The electronic excitation transfer cross section between identical atoms in S and P states in the gas phase was investigated theoretically in the low-incident-energy range by means of the impact-parameter method. With respect to the P states of an atom, all three degenerate P states of mutually orthogonal polarizations were taken into account. The direction of P polarization was taken into account using two different methods. These methods were the "fixed-atom approximation" and the "rotating-atom approximation," respectively. The difference between the solution from coupled equations with respect to the direction of P-state polarization and those from the respective approximations mentioned above was studied. The fixed-atom approximation was found to be better than the rotating-atom approximation for the computation of the over-all cross section of S-P-type excitation transfer. The cross section obtained from the coupled equations was nearly one-half of that from the rotating-atom approximation and nearly 1.5 times as much as that from the fixed-atom approximation. It is shown that the total cross section can be written as σ=3.36πe2μ2ℏv, where v represents the relative velocity of an incident atom, e the electronic charge, and μ the transition dipole matrix element between the S and P states under consideration.