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At distances not exceeding 1500 km, it is convenient to calculate the field strength of a vlf transmitter by geometrical optics. In such computations, it is usual to assume some equivalent height for the (ionospheric) reflecting layer with a reflection coefficient that does not vary with angle of incidence. In the present paper, the ionosphere is taken to be a homogeneous ionized medium with a sharp lower boundary. The reflection coefficient, which is a function of angle of incidence, is utilized to compute the strength of the single and multiple hop sky waves. Combining these with the numerical results of the amplitude and phase of the ground wave, the total field is obtained. The theoretical field-strength-vs-distance curves compare favorably with the experimental data of Heritage for frequencies of 16.6, 18.6, and 19.8 kc over daytime paths in the Pacific Ocean. Finally, diffraction by the earth's bulge of the first hop sky wave is considered. This effect is important at ranges greater than 1200 km or so.