Following a brief discussion of the Hahn theory of velocity modulation in which there is explained the basic velocity-modulation tube phenomena by means of space-charge waves propagating along the electron beam, the wave theory is reformulated by means of the retarded potentials for the most important case, that of a magnetically focused electron beam. The use of the potentials is believed to result in sufficient simplification to merit consideration in choosing the best attack on the theory. The electron beam is seen to be a medium for space-charge-wave propagation, the input signal serving to excite waves which propagate with beneficial change down the tube and induce output current in the output circuit. It is shown that important design constants for velocity-modulation tubes, such as optimum-drift tube length and the amount and phase of the transconductance, may be computed by use of the wave theory. Numerical values are given for a special case as an example.