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In an earlier paper, Thompson has shown experimentally that sharp electron beams can be obtained if the relative electrode potentials on the anode and the grid of a vacuum tube are properly adjusted. However, theoretical interpretation of this effect was lacking. In the present paper the effects of the grid-support wires and of the various tube dimensions on the angle of electron emission are investigated theoretically. The investigation indicates that Thompson's interpretations are in the right direction. Quantitative check with the experimental results cannot be expected, because the theoretical computations are based upon pure electrostatic considerations at the cathode surface, while in actual experiments the angle of beam current at the anode is measured. Thus, the focusing and defocusing effects of the field distribution in space and the space charge existing near the cathode will cause a wide deviation between the angle of electron emission at the cathode and that of the beam current at the anode.