Advertisement

Equations and Units

  • Eugen Skudrzyk

Abstract

We must distinguish between dimensional equations that are valid in all self consistent systems of units and equations that give the numerical values only in a specified system of units. A dimensional equation, for instance, is
$$ {\text{u = Ri}}{\text{.}} $$
(1)
This equation holds regardless of what the units are. In contrast, the equation
$$ u=\underline{23}i\ , $$
(2)
where u represents a voltage and i a current, holds only in the system of units for which the numerical value 23 has been specified. Strictly speaking, this equation is incorrect in the form written because 23 is a number of zero dimension; and volts as given by the left-hand side, can never be amperes, as given by the right-hand side. To draw attention to this fact, 23 is underlined to indicate that it is not just a number, but also has a dimension. It is poor practice to omit dimensional symbols, because a dimensional check is always the first step in tracing computational errors. The equations in this book, therefore, refer to dimensional magnitudes almost without exception, and they hold for every coherent system of units.

Keywords

Magnetic Flux Electric Displacement Coherent System Dimensional Equation Standard Resistor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. The American Society of Mechanical Engineers, “Letter Symbols for Acoustics”, New York, N. Y. 1959.Google Scholar
  2. American Standards Association, New York, N. Y. 1960: Incorporated, “Acoustical Terminology”; C 61. 1–1961 Quantities and Units Used in Electricity, 1966.Google Scholar
  3. Bodea, E.: Giorgis rationales MKS-Maßsystem mit Dimensionskohärenz für Mechanik, Elektromagnetik, Thermik, fundiert auf Kalantaroff’s (LTQ)-System, 2. Aufl. Basel: Birkhäuser. 1949.Google Scholar
  4. Bridgeman, P. W.: Theorie der physikalischen Dimensionen. Leipzig, Berlin: Teubner. 1932; Dimensional analysis. New Haven and London: Yale University Press. January.Google Scholar
  5. Cornelius, P.: The rationalized Giorgi system with absolute volt and ampere as applied in electrical engineering. Philips techn. Rev. 10 (1948) 79–86.Google Scholar
  6. Cornelius, P., Hamaker, H. C.: The rationalized Giorgi system and its consequences.Philips Res. Rep. 4 (1949) 123–142.Google Scholar
  7. Cowan, E. W.: Basic electricity magnetism. New York, N. Y.: Academic Press. 1968.Google Scholar
  8. Curtis, H. L.: Electrical measurements. New York, N. Y.: McGraw-Hill. 1937.Google Scholar
  9. Dunconson, W. E.: The dimensions of physical quantities. Proc. Physic. Soc. London 53 (1941) 432–448.ADSCrossRefGoogle Scholar
  10. Golding, E. W.: Electrical measurements and measuring instruments (Kap. II). London: Pitman and Sons. 1933.Google Scholar
  11. Groot, W. De: Die Entstehungsgeschichte des Giorgi-Systems der elektrischen Einheiten. Philips techn. Rdsch. 10 (1948/49) 54–60.Google Scholar
  12. Guggenheim, E. A.: Units and dimensions. Philos. Mag. 33 (1942) 479–496.Google Scholar
  13. Halsey, R. J.: The rationalised M.K.S. system of electrical units. Post Office Electr. Engr. J. 46, 4, 187–190.Google Scholar
  14. Hecht, H.: Betrachtungen zum physikalischen Maßsystem. Göttingen: Wissenschaftl. Verlag Musterschmidt. 1951.Google Scholar
  15. Jackson, L.: Classical electrodynamics. New York, N. Y.: Wiley. 1962.Google Scholar
  16. Knetssler, L.: Über das Meter-Kilogramm-Sekunden-System (System Giorgi). E und M 54(1936) 1–2.Google Scholar
  17. Oberdorfer, G.: Das natürliche Maßsystem. Wien: Springer. 1949.Google Scholar
  18. Sralicky, M.: Die neuen elektrischen absoluten Maßeinheiten. Siemens Austria Z. 1 (1949) 25–27.Google Scholar
  19. Verheulen, R.: Normung akustischer Größen. Philips techn. Rdsch. 5 (1940) 250–251;Google Scholar
  20. Verheulen, R.: Dimensional analysis, units and rationalisation. Philips Res. Rep. 7 (1952) 432–441.Google Scholar
  21. Wallot, J.: Größengleichungen und Zahlenwertgleichungen. E.T.Z. 64 (1943) 13–16;Google Scholar
  22. Wallot, J.: Elektrische Maßsysteme. E.T.Z. 64 (1943) 299–303.Google Scholar
  23. Williams, H. P.: Electrical units and the MKS System. Electr. Communic. 23 (1946) 96–105.Google Scholar
  24. United States Department of Commerce: Stans, M. H., ASTIN, A. V.: The English and metric systems of measurement (Special Publication 304 A, issued 1968, revised 1969), available from the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402.Google Scholar
  25. New Values for the Physical Constants,Recommended by NAS-NRC, NBS Technical News Bulletin, October 1963, also NBS Technical News Bulletin, May 1965 (For sale by the uperintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402).Google Scholar
  26. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part I-1965 Basic quantities and units of the SI.Google Scholar
  27. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.: R 31-Part II-1958 Quantities and units of periodic and related phenomena.Google Scholar
  28. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part III-1960 Quantities and units of mechanics (Z 10.3–1948, [R 1953]).Google Scholar
  29. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part IV-1960 Quantities and units of heat (Y 10.4–1957).Google Scholar
  30. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part V-1965 Quan tities and units of electricity and magnetism.Google Scholar
  31. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part VII-1965 Quantities and units of acoustics.Google Scholar
  32. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:R 31-Part XI-1961 Mathematical signs and symbols for use in the physical sciences and technology.Google Scholar
  33. International Organization for Standardization,available from the USA. Standards Institute, 10 East 40th St., New York, N. Y.:Y 10.19–1967 Letter symbols for units in electrical • science and electrical engineering [(I.E.E.E. No. 260), September 1968].Google Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations