The theoretical problem of a weakly ionized, constant temperature, three particle plasma in an externally generated magnetic field is reformulated by transforming the set of 14 macroscopic plasma equations (continuity and momentum equations for ions and electrons plus Maxwell's equations) in 14 unknowns (ion and electron number densities and velocities plus the effective electric and magnetic fields) into an equivalent set of 4 integral equations in 4 unknowns. In the course of this transformation, it is shown that the plasma behavior can be interpreted in terms of three ambipolar processes : drift, deformation, and diffusion. Plasma diffusion is characterized by two diffusion coefficients : the usual Schottky formula applying in the direction parallel to the effective magnetic field and a new expression for the ambipolar transverse diffusion coefficient applying in directions perpendicular to the effective magnetic field. The new ambipolar coefficient differs markedly from the familiar ambipolar coefficient associated with the names of Bickerton, Lehnert, Holway, Allis, and Buchsbaum; and, in general, it gives values for the transverse diffusion coefficient which are two orders of magnitude larger than those given by the latter. It is concluded that ambipolar diffusion can produce a transverse diffusion coefficient large enough to account for the diffusion rates measured by Bohm, Burhop, Massey, and Williams in argon arc discharges.