The Combination of Observations (Classic Reprint)

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Excerpt from The Combination of Observations The aim of this book is to give an account of the method of Least Squares, without entering into elaborate descriptions of instruments or of experimental methods. The reader who wishes to apply the method to his own subject can find the experimental details in the textbooks relating to his own special subject, and any attempt to include such details in the present volume would have meant a considerable addition to its size. Hence it has been the author's aim to show how to obtain the best interpretation of the results of experiment, without consideration of the way in which these results are to be obtained. It cannot be too strongly insisted upon that the methods of Least Squares cannot in any way improve upon the actual observations. The application of these methods to a large number of carelessly conducted experiments cannot in general be expected to yield results as reliable as could be obtained from two or three carefully conducted experiments. The proof of the Normal Error Law has been based on Hagen's hypotheses regarding errors of observation. In most of the problems of Astronomy, Geodetics, and Physics the errors of observation satisfy the hypotheses, and the application of least square methods is justified. But cases may arise in which particular care is necessary in applying these methods. This is especially true of Biological problems. For organic variability is the resultant of A large number of contributory causes, some of which may have a definite tendency to act always in one direction. The effect of such a bias is to produce an unsymmetrical frequency distribution, and the application of ordinary least square methods is then meaningless. It is thus in no way justifiable to regard Least Squares as a magical instrument applicable to all problems. Of the arrangement of this volume little need be said. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.