Excerpt from Excitation and Propagation of Surface WavesRays in Space can be defined in terms of the propagation velocity by Fermat's principle or by the differential equations which follow from it. Complex rays can be defined by applying Fermat's principle to complex curves, or by considering complex solutions of the ray equations. In either case it is necessary that c(x) be defined for complex values of x which is the case if is an analytic function of x. 'we can also define complex surface rays by applying Fermat's principle to complex curves on the surface S or by considering complex solutions of the equations for surface rays. In this case it is necessary that both the velocity c1(x) and the surface S be defined for complex 2.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.