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On the Nature of Dimensions

Published online by Cambridge University Press:  14 March 2022

Brian Ellis*
Affiliation:
University of Melbourne

Abstract

In the first part of this paper it is shown that unit names, whether simple or complex, whether of fundamental, associative or derivative measurement, may always be regarded as the names of scales. In the second it is shown that dimension names, whether simple, like “[M]”, “[L]” and “[T]”, or complex dimensional formulae, may always be regarded as the names of classes of similar scales. Thus, a new foundation for the theory of dimensional analysis is provided, and in the light of this, its nature and scope are examined. Dimensional analysis is shown to depend upon certain conventions for expressing numerical laws.

Type
Research Article
Copyright
Copyright © 1964 by the Philosophy of Science Association

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References

[1] Bridgman, P. W. Dimensional Analysis, Yale, 1931.Google Scholar
[2] Campbell, N. R. Foundations of Science, Dover, 1957.Google Scholar
[3] Campbell, N. R. An Account of the Principles of Measurement and Calculation, Longmans Green, 1928.Google Scholar
[4] Ellis, B.Some Fundamental Problems of Direct Measurement”, Australasian Journal of Philosophy, Vol. 38, No. 1, May, 1960.CrossRefGoogle Scholar
[5] Ellis, B.Some Fundamental Problems of Indirect Measurement”, Australasian Journal of Philosophy, Vol. 39, No. 1, May, 1961.CrossRefGoogle Scholar
[6] Focken, C. M. Dimensional Methods and their Applications, London, 1953.Google Scholar
[7] Stevens, S. S.On the Theory of Scales of Measurement”, Science, Vol. 103, No. 2684, 1946.CrossRefGoogle ScholarPubMed
[8] Stevens, S. S.Measurement, Psychophysics and Utility”, Measurement: Definitions and Theories, edited by Churchman, C. W. and Ratoosh, P., Wiley, 1959 (pp. 1863).Google Scholar