The bulletin of mathematical biophysics

, Volume 27, Supplement 1, pp 131–133 | Cite as

Biological similarity relative to allometric quantities

  • Hugo M. Martinez


It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation
$$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$
A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.


Metabolic Rate Dimensional Analysis Constant Density Empirical Fact Plausible Assumption 
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  1. Günther, B. and B. Leon de la Barra. 1965. “Theory of Biological Similarities, Non-Dimensional Parameters and Invariant Numbers.”Bull. Math. Biophysics, in press.Google Scholar
  2. Günther, B. “Thermal Similarity Principle, Dimensional Analysis and Homeothermy.” (Unpublished paper, private communication).Google Scholar
  3. Langhaar, H. L. 1951.Dimensional Analysis and Theory of Models. New York: Wiley and Sons.MATHGoogle Scholar

Copyright information

© N. Rashevsky 1965

Authors and Affiliations

  • Hugo M. Martinez
    • 1
  1. 1.Department of MathematicsU.S. Naval Postgraduate SchoolMonterey

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