The conductivity of ionized gases is treated by a method similar to that used by Alfven in his book "Cosmical Electrodynamics". The results differ from those of Alfven. In particular, it is shown that Alfven's conclusion, that whenever the Hall current disappears the conductivity becomes independent of the magnetic field, is not true in general. Moreover, it is not true under just the conditions of interest for the "Pinch Effect". The main conclusions of the present paper are (1) of currents down a tube, the ion component is the small fraction of m/M of the electron current, regardless of the magnitude of the magnetic field; (2) the conduction along the tube depends on the transverse motion of neutral mass, i.e. on the radial velocity of u(r) of the gas in the tube.