With some interest, I have read that Pappert, Gossard, ;1nd Roth· muller have developed a comprehensive computer program to obtain numerical results for the propagation . constants of an earth-ionosphere waveguide with an arbitrary electron-density profile. The overall agreement between their approach based on Budden's (1961) work and our method (e.g., Wait and Spies, 1960;Wait, 1960) is quite reassuring. If nothing else, it should lay to rest the contro· versies which have arisen in connection with the importance of accounting properly for earth curvature in calculating the charac· teristics of the least attenuated modes.In their paper, Pappert, Gossard, and Rothmuller (1967) show good agreement with some of our numerical results for the firstorder mode in daytime but they get only partial agreement for the second-order mode in daytime. Actually, the differences are not to be unexpected. As we explained in our technical note (Wait and Spies, 1964): · "In summary, the calculations given in this technical note are strictly correct for an earth-ionosphere waveguide which is bounded by a homogeneous smooth earth and a reflecting layer at height h with a normalized surface impedance ~-'The applicability of the results to an actual diffusely bounded ionosphere requires a number of approximations which are justified mainly an physical grounds. The principal assumption is that ~ is assumed at the outset and then the mode· equation is solved to yield the propagation characteristics. A fundamental question may arise in that the angle of incidence is complex for modes in a lossy waveguide. However, it is fortunate that the cosine C' of the angle of incidence at the ionosphere is approximately equal to (2h/a+{7JI/2 where Cis related to the parameter t, in (13), by

THETASKOFCOMMUNICATING withasatellite from a fixed or moving station on or near the earth is becoming one that must be accom-107