The influence of the ratio of magnetic field to gas pressure on the perpendicular and transverse drift velocity of an electron swarm is examined quantitatively for H2, N2, O2, air and C2H6 for mean energies from 0?1 to 10 ev. Whereas the perpendicular drift velocity reaches a peak value when the electron collision frequency is approximately equal to the cyclotron frequency, the transverse velocity starts to decline when this equality is reached. In contrast, the ratio of the perpendicular to transverse velocity, which is shown to be an important quantity governing gaseous discharge movement, continues to increase with B/p; the increase is almost linear throughout except for gases exhibiting the Townsend-Ramsauer effect. Expressions are derived for the low and high magnetic field case and values in the intermediate region, which lies in the range 10-3 B/p 10-1 Wb m-2 torr-1, are obtained numerically. The mobility values for the different gases at a fixed value of mean energy and B/p differ by up to a factor of 10, and this should allow discharge propagation velocities to be identified with particular movement mechanisms unless obscured by feedback processes. At low magnetic fields the perpendicular drift velocity is derived as a function only of B/p and E/p. If the equivalent pressure concept were used in the derivation of Amp?re's law, the magnitude of the force on a conductor in a crossed magnetic field would be higher than hitherto accepted. The relevance and application of the calculated magnetic transport data to practical discharges are mentioned briefly.