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Chapter I. The performance of an oscillating pliotron is determined by accertaining at intervals of a few degrees the instantaneous plate loss, grid loss, input, and so on. These values are then averaged over the cycle to determine tube output and efficiency. By performing this operation with a variety of plate and grid voltages, the optimum conditions for a given output are obtained. In this way a combination of plate and grid voltages and grid bias is obtained which is independent of frequency and can be used for the design of any free oscillating circuit where sinusoidal plate and grid voltages are obtained 180 degrees out of phase. It is shown that the conditions of starting of oscillations can be obtained by assuming zero grid bias and determining the circuit resistance which will just absorb the tube output for small amplitude oscillations. The phenomenon of "blocking" is shown to be due to secondary electron emission from the grid. By knowing under what conditions this secondary emission takes place the circuit may be so designed that all will not occur simultaneously. Chapter II. For qualitative investigations of vacuum tube performance the plate circuit is assumed to be a portion of a sine wave. This permits mathematical integration to be substituted for the step-by-step integration of the first chapter. By using the mathematical form a qualitative investigation of the effects of space charge, variations in plate voltage and other factors can be made.