A radio-frequency sheath model for a spherical probe in a collisionless plasma is presented. The method of solution is based on the quasi-static approximation and the electrostatic probe theory of Bernstein and Rabinowitz. The resistive part of the admittance is ascribed to the sheath transit-time collisionless dissipation mechanism suggested by Mayer and developed by Gould. Expressions are obtained for the effective sheath thickness and the equivalent resistance of the transit-time dissipation. The sheath model and, hence, the admittance are completely determined in terms of the bias potential, the probe radius, the plasma frequency, and the Debye length; i.e., there are no adjustable parameters in our theory which are to be determined by experiment. Our results agree favorably with Cohen and Bekefi's experimental data on the conductance resonant frequency and the width of the conductance peak.