Metabolic rates

Roughly, surface area, A, of an animal scales as its length, L, squared
A = L2
and the mass, M, scales as L cubed
M = L3
Heat is dissipated across the surface, and metabolic rate is proportional to heat dissipation, so
metabolic rate ≈ L2 = M2/3
(metabolic rate)/(unit mass) ≈ M-1/3
Seems reasonable. Pulse rate is related to metabolic rate per unit mass, and we know smaller animals have faster heartbeats.
However, extensive and careful measurements by Kleiber showed that metabolic rate per unit mass scales as M-1/4, instead of M-1/3. Why should this be?
More heat is lost through the lungs than across the skin surface, so the fractal structure of the lungs may account for this difference.

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