SEQUEL TO THE GENERALIZATION. 117 



descent of the particles and the potential ascent; or, 

 in other words, the conservation of vis viva. This 

 was the first analytical treatise ; and the analysis is 

 declared by Lagrange to be as elegant in its steps as 

 it is simple in its results. Maclaurin also treated 

 the subject ; but is accused of reasoning in such a 

 way as to show that he had determined upon his 

 result beforehand ; and the method of John Ber- 

 noulli, who likewise wrote upon it, has been strongly 

 objected to by D'Alembert. D'Alembert himself 

 applied the principle which bears his name, to this 

 subject ; publishing a Treatise on the Equilibrium 

 and Motion of Fluids in 1744, and on the Resist- 

 ance of Fluids in 1753. His Reflexions sur la 

 Cause Generate des Vents, printed in 1747, are also 

 a celebrated work, belonging to this part of mathe- 

 matics. Euler, in this as in other cases, was one of 

 those who most contributed to give analytical ele- 

 gance to the subject. In addition to the questions 

 which have been mentioned, he and Lagrange 

 treated the problems of the small vibrations of 

 fluids, both inelastic and elastic ; a subject which 

 leads, like the question of vibrating strings, to some 

 subtle and abstruse considerations concerning the 

 significations of the integrals of partial differential 

 equations. Laplace also took up the subject of 

 waves propagated along the surface of water ; and 

 deduced a very celebrated theory of the tides, in 

 which he considered the ocean to be, not in equili- 

 brium, as preceding writers had supposed, but agi- 



