Preface
The main object of the work here submitted to the reader is to exhibit a view of the labours of successive enquirers in establishing a knowledge of the mechanical principles which regulate the movements of the celestial bodies, and in explaining the various phenomena relative to their physical constitution which observation with the telescope has disclosed. It may, perhaps, be desirable to trace out briefly the plan I have pursued in attempting to execute this undertaking.
The first part of the work, extending to the close of the thirteenth chapter, is devoted to the history of the Theory of Gravitation. In the first and third chapters I have endeavoured to give some account of the immortal discoveries by which Newton established this theory in its utmost generality. The researches of the learned Prof. Eigaud have recently disclosed some interesting details respecting the original publication of the Principia, of which I have not failed to avail myself in the execution of this portion of the work.
The future history of Celestial Mechanics naturally admits of a division into two distinct periods. The first comprehends the researches of geometers from the time of Newton to the commencement of the nineteenth century. Towards the close of this period the analytical methods devised for the developement of the Theory of Gravitation had attained a high state of perfection, and the various phenomena which had seemed irreconcilable with its principles, were all satisfactorily accounted for. The second period embraces the further developement of the theory down to the present time.
The third and following chapters to the ninth inclusive, are devoted to the first of the above-mentioned periods. The third chapter contains an account of the early researches of Euler, Clairaut, and D'Alembert on the Problem of Three Bodies, and of the application of their respective solutions to the lunar theory. The difficulty which for some time attended the computation of the movement of the lunar apogee, was at length effectually removed by Clairaut, and the triumph of the Newtonian principles was practically exhibited in the construction of lunar tables by Mayer, which possessed sufficient accuracy to be employed with confidence in the solution of the great Problem of the Longitude.
It is a curious fact that, in the original edition of the Principia, Newton gave the results of an investigation of the movement of the lunar apogee, which seemed to imply that he had treated the subject by a method of a sufficiently comprehensive character. These results were suppressed by him in the second edition, doubtless in consequence of their not exhibiting so
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complete an accordance with observation as was manifest in his other researches on the hmar theory *. That Newton really was in possession of a method adequate to a complete investigation of the subject, is rendered still further probable by the recent researches of Mr. Adams, who, by the aid of geometrical considerations, analogous to those expounded with so much elegance in the Principia, has obtained results relative to the movement of the lunar apogee, which present a complete accordance with observation.
The fourth chapter is devoted to the early researches of geometers on the perturbations of the planets and the stability of the planetary system. While occupied with the former of these subjects, the illustrious Euler devised a method of investigation which must be regarded as one of the most remarkable in the annals of science. It consisted in regarding the perturbations of a planet as arising from an incessant change in the elements of its elliptic motion. This fertile idea was destined to acquire an immense developement from the labours of succeeding geometers.
The sublime results which the analytical researches of Lagrange and Laplace have disclosed, relative to the stability of the planetary system, while they have served to invest astronomical science with additional features of interest, are entitled to be classed among the noblest triumphs v/hich the human mind has achieved in the investigation of the laws of the physical universe. The labours of these great geometers, which w^ere of a kindred nature throughout their whole career, are on this occasion more especially interlaced. As some misapprehension appears to have not unfrequently arisen from this circumstance, I have endeavoured, by a careful reference to the volumes of the Academy of Sciences and other original sources, to exhibit the results independently arrived at by each geometer in the course of his researches on the subject.
The fifth chapter contains an account of the physical explanation of the great inequality in the mean longitudes of Jupiter and Saturn, and of the secular inequality in the mean motion of the Moon, as well as an allusion to several points of minor importance in the Theory of Gravitation. The irregularities in the mean longitudes of Jupiter and Saturn long continued to form an inexplicable enigma to geometers. In vain did Euler employ all the resources of his fertile genius in endeavouring to account for their existence by the principles of the Theory of Gravitation. Equally fruitless was the result of Lagrange's application of his commanding powers of analytical research to the subject. It was reserved for Laplace to detect the true origin of these anomalous phenomena in the mutual action of the two planets.
Perhaps a still more remarkable result, due to the same geometer, was the explanation of the secular inequality in the mean motion of the Moon. The records of certain eclipses of the Moon observed at Babylon about seven hundred years before the Christian era, when compared with observations of similar phenomena by the Arabian astronomers about the tenth
* Sea Appendix IV.
