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Ray paths and focusing properties are calculated for the deflection and acceleration fields of a flat picture tube with lateral beam injection such as has been introduced to the art by W. R. Aiken. The results give insight into the measures which must be taken to achieve linearity of deflection and to assure sharp spot focus over the picture area. Specifically, it is found that linear deflection can be obtained by the application of voltage variations to the deflection electrodes which do not depart greatly from linear variations between the prescribed maximum and minimum values. Horizontal focus is determined almost entirely by the focusing action of the gun and the horizontal deflection plates. The focusing action of the latter is such that the beam incident on the deflection field must be, in general, divergent. The point of divergence required shifts with the horizontal scan, resulting in the need for some kind of dynamic control of gun focus. The horizontal deflection fields, the fields between the accelerating electrodes, and the vertical deflection fields all contribute to vertical focusing. If the separation of the side plates of the horizontal deflection system is of the same order as or less than the height of the deflection structure, the first focus formed by the horizontal deflection field is re-imaged at the screen by the remaining focusing elements. The vertical deflection field alone will not focus a parallel incident pencil in the plane of the screen.