The importance of these deductions lies in the fact that an electric charge in motion, quite independently of any material nucleus, possesses an apparent mass in virtue of its motion, and that this mass is a function of the speed. Indeed, we shall see later (see section 82) that the apparent mass of the particles constituting the cathode stream can be explained in virtue of their charge, without the necessity of assuming a material body in which the charge is distributed. This has led to the suggestion that all mass may be electrical in origin, and due purely to electricity in motion. =49. Action of a magnetic field on a moving ion.= Let us consider the case of an ion of mass _m_ carrying a charge _e_ and moving freely with a velocity _u_. If _u_ is small compared with the velocity of light, the ion in motion corresponds to a current element of magnitude _eu_. If the ion moves in an external magnetic field of strength _H_, it is acted on by a force at right angles both to the direction of motion, and to that of the magnetic force and equal in magnitude to _Heu_ sin θ, where θ is the angle between the direction of the magnetic force and the direction of motion. Since the force due to the magnetic field is always perpendicular to the direction of motion, it has no effect upon the velocity of the particle, but can only alter the direction of its path. If ρ is the radius of curvature of the path of the ion, the force along the normal is equal to _mu²_ -----, ρ and this is balanced by the force _Heu_ sin θ. If π θ = ---, 2 _i.e._ if the ion is moving at right angles to the direction of the magnetic field _mu²_ _Heu_ = ----- ρ or _m_ _H_ρ = ---- _u_ _e_ Since _u_ is constant, ρ is also constant, _i.e._ the particle describes a circular orbit of radius ρ. The radius of the circular orbit is thus directly proportional to _u_, and inversely proportional to _H_. If the ion is moving at an angle θ with the direction of the magnetic field, it describes a curve which is compounded of a motion of a particle of velocity _u_ sin θ perpendicular to the field and _u_ cos θ in the direction of the field. The former describes a circular orbit of radius ρ, given by _m_ _H_ρ = --- _u_ sin θ; _e_ the latter is unaffected by the magnetic field and moves uniformly in the direction of the magnetic field with a velocity _u_ cos θ. The motion of the particle is in consequence a helix, traced on a cylinder of radius