Discussion Of The Precision Of Measurements. With Examples Taken Mainly From Physics And Electrical Engineering

PREFACE. THE material presented in this volume is the outcome of several years teaching of the subject. In a less complete form it was prepared for lecture notes and was printed in pamphlet form, but not published, by the Massachusetts Institute of Technology in 1888, having appeared in the Tech- nology Quarterly and in the Electrical Engineer in 1887. In this revised form, the author has felt that it perhaps possessed sufficient completeness and originality to be of interest or value to students and teachers, and therefore to merit publication. In venturing to urge the importance of the subject as a course of study for engineers and for students of physics or other pure sciences, the author would suggest the value of the attitude of mind produced by it. One who has in any reason- able degree mastered its methods, although hemay never apply them directly, will not only have increased his power to intelligently scrutinize experimental results, but will have acquired a tendency to do so. And it is perhaps not too much to hope that he may acquire a notion of a judicious distribution of effort which, with the best of results to himself, he may carry into quite other matters. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, BOSTON, September, 1892. SILAS W. HOLMAN. Introductory CONTENTS. PRECISION OF MEASUREMENTS. DIRECT MEASUREMENTS. PAGE Direct Measurements 4 Indirect Measurements 4 Quantities Independent, Conditioned 5 Sources of Error 5 Errors of Single Observations.- 6 Variable Part 6 Constant Part, Constant Error 7 Elimination of Constant Error, 7 Corrections 8 Example I. A, B, C. Distance by Steel Tape 9 Determinate and Indeterminate Errors 10 Residuals II Accuracy or Error of Result 13Deviations 14 General Law of Deviations 15 Mean Best Representative Value 16 Deviation Measure 16 Average Deviation 16 Example II 18 Negligible Amounts 20 Places of Figures in d.m. and Best Value of n 22 Other Deviation Measures 23 Special Law of Deviations, 24 Precision Measure of Result 25 in P.M 26 To Make Residuals Negligible ., Criterion 26 Best Value of Residuals Equal Effects 27 Fractional Deviation, Fractional Precision 29 Mistakes 30 v I VI CONTENTS. FACET Criterion for Rejection of Doubtful Observations 30 Weights 31 Meaning of Estimated Accuracy of Direct Result 32 Forms of Problems on Accuracy of Result 33 Data Required to Substantiate Result 36 Planning of Direct Measurement, 36 Solutions of Illustrative Problems in Direct Measurements 37 Example III. Weighing. Balance 37 Example IV. Voltmeter Calibration 41 INDIRECT MEASUREMENTS. Estimate of Accuracy of Indirect Result 45 Error of Method 46 Check Methods 47 Relation between P.M. of Results and of Components 47 Types of Problems 47 General Formulae .... 48 Notation 49 Separate Effects. I, II. Formulae, 49 Resultant Effects. Ill 1,2. Formulae 50 Equal Effects. Formulae 53 Application to Precision Discussions 54 Formulae for General and Special Functions 55 Simple Functions 56 Separation into Factors which are Functions of . . Single Components. 61 Separation into Groups 63 Critera for Negligibility of 8 in Components 67 Numerical Constants 70 Equal Effects. Demonstration 70 Estimated Precision Measures of Components 72 Components with Special Laws of Deviations 73 Preparation of Functions for Discussion 73 Simplification of Functions 75 Significant Figures 76 Rules for Significant Figures...