LXVII.On the application of least squares.—II

Abstract

A solution of the general problem in least squares, together with examples of its applications to several special cases, was given in a previous paper. The author now presents further illustrations of the adjustment of observations and determination of parameters, together with suggestions for systematic procedure in computation. The problems here treated are the logarithmic decrement of a balance, the exponential law, and the laws represented by the equations ya^x =b, yz^x =b, and yz^x =w, wherein a and b are parameters, arid x, y, z, w are observed coordinates. The last three equations are respectively the ones needed in the determination of e and h (electronic charge and Planck's constant) under the three situations: (a) neither e nor h directly observed, (b) direct observations on e included, (c) direct observations on both e and h included. Provisions in the general solution allow any relation, between e and h to be forced. In particular, the normal equations are set up and illustrated with Eddington's relation hc/2πe ²=137 forced or released at will, using Birge's weighting. The disparity between the two pairs of values of e and h that are obtained with and without forcing any theoretical relation constituted a basis for accepting or rejecting the theory.