Background
Hill, George William was born on March 3, 1838 in New York, United States. Son of John William and Catherine (Smith) Hill.
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(This work has been selected by scholars as being cultural...)
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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(Excerpt from The Collected Mathematical Works of George W...)
Excerpt from The Collected Mathematical Works of George William Hill, Vol. 3 Jupiter and Saturn must have presented to the earliest observers of the celestial motions less difficulties than the interior planets. The first things noted, undoubtedly, were, that the first made a circuit of the heavens in about twelve and the second in about thirty years. Then the retrograde motion, at the time of Opposition, and its extent would be perceived. The slowness and steadiness of the motion would natur ally suggest the hypothesis of circular motion, but it was certainly reserved for a later and more philosophic age to explain the later-observed phenomenon by means of an epicycle. 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.
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(This is a reproduction of a book published before 1923. T...)
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(This historic book may have numerous typos and missing te...)
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...cosines instead of circular. The differential equations of this problem, in the case where the radii are supposed to describe no areas, were first integrated by Binet. But the addition, to the forces, of the terms arising from centrifugal action, much enhances the interest of the problem. See Liouville, Journal de MatlUmatiquet, First Ser., Tome II, p. 457. MEMOIR No. U. On the Interior Constitution of the Earth as Respects Density. (Annals of Mathematics, Vol. IV, pp. 19-29, 1888.) Nearly all the matter accessible to us is found to be porous. Thus the application of pressure to it tends to reduce the amount of porosity and, in consequence, augments the density of the mass. Moreover, the greater the pressure the greater is the increment of density. A familiar instance of this is the case of atmospheric air or a gas in which, provided the temperature remains constant, the density varies directly as the pressure. It is natural to think that the matter of which the earth is composed is not excepted from this law. At small depths, it is true, the rigidity of the earth's mass interferes with its exerting any pressure, as the existence of caves shows. But at great depths where the weight of the superincumbent mass becomes very great, it is extremely probable the molecular force of cohesion gives way in a manner which allows pressure to act; which is illustrated by the behavior of ice in a glacier. I propose to see what conclusions we are led to by adopting this relation between the density p and the pressure £, P = A + Bp. A and B are constants, A denoting the density at the surface, and B the rate of increase of the density per unit of pressure. In applying this formula to the atmosphere and gases, we have by Boyle's law A--0. Let V denote the potential of ...
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(This book was originally published prior to 1923, and rep...)
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(This book was originally published prior to 1923, and rep...)
This book was originally published prior to 1923, and represents a reproduction of an important historical work, maintaining the same format as the original work. While some publishers have opted to apply OCR (optical character recognition) technology to the process, we believe this leads to sub-optimal results (frequent typographical errors, strange characters and confusing formatting) and does not adequately preserve the historical character of the original artifact. We believe this work is culturally important in its original archival form. While we strive to adequately clean and digitally enhance the original work, there are occasionally instances where imperfections such as blurred or missing pages, poor pictures or errant marks may have been introduced due to either the quality of the original work or the scanning process itself. Despite these occasional imperfections, we have brought it back into print as part of our ongoing global book preservation commitment, providing customers with access to the best possible historical reprints. We appreciate your understanding of these occasional imperfections, and sincerely hope you enjoy seeing the book in a format as close as possible to that intended by the original publisher.
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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.
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(Excerpt from The Collected Mathematical Works of George W...)
Excerpt from The Collected Mathematical Works of George William Hill, Vol. 4 In Nos.220 and 221 of this Journal appears an article by Mr. Stockwell, in which, in opposition to all previous investigators, an acceleration is found for the motion of this element of the lunar orbit. The introductory history of this matter given by the author is incomplete, as he passes over without notice the most recent, and perhaps the only correct, determination of the coefficient, viz. : that by Delaunay (Comptes Rendus, Tome LXXIV, pp. 152, 153). Delaunay finds that, assuming - 1270" i-as the value of ns(e1² - e10²)dt, the coefficients of i² in the motions of the perigee and node are severally -39".986 and +6".778. Before astronomers accept the new values advanced by Mr. Stockwell, in order to judge intelligently about the matter, they doubtless would like to know how it happens that the author differs so greatly from his predecessors. No information in the article itself is given on this point; it is strange that the author should deem this a matter of no importance. The explanation is not far to seek; the quantities e and w, which appear in the author's equation (1), are treated as though they suffered no periodic perturbations. Yet the equation is not true unless these two symbols denote severally the eccentricity and longitude of the perigee in the instantaneous orbit which the moon is, at the moment, describing. All the previous investigators, while they do not employ equation (1), have employed methods in which this principle is tacitly admitted. 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.
