The Theory of Errors and Method of Least Squares (Classic Reprint)

William Woolsey Johnson

ISBN 10: 1332339131 / ISBN 13: 9781332339136

Published by Forgotten Books, 2016

About this Item

Print on Demand. This book details the mathematics behind the theory of errors in measurement. The author begins by highlighting the fact that measurements are imprecise and subject to errors due to a variety of factors. The author then introduces the concept of probability, providing a foundation for assessing the likelihood of different outcomes. With this framework, the author introduces the idea of an error distribution, which can be used to quantify the expected accuracy of a measurement. The mathematical proof for the "Principle of Least Squares" is included, which posits that the most likely value of a measured quantity is the one that minimizes the sum of the squared errors. The author also provides a way to determine the precision of a measurement and explores how to combine the results of multiple measurements to improve accuracy. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781332339136_0

Bibliographic Details

• Title: The Theory of Errors and Method of Least Squares (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2016
• Language: English
• ISBN 10: 1332339131
• ISBN 13: 9781332339136
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Statistics

About this title

Synopsis

Excerpt from The Theory of Errors and Method of Least Squares

The basis adopted in this book for the theory of accidental errors is that laid down by Gauss in the Theoria Motus Corporum CaUstium (republished as vol. vii of the Werke) which may be described for the most part in his own words, as follows:

"The hypothesis is in fact wont to be considered as an axiom that, if any quantity has been determined by several direct observations, made under similar circumstances and with equal care, the arithmetical mean between all the observed values presents the most probable value, if not with absolute rigor, at least very nearly so, so that it is always safest to adhere to it." (Art.177.)

Then introducing the notion of a law of facility of error to give precise meaning to the phrase "most probable value," we cannot do better than to adopt that law of facility in accordance with which the arithmetical mean is the most probable value. After deriving this law and showing that it leads to the principle of least squares, he says: "This principle, which in all applications of mathematics to natural philosophy admits of very frequent use, ought everywhere to hold good as an axiom by the same right as that by which the arithmetical mean between several observed values of the same quantity is adopted as the most probable value." (Art. 179)

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