162 SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. [23 



In the next place I would remark that the error which I attribute 

 to M. Plana's theory on this point is not one of calculation which might 

 require long and complicated numerical processes to be gone through for 

 its correction, but that it is an error of principle, about which a mathe- 

 matician ought not to have much difficulty in making up his mind. I am 

 therefore inclined entirely to agree with M. de Ponte'coulant's opinion, that 

 the prolonged discussion of this subject would not be creditable to science, 

 and indeed, considering the importance of the question, and the length of 

 time which has passed since the publication of my Memoir, I cannot but 

 think it strange that any controversy respecting it should still exist at all. 



Some persons appear to be under the impression that the contest lies 

 between two values of the secular acceleration, that M. Delaunay and I 

 agree in one value, and that MM. Plana, de Pontecoulant, and Hansen, 

 agree in a larger value ; but this is by no means the true state of the 

 case. Between M. Delaunay's result and my own, indeed, there is a perfect 

 agreement. He has carried the approximation much further than I have 

 done, but all of the terms which I have calculated have been confirmed 

 by him. Again, before publishing my Memoir in 1853, I had obtained my 

 result by two different methods, and I have since confirmed and extended 

 it by means of a third. M. Delaunay arrived at his result by an inde- 

 pendent method of his own, and he has lately found exactly the same 

 result by following the method given by Poisson. 



On the other hand, among our opponents there is far from being the 

 same satisfactory agreement. 



In his theory of the Moon, M. Plana obtained one value of the secular 

 acceleration. In 1856 he printed a paper in which he admitted that his 

 theory was wrong on this point, and actually deduced my result from his 

 own equations. Soon afterwards, however, M. Plana retracted his admission 

 of the correctness of my result, and obtained a third result, differing both 

 from his former one and from my own. 



Again, M. de Pontecoulant, in the last communication which I received 

 from him, gives two different values of the secular acceleration, one of which 

 he has obtained by using the time, and the other by using the Moon's 

 longitude as the independent variable. Strange to say, however, he does 

 not appear at all startled at obtaining two contradictory values, but seems 

 fully inclined to defend both. Indeed, judging from the last paragraph of 



