Resonant charge transfer cross sections are calculated for collisions between atomic ions and atoms in the energy range .1 ev < E < 100 ev using an energy impact parameter method in which the motion of the collision complex is treated classically. Both rectilinear and induced dipole trajectories are considered. Calculations using the induced dipole orbit were carried out on a computer. The results indicate that the classical induced dipole force tends to increase the charge transfer cross section in the low-energy region, and approaches the rectilinear orbit approximation in the higher energy region considered in this thesis.