Excerpt from Investigation of Inequalities in the Motion of the Moon Produced by the Action of the Planets The immediate incentive to the present work was the hope of explaining by gravitational theory the observed variations in the mean longitude of the Moon, shown by more than two centuries of observation to exist, but not yet satisfactorily accounted for. The author has published a number of papers and memoirs on this subject during the last forty years, terminating with a summary of the case, which appeared in the Monthly Notices of the Royal Astronomical Society for March, 1904. The deviations in question offer the greatest enigma yet encountered in explaining the motions of the heavenly bodies, and the present paper may be regarded as a contribution to the study of the problem thus offered. While the work was in progress the completing chapter of Professor Brown's Theory of the Moon's Motion appeared. The actual work being based on Delaunay's theory, it seemed to be desirable to revise and correct it by Brown's results. In doing this the imperfections of Delaunay's theory as a basis became so evident, and the later theory proved to be so much better adapted to the purpose of the investigation, that the completed work gradually became step by step practically based upon Brown's theory, except in those parts requiring derivatives which could not be readily obtained except from Delaunay's literal expressions. Acknowledgment is due to Professor Brown for courteous advice and assistance which facilitated the use of his work for the purpose. The theory of the action of the planets on the Moon being, in several points, the most intricate with which the mathematical astronomer has to deal, it is important that its development should be presented in a form to render as easy as possible the detection of errors or imperfections. In the arrangement of the work this end has been kept constantly in view. It is hoped that any investigator desiring to test the processes will find few difficulties except those necessarily inherent in the nature of the work. To form a general conception of the arrangement it may be stated that the work naturally divides itself into four parts. One of these treats of the theory of the subject, including under this head not only the general equations, but the numerical details on which all the computations are based. In this part the fundamental quantities are reduced to products of two factors, one of which depends upon the coordinates of the planet; the other upon the geocentric coordinates of the Moon. The first factors, termed planetary, are numerically developed in Part II. This development falls into two parts, one treating the direct action of the planet, the other the indirect action through the Sun. 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.