Measures for this purpose have been carried on or are in progress in most civilized coun tries. The exact form and size of the earth cannot be determined in the best way through observations in any one country, but require a combination of the geodetic surveys of various countries as widely separated as possible. With a view of securing co-operation in the solution of the problem, an International Geodetic Asso ciation was formed, comprising the United States and the leading countries of Europe. This association, represented by members from the various countries, meets from time to time to carry out the co-operative work of the asso ciation, and decide upon the best way of com bining the several geodetic surveys.
The accompanying map shows the principal modern geodetic arcs which have been com pletely measured in different parts of the world, and affords a comparison of the work done by the United States with that of foreign countries. The two arcs already completely measured in the United States are those of the thirty-ninth parallel of latitude, and the eastern oblique arc. The arc along the thirty-ninth parallel extends across the country from Cape May, N. J., to Point Arena, Cal., a distance of 2625 statute miles (4225 kilometers). Its triangulation in cludes 10 base lines having an aggregate length of 53.5 miles, one of them being nearly 11 miles long. In the Rocky Mountain region many of the triangle sides are over 100 miles in length, and some of the triangulation stations are more than 14,000 feet (4300 meters) above the level of the sea. To fix the position of this arc on the surface of the earth, and to determine the true direction of the lines of triangulation, the latitude was accurately determined at 109 stations, the longitude at 29 stations, and the azimuth at 73 stations.
The eastern oblique arc extends from Calais, Maine, to New Orleans, La., a distance of 1623 miles (2612 kilometers). The triangulation in dudes six base lines. The latitude was deter, mined at 71 stations, the longitude at 17, and the azimuth at 56. The measurement of the arc is result obtained from the triangulation which forms the primary control of the surveys .of the Atlantic executed by the United States Coast and Geodetic Survey.
Of the work now in progress, the principal measurement is that of an arc of the ninety eighth meridian west of Greenwich. This work is practically completed within the limits of the United States, and preparations are being made for its extension northward into Canada, and southward into Mexico.
The principal arcs measured in foreign countries are the Anglo-French meridional arc extending from the north of the British Isles southward through France and Spain into Africa; the great Russian meridional arc ex tending from the Arctic Ocean to the northern boundary of Turkey; the European latitudinal arc extending from the southern nart of Ireland eastward into central Russia; and the great Indian meridional arc extending from the south ern point of the Peninsula of India northward to the Himalayas.
The total length of all the arcs completely measured in all parts of the world during the modern period amounts to a little more than two-fifths of the girdle of the earth along a great circle.
The exact form of the earth as given by these measurements is such, that with consider able exactness all parallels of latitude are circles, and all meridional great circles are ellipses. The dimensions and form of the spheroid, or more properly, ellipsoid of revolu tion given by these co-ordinate circles and ellipses are usually stated in terms of its equatorial and polar radii, or diameters, and the two most notable computations of these dimensions are those made by Bessel in 1841, and those made by Clarke in 1866. The dimen sions as determined by these computations and the compression values deduced therefrom, which are applied to all calculations in connec tion with modern geodetic work, and in the preparation of maps for exact surveys, are given in the following table, both the Bessel and Clarke computations being riven in meters and English statute miles.
Both sets of dimensions very closely approxi mate to the truth, but the number of recent measurements is insufficient to determine which of the two is more nearly correct. It is quite probable that the true dimensions lie between the two. A very clear idea of the small amount of flattening at the poles indicated by the figures of either set may be had by constructing a globe approximately five feet in diameter. In order to represent the shape of the earth, the equatorial diameter of the globe will have to be made ono-fifth of an inch longer than its polar diameter. The consequent distortion from a perfect sphere will be unappreciable to the eye unaided by the use of measuring instruments.