Laplace's calculations of length of the meter

Abstract

Laplace's calculations to derive the length of the meter are described. It is noted that any form of the method of least squares is not used in his determination of the length of the meter. Instead, he used two equations to solve for two unknowns that are necessary to determine the length of the meter. In Appendix 1, these two equations are derived as the asymptotic expansion of the elliptic integral derived by Bessel. Some estimation results obtained by the method of least squares, namely, results of calculations by Legendre and by Stigler, are summarized in Appendix 2.