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Newton Papers : Papers Connected with the Principia on Lunar Theory

Newton, Isaac, Sir, 1642-1727

Newton Papers

<p style='text-align: justify;'>Add. 3966 is a collection of papers connected with the <i>Principia </i>on lunar theory. Newton’s interest in providing a mathematical treatment of the moon’s motion was prompted by two distinct <i>desiderata</i>.</p><p style='text-align: justify;'>First, accurate lunar tables might be used to calculate the longitude. The problem of establishing longitude was extremely important for the science of navigation and was eventually a major concern of national investment in scientific research during Newton’s lifetime. Equipped with lunar tables, a sailor on the high seas would be able to proceed as follows. Firstly, observe the position of the moon. On the basis of this observation, read what now is known as Greenwich Mean Time on the tables, and by comparing this with the local time, determine longitude. Newton became a member of the Parliamentary Committee for the Board of Longitude in 1714, which established that a prize would be awarded to those who could solve the problem of longitude with the required precision (see <a href='/view/MS-ADD-03972'>Add. 3972</a>).</p><p style='text-align: justify;'>Second, Newton wished to obtain a stringent test of gravitation theory. The orbit of the moon, due to its gravitational interaction with the earth and the sun, is particularly complex. Predicting the moon’s motion from theory would have been a great success. This success was achieved only in part. Most notably, Newton was unable to predict the motion of the moon’s apogee (the point in the orbit of the moon at which it is furthest from the earth). In Section 9, Book 1, of his <i>Principia</i>, Newton formulated a mathematical model which accounted for only half of the motion of the moon’s apogee. In Book 3, Newton was unable to provide a successful mathematical model.</p><p style='text-align: justify;'>Newton’s attempts to develop a theory for the moon’s apogee are documented in <a href='' onclick='store.loadPage(208);return false;'>Add. 3966.12</a>. The handwriting is that of his amanuensis Humphrey Newton, and there are additions and corrections in the hand of Isaac Newton himself. Most probably, Newton dictated and emended these pages while, in late 1686 or early 1687, he was completing Book 3 of <i>Principia</i>. The possibility that they were composed in 1688, after the publication of the <i>Principia</i> should also be considered. The two lemmas did not fail to attract the attention of the astronomer John Couch Adams and the physicist George Stokes, two of the members of the Committee that was in charge of studying the manuscripts donated by the fifth earl of Portsmouth to Cambridge University in 1872. Indeed, the two lemmas were considered of particular importance and printed in <i>A catalogue of the Portsmouth collection of books and papers written by or belonging to Sir Isaac Newton </i>(1888), Appendix III to the Preface on pp. xxvi-xxx.</p><p style='text-align: justify;'>A first successful theory of the motion of the moon was achieved much later, in the middle of the eighteenth century, by Alexis-Claude Clairaut, Leonhard Euler and Jean Le Rond D’Alembert. </p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>


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