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The mathematical theory of the operation of the plate line of a distributed amplifier is developed using matrix algebra as a tool. The effects of a finite number of current generators placed at regular intervals on what would otherwise be an ordinary lumped-constant transmission line are determined. The theory predicts the manner in which the output of a distributed amplifier is changed with propagation constant of the grid and plate lines, termination of the grid and plate lines, number of tubes, and grid driving voltage. Some of the deductions made were tested using a six tube distributed amplifier; and, the experimental results were found to be in general agreement with predicted results.