The inclusion of the variation of the equilibrium magnetic field across the Larmor orbits of the resonant particles is crucial for a self-consistent treatment of cyclotron resonance in plasmas. Two contrasting nonrelativistic self-consistent calculations [T. M. Antonsen and W. M. Manheimer, Phys. Fluids 21,2295 (1978); C. N. Lashmore-Davies and R. 0. Dendy, Phys. Fluids B 1, 1565 ( 1989) ] which analyze perpendicular propagation in the same nonuniform magnetic field are compared. It is shown that the first of these, which is a full wave calculation, makes an approximation that eliminates the damping found in the second, which calculates optical depth via a Wentzel-Kramer-s-Brillouin (WKB) approximation. A new expansion of the exact integral equation describing the problem is given, producing full wave equations which incorporate the perpendicular damping. The equations are of the correct form to ensure energy conservation and can easily be obtained to any order in an expansion in terms of the ratio of Larmor radius to perpendicular wavelength.