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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
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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

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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

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