PREFACE. -I'V
century, seemed to indicate that the Moon's angular velocity round the Earth was subject to a slow acceleration. This fact was confirmed beyond all doubt by the observations of modern astronomers ; but its existence seemed absolutely irreconcilable with the results to which geometers were conducted by their researches on the Theory of Gravitation. The physical cause of this acceleration continued to escape the analytical scrutinies of Euler, Lagrange, and Laplace, until at length the sagacity of the last-mentioned geometer led to its detection.
The sixth chapter is devoted to an account of the labours of geometers on the Figure of the Earth, the Precession of the Equinoxes, the Libration of the Moon, and other kindred subjects. By an ingenious application of his researches on the attraction of spheroids, Newton rigorously determined the ellipticity of the Earth, upon the supposition of its density being uniform, and of the figure of an oblate spheroid being compatible with the conditions of equilibrium of a fluid mass. The truth of the last-mentioned supposition was afterwards demonstrated by Maclaurin with all the elegance and rigour of the ancient geometry. With respect to the internal structure of the Earth, the ellipticity deduced from the measurement of arcs of the meridian was totally at variance with the supposition of its homogeneity. It was reserved for Clairaut to determine the ellipticity on the more probable hypothesis of the strata increasing in density towards the centre of the Earth.
The Precession of the Equinoxes is beyond doubt the most remarkable of all the perturbative effects by which the planetary system is characterised. Its original discovery as a sidereal phenomenon is due to the great astronomer Hipparchus. The explanation of its true character was first given by Copernicus, who shewed that it might arise from a conical motion of the Earth's axis. The question relative to the physical cause of this singular movement continued to be involved in impenetrable mystery, until at length Newton discovered its origin in the disturbing action of the Sun and Moon upon the redundant matter accumulated round the terrestrial equator. The subsequent discovery of the Nutation of the Earth's Axis by Bradley introduced a new cause of complication into the subject. The complete sohition of the problem of the Earth's motion round its centre of gi'avity, by a rigorous application of the principles of Mechanical Science, was reserved for D'Alembert. The subject of the Libration of the Moon, which is noticed in the same chapter, exhibits another striking illustration of the comprehensive character of the Theory of Gravitation in assigning the physical explanation of the various phenomena relative to the movements of the celestial bodies. The researches of Newton on this subject were perfected by Lagrange, who succeeded in obtaining results which accorded in a most satisfactory manner with those deduced from observation.
The seventh and eighth chapters embrace a somewhat detailed history of the theory of Jupiter's satellites. In the seventh chapter I have given an account of the original discovery of tliese bodies by the illustrious
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Galileo, and of the labours of subsequent astronomers in establishing the laws of their complicated movements. The eighth chapter exhibits a view of the researches of geometers, having for their object the explanation of these laws by the Theory of Gravitation. Some of the most curious effects of perturbation occur in this beautiful system. The results are mainly due to Lagrange and Laplace. The powerful character of the analysis which Laplace employed in these researches, is remarkably exhibited in the determination of the ellipticity of Jupiter by means of the derangements which the redundant matter accumulated round the equator of the planet occasions in the motions of the satellites. The illustrious geometer even boldly asserted, that the result thus derived from theory was entitled to greater reliance than that obtained by direct measurement with the micrometer !
The ninth chapter commences with a brief notice of the labours of geometers on some of the more hidden effects of perturbation. One of the most interesting of these is the gradual diminution of the obliquity of the ecliptic, occasioned by the disturbing action of the planets on the earth. The sublime results arrived at by Lagrange and Laplace, relative to the stability of the planetary system, assure us that such a diminution will not continue indefinitely, but that after a certain limit of obliquity has been attained, the angle contained between the planes of the ecliptic and the equator will then commence to open out. This process will continue until the obliquity attains a certain maximum value, when the increase will be converted again into a diminution, and thus the inclination of the two planes will continually oscillate between fixed limits prescribed by the intensity of the disturbing forces. It follows as a necessary consequence, that the climate of any particular country will not undergo an essential change from this cause, such as would inevitably "ensue if the equator and ecliptic were ever to coincide, or to form with each other an angle of ninety degrees. Thus the more profoundly does analysis penetrate into the operations of nature, the more admirable is the harmony which appears to pervade her various arrangements.
