This thesis is concerned primarily with determination of statistics for the velocities of propagation of an electromagnetic wave in a dispersive medium. The velocities of propagation are discussed in terms of a plane travelling wave solution of Maxwell's equations obtained using the multiple Laplace transformation and complex inversion integrals. The types of dispersion discussed correspond to a magneto-ionic, electron displacement and polar resonances of the ionosphere and troposphere. The physical nature of the randomness of the dispersive index of refraction is derived from considerations of statistical turbulence theory. Expressions are then obtained for determining the mean, mean square and variance of the signal, group and phase velocity of an electromagnetic wave. It is proposed by S. M. Harris (IRE Trans. Vol. AP-9, No. 2, pp. 207-210, Mar., 1961) that the group velocity and phase velocity of an electromagnetic wave propagated in the ionosphere may be averaged to obtain a velocity estimate free of refraction to within second order refractive effects. The basis for this procedure is that for an operating frequency considerably above the critical frequencies of the ionospheric medium, the group velocity is slightly less than the velocity of light.
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