Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-09T08:23:02.599Z Has data issue: false hasContentIssue false
  • English
  • Français

Derived Measurement, Dimensions, and Dimensional Analysis

Published online by Cambridge University Press:  14 March 2022

Robert L. Causey
Robert L. Causey*
Affiliation:
The University of Texas at Austin
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a representational theory of derived physical measurements. The theory proceeds from a formal definition of a class of similar systems. It is shown that such a class of systems possesses a natural proportionality structure. A derived measure of a class of systems is defined to be a proportionality-preserving representation whose values are n-tuples of positive real numbers. Therefore, the derived measures are measures of entire physical systems. The theory provides an interpretation of the dimensional parameters in a large class of physical laws, and it accounts for the monomial dimensions of these parameters. It is also shown that a class of similar systems obeys a dimensionally invariant law, which one may safely subject to a dimensional analysis.

Type
Research Article
Information
Philosophy of Science , Volume 36 , Issue 3 , September 1969 , pp. 252 - 270
Copyright
Copyright © 1969 by The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

This paper reports part of the research presented in my dissertation at the University of California, Berkeley (1967). The dissertation has been reprinted as [7]. I have benefited from discussions with William Craig, R. D. Luce, and especially E. W. Adams, my dissertation advisor. I also wish to thank the referees for some helpful suggestions concerning the text.

References

[1] Aczél, J., Lectures on Functional Equations and Their Applications, Academic Press, New York, 1966.Google Scholar
[2] Adams, E. W., “On the Nature and Purpose of Measurement,” Synthese, vol. 16, 1966, pp. 125–169.CrossRefGoogle Scholar
[3] Birkhoff, G., Hydrodynamics, revised edit., Princeton University Press, Princeton, 1960.Google Scholar
[4] Bridgman, P. W., Dimensional Analysis, revised edit., Yale University Press, New Haven, 1931.Google Scholar
[5] Büchi, J. R., and Wright, J. B., “The Theory of Proportionality as an Abstraction of Group Theory,” Mathematische Annalen, vol. 130, 1955, pp. 102–108.CrossRefGoogle Scholar
[6] Campbell, N. R., Foundations of Science, Dover, New York, 1957.Google Scholar
[7] Causey, R. L., Derived Measurement and The Foundations of Dimensional Analysis, Technical Report No. 5, Measurement Theory and Mathematical Models Reports, University of Oregon, Eugene, Oregon, 1967.Google Scholar
[8] Einstein, A., “Elementare Betrachtungen über die thermische Molekularbewegungen in festen Körpern,” Annalen der Physik, vol. 35, 1911, pp. 679–694.Google Scholar
[9] Ellis, B., Basic Concepts of Measurement, Cambridge University Press, Cambridge, 1966.Google Scholar
[10] Ellis, B. D., “On the Nature of Dimensions,” Philosophy of Science, vol. 31, 1964, pp. 357–380.CrossRefGoogle Scholar
[11] Luce, R. D., “On the Possible Psychophysical Laws,” Psychological Review, vol. 66, 1959, pp. 81–95.CrossRefGoogle ScholarPubMed
[12] Sedov, L. I., Similarity and Dimensional Methods in Mechanics, 4th edit., Moscow, 1957 (English translation, Academic Press, New York, 1960).Google Scholar
[13] Suppes, P., and Zinnes, J. L., “Basic Measurement Theory,” in Luce, R. D., Bush, R. R., and Galanter, E. (eds.), Handbook of Mathematical Psychology, vol. 1, Wiley, New York, 1963.Google Scholar
[14] Tolman, R. C., “The Principle of Similitude,” Physical Review, vol. 3, 1914, pp. 244–255.CrossRefGoogle Scholar