The longitudinal mangetoconductivity of thin metallic wires has been studied by several authors [1][2][3][4][5] but no integrable equation has been obtained, except in limiting cases. As a recent study [6] has yielded evidence for the efficiency of the mean free path in representing the effects of partial scattering of electrons at a wire surface, we have attempted to extend this procedure to the case where both longitudinal electric and magnetic fields are operative, in order to propose a simple equation for the magnetoconductivity. The results are given in this letter.Let us consider a cylindrical wire, of axis 0z, whose cross-section in the xOy plane (perpendicular to 0z) has a circular shape (Fig. 1). The electron velocity v, is defined from its magnitude v, the angle, 0, of v with 0z, and the azimuth angle, 95, in the xOy plane (Fig. 1). Under the combined action of longitudinal electric and magnetic fields an electron moves on a helical trajectory [7 9]. An electron starting from a point A of the wire surface (of diameter 2a) with a radial velocity at angle 95 with respect to the radius of the wire, OA, moves on a helix whose projection in the xOy plane is a circle C of centre E and radius R withwhere m is the electron effective mass, e the absolute charge of the electron and B the magnitude of the magnetic field (Fig. 2). The electron is scattered by the wire surface to a point M, whose projection on the x-y plane is S, ; the projection of the electron path on the x-y plane traverses an angle 0 around the circle C. It is clear thatand ASI/AM 1 = Isin 0lThe angle ~ can be implicitly defined by calculating AS, AS, = 2Rsin-~l Assuming that an electronic specular reflection coefficient at wire surface, p, can be defined as usual [7,9] a mean-free path related to the size effect in the presence of magnetic field, 2s(0, 95, Ro/a) can be calculated according to the procedure previously defined 0261 8028/87 $03.00 + .12