414 D'ALEMBERT. 



du Deffand, and his participation in the labours and 

 factions of the Encyclopaedists, the Diderots, the Holbachs, 

 the Voltaires, shew sufficiently that he had exchanged 

 the peace of geometry for the troubled existence of 

 coterie and party. 



We ought, while on this subject, to add the just and 

 judicious remark of Bossut on the circumstance of James 

 Bernouilli having anticipated in some sort D'Alembcrt's 

 method of treating dynamical problems : " That the 

 latter seemed to prove, by the numerous and important 

 applications which he had made of his Principle, that in 

 all probability he owed the discovery of it solely to 

 himself." ('Hydrodyn/ L, xv.) 



In treating of Hydrodynamics D'Alembcrt had found 

 the ordinary calculus insufficient, and was under the 

 necessity of making an important addition to its pro- 

 cesses and its powers, already so much extended by the 

 great improvements which Eulcr had introduced. This 

 was rendered still more necessary when, in 1746, he came 

 to treat of the winds, and in the following year when he 

 handled the very difficult subject of the vibration of cords, 

 hitherto most imperfectly investigated by mathema- 

 ticians.* In all these inquiries the differential equations 

 which resulted from a geometrical examination of the 

 conditions of any problem, proved to be of so difficult 



* Taylor ('Methodus Incrementum') had solved the problem of the 

 vibrating cord's movement, but upon three assumptions that it de- 

 parts very little from the axis or from a straight line, that all its points 

 come to the axis at the same moment, and that it is of a uniform 

 thickness in its whole length. D'Alembert's solution only requires 

 the last and the first supposition, rejecting the second. The first, 

 indeed, is near the truth, and it is absolutely necessary to render 

 the problem soluble at all. The third has been rejected by both 

 Euler and Daniel Bernouilli, in several cases investigated by them. 



