TRAVERSE ADJUSTMENT: WHY NOT “LEAST SQUARES”?

Abstract

I. Introduction.—The literature of least squares is extensive and much of it is theoretical and prosy. I propose, therefore, in the present paper to scrape the jam off the bread, so to speak, and present the pabulum to the reader first; in other words, to give first the solution in as simple and neat a form as possible, then the proof, and finally an example and some notes. The problem is that of adjusting in plane coordinates a traverse beginning at a known point and closing on a known point, having also in the general case an angular closure. If, as I believe, the proof does not appear anywhere else in its present form and nowhere in the English language, I am at a loss to know why. It is not enough to say that the traverse is not a precise enough form of survey to warrant a practical application of the method of least squares. Nor does the admitted difficulty of assigning relative probable errors to linear and angular measurements, coupled with a tendency for the linear errors to be systematic, quite account for it. One has only to read what little there is on the subject of simple traverse adjustment in the English language to detect diversity, vagueness, and sometimes even uneasiness in the statements on it.