The Doctrine of Germs

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Excerpt from The Doctrine of Germs: Or the Integration of Certain Partial Differential Equations Which Occur in Mathematical Physics The method of integration by means of Germs adopted in this Treatise is based on the admitted principle that in the work of integrating a proposed differential equation we are free to avail ourselves of the advantages offered by any distinctive peculiarities that are perceived to exist in the equation itself prior to its integration. Any such peculiarity will, as a matter of course, impress a corresponding peculiarity on the integral to be found. Equations will therefore be classified according to their distinctive peculiarities, those peculiarities being indicated by the particular ways in which germs may be connected with the variables of a differential equation without disturbing or in any way affecting its form. In this Treatise the differential equations that will be brought before the reader are all linear and partial, in consequence of which the doctrine of germs suitable for such equations admits of being presented in a form that is easily reduced to a system of singular efficiency. But there are certain other equations that are not linear, and which therefore do not fall under the system that will be developed in the following pages. 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.