Scaling of human body mass with height: the Body Mass Index revisited

We adapt a biomechanical argument of Rashevsky, which places limits on the stress experienced by a torso supported by the legs, to deduce that body mass $m$ of growing children should scale as the $p$th power of height $h$ with $7\mathrm{/}3<p<8\mathrm{/}3$. Further arguments based on stability and heat loss suggest that $p$ should be close to 8/3. The arguments are extended to suggest that waist circumference $w$ should scale as $h^q$ with $q$ near the lower end of $2/3\leq q \leq 1$. Data from Hong Kong and British children are consistent with these hypotheses.