D'ALEMBERT. 467 



and from thence he deduces 



dz = KS(dx-{-'Rd a)f : T + * ^ = 



= Bd/:T -M^-? and 

 consequently z = B/: T. 



It is thus clear, that Euler had, in or before 1734, in- 

 tegrated an equation of Partial Differences ; and it must 

 further be remarked, that D'Alembert, in his paper on the 

 Winds, the first application of the calculus, quotes Euler's 

 paper of 1734. D'Alembert always differed with Euler re- 

 specting the extent to which this calculus can be applied, 

 holding, contrary to Euler's opinion, that it does not include 

 irregular and discontinuous arbitrary functions.* 



III. 



The Vitriere's house, in which D'Alembert was brought 

 up and lived afterwards for so many years, can no longer be 

 ascertained. I have examined this matter with some care 

 in the street in which it stood, Rue Michel-le-Comte. That 

 street is very narrow, in no place above eighteen or nineteen 

 feet wide, and the houses on both sides are lofty. D'Alem- 

 bert, therefore, did not exaggerate when, in his letter to 

 Voltaire, he said he could only see a yard or two of the sky 

 from his room, The street is near the Rue St. Martin, at 

 some distance north of the H6tel-de-Ville. The church of 

 St. Jean-le-Rond, at the gate of which he was exposed, and 

 from which he took his name, stood near the cathedral of 

 Notre Dame, and was pulled down in 1748. It was a bap- 

 tistery of Notre Dame, near the Foundling Hospital, and 

 touched the Cathedral Church. Of the Vitriere's house I 

 have inquired everywhere, not only in the Rue Michel-le- 

 Comte, but at the Prefecture (H6tel-de-Ville), and among 

 my brethren of the Institute ; I can discover no traces of 

 it. D'Alembert's Address given on his admission to the 

 Academy in 1741, only mentions the street without giving 

 any number. 



* Cousin has mentioned the anticipation of Euler. ' Astronomie, Disc. 

 Prelim.' 



