BIOGRAPHICAL NOTICE. xxxvii 



the paper seems to have attracted no attention, but it then became the object of a 

 long and bitter controversy. Plana, who was the person most concerned in the matter, 

 published, in 1856, a memoir in which he admitted that his own theory was wrong upon 

 this point, and he deduced Adams's result from his own equations. But shortly after- 

 wards he retracted his admission, and, rejecting some of the new terms which he had 

 obtained, arrived at a result which differed both from his original value and from Adams's. 

 The question was in this state when Delaunay, by employing his own special method 

 of treating the Lunar Theory and extending the investigation only to the fourth order, 

 had the satisfaction of obtaining Adams's coefficient -^\-, a result which he brought before 

 the French Academy in January, 1859. This caused Adams to communicate to the Academy, 

 in the same month, the values which he had obtained some time before for the terms 

 in m 5 , m s , and m 7 ; and he pointed out at the same time that, when these terms were 

 included, the value of the acceleration was reduced to 5""78, and, inferring that the 

 remainder of the series would be nearly equal to 0"'08, he concluded that the total value 

 of the acceleration was about 5"'70. Soon afterwards Delaunay carried his approximation 

 as far as terms of the eighth order, and by reducing the forty-two terms in the ana- 

 lytical expression to numbers he obtained the value 6"'ll. Delaunay 's result, which was 

 communicated to the Academy in April, 1859, confirmed the accuracy of Adams's values 

 of the terms in m 5 , m e , and m 7 , and also those of m 2 e 2 , and m lf f, which Adams had 

 communicated to him privately. A month after the publication of this paper Pontecoulant 

 made a vigorous attack on the new terms introduced by Adams, which he said had been 

 rightly ignored by Laplace, Damoiseau, Plana, and himself, as they had no real existence. 

 He also objected that if the result of Adams were admitted, it would "call in question 

 what was regarded as settled, and would throw doubt on the merit of one of the most 

 beautiful discoveries of the illustrious author of the Mecaniqiie Celeste." Shortly after- 

 wards he communicated a paper to the Monthly Notices of the Royal Astronomical 

 Society on " the new terms introduced by Mr Adams into the expression for the co- 

 efficient of the secular equation of the Moon," in which he characterised the mathematical 

 process by which these terms had been obtained as "une veVi table supercherie analytique 1 ." 

 It would appear that Le Verrier did not accept Adams's value, for in presenting a note 

 by Hansen to the Academy in 1860 he states that Hansen's tables afford an irrefragable 

 proof of the accuracy of the value 12" which is there attributed to the acceleration. 

 Referring then to the fact that according to Delaunay the secular acceleration should 

 be reduced to 6" he proceeds : " Pour un astronome, la premiere condition est que ses 

 theories satisfassent aux observations. Or la theorie de M. Hansen les repre"sentc toutes, 

 et Ton prouve a M. Delaunay qu'avec ses formules on ne saurait y parvenir. Nous con- 

 servons done des doutes et plus que des doutes sur les formules de M. Delaunay. Tres 

 certainement la vdrite^ est du cote de M. Hansen 1 ." 



1 Hansen stated in 1866 (Monthly Notices, xxvi. p. m, and found the result to be 5"-70. Hansen says that 

 187) that he had never disputed the correctness of Adams's Adams's theory appeared too late to permit of his using 

 theory, but that he was not satisfied with " the develop- it; "and it was well that it so happened, for I had already 

 ment of the divisors into series." If this refers to the found by my own theory a coefficient which represents 

 expansion of the acceleration-coefficient in powers of m, ancient eclipses as well as could be desired." It is there- 

 it should be noticed that Adams stated (Vol. xxi. p. 15) fore to be inferred that in this theory the new terms were 

 that he had calculated the value of the acceleration by omitted by Hansen, as they had been by Plana and 

 a method that did not require any expansion in powers of Damoiseau. 



