Systems of Electrical Units

NBS MONOGRAPH 56 Systems Of Electrical Units U.S. DEPARTMENT OF COMMERCE HATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical prob- lems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Research projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's research are published either in the Bureau's own series of publications or in the jom-nals of professional and scientific societies. The Bureau itself publishes three periodicals available from the Government Printing Office: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio com- munications throughout the world. There are also five series of nonperiodical publications: Mono- graphs, Applied Mathematics Series, Handbooks, Miscellaneous Publications and Technical Notes. A complete listing of the Bureau's publications can be found in National Bureau of Standards Circular 460, Pubhcations of the National Bureau of Standards, 1901 to June 1947 ($1.25), and the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957 ($1 .50), and Miscellaneous Publication 240, July 1957 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) ($2.25); available from the Superintendent of Documents, Govern- ment Printing Office, Washington 25, D.C. • ERRATA TO ACCOMPANY NATIONAL BURBIAU OF STANDARDS MONOGRAPH 56, SYSTEMS OF ELECTRICAL UNITS Page Column Line Now reads in part Should read « • a « 15 2 ft • « « eQ 4»4»1» • {A^}p=2,657W2 (25..... two times 14 2 < four times V quantities 16 1 < 2 physical v. 22 1 27 the henry/ampere .... the henry/meter 34.5 February 15, I UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary NATIONAL BUREAU OF STANDARDS . A. V. Astin, Director Systems of Electrical Units Francis B. Silsbee Reprinted from the Journal of Research of the National Bureau of Standards^— C. Engineering and Instrumentation Vol. 66C, No. 2, April-June 1962 National Bureau of Standards Monograph 56 Issued September 20, 1962 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 30 cents Foreword As part of its mission to provide a basis for exact measurements in science and industrj', the National Bureau of Standards from time to time publishes survey material on the status of important areas of measurement. This publication sm'veys the various systems of units used in the hterature on electricity and magnetism and briefly traces their historical development. In electricit}- there has been a gradual evolution over the past half-century both in the definition of units and in the experimental methods for realizing and maintaining them in the laboratory. A significant change was the establishment by international agreement of the "absolute" system of electrical units on January 1, 1948 as announced in NBS Circular 459, Announcement of Changes in Electrical and Photometric Units. Additional details regarding the change were given in XBS Cii'culars C475, Establishment and Alaintenance oj the Elec- trical Units, and C531, Extension and Dissemination of the Electrical and Mag- netic Units by the National Bureau of Standards. However, since these pubHcations were issued, fm'ther uuprovements have been made m experimental procedures. Furthermore, smce the publication in 1916 of NBS Circular 60, Electric Units and Standards, and NBS Scientific Paper 292, International System of Electric and Magnetic Units, preferences and plailosophies regarding alternative systems of units have changed substantially. These latter develop- ments are currently under discussion by such international standardizing bodies as the International Electrotechnical Commission, the International Union of Pure and Applied Physics, and the International Organization for Standardization. It is hoped that the survey included in the present pubhcation will serve as a stimulus to the further development, understanding, and utilization of systems of electrical units. A. V. AsTiN, Director. iii Systems of Electrical Units Francis B. Silsbee (January 19, 1962) The various sj-stems of measurement, with their respective sets of units, used in the literature on electricity and magnetism are described in detail. Their historical development is summarized. The manner in which each is derived from either of the two alternative points of view of the experimentalist and the theoretician is compared and contrasted. The desirability of recognizing both points of view in international standardization, particularly when discussing rationalization, is pointed out. The present status of the absolute measurements on which all electrical units are based is reported, and tables are included for the conversion of equations and numerical values from one sj^stem to another. Contents 1. Introduction 1 6. Systems of measurement and representation 20 20 2. Historical summary 2 6.1. Sizes of units 6.2. Nomenclature of systems of measurement. - 21 3. Fundamental philosophies 4 6.3. Development of MKSA systems 21 4. Experimental approach 6 6.4. CGS systems 23 4.1. Nomenclature of units and standards 6 6.5. Practical and "international" systems 25 4.2. Measurement 9 6.6. IMiscellaneous svstems 25 4.3. Present experimental basis for electrical 6.7. The "fourth unit" problem 26 units 11 7. Dimensions 27 4.4. Experimental estabhshment of physical 8. Rationalization 29 laws 13 9. Summary and conclusions 32 4.5. Derivation of germane systems of measure- 10. Appendixes 34 ment by the Realist 16 10.1. Tables (for table 6 see p. 29) 34 5. Theoretical approach 17 10.2. Chronology 38 5.1. The mathematical model 17 10.3. Notation, glossary, and organizations 39 5.2. Coherent abstract units 19 10.4. References 41 1. Introduction opinion, merely one particularly striking indication of a very deep-seated difference in the points of This paper has been prepared with several objec- view and resulting philosophies of two major classes tives in mind. The first is to provide a definite of workers and thinkers in the field of physics. account of the authorities and procedures on which Hence, the fourth objective of this monograph is to measurements of electrical and magnetic quantities reconcile these contrasting philosophies by disen- are currenth' based. A second is to ofi^er a nomen- tangling them as completely as possible, even at the clature in the field of units and standards which is expense of a possibly excessive amount of circum- fairly consistent with current usage and which if locution and repetition in the text. generally adopted would minimize semantic con- In the development of this paper, a brief historical fusion in the field. A thu'd is to provide a brief summary will meet the third objective; the major historical survey to record the successive steps in division of the two philosopMes will then be out- the evolution of the various systems of electrical lined, the basic prmciple of the first (experimental) units, together with a systematic tabulation for philosophy being also appropriate for introducing converting equations and data from one system to digi-essions to cover the first and second objectives. another. A fourth objective is to reconcile the The contrastmg theoretician's philosophy will then current controversy which was triggered by the be described on the foundation of the quantity cal- 1950 decision of the International Electrotechnical culus. The various systems of equations and imits Commission to recommend the use in the future in the electrical field" will then be listed and com- will be followed by a brief discussion of a "rationalized" system of measurement. pared. This of the subject of dimensions from both points of The sharpness of this conflict is illustrated con- ^-iew. The process of rationalization as seen from cisely by comparing the following statements: the theoretician's point of view will contrast with (a) "1 oersted = 1,000 ampere-turns/meter." = that described earliei-, and the suggestions of various (b) "The number of ampere-turns per meter other writers who have recently attempted to cor- 1,000/4t times the number of oersteds." relate or reconcile the philosophies will be discussed. Each of these statements has

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