The subject of Comets was one of the severest tests to which the Theory of Gravitation was submitted during the early period of its history. These bodies seemed to be so destitute of any coherent structure, and at the same time so capricious in their movements, that the attempt to make them the groundwork of strict investigation was long considered to be attended with insuperable difficulties. Newton, however, perceived, with characteristic sagacity, that, however evanescent might be the physical constitution of Comets, their material structure would subject them to the influence of the principle of Gravitation ; and, in pursuance of this idea, he framed a theory of their movements, according to which they all revolved in orbits resembling one or other of the conic sections, having the sun in the common focus. The apparition of the great comet of ] 680 furnished him with the means of obtaining a complete verification of his theory. By a rigorous discussion of its observed positions he demonstrated incon-
PREFACE. ^:<Yii
testably that the comet revolved in an orbit which sensibly coincided with a parabola, and that the line joining it and the sun described equal areas in equal times. Halley applied Newton's theory to a vast number of recorded observations of comets, and among the results to which he was led he arrived at the conclusion that the comet of 1682 would again pass through its perihelion in the year 1758 or 1759. The actual return of this celebrated comet, agreeably to the prediction of Halley, is familiar to every reader. The effects of planetary perturbation were calculated beforehand by Clairaut, who succeeded in fixing the time of return with remarkable precision. This was unquestionably one of the greatest triumphs which had yet been achieved in the developement of the Theory of Gravitation. The general theory of the Perturbations of Cometary Bodies was a few years afterwards simplified and improved by Lagrange.
The ninth chapter closes with a brief allusion to the Mecanique Celeste. The publication of that immortal work forms an important landmark in the history of Physical Astronomy. The Theory of Gravitation, after being subjected to a succession of severe ordeals, from each of which it emerged in triumph, finally assumes an attitude of imposing majesty, which repels all further question respecting the validity of its principles.
The tenth chapter introduces the second period in the history of the Theory of Gravitation. It commences with an account of the interesting results obtained by geometers, about the beginning of the present century, relative to the variations of the elements of the planetary orbits. The highly-refined method of investigation due originally to the genius of Euler, by which the perturbations of a planet are supposed to arise from a continuous variation of the elements of elliptic motion, was now carried to a state of unexampled perfection by Lagrange, and by the combined labours of that illustrious geometer and Poisson, was rendered applicable to all the great problems of the system of the W'orld.
After a brief notice of some of the methods employed by modern geometers in their researches on planetary perturbation, the chapter closes with an account of the recent improvements in the lunar theory. The irregularities in the Moon's longitude, which, throughout the greater part of the nineteenth century, continued to occasion great embarrassment to astronomers and mathematicians, finally assumed a definite character, which rendered them a feasible subject of investigation with respect to their physical origin, when the vast mass of the Greenwich observations, extending from 1750 to 1830, were subjected to a comprehensive discussion by the present Astronomer Koyal, and new corrections of the elements of the lunar orbit w-ere deduced. Moreover, some- hidden inequalities, which hitherto had totally escaped the notice of astronomers, and which seemed to be irreconcilable with theory, emerged from this important discussion. The explanation of the origin of these various anomalies by M. Hansen, forms an epoch of great importance in the history of Physical Astronomy. The complicated movements of the
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Moon, which had occupied the attention of mankind from the earliest ages in the history of civilisation, npon ^Yhich a long succession of illustrious astronomers and mathematicians had exerted their utmost powers of research, were at length completely analyzed, their laws clearly traced out, and the various resulting inequalities accounted for in strict accordance with the Theory of Gravitation. The consummation of this great achievement constitutes a new laurel in the wreath of the Royal Observatory of Greenwich, w4iile it imperishably associates the already illustrious names of Airy and Hansen with the history of one of the most important departments of Astronomical Science.
