  We give a precise formula for the value of the canonical Green's function at
a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we
express the 'energy' of the Weierstrass points in terms of a spectral invariant
recently introduced by N. Kawazumi and S. Zhang. It follows that the energy is
strictly larger than log 2. Our results generalize known formulas for elliptic
curves.
