Applications of operational calculus to ground-wave propagation, particularly for long waves

All results of the approximative diffraction theory dealing with the propagation of radio waves around a smooth spherical earth (surrounded by a homogeneous atmosphere) can be derived from a one-dimensional integral equation originally discussed by Hufford. This equation can be solved in terms of operational calculus which leads, first of all, to the well-known residue series. In this treatment the Sommerfeld theory for a fiat earth appears at once as a limiting case; moreover, analytic expressions for correction terms accounting for the finite value of the earth´s radius are easily determined. Finally, the equation in question can also be used for the extension to inhomogeneous soil conditions, without neglecting the earth´s curvature.