ON THE LUNAR THEORY, WITH A BRIEF SKETCH OF THE HISTORY OF THE PROBLEM UP TO THE TIME OF NEWTON. BY HUGH GODFRAY, M.A. OF ST. JOHN'S COLLEGE, CAMBRIDGE. SECOND EDITION, REVISED. MACMILLAN AND CO. CAMBRIDGE: AND 23, HENRIETTA STREET, COVENT GARDEN, LONDON. 1859. PREFACE TO THE FIRST EDITION. OF all the celestial bodies whose motions have formed the subject of the investigations of astronomers, the Moon has always been regarded as that which presents the greatest difficulties, on account of the number of inequalities to which it is subject; but the frequent and important applications of the results render the Lunar Problem one of the highest interest, and we find that it has occupied the attention of the most celebrated astronomers from the earliest times. Newton's discovery of Universal Gravitation, suggested, it is supposed, by a rough consideration of the motions of the moon, led him naturally to examine its application to a more severe explanation of her disturbances; and his Eleventh Section is the first attempt at a theoretical investigation of the Lunar inequalities. The results he obtained were found to agree very nearly with those determined by observation, and afforded a remarkable confirmation of the truth of his great principle; but the geometrical methods which he had adopted seem inadequate to so complicated a theory, and recourse has been had to analysis for a complete determination of the disturbances, and for a knowledge of the true orbit. |