23] SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. 175 



methods as a fact mathematically inadmissible. On the contrary, it appears 

 to me a palpable absurdity to suppose that the result of a mathematical 

 investigation can be different according as one independent variable or an- 

 other is employed in obtaining it, or that two methods of solving the same 

 problem may both be correct and yet lead to contradictory results. 



In order, however, to shew this mathematical inadmissibility, M. de 

 Pontecoulant goes on to say, " En effet, M. Adams convient quelque part, 

 je crois, et d'ailleurs, je le demontrerais bientot jusqu'a I'eVidence, que la 

 consideration de la variability de 1'orbe terrestre, n'exerce aucune influence 

 sur la determination de 1'inegalite seculaire, lorsqu'on emploie pour 1'obtenir 

 les formules directes que j'ai adoptees dans ma theorie." 



In thus stating that I admit that one of the methods of determining 

 the secular acceleration is unaffected by the consideration of the variability 

 of the eccentricity of the Earth's orbit, M. de Pontecoulant overlooks " une 

 petite difficulte," viz., that instead of admitting this, I assert, in so many 

 words, the exact contrary. In the concluding sentence of my Memoir I 

 say, " when both processes were corrected by taking into account the new 

 terms whose existence I had already recognized, I had the satisfaction of 

 finding a perfect agreement between the results." 



For M. de Pontecoulant's demonstration "jusqu'a 1'evidence," I am not 

 responsible, and indeed, I think his paper tends to shew that he has 

 peculiar ideas as to what constitutes demonstration. 



In the next place M. de Pontdcoulant offers " une reflexion tres simple," 

 which he thinks ought to have struck me. " Qui est-ce apres tout que 

 le coefficient de I'e'quation seculaire ? une certaine fonction des elements des 

 orbites de 1'astre trouble et de 1'astre perturbateur, qui se deduit des 

 formules diffeVentielles du mouvement ; cette fonction est la meme, selon 

 M. Adams, par quelque methode qu'on 1'obtienne, dans le cas ou Ton con- 

 sidere comme variable 1'excentricite de 1'orbe terrestre; a plus forte raison elle 

 doit 1'etre dans le cas ou Ton regarde cette excentricite comme constante." 

 I am at a loss to imagine what can be the meaning of this last clause, 

 since the secular equation in question is entirely due to the variability of 

 the eccentricity of the Earth's orbit, and would not exist at all if this 

 eccentricity were constant. 



It must be admitted that my new determination of the secular accelera- 

 tion has, as M. de Pontecoulant says, " 1'inconvdnient d'alterer profonde"ment 



