PEE FACE.

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testably that the comet revolved in an orbit which sensibly coincided witha parabola, and that the line joining it and the sun described equal areasin equal times. Halley applied Newton’s theory to a vast number ofrecorded observations of comets, and among the results to which he wasled he arrived at the conclusion that the comet of 1082 would again passthrough its perihelion in the year 1758 or 1759. The actual return ofthis celebrated comet, agreeably to the prediction of Halley , is familiarto every reader. The effects of planetary perturbation were calculatedbeforehand by Clairaut , who succeeded in fixing the time of return withremarkable precision. This was unquestionably one of the greatest tri-umphs which had yet been achieved in the developement of the Theory ofGravitation. The general theory of the Perturbations of Cometary Bodieswas 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 inthe history of Physical Astronomy. The Theory of Gravitation, afterbeing subjected to a succession of severe ordeals, from each of which itemerged in triumph, finally assumes an attitude of imposing majesty,which repels all further question respecting the validity of its prin-ciples.

The tenth chapter introduces the second period in the history of theTheory of Gravitation. It commences with an account of the interestingresults obtained by geometers, about the beginning of the present century,relative to the variations of the elements of the planetary orbits. Thehighly-refined method of investigation due originally to the genius ofEuler , by which the perturbations of a planet are supposed to arise froma continuous variation of the elements of elliptic motion, was now carriedto a state of unexampled perfection by Lagrange, and by the combinedlabours of that illustrious geometer and Poisson , was rendered applicableto all the great problems of the system of the world.

After a brief notice of some of the methods employed by moderngeometers in their researches on planetary perturbation, the chaptercloses with an account of the recent improvements in the lunar theory.The irregularities in the Moon ’s longitude, which, throughout the greaterpart of the nineteenth century, continued to occasiou great embarrassmentto astronomers and mathematicians, finally assumed a definite character,which rendered them a feasible subject of investigation with respect totheir physical origin, when the vast mass of the Greenwich observations,extending from 1750 to 1830, were subjected to a comprehensive discus-sion by the present Astronomer Royal, and new corrections of theelements of the lunar orbit were deduced. Moreover, some hiddeninequalities, which hitherto had totally escaped the notice of astronomers,and which seemed to be irreconcilable with theory, emerged from thisimportant discussion. The explanation of the origin of these variousanomalies by M. Hansen, forms an epoch of great importance in thehistory of Physical Astronomy. The complicated movements of the