NETWORK ADJUSTMENT BY LEAST SQUARES—ALTERNATIVE FORMULATION AND SOLUTION BY ITERATION

Abstract

Given a network, as in a gravity survey, comprising observed differences in the values of adjacent points, any adjustment of the network, however obtained, is shown to be a least square adjustment if (1) the sum of the corrected observations around any circuit is zero and (2) the sum of the weighted corrections at any junction is zero. This principle provides a means of controlling necessary approximations such as the subdivision of a large network, and simplifies subsequent adjustments made necessary by extension or revision of the observations. It also serves in some cases to reduce the number of equations and in others to eliminate the equations entirely. The paper outlines a time‐saving trial and error method of solving network equations, applicable to electric circuits as well as observational network problems.