On the other hand, a comparison of various measurements of arcs of the meridian in different latitudes gave some support to the view that the earth was elongated towards the poles and flattened towards the equator, a view championed with great ardour by the Cassini school. It was clearly important that the question should be settled by more extensive and careful earth-measurements.
The essential part of an ordinary measurement of the earth consists in ascertaining the distance in miles between two places on the same meridian, the latitudes of which differ by a known amount. From these two data the length of an arc of a meridian corresponding to a difference of latitude of 1° at once follows. The =latitude= of a place is the angle which the vertical at the place makes with the equator, or, expressed in a slightly different form, is the angular distance of the zenith from the celestial equator. The =vertical= at any place may be defined as a direction perpendicular to the surface of still water at the place in question, and may be regarded as perpendicular to the true surface of the earth, accidental irregularities in its form such as hills and valleys being ignored.[123]
The difference of latitude between two places, north and south of one another, is consequently the angle between the verticals there. Fig. 78 shews the verticals, marked by the arrowheads, at places on the same meridian in latitudes differing by 10°; so that two consecutive verticals are inclined in every case at an angle of 10°.
[Illustration: FIG. 78.—The varying curvature of the earth.]
If, as in fig. 78, the shape of the earth is drawn in accordance with Newton’s views, the figure shews at once that the arcs A A_{ 1}, A_{ 1} A_{ 2}, etc., each of which corresponds to 10° of latitude, steadily _increase_ as we pass from a point A on the equator to the pole B. If the opposite hypothesis be adopted, which will be illustrated by the same figure if we now regard A as the pole and B as a point on the equator, then the successive arcs _decrease_ as we pass from equator to pole. A comparison of the measurements made by Eratosthenes in Egypt (chapter II., § 36) with some made in Europe (chapter VIII., § 159) seemed to indicate that a degree of the meridian near the equator was longer than one in higher latitudes; and a similar conclusion was indicated by a comparison of different portions of an extensive French arc, about 9° in length, extending from Dunkirk to the Pyrenees, which was measured under the superintendence of the Cassinis in continuation of Picard’s arc, the result being published by J. Cassini in 1720. In neither case, however, were the data sufficiently accurate to justify the conclusion; and the first decisive evidence was obtained by measurement of arcs in places differing far more widely in latitude than any that had hitherto been available. The French Academy organised an expedition to Peru, under the management of three Academicians, _Pierre Bouguer_ (1698-1758), _Charles Marie de La Condamine_ (1701-1774), and _Louis Godin_ (1704-1760), with whom two Spanish naval officers also co-operated.