Breaking a “vicous circle”: Unscrambling A.-C. Clairaut's iterative method of 1743

AbstractIn this paper I show how in 1743 A.-C. Clairaut applied an iterative method to calculate the ellipticity of an infinitesimally flattened, homogeneous ellipsoid of revolution in equilibrium, taken to represent the earth. Clairaut did not make very clear what he was doing and, as a result, left certain readers in the dark. They could not understand the point of the calculation and erroneously thought that Clairaut was going around in circles. The paper ends with a discussion of Clairaut's clarification of the calculation, published in 1760 in response to the criticisms of John Muller, and a brief comparison of Clairaut's iterative method with the “Newton-Raphson Method.