Excerpt from Basic Mathematical Research for Electromagnetic Theory Though the effect of the ionosphere on electromagnetic wave propagation has been studied for fifty years, definitive results are lacking. The reason is that the ionosphere in the presence of the earth's magnetic field presents a nonhomogeneous anisotropic medium with several parameters such as collision frequency, the gyromagnetic frequency of the electrons, and density of the electrons, each varying as a function of position and time, about which quanti tative knowledge is fragmentary. Even if the parameters and consequently the dielectric tensor were known precisely the mathematical problem of predicting the behavior of a plane wave or dipole field which enters the ionosphere from below is still beyond the full powers of present-day mathematics. Awareness of this fact has led us to undertake fundamental theoretical work bearing on this problem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.