Method of Least Squares Applied to Estimating Errors in Coal Analysis (Classic Reprint)

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Excerpt from Method of Least Squares Applied to Estimating Errors in Coal AnalysisIn this paper, which is published by the Bureau of Mines as a contribution to the increase of efficiency in, the utilization of fuel, the authors have sought to describe a definite method for estimating the probable limits Of error in analyzing samples of coal, and to show how this method, that of least squares, should be applied.Bailey 0 has shown that the method of least squares is applicable to the problem of sampling coal, it can be used to determine the limits of accuracy of sampling and for preparing standardized methods of sampling, but so far as the authors know the accuracy of the ordinary methods oi analyzing coal has not yet been investi gated by a mathematical method. It is customary to estimate the limits of accuracy of analysis by observing the agreement of duplicate determinations, that is, from general experience with a given kind of analysis. Hence, as some sets of duplicates are found to agree more closely than others, this question arises: What is the widest variation and What is about the average variation reasonably to be expected? Or, in other Words the question is: What is the magnitude of the probable error of a single determination and what is the maximum error to be expected, say, once in determinations?About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.