The eleventh chapter is devoted to an account of the recent researches of geometers on the particular cases of perturbation which occur in the planetary system. Among the more important subjects which it embraces may be mentioned the discovery of the long inequality in the mean longitudes of the Earth and Venus, by Airy ; the investigation of the perturbations of Halley's comet, on the occasion of its passage of the perihelion in 1835, by Rosenberger, Pontecoulant, and other geometers ; the interesting researches of Le Verrier on various cases of cometary perturbation ; the completion of Lagrange's labours on the Libration of the Moon, by Poisson; the determination of the ellipticity and mean density of the Earth, by Bessel and other enquirers ; the final researches of Poisson on the motion of the Earth about its centre of gravity, and the invariability of the Sidereal Year ; and the definitive detection of periodical oscillations in the Atmosphere depending on the perturbative influence of the Moon*
In the twelfth and thirteenth chapters I have endeavoured to give an account of the theoretical discovery of the planet Neptune, as it resulted from an investigation of the perturbations produced in the motion of Uranus. This may perhaps be regarded as the most astonishing conquest which the human mind has ever achieved in unfolding the arrangements of the material world. Nor does it tend to diminish our admiration of this great discovery, that it is due to the independent researches of two contemporary geometers, who, by methods totally dissimilar in their details, if not in their essential character, succeeded nearly about the same time in determining the position of the disturbing body. The brilliant researches of M. Le Verrier on this subject constitute the strongest title which he has yet earned to the admiration of the scientific world; while those of Mr. Adams, the other discoverer of the planet, may be justly regarded as the noblest tribute which he could offer to the memory of his illustrious countryman, the great founder of Phj^sical Astronomy. Some remarks suggested by this discovery, which it would have been inconvenient to have inserted in the body of the work, will be found in an Appendix at the end.
The thirteenth chapter closes the history of Celestial Mechanics. Physical Astronomy, as usually understood, is confined to the researches of geometers on this subject; but in its more comprehensive sense it may be supposed to embrace the consideration of all the physical
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principles wliicli are known to exercise an influence on celestial ]Dhenomena, as well as the study of those facts respecting the structure of the celestial bodies which admit of being explained by reference to established principles of physics. In accordance with this more enlarged signification, the subjects noticed in the greater portion of the remainder of the work ought to be considered as forming an essential part of Physical Astronomy.
The invention of the telescope about the beginning of the seventeenth century furnished the astronomer with an instrument of observation, the mighty efficacy of which can only be compared with the aid which the infinitesimal calculus affords to the geometer in his researches on the effects produced by' the continuous agency of those forces which Nature employs in her operations. Armed with such an instrument, the sagacious Galileo was soon enabled to announce a multitude of discoveries in the heavens, of startling novelty and of the highest importance. Myriads of stars whose existence had eluded the scrutinies of the naked eye, were now seen to illumine the unfathomable regions of space. The investigation of the cosmical arrangement of the celestial bodies, and the study of their individual structure, w-ere problems unexpectedly found to be within the reach of the human faculties. This department of astronomical science, no less remarkable for the sentiments wdiich it is calculated to iuspire respecting the grandeur of the material universe, than for the multitude of instructive and delightful views of tlie physics of the celestial regions which it unfolds, has been prosecuted with ardour by a succession of eminent astronomers from Galileo's time down to the present day.
The fourteenth chapter exhibits a view^ of the progress of researches on the physical constitution of the bodies of the solar system, and also includes an account of the various discoveries by which it has been enriched in modern times. The observations of the solar spots have suggested some highly interesting speculations respecting the great central body which forms the source of the light and heat of the system. The Moon, from her comparative proximity, has naturally given rise to much physical enquiry. The observations of the planets have disclosed a multitude of facts of a highly interesting character. Their rotatory movements round fixed axes with corresponding elliptical figures, and the diversified appearance of their surfaces, constitute striking points of analogy between them and the Earth. The remarkable phenomena visible in the polar regions of Mars, the belts of Jupiter and Saturn, and the wondrous rings of the latter planet, have all furnished abundant materials of observation and research. Nor are the satellites wanting in physical features of an important character. The relation of equality between their periods of rotation and revolution, which a variation of their brightness, in several instances, has served to establish, constitutes a striking point of analogy between them and the terrestrial satellite. The phenot-x PEEFACE.
rnena accompanying their transits and occultations are also suggestive of some interesting speculations.
This chapter introduces a name which occupies a prominent place in the remaining portion of the work— it is the immortal name of William Herschel. To the bulk of the intelligent class of readers this illustrious individual appears in the character of an astronomer distinguished by his skilful construction of huge telescopes, which he employed with marvellous success in exploring the heavens. To the student who has advanced within the precincts of astronomical science, he forms a more exalted object of admiration, as an observer of almost unrivalled acuteness and sagacity, whose exquisite faculty of discernment frequently enabled him to arrive at results far beyond the scope of the mere instrumental resources available to him ; and as a philosopher of the highest order, who, by his originality of thought and capacity for comprehensive speculation, succeeded in establishing the principles of Sidereal Astronomy upon a broad and indestructible basis.
