In the magnetized plasma of a hollow cathode arc the longitudinal and rotational drift velocities of ions have been measured, together with the electron and neutral densities and the temperatures of ions, electrons, and neutrals. The radial and longitudinal gradients of these quantities have been established. The ions drift against the electric field towards the anode with velocities between about 500 and 2500 m/s, driven by the plasma pressure gradient which is balanced by viscous deceleration and by friction against the surrounding neutral gas. The classical theory of the momentum balance with a turbulent contribution to the viscosity provides a good description of the longitudinal ion transport and explains direction and magnitude of the occurring drift velocity.