Biological similarity relative to allometric quantities

Abstract

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.