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 A1, A1 A2, 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.
The expedition started in 1735, and, owing to various difficulties, the work was spread out over nearly ten years. The most important result was the measurement, with very fair accuracy, of an arc of about 3° in length, close to the equator; but a number of pendulum experiments of value were also performed, and a good many miscellaneous additions to knowledge were made.
But while the Peruvian party were still at their work a similar expedition to Lapland, under the Academician Pierre Louis Moreau de Maupertuis (1698-1759), had much more rapidly (1736-7), if somewhat carelessly, effected the measurement of an arc of nearly 1° close to the arctic circle.
From these measurements it resulted that the lengths of a degree of a meridian about latitude 2° S. (Peru), about latitude 47° N. (France) and about latitude 66° N. (Lapland) were respectively 362,800 feet, 364,900 feet, and 367,100 feet.[124] There was therefore clear evidence, from a comparison of any two of these arcs, of an increase of the length of a degree of a meridian as the latitude increases; and the general correctness of Newton’s views as against Cassini’s was thus definitely established.
The extent to which the earth deviates from a sphere is usually expressed by a fraction known as the ellipticity, which is the difference between the lines C A, C B of fig. 78 divided by the greater of them. From comparison of the three arcs just mentioned several very different values of the ellipticity were deduced, the discrepancies being partly due to different theoretical methods of interpreting the results and partly to errors in the arcs.
A measurement, made by Jöns Svanberg (1771-1851) in 1801-3, of an arc near that of Maupertuis has in fact shewn that his estimate of the length of a degree was about 1,000 feet too large.
A large number of other arcs have been measured in different parts of the earth at various times during the 18th and 19th centuries. The details of the measurements need not be given, but to prevent recurrence to the subject it is convenient to give here the results, obtained by a comparison of these different measurements, that the ellipticity is very nearly 1∕292, and the greatest radius of the earth (C A in fig. 78) a little less than 21,000,000 feet or 4,000 miles. It follows from these figures that the length of a degree in the latitude of London contains, to use Sir John Herschel’s ingenious mnemonic, almost exactly as many thousand feet as the year contains days.
222. Reference has already been made to the supremacy of Greenwich during the 18th century in the domain of exact observation. France, however, produced during this period one great observing astronomer who actually accomplished much, and under more favourable external conditions might almost have rivalled Bradley.