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The paths of electrons in a uniform magnetic field, under the influence of forces transverse to the magnetic field, are of interest in a variety of vacuum tubes. In general, the force experienced by the electron varies with time. The time variation may arise from motion of the electron through an electrostatic field, from motion of the electron along the lines of a curved magnetic field (inertial forces), or from the deliberate application of a time-varying electric field. A graphical method for obtaining the electron paths is described as follows; the given transverse-field versus time curve is approximated by tangent sections; the complete analytic solution is obtained for any tangent section; the analytic solution is interpreted graphically; and a method for joining graphical solutions of neighboring sections is developed. Emphasis is placed on the resultant velocity components and displacement after the field has ceased to act. The graphical method is used to analyze the motion of electrons in the orthicon and image orthicon, television pickup tubes in which the velocity components of the scanning beam critically affect performance. Problems considered are: magnetic and electrostatic deflection in a magnetic field, an electrostatic lens immersed in a magnetic field, the effect of "tapering" the applied forces, and the possibility of canceling unwanted velocity components introduced in one part of the tube by equal and opposite components introduced in another part.