D'ALEMBERT. 409 



truncated cone which he called a vein ; and his correc- 

 tion of the former result was a matter of much con- 

 troversy among mathematicians. Daniel Bernouilli at 

 first maintained it to be erroneous against Riccati and 

 others, but he afterwards acquiesced in Newton's view. 

 He however always resisted the hypothesis of the cataract, 

 as indeed did most other inquirers. Newton's assumptions, 

 in other parts of this very difficult inquiry, have been 

 deemed liable to the same objections; as where he leaves 

 the purely speculative hypothesis of perfectly uncom- 

 pressed and distinct particles, and treats of the interior 

 and minute portions of fluids, as similar to those which 

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

 ever, be admitted as D'Alenibert 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 hav- 

 ing, after resorting to hypotheses which the experiments 

 refuted, abandoned their doctrines as equally unsatisfac- 

 tory, 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 pressure 

 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 manifest that the prin- 

 ciple may be applied. Thus, if a fluid contained in a 

 vessel of any shape be conceived divided into layers per- 

 pendicular to the direction of its motion, and if v repre- 

 sent generally the velocity of the layers of fluid at any 



