Excerpt from The Bell System Technical Journal, 1939, Vol. 18: A Journal Devoted to the Scientific and Engineering Aspects of Electrical CommunicationCertain types of electrostatic fields may be used as lenses to focus electron beams. The theory of these lenses is developed for electric fields that are symmetrical about a central axis. The introduction of two velocity functions exactly reduces the partial differential equations of electron motion to a series of ordinary differential equations. The first equation describes the action of a lens for electron paths near the axis, the remaining equations determine the higher order aberration terms. Sections on the following subjects are included: the general equations of electron optics, thin lenses, thick lenses, aberration, the reduction of aberra ration, apertured plates, and concentric tubes. A list of symbols and lens equations is also included at the end of the article.N certain types of modern vacuum tubes, a beam of electrons is brought to a focus by an electrostatic field whose action on the beam is analogous to that of an optical lens on a beam of light. An electrostatic field which acts in this manner is called an electron lens. Such lenses are rapidly finding applications in amplifier tubes, tele vision and oscillograph tubes, electron microscopes, and various types of experimental apparatus. As the extent of their application widens, the theory of these lenses naturally assumes a corresponding importance.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.