Numerical values of the path integrals for the first five hops are given as a function of distance from 1000 km to 8000 km, for frequencies of 10, 20, 30, 60, 100, 150, and 200 kHz., for sea paths, and for land paths with conductivities of 0 * .01 and 0.001 mhos/m, assuming reflection heights of 60, 70, 80, 90, and 100 km.For convenience, ground wave curves for the same parameters are given.Using these values, and any ionospheric reflection coefficients, the individual time modes, and the total field can be calculated simply.The calculation is valid near the caustic and in the shadow region.The path integrals can also be used to extract ionospheric reflection coefficients from experimental data. (Author).