The inertial motion of a free particle on a β-plane is studied here. Analytical solutions are found, and discussed in a phase diagram. Asymptotic cases are also given some attention. Eastward and westward drift velocities are computed analytically as a function of the parameter β and an angle of incidence. Particles which do not cross the equator always drift westward, while particles which cross the equator drift either eastward or westward or describe a stationary pattern. Trajectories are also discussed on a rotating globe. Finally, the results are related to Lagrangian studies and to the stability analysis of zonal equatorial currents.