THEORIE DE LA FIGURE DE LA TERRE,

8vo, pp. xl, 305, [1] errata], [3] contents, [1] imprimatur; engraved headpieces throughout, and the vast majority of pages illustrated with engraved diagrams; some foxing throughout, only heavy in one or two places; ownership signature of Wm. Wilson, dated 1913, on front free endpaper; in contemporary calf, spine gilt in compartments with raised bands, gilt morocco lettering-piece; very light wear but an attractive copy.

First edition of the best-known work of the French mathematician and physicist Alexis Claude Clairaut (1713-1765), in which he demonstrates that the shape of the Earth was that of an oblate spheroid, flattened at the poles and wider at the equator, being held in hydrostatic equilibrium.

The observational underpinnings to Clairaut's conclusions came from an expedition he had taken in 1736 to Lapland, under the auspices of the Académie des sciences, in the company of Maupertuis, Celsius, and others, with the aim of measuring the length of one degree of latitude; Clairaut's role in the expedition was to extrapolate from these measurements the shape of the earth. His answer, that the earth was an oblate ellipsoid, had almost immediately been published by Maupertuis in 1738, but it was in the Theorie de la figure de la terre that Clairaut's theoretical basis for his conclusions was fully articulated for the first time. Drawing on both Newton's theories of gravitation and on Huygen's work on centrifugal force, Clairaut proposes a formula to calculate the acceleration due to gravity on the surface of a spheroid at any given latitude; on the basis that the shape of the earth is dependent on a combination of gravity and the centrifugal forces resulting from its rotation around an axis, Clairaut was able to use this formula, now known as Clairaut's theorem, to correct Newton's estimation of the shape of the earth.

See DSB III, 282.