416 D'ALEMBERT. 



equation to the radius, after obtaining, by a first inves- 

 tigation, the value of the third term above given in 

 that equation 



_ 



d v 1. ( as above given.) 



w 3 (A 2 + &c. 



This omission he now supplied, and he found that 

 the result, when applied to the case, made the pro- 

 gression of the moon's apogee twice as quick as the 

 former operation had given it, or nine years, agreeing 

 with the actual observation. He deposited, in July, 

 1746, with the secretary of the Academy, as well as 

 with Sir Martin Folkes, president of the Royal Society, 

 a sealed paper containing the heads of his analysis, but 

 delayed the publication of it until he should complete 

 the whole to his satisfaction : a most praiseworthy cau- 

 tion, after the error that had been committed in the 

 first instance. He announced, however, the result, 

 and its confirming the Newtonian theory, in May of 

 the same year; and added, that his reasoning was 

 purely geometrical, and had no reference to vague 

 topics, giving, at the same time, a conclusive exposition 

 of Bufibn's ignorance in his hot attack, which showed 

 him to be wholly incapable of appreciating any part 

 of the argument. In May, 1752, the Memoir itself was 

 given to the Academy, and it appears in the volume 

 for 1748.* It is entitled, " De 1'Orbite de la Lune, en 

 ne negligeant pas les quarres des quantites de meme 

 ordre avec les forces perturbatrices ; which has misled 

 many in their conception of the cause to which the 

 error must be ascribed. But in the volume for 1748, 

 p. 433, he leaves no doubt on that cause ; for he states 



* For an account of the irregular and irrational manner in -which the 

 Memoirs of the Academy were published, see ' Life of Lavoisier.' The 

 inconvenience of it meets us everywhere. 



