The Julia set B for an N'th degree polynomial T and its equilibrium electrostatic measure /x are considered. The unique balanced measure on B is shown to be ix. Integral properties of /J. and of the monic polynomials orthogonal with respect to /J., P n , n = 0 , 1 , 2 , . . . , are derived. Formulae relating orthogonal polynomials of the second kind of different degrees are displayed. The measure ju is recovered both in the limit from the zeros and from the poles of the [N" -1/N n ] Pade

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... mant to the moment generating function to /A. For infinitely many polynomials of each degree N the zeros and poles all lie on an increasing sequence of trees of analytic arcs contained in B. The properties of these Pade approximant sequences support conjectures of George Baker which have not previously been tested on measures supported on sets nearly as complicated as Julia sets spread out in the complex plane.