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Clairaut's theorem is a general mathematical law applying to spheroids of revolution. Published in 1743 by Alexis Claude Clairaut in his ''Théorie de la figure de la terre, tirée des principes de l'hydrostatique'',〔(From the catalogue of the scientific books in the library of the Royal Society. )〕 which synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid,〔 A reprint of the original work published in 1908 by Cambridge University Press.〕 it was initially used to relate the gravity at any point on the Earth's surface to the position of that point, allowing the ellipticity of the Earth to be calculated from measurements of gravity at different latitudes. ==Formula== Clairaut's formula for the acceleration due to gravity ''g'' on the surface of a spheroid at latitude φ, was:〔( W. W. Rouse Ball ''A Short Account of the History of Mathematics'' (4th edition, 1908) )〕 : where is the value of the acceleration of gravity at the equator, ''m'' the ratio of the centrifugal force to gravity at the equator, and ''f'' the flattening of a meridian section of the earth, defined as: : (where ''a'' = semimajor axis, ''b'' = semiminor axis). Clairaut derived the formula under the assumption that the body was composed of concentric coaxial spheroidal layers of constant density. This work was subsequently pursued by Laplace, who relaxed the initial assumption that surfaces of equal density were spheroids.〔 Reprint of the original edition of 1873 published by Macmillan and Co.〕 Stokes showed in 1849 that the theorem applied to any law of density so long as the external surface is a spheroid of equilibrium. A history of the subject, and more detailed equations for ''g'' can be found in Khan.〔(NASA case file ''On the equilibrium figure of the earth'' by Mohammad A. Khan (1968) )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Clairaut's theorem」の詳細全文を読む スポンサード リンク
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