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Solution of Maxwell's equations for a cold, uniform magnetoplasma bounded by conducting walls shows (i) how plane waves evolve in the space of (??/??c,??p/??c) with (kc/??c) as parameter, and (ii) the range of parameters in which whistler mode propagation without Wieder's fine structure can be expected. In this space, the whistler evolves from an electrostatic mode at low densities, the whistler characteristic appears in a range of densities where the static approximation is invalid, and at still higher densities, residual effects of boundaries show up in the fine structure, as accounted for by J. C. Lee. The asymptotic form of the solution when lateral dimensions are large shows the existence of classes of solutions which are inadmissible because none can be reached along a continuous locus in this space. Effects of finite boundaries on the dispersion characteristic and the interpretation of experimental data are discussed.