  What determines the caliber of axonal branches? We pursue the hypothesis that
the axonal caliber has evolved to minimize signal propagation delays, while
keeping arbor volume to a minimum. We show that for a general cost function the
optimal diameters of mother ($d_0$) and daughter ($d_1$, $d_2$) branches at a
bifurcation obey a branching law: $d_{0}^{\nu+2}=d_{1}^{\nu+2} +
d_{2}^{\nu+2}$. The derivation relies on the fact that the conduction speed
scales with the axon diameter to the power $\nu$ ($\nu=1$ for myelinated axons
and $\nu=0.5$ for non-myelinated axons). We test the branching law on the
available experimental data and find a reasonable agreement.
