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The problem of radiation of a surface wave by an elemental vertical electric dipole on an impedance plane is formulated in terms of a surface integral. This integral is solved approximately in one dimension, while integration with respect to the second dimension is achieved through Laplace transform methods. The result is the same as that obtained through the classical formulation using a spectrum of plane waves, but the use of a constant surface impedance avoids the difficulties of solving a boundary-value problem. The influence of the Fresnel zones is clearly indicated, and the effect of electrical parameters of the surface is discussed. Since the treatment is simpler and more compact than the usual classical solution, while retaining nearly all the salient features of the latter, it may prove useful as an introduction to surface wave propagation at the introductory graduate level.