The fifteenth chapter contains an account of the progress of enquiry on the physical constitution of Comets, These mysterious bodies, beyond doubt, perform some important function in the economy of nature, which can only be ascertained by attentive observations of the phenomena which accompany their various apparitions.
The sixteenth chapter is devoted to those physical principles whose influence in disturbing the apparent positions of the celestial bodies, or in modifying the features of celestial phenomena, must necessarily be taken into account before astronomical observations can be rendered available as the groundwork of ulterior enquiry. It comprehends an account of the progress of researches on Precession, Kefraction, Aberration, Nutation, Diffraction, and Irradiation. In the history of Kefraction the mighty names of Newton and Laplace reappear with transcendant lustre. The correspondence between Newton and Flamsteed, published by the late Mr. Baily, has supplied some interesting materials connected with the researches of Newton on this subject. The uncertainty which so long existed respecting the construction of Newton's table of refractions, which Halley originally communicated to the Royal Society — whether it was based upon some physical theory of the subject, or whether it was calculated merely by an empiric process— has been effectually removed by the correspondence above referred to. It appears that Newton studied profoundly the theory of Astronomical Refraction, and succeeded in determining the results corresponding to various hypotheses respecting the physical constitution of the atmosphere. His suggestion to Flamsteed, recommending the practice of noting the indications of the barometer and thermometer, as a desirable accompaniment to astronomical observations, constitutes a striking illustration of the sagacity by which that great philosopher was distinguished above ordinary enquirers.
The subjects of Aberration and Nutation are introduced, with an account of the original discovery of these phenomena by the immortal
PREFACE. *X1
Bradley. The chapter closes with an account of the most important results ^Yhich have been elicited by the labours of successive enquirers on the subject of the Irradiation of Light.
The seventeenth chapter is devoted to the history of the physical enquiries connected with eclipses of the Sun and Moon, the transits of the inferior planets, and other occurrences of a similar character. These phenomena are all influenced in so great a degree by Refraction, and the other affections of light, that it would have been inconvenient to have alluded to them at an earlier stage of the work. This chapter contains a somewhat detailed exposition of the most important facts which have been observed on the occasion of the various total eclipses of the Sun recorded in history, including an investigation of the conclusions which they are calculated to suggest respecting the physical constitution of the great central body of the planetary system. The subject of the transits of Venus has naturally suggested a brief notice of the life and labours of the lamented Horrocks. There is a deep interest associated with the fate of this youthful astronomer. Although dwelling in a remote district of Lancashire, in almost entire seclusion from the rest of the scientific world, he unquestionably arrived at a juster appreciation of Kepler's discoveries than any of the successors of that great astronomer had hitherto done ; v.hile the sagacity and originality of his views on various points relating to astronomy, his fertile and glowing imagination, and his ardent enthusiasm in the pursuit of science — all seemed to foreshadow a career of uncommon brilliancy, which a premature death unfortunately soon brought to a close. Even his brief labours, however, have assured to him a reputation which will live imperishably in the annals of science. By his own countrymen he cannot fail to be regarded with peculiar interest, as the morning star of a galaxy of men of genius, who continued for about a century to adorn these isles by their successful cultivation of the physico-mathematical sciences. The names of Horrocks, Gascoigne, Brouncker, Barrow, Wallis, Wren, Gregory, Hooke, Newton, Taylor, Bradley, Simpson, and Maclaurin, represent a constellation of scientific enquirers, which for splendour of genius and high intellectual endowments has never been surpassed, and rarely equalled, during a similar period in the history of any nation, whether of ancient or modern times.
As any work relating to astronomical science would be incomplete without some allusion to the important subject of observation, the eighteenth chapter has been devoted to a condensed account of the progress of Practical Astronomy, from the earliest ages down to the present time. The annals of physical science do not, perhaps, furnish a more interesting picture of gradual advancement towards perfection than that which exhibits the successive improvements effected in this department of astronomy — from the naked estimations of the Chaldean priests to the refined and complicated methods of observation practised by modern astronomers— from the gnomon and the clepsydra, in their most rudimentary forms, to the transit circle of the Greenwich Observatory, the pendulum
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clock of the most improved construction, and the electro-magnetic recording apparatus of the American astronomers.
