Errors of Observation and their Treatment
This little book is written in the first place for students in technical colleges taking the National Certificate Courses in Applied Physics; it is hoped it will appeal also to students of physics, and pernaps chemistry, in the sixth forms of grammar scho
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ERRORS OF OBSERVATION AND THEIR TREATMENT by
J. TOPPING, PH.D., F.lNST.P. Forllll!l"h Vicl!-Clwncellor. Brunel G'nirer,lin'
FO\JRTH
[DITIO~
CHAPMAN AND HALL SCIENCE PAPERBACKS
First published 1955 Reprinted once Second edition 1957 Reprinted twice Third edition 1962 Reprintedjive times Fourth edition 1972 Reprinted 1975 Chapman and Hall Ltd., 11 New Fetter Lane, London EC4P 4EE
© 1972J. Topping Whitstable Litho Ltd., Whitstable, Kent. ISBN-13: 978-0-412-21040-2 e-ISBN-13: 978-94-011-6928-8 DOI: 10.1007/978-94-011-6928-8
This paperback edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated withollt the pllblisher' s prior consent in any form of binding or cover other than that in which it is published and withollt a similar condition inc/uding this condition being imposed on the subsequent purchaser. All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission il1 writing from the Pllblisher.
Distributed in the U.S.A. by HALSTED PRESS, A DIVISION OF JOHN WILEY & SONS, INe .• NEW YORK
PREFACE This little book is written in the first place for students in technical colleges taking the National Certificate Courses in Applied Physics; it is hoped it will appeal also to students of physics, and pernaps chemistry, in the sixth forms of grammar schools and in the universltIes. For wherever experimental work in physics, or in science generally, is undertakcn the degree of accuracy of the measurements, and of the res,!lts of the experiments, must be of the first importance. Every teacher of experimental physics knows how "results" given to three or four decimal plaees are often in error in the first place; students suffer from "delusions of accuracy." At a higher level too, more experieneed workers sometimes claim a degree of accuracy which cannot be justified. Perhaps a consideration of the topics discussed in this monograph will stimulate in students an attitude to experimental results at onee more modest and more profound. The mathematical treatment throughout has been kept as simple as possible. It has seemed advisable, however, to explain the statistical concepts at the basis of the main considerations, and it is hoped that Chapter 2 contains as elementary an account of the leading statistical ideas involved as is possible in such small compass. It is a necessary link between the simple introduction to the nature and estimation of errors given in Chapter 1, and the theory of errors discussed in Chapter 3. Proofs have usually been omitted but references to other works are given in the text. There is also a list of books for further reading. I am much indebted to other writers, wh ich will be obvious, and to many groups of students particularly those at The Polytechnic, Regent Street, London, who bor
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