is is only necessary to assume a center, equal; that is, one man journeys, say, draw a system system of rectangular axis two thousand miles, while the two ac- through this point, find the moments of complish one thousand each. In other the fifteen persons with regard to each words, to introduce from the science of of these two lines, note the prepondermechanics a term which it will frequently ance of moments on one side of each of be found convenient to use in this dis- the axis, divide this surplusage by the cussion, the moment of the man from entire population under discussion, and San Francisco about the rendezvous is the result will be the amount of disequal to the moment of the two men from New York with respect to the same point. The west moment is in equilibrium with the east moment, and the fulcrum about which they balance is the center of this population of three per

sons.

A moment is the product of a force by its shortest distance from some point, line or plane, to which it is referred, this distance being known as the leverage. The intensity of the force and the length of the leverage are counted in

placement of the axis from its rightful position. Adjust these lines so as to compensate for that error, and their intersection will be at the true center of population.

This is the general method to be employed in finding the center of population of the country at large. But as it would be an infinite labor to consider its fifty millions of inhabitants individually, determining their moments one by one, it becomes necessary to handle them by groups, such as states, counties, town

ships, or square degrees, proceeding there. Through all of these vicissi upon the assumption that the people of tudes, however, there is a constant proeach of these groups are massed either gress to the West, and, its recurring in the geometrical center of the area oc- positions upon a map being ordinarily cupied by them, or at some other point symbolized by a star, this conventional which, from an inspection of the map, sign becomes literally the star of empire aided, perhaps, by local calculations, of whose westward way so much is seems to be their population center. written and said. It is now in Ohio. Whatever divisions of area may be The center of the population of any adopted for this purpose, it is always well to obtain separately the moments of those cities which, owing to size or remoteness from either axis of co-ordinates, will exert most influence on the center; the gain in accuracy will more than repay for the extra trouble incurred.

The center of population of the United States may, therefore, be defined as that point at which, if all of the people should assemble there, the amounts of travel performed on any two sides would balance; in less popular language, the moments of the population with respect to any great circle passing through that point, taken as an axis, are in equilibrium. It may sound strange to call an arc of a circle an “axis," but in the treatment of a new subject like this, it is permitted to take some liberties with language; in the words of King John to Katharine: "We are the makers of manners."

portion of the earth's surface has been aptly compared to the center of gravity of a spherical shell of equal extent, having weight, in any locality, in proportion to the density of its population; but for tunately the determination of the former center is not so intricate a problem as that of the latter would prove to be. In all ordinary discussions of the center of gravity, the objects considered are so limited in dimension that the forces of gravitation may be supposed to act in parallel lines; but in treating a section of the earth's area, one-eighth of a circumference in extent, this assumption can no longer be permitted. Here gravity acts along the normals to the surface, which converge, approximately, at the center of the earth.

Again, even supposing that the forces of gravity influencing this spherical shell acted in lines parallel to each other, and to the normal to the surface through their center, the moment of each of these forces would then be the product of its intensity by its perpendicular distance from the center; that is, by the sine of the arc included between its point of application and the center. But, in getting the center of population, it is evident that the leverage to be taken as a factor in obtaining the moment of any group of people is the distance that they would have to travel in order to reach that center. People do not travel along the sine of an arc, however; they follow the arc itself, and in theoretical journeys, as all of the migration of this discussion must be, they take the shortest route, that is, the great circle.

A knowledge of the whereabouts of this pivotal point is useful in various ways. It has a practical value in the location of a national capital, university, industrial fair, or other institution whose situation should be central and equally convenient of access on all sides. To the historian and political investigator its successive positions, as shown by census after census, graphically exhibit the movement and advance of our people in a wave which is at one time accelerated by the settlement of the Pacific coast, in the next decade checked by the loss of life and enterprise incident to our civil war, deflected to the North in 1870 by the excessive devastation of the Southern States; again to the South By thus considering that all leverages in 1880 by the rapid recovery and growth reaching from the center of population, of that desolated region, and probably or the axis passing through the same, to to be turned northward again in 1890 the distant city or state, are measured by the occupation of the region to be along the earth's surface, we are relieved opened by the Northern Pacific Railway, from one of the embarrassments which and by a rush of emigration to the affect the determination of the center of mineral regions of Alaska, and the es- gravity; and by further assuming that tablishment of a territorial government these measured arcs are stretched out

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