In this chapter I have given a somewhat detailed account of the E,oyal Observatory of Greenwich, from its origin down to the present time. The observations which have emanated from that noble establishment have proved of incalculable service to astronomical science. No other similar institution, whether of ancient or modern times, can compare with it in this respect. Its history affords an instructive lesson regarding the advantage to be derived from applying the resources of an observatory to some definite object, and maintaining that object in view with unswerving constancy of purpose. An uninterrupted succession of eminent astronomers, who have directed the labours of this establishment, have contributed to render it the storehouse from which the materials for determining the elements of Astronomical Science have been mainly derived in modern times. With the triumphs of the Theory of Gravitation its history is inseparably associated. During the early period of its existence, it had the glory of supplying Newton with a series of observations, which served as a valuable guide to him while engaged in threading his way through the intricacies of the lunar theory, and it has continued ever since to furnish almost exclusively the astronomical facts, by an appeal to which the successors of that illustrious geometer have been enabled to establish the accuracy of their theoretical results. The recent reduction of the entire mass of the Greenwich Observations of the Moon and Planets, extending from 1750 to 1830, under the superintendence of the present Astronomer Koyal, is an achievement which, while in respect of vastness it has few parallels in the annals of science, at the same time forms one of the most valuable acquisitions which Astronomy has received during the present century.
As a fitting sequel to the subject above-mentioned, the nineteenth chapter contains a brief account of the labours of astronomers in the construction of Catalogues of Stars. It is impossible to exaggerate the importance of this department of Astronomical Science. The places of the stars constitute so many fundamental facts, upon which depend all exact conclusions relative to the movements of the planetary bodies. The labours connected with their determination afford ample scope for talents of the highest order ; but it must be acknowledged that they offer little to captivate either the imagination or the intellect, while at tlie same time they demand the most arduous exercise of the attention, and the most unflinching perseverance. Despite these disadvantages, there have not been wanting numerous examples of astronomers who, disregarding the eclat which usually attends discovery, have devoted the best portion of their lives to the construction of a Catalogue of Stars. Lacaille, Piazzi, and Groombridge will be especially remembered in the annals of astronomy, as individuals who sacrificed their days and nights with unwearied assiduity to this object, cheered only by the consciousness of the advantages which posterity would derive from their labours, and niEFACE.
by the secret charm which a constant intercourse with nature never fails to yield.
The twentieth chapter contains the history of the Telescope. The researches of Van Swinden have recently contributed to throw much interesting light upon the original invention of that instrument.
The twenty-first chapter, which completes the work, is devoted to a condensed account of the progress of researches in Stellar Astronomy. The labours of modern enquirers in this department of Astronomical Science have led to some conclusions of a highly interesting and important nature. The existence of a sensible parallax in the fixed stars — a question which has occasioned much anxious investigation from the time of Copernicus down to the present day— has at length been definitively established in several instances by the labours of Bessel, Henderson, Struve, Peters, and Maclear. It is now ascertained beyond all doubt, that light, travelling at the rate of 192,000 miles in a second, would require three years and a half to traverse the space between one of the nearest of those luminaries and the earth ! The motion of the solar system in space, is another of those sublime conclusions which have been established by the researches of modern astronomers. It appears from the labours of Sir William Herschel and his successors on this subject, that not only do the satellites move round the planets, and the planets round the Sun, but that the Sun, with his whole cortege of planets and satellites, is being constantly transported through space to a determinate point in the heavens, revolving, in all probability, round the centre of gravity of some vast system of suns, of which it forms one of the constituent members. Thus the farther the human mind is allowed to penetrate into the mechanism of the phj^sical universe, the more overwhelming is the impression produced of the surpassing grandeur of its movements, and the more exalted is the conception formed of the Omnipotent Being who constantly presides over its countless arrangements.
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You’ve reached the end of History of physical astronomy, from the earliest ages to the middle of the 19th century. Comprehending a detailed account of the establishment of the theory of gravitation by Newton, and its development by his successors; with an exposition of the progress of research on all the other subjects of celestial physics.
