The Collected Mathematical Works of George William Hill, Vol. 4 (Classic Reprint)
(Excerpt from The Collected Mathematical Works of George W...)
Excerpt from The Collected Mathematical Works of George William Hill, Vol. 4
In this care must be taken to have a, e and y of the same signification in all the factors. When we neglect the inclination of the lunar orbit the last term may be neglected.
The advantage of the employment of such a formula as this over the one employed by Mr. Stockwell consists in the circumstance that since the first factors are non-periodic, the second may be limited to their non-periodic terms. The expression is correct, however far we may wish to push the approximation in reference to powers of the solar disturbing force.
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The Collected Mathematical Works of George William Hill, Vol. 1 (Classic Reprint)
(Excerpt from The Collected Mathematical Works of George W...)
Excerpt from The Collected Mathematical Works of George William Hill, Vol. 1
Le travail quotidien da Nautical Almanac, qui est fort absorbant, lui lais sait cependant assez de temps pour ses recherches originales, dont quelques unes portent sur des objets étrangers a ses études habituelles. Dans les premieres années surtout, on trouve fréquemment son nom dans ces recueils périodiques, Oh les amateurs de mathématiques pures se proposent de petits problemes et se complaisent dans 'élégance des solutions, par exemple, dans The Analyst.
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.
Tables of Venus, Prepared for the use of the American Ephemeris and Nautical Almanac
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The Collected Mathematical Works of George William Hill
(
This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.
This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.
As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.
This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.
As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
George William Hill was an American astronomer, mathematician and scientist. He was one of the scientists who made major contributions to celestial mechanics and to the theory of ordinary differential equations.
Background
George William Hill Hill was born on March 3, 1838 in New York City, New York, United States. He was the son of John William Hill, an artist and engraver, and Catherine (Smith) Hill of English and Huguenot descent. His paternal grandfather was John Hill. In 1846 the family moved to a farm in West Nyack.
Education
In West Nyack Hill attended the local school. Later he went to Rutgers College and had the good fortune to come under an able teacher, Doctor Theodore Strong, who gave him a thorough grounding in the fundamentals of mathematics and celestial mechanics by making him study the classical treatises of Euler, Lacroix, Laplace, Lagrange, and Legendre. He took his degree in 1859.
Career
During the following thirteen years Hill must have spent a good deal of time mastering the later works on the lunar and planetary theories, especially those of Delaunay and Hansen. His own publications on those subjects began in 1872. It was this training that probably gave the trend to all his work--the application of mathematical analysis to the investigation of natural phenomena, with the final step of reducing the results to numerical data. In 1861 he joined the staff of the Nautical Almanac Office and spent a year or two in Cambridge, Massachussets, which was its headquarters at that time. Soon, however, he obtained permission to do his work at his home in West Nyack, and from then to the time of his death his only absences for any considerable period were the ten years, 1882-1892, which he spent in Washington working on the theory and tables of Jupiter and Saturn, a trip to Europe, and two holidays in the northwest of Canada.
His ability was first decisively shown in a memoir entitled "Researches in the Lunar Theory, " which appeared (1878) in the opening number of the newly founded American Journal of Mathematics. In this paper he calculated the first step in a new method for treating the motion of the moon under the attractions of the earth and sun. What proved to be equally important in the paper was the initiation of the "periodic orbit"--an idea which has had a profound effect on the later development of celestial mechanics. In the hands of H. Poincare, G. H. Darwin, and many others, it has greatly changed the approach to the study of the motions of three mutually attracting bodies. Its publication gave new life to a subject which had seemed to be marking time in merely securing higher numerical accuracy for the various gravitational theories of the bodies in the solar system, and the impetus is not yet exhausted. Another useful idea, the surface of zero velocity, is also set forth in this paper.
The second step, which was actually published the previous year in a paper, On the Part of the Motion of the Lunar Perigee Which is a Function of the Mean Motions of the Sun and Moon (1877), displays Hill's analytical skill in a marked degree. His initiation of the infinite determinant and the devices which he used to calculate its value to a high degree of accuracy were nearly all new. In this paper, also, he showed his unusual capacity to carry out accurately a long and intricate calculation.
Shortly after the publication of these papers Hill was persuaded by Simon Newcomb to undertake a new theory of the motions of Jupiter and Saturn. This theory and the formation of the necessary tables occupied him until 1892. In order to avoid delay in completing the work, which was mainly a laborious and involved set of computations, Hill used a well-known method, that of Hansen. This was perhaps unfortunate, for Hill was then at the height of his powers and if given more time he might have produced a new method which would have been of service in other similar problems. He was unwilling to use routine computers, finding it more trouble to explain what was to be done than to do it himself. The final result is one of the most important contributions to mathematical astronomy of the past century.
Among his later papers is a noteworthy contribution for calculating the effects of the planets on the motion of the moon. This is, in effect, a particular case of the problem of four bodies. While Hill was essentially a mathematician, he was interested in the subject only in so far as it could be used to deduce astronomical and other phenomena, and particularly those which depend on the law of gravitation. He had little interest in the modern developments of mathematics. His work bears in many respects a striking similarity to that of his contemporary, J. C. Adams, of Cambridge, England, the codiscoverer with Leverrier of the planet Neptune. In fact, immediately after the appearance of Hill's paper on the lunar perigee, Adams published one which showed that he had worked on the same lines and even had constructed and evaluated the infinite determinant. Adams, however, had kept to the lunar problem, while Hill, as mentioned above, extended the idea in a general manner.
He was a lecturer at Columbia University, 1898-1901, but characteristically returned the salary, writing that he did not need the money and that it bothered him to look after it.
His needs like his income were small. He was not gifted as an expositor. His papers while clearly expressed are very concise. On one occasion the method of deducing a long algebraical development which required special devices and several weeks of concentrated work is dismissed in a line. Most of his published papers have been reprinted by the Carnegie Institution of Washington in four quarto volumes, with a preface by Henri Poincare, The Collected Mathematical Works of George William Hill (1905-1907).
(Excerpt from The Collected Mathematical Works of George W...)
Membership
Hill became president of the American Mathematical Society in 1894, serving for two years. He was elected to the Royal Society of Edinburgh in 1908, as well as to the academies of Belgium (1909), Christiania (1910), Sweden (1913), the Netherlands (1914) among others.
Personality
Hill was essentially the type of scholar and investigator who seems to feel no need of personal contacts with others. While the few who knew him speak of the pleasure of his companionship in frequent tramps over the country surrounding Washington, he was apparently quite happy alone, whether at work or taking recreation. This isolation seems to have had no effect on him other than to preserve the independence of his ideas and to emphasize a natural indifference to externals: his intellectual outlook was always essentially sane.
Interests
Hill's one mild extravagance, the buying of books, was probably due to his desire to remain at home. He read somewhat widely, especially in botany, his hobby.
Connections
Hill never married. His later life he spent alone on his farm, taking his meals with a married brother who lived nearby.