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skilful observers. Mathematical analysis has beencarried to an unhoped-for degree of perfection toaccount for peculiarities of lunar motion revealed byobservation. Observation has been pushed to theutmost point of delicacy to detect peculiarities oflunar motion predicted by mathematical analysis.The history of the contest is adorned by the namesof nearly all the leading observers and mathematiciansof the last century and a half;—Laplace andLagrange; Euler , Clairaut , and d’Alembert ; Airy,Leverrier , Adams, and Cayley; Hansen, Delaunay,Peirce, and Newcomb; a host, in fine, of names sodistinguished, that it becomes almost invidious toparticularize any among them. In the wholehistory of the researches by which men have endea-voured to master the secrets of nature, no chapteris more encouraging than that which relates to theinterpretation of the lunar motions.
Note .—Since this chapter was in type, I have found that Prof.Grant, in an appendix to his “ History of Physical Astronomy,”records how Newton , in the original edition of the “Principia ”(1687), gives very satisfactory values of the progression of theperigee in sizygy and its regression in quadrature. Thus he found11° 21' for the monthly progression, and 8°1' for the monthlyregression ; and a mean annual advance of 40°. Modern tablesassign 11°, 9°, and 40° 40' 32" for these quantities respectively.Newton refrained from publishing the details of his researches, butas Prof. Grant remarks, whatever Newton ’s method may havebeen, “ it was manifestly one which was capable of grappling withthe main difficulties of the question.”