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 7/3 < p < 8/3. 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 hq with q near the lower end of 2/3 < or = q < or = 1. Data from Hong Kong and British children are consistent with these hypotheses.