The Adjustment of a Level Net

Two closely related methods of obtaining a “least squares” adjustment of the closing errors in a level net are described in this paper. The first method involves the writing, by inspection, of the appropriate normal equations and their subsequent solution by a process of converging increments; the second utilizes the principle of successive distributions, and is suggested by the Cross method of moment distribution.

Both methods are well adapted to the use of the slide-rule and possess the advantages of simplicity and brevity, as compared with the conventional least squares solutions. They are intended to apply primarily to surveys of ordinary extent and accuracy, such as those executed by municipal and highway engineering organizations.

Beyond the consideration that, in practice, one method may appeal more than the other to a given individual, the reasons for presenting a dual treatment of the subject include the following: (a) The first method derives immediately from the principal hypothesis of the theory of least squares, and thus serves to substantiate the correctness of the second method; (b) the process utilized (in the first method) for solving the normal equations may be successfully applied to various other types of engineering problems (for example, to indeterminate structures); and (c) the parallel solutions show the inter-relations of the two methods and suggest a procedure that may be used to advantage in devising extensions of the distribution method to new types of problems.