CALCULUS OF PARTIAL DIFFERENCES. 51 



distance of that body from each of the two others, and the 

 almost elliptical path of the one whose orbit was sought, 

 leaving its deviation from that path alone to be sought after. 

 Accordingly, the paper of 1743 did not satisfy its illustrious 

 author, who, in 1747, produced another worthy of the subject 

 and of himself. This was read 15th November, 1747, but 

 part of it had been read in August. He asserts positively in 

 a note (Mem.' 1745, p. 335), that though Euler's first paper 

 had been sent in the same year, he had never seen it till after 

 his solution was obtained ; therefore, Lalande had no right to 

 state in his note to the very bad edition of Montucla which 

 he published, that Fontaine always said that Clairaut was 

 enabled to obtain his solution by the paper of Euler (vol. iv. 

 p. 66). 



At the time that Clairaut was engaged in this investigation, 

 D'Alembert, unknown to him, was working upon the same 

 subject. Their papers were presented on the same day, and 

 Clairaut's solution was unknown to D'Alembert ; but so 

 neither could D'Alembert's solution have been known to 

 Clairaut, because the paper is general on the problem, anc. 

 the section applicable to the moon's orbit was added after the 

 rest was first read, and was never read at all to the Academy, 

 Nothing, therefore, can be more clear than that neither of 

 these great geometricians borrowed from the other, or from 

 Euler. It is just possible that Euler in his complete solution 

 of 1752 might have had the advantage of their previous ones 

 but as it clearly flowed from his earlier paper, there is nc 

 doubt also of his entire originality. Nevertheless, when 

 D'Alembert's name became mixed up with the party proceed- 

 ings among the literary and fashionable circles of Paris, there 

 were not wanting those who insisted that the whole fame oi 

 this great inquiry belonged to Clairaut ; and it is painful to 

 reflect on the needless uneasiness which such insinuations 

 gave to D'Alembert. 



Thus, in investigating this famous "Problem of the Three 

 Bodies," all the three geometricians, without communicating 



E 2 



