PREFACE.

The main object of the work here submitted to the reader is to exhibit aview of the labours of successive enquirers in establishing a knowledgeof the mechanical principles which regulate the movements of the celestialbodies, and in explaining the various phenomena relative to their physicalconstitution which observation with the telescope has disclosed. It may,perhaps, be desirable to trace out briefly the plan I have pursued inattempting to execute this undertaking.

The first part of the work, extending to the close of the thirteenthchapter, is devoted to the history of the Theory of Gravitation. Inthe first and third chapters I have endeavoured to give some accountof the immortal discoveries by which Newton established this theoryin its utmost generality. The researches of the learned Prof. Rigaudhave recently disclosed some interesting details respecting the originalpublication of the Principia , of which I have not failed to avail myself inthe execution of this portion of the work.

The future history of Celestial Mechanics naturally admits of a divisioninto two distinct periods. The first comprehends the researches ofgeometers from the time of Newton to the commencement of the nine-teenth century. Towards the close of this period the analytical methodsdevised for the developement of the Theory of Gravitation had attained ahigh state of perfection, and the various phenomena which had seemedirreconcilable with its principles, were all satisfactorily accounted for.The second period embraces the further developement of the theory downto the present time.

The third and following chapters to the ninth inclusive, are devoted tothe first of the above-mentioned periods. The third chapter contains anaccount of the early researches of Euler , Clairaut , and D’Alembert onthe Problem of Three Bodies , and of the application of their respectivesolutions to the lunar theory. The difficulty which for some time at-tended the computation of the movement of the lunar apogee, was atlength effectually removed by Clairaut , and the triumph of the Newtonianprinciples was practically exhibited in the construction of lunar tables byMayer, which possessed sufficient accuracy to be employed with confidencein the solution of the great Problem of the Longitude .

It is a curious fact that, in the original edition of the Principia , Newtongave 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 suf-ficiently comprehensive character. These results were suppressed by himin the second edition, doubtless in consequence of their not exhibiting so

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