  We examine the scaling law $B \propto M^{\alpha}$ which connects organismal
metabolic rate $B$ with organismal mass $M$, where $\alpha$ is commonly held to
be 3/4. Since simple dimensional analysis suggests $\alpha=2/3$, we consider
this to be a null hypothesis testable by empirical studies. We re-analyze data
sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels,
Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting
$\alpha=2/3$ in favor of $\alpha=3/4$. For mammals, we find a possible
breakdown in scaling for larger masses reflected in a systematic increase in
$\alpha$. We also review theoretical justifications of $\alpha=3/4$ based on
dimensional analysis, nutrient-supply networks, and four-dimensional biology.
We find that present theories for $\alpha=3/4$ require assumptions that render
them unconvincing for rejecting the null hypothesis that $\alpha=2/3$.
