xxxviii BIOGRAPHICAL NOTICE. 



In the Monthly Notices for April, 1860, Adams replied to his objectors, pointing out 

 simply and clearly the errors into which they had fallen. He mentions that before 

 publishing his memoir of 1853 he had obtained his result by two different methods, and 

 that he had subsequently confirmed and extended it by a third. In a series of letters 

 addressed to Lubbock in June, 1860, Plana began by objecting to Adams's value of the 

 term in m\ but he soon admitted its accuracy. Lubbock also was led to apply his own 

 formulae to the question, and he too arrived at Adams's result. Another calculation was 

 made by Cayley, who, by an entirely different method, also obtained the same result. As 

 Pontdcoulant still continued his reiterated attacks upon the accuracy of the new terms, 

 Cayley's calculation was printed in extenso in the Monthly Notices, where it occupies 

 fifty-six pages. Delaunay had also made another calculation, in which, by following the 

 method indicated by Poisson in 1833, he was led to the same value. The coefficient 

 of m* had also been verified in 1861 by Donkin, who used Delaunay's method of the 

 variation of the elements. Thus Adams's value of the term in m 4 was obtained by himself 

 in three ways, by Delaunay in two ways, and by Lubbock, Plana, Donkin, and Cayley. 

 Pontecoulant continued his attacks with no abatement of violence in the Comptes Rendus. 

 Ultimately he abandoned Plana's value and obtained one of his own, which differed both 

 from Adams's and Plana's. 



The whole controversy forms a very extraordinary episode in the history of physical 

 astronomy ; the indifference with which the memoir of 1853 was at first received, in 

 spite of the interest and importance of the subject, being followed by the violent 

 controversy which resulted in so many independent investigations by which Adams's 

 result was confirmed. It is not known why Laplace did not carry the calculation 

 beyond the term in m 2 ; but it may be supposed that he regarded the subsequent 

 terms as not likely to modify the value of the first term to any considerable extent. 

 Damoiseau's and Plana's theories passed under the review of Laplace, and may be 

 regarded as having received his sanction. Thus Adams's result not only unsettled a 

 matter which after years of difficulty and struggling had apparently received its full 

 and final explanation, but it detracted from the completeness of a discovery which had 

 long been regarded as one of the greatest triumphs of Laplace's genius. Although 

 the point in dispute relates entirely to the mathematical solution of differential 

 equations, in which observation in no way entered, there can be no doubt that the 

 fact that Plana's result agreed with observation, while Adams's did not, created in 

 the minds of many a presumption against the accuracy of the latter. This view was 

 certainly taken by Le Verrier in the passage quoted above, and it seems also to have 

 influenced Hansen. It is curious that it should have been possible for so much dif- 

 ference of opinion to exist upon a matter relating only to pure mathematics, and with 

 which all the combatants were fully qualified to deal, as is clearly shown by their 

 previous publications. The whole controversy illustrates the peculiar nature of the lunar 

 problem, and of the analysis by means of which the results are reached. The com- 

 plete solution being unattainable by any of the methods which have as yet been 

 applied, the skill of the mathematician is shown in selecting from a vast number of 

 terms those which will produce a sensible influence in that particular portion of the 

 complete solution which is under consideration. 



A most admirable account of the whole discussion was given by Delaunay in the 



