The extended WKB method is employed to obtain a solution of the differential equation governing the dependence of field strength on height. The excess permittivity is represented as an exponential function of height. The method yields asymptotic solutions which become less accurate as the frequency decreases. It is found that the first-order solution can be used down to 300 kHz. For lower frequencies, the more complicated second-order solution is necessary, which can then be used down to 10 kHz. The results are compared with those based on an airless earth and an equivalent earth of 4/3 times the true radius.