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(This book, "The collected mathematical Works of George Wi...)
This book, "The collected mathematical Works of George William Hill Memoir No. 50. A New Theory of Jupiter and Saturn Astronomical, Papers of the American Ephemeris. Vol. IV. 1", by George William Hill, is a replication of a book originally published before 1905. It has been restored by human beings, page by page, so that you may enjoy it in a form as close to the original as possible. This book was created using print-on-demand technology. Thank you for supporting classic literature.
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(The Collected Mathematical Works of George William Hill w...)
The Collected Mathematical Works of George William Hill was written by George William Hill in 1906. This is a 350 page book, containing 86713 words and 3pictures. Search Inside is enabled for this title. (Typographical errors above are due to OCR software and don't occur in the book.) About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology. Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org
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(This historic book may have numerous typos and missing te...)
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 edition. Excerpt: ... n + tan u _ sin (n + u) tan n--tan o--sin (/--o) _ 2 tan ii tan o _ cos (/i--o)--cos (/i + o)--tan /--tan u sin (ji--o) It will be more convenient to employ as the variables % = ft + f and 1 =--v. Then as a constant quantity, £(7' = + v = Bip' + (cos /-cos sin' j But, if 2_1 is put for Xs + y2 + 1, this equation can be given the form u--u cos / cos 0 = sin' 0. This equation constitutes the relation between the true and mean anomalies in Ptolemy's theory of eccentric circles. It holds for each of the three observations, and we thus have the data requisite for the determination of the three unknowns u, % and. If the latter symbols are used for the first observation we should add to them certain known arcs for the second and third observations. But it is conducive to symmetry to suppose that the known arcs to be added to % and 41 m the several observations in their order are ax, a2, a8, and again (3U /?2, /3S. It will shorten the writing of some of the formulas if we impose upon the ft the condition /2i+&+/3s=0. As to the a, the computation is shortened if we suppose one of them vanishes. To abbreviate we write 4 for + (3ly then the equations for solution are u--u cos (x + ax) cos = sin21/1 u--u cos (x + ) cos ji2 = sin i//t U--U COS (x + a) 008 0a; 8in2 0a By developing cos (% + a) we have the modified form: u--cos Oj cos. u cos x + sin aicos 0i u 8U1X--8in 0i u--cos aa cos 02. u cos x + sin o2 cos f/2. u sin x = sin 02 u--cos a„ cos 03. u cos x + sin a-3 cos 0,. u sin x = sin 0a Let these equations be regarded as linear, and as determining the unknowns it, u cos %, and u sin %. Employ A to denote the determinant formed from the coefficients of the equations, and S to denote summation By moving froTM...
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Hill, George William was born on March 3, 1838 in New York, United States. Son of John William and Catherine (Smith) Hill.
Bachelor of Arts, Rutgers, 1859, Master of Arts, 1862. (honorary Doctor of Philosophy, Rutgers, 1872. Doctor of Science, University of Cambridge, England, 1892.
Doctor of Laws, Columbia, 1894, Princeton, 1896).
Unmarried.
And Catherine Smith Hill. He moved to West Nyack with his family when he was eight years old. In 1861 he was hired by John Daniel Runkle at the Nautical Almanac Office in Cambridge, Massachusetts.
His work focused on the mathematics describing the three-body problem, later the four-body problem, to calculate the orbits of the Moon around the Earth, as well as that of planets around the Sun.
The Hill sphere, which approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits, was described by Hill. He 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 Hill died in West Nyack, New New York
(This book was originally published prior to 1923, and rep...)
(This book was originally published prior to 1923, and rep...)
( This work has been selected by scholars as being cultur...)
(This work has been selected by scholars as being cultural...)
( This work has been selected by scholars as being cultur...)
(This volume is produced from digital images from the Corn...)
(The Collected Mathematical Works of George William Hill w...)
(This book, "The collected mathematical Works of George Wi...)
(Excerpt from The Collected Mathematical Works of George W...)
(Excerpt from The Collected Mathematical Works of George W...)
(This historic book may have numerous typos and missing te...)
(This historic book may have numerous typos and missing te...)
(This is a reproduction of a book published before 1923. T...)
Royal Society; Royal Swedish Academy of Sciences. Royal Academy of Science, Letters and Fine Arts of Belgium. Norwegian Academy of Science and Letters.
Royal Netherlands Academy of Arts and Sciences.
Lincean Academy; Royal Society of Edinburgh.