D'ALEMBERT. 399 



interior and minute portions of fluids, as similar to those 

 which we know. (Lib. ii. prop. 37, 38, 39.) It must, 

 however, be admitted as D'Alembert has observed, 

 (' Encyc.' v. 889, and ' Resistance des Fluides,' xvii.) 

 that "those who attacked the Newtonian theory on 

 this subject had no greater success than its illustrious 

 author; some having, after resorting to hypothesis 

 which the experiments refuted, abandoned their doc- 

 trines as equally unsatisfactory, and others confessing 

 their systems groundless, and substituting calculations 

 for principles." 



Such was the state of the science when D'Alembert 

 happily applied his Dynamical principle to the pres- 

 sure and motion of fluids, and found that it served 

 excellently for a guide, both in regard to non-elastic 

 and elastic fluids. In fact the particles of these being 

 related to one another by a cohesion which prevents 

 them not from obeying an external impulse, it is'mani- 

 fest that the principle may be applied. Thus, if a fluid 

 contained in a vessel of any shape be conceived divided 

 into layers perpendicular to the direction of its motion, 

 and if v represent generally the velocity of the layers 

 of fluid at any instant, and d v the small increment of 

 that velocity, which may be either positive or negative, 

 and will be different for the different layers, v + dv 

 will express the velocity of each layer as it takes the 

 place of that immediately below it ; then if a velocity 

 + dv alone were communicated to each layer, the fluid 

 would remain at rest. ('Traite de Fluides,' Liv. ii. ch. 

 1. Theor. 2.) Thus the velocity of each part of the 

 layer being taken in the vertical direction is the same, 

 and this velocity being that of the whole layer itself, 

 must be inversely as its horizontal section, in order 

 that its motion may not interfere with that of the other 

 layers, and may not disturb the equilibrium. This, then, 

 is precisely the general dynamical principle already ex- 

 plained applied to the motion of fluids, and it is impos- 

 sible to deny that the author is thus enabled to demon- 



