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Existing formulas for the amplification factor of the 3-electrode vacuum tube implicitly assume, among other things, that the distance between the grid and anode is large compared to the distance between turns of the grid. Formulas are developed here for the calculation of the amplification factor for plane and cylindrical structures for which this assumption is not permissible. The results given by the new formulas become identical with those obtained from existing formulas when the foregoing assumption is legitimate. A satisfactory experimental verification, made by determining the amplification factor for an ideal scale model of a plane structure immersed in an electrolytic trough, is also presented.