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 lastmentioned 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 solution of the problem of the Earth's motion round its centre of gravity, 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 these bodies by the illustrious

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 1680 furnished him with the means of obtaining a complete verification of his theory. By a rigorous discussion of its observed positions he demonstrated incon

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 Mécanique 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 world.

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 Royal, and new corrections of the elements of the lunar orbit were 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

Moon, which had occupied the attention of mankind from the earliest ages in the history of civilisation, upon which 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, while 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, Pontécoulant, 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 Physical 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

principles which are known to exercise an influence on celestial phenomena, 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, were problems unexpectedly found to be within the reach of the human faculties. This department of astronomical science, no less remarkable for the sentiments which it is calculated to inspire respecting the grandeur of the material universe, than for the multitude of instructive and delightful views of the 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 pheno