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HISTORY OF PHYSICAL ASTRONOMY.

Sir John Lubbock has investigated the lunar perturbations in somevaluable papers which have appeared in the volumes of the Royal Society ,and also in a special treatise on the subject. The most remarkable innovation which he has introduced into his researches is that of employingthe mean longitude of the moon as the independent variable. This isthe practice which had always been pursued in the planetary theory, hutin the lunar, it had been hitherto deemed more convenient to derive themean longitude in terms of the true, considered as the independentvariable, and then by the reversion of series to obtain the expression forthe true longitude in terms of the mean. The eminent geometer justmentioned conceives, however, that the use of the mean longitude as theindependent variable conduces to greater simplicity in practice, even whenthe question relates to the lunar perturbations. His example was soonafterwards followed by Poisson , who introduced another important innova-tion into the lunar theory, by employing in his researches the method ofthe variation of elements *.

The only difficulty which still continued to attach to the lunar theoryarose from the errors in the mean longitude, which had occasioned somuch fruitless discussion since the commencement of the nineteenthcentury. Although the inequality of long period, depending on the actionof the sun, which Laplace suggested as the probable explanation ofthese anomalies, was generally believed to be insensible, still, as noattempt had been made to calculate its real value, the question as to itsadequacy to account for the errors of the tables continued to be involved indoubt. Poisson , having examined this point with great attention, dis-covered the important fact that the disturbing action of the sun could notproduce an inequality in the moon’s mean longitude of the form indicatedby Laplace. He then considered the inequality depending on thedifference in the compression of the two hemispheres, and he found, asLaplace had already done, that it was quite insensible. Sir John Lubbock ,about the same time, very simply arrived at a similar conclusion by theaid of his own formulae.

Doubts now began to be entertained respecting the accuracy with whichthe observations were reduced, for the theory of gravitation was found tobe so satisfactory in all other respects that it seemed impossible to ques-tion its adequacy to account for all the real irregularities in the motions ofthe heavenly bodies. A step, how'ever, was at length taken which esta-blished in the clearest light the actual existence of the phenomenon, andterminated in the triumphant vindication of Newton’s principles. Forsome years past all the observations on the sun, moon, and planets, whichhave been made at Greenwich since the middle of the last century, havebeen undergoing a course of reduction conformably to a uniform plan,under the able superintendence of the present Astronomer Royal. Inthe summer of 1846, the lunar observations were so far completed as toenable Mr. Airy to obtain fresh corrections for the elements, and withthese the epochs were calculated for different times and compared withcorresponding observations. This comparison had the effect of confirmingby the most decisive evidence the researches of Burg and other astrono-mers. It appeared evident that the epoch was affected by some inequalityof very long period, and probably of a very complicated form. Mr. Airy,aware that M. Hansen was then engaged with the lunar theory, transmitted

* Mem. Acad, des Sciences, 1835.