40 DYNAMICAL PRINCIPLE. 



ing the means of a strict and direct solution, Newton had 

 recourse to assumptions marked by the most refined ingenuity, 

 but admitted to be gratuitous and to be unauthorised by the 

 facts. The celebrated Cataract is of this description. He 

 supposes (' Principia,' lib. ii. prop* 36), that a body of ice 

 shaped like the vessel, comes in contact with the upper 

 surface of the liquid and melts immediately on touching it, so 

 as to keep the level of the fluid always the same, and that a 

 cataract is thus formed, of which the upper surface is that of 

 the fluid, and the lower that of the orifice. His first investi- 

 gation assumed the issuing column to be cylindrical, but he 

 afterwards found that the lateral pressure and motion gave it 

 the form of a truncated cone which he called a vein ; and his 

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

 troversy among mathematicians. Daniel Bernoulli 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 uncompressed 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, 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 hypotheses which the experiments 

 refuted, abandoned their doctrines as equally unsatisfactory, 

 and others confessing their systems groundless, and substi- 

 uting 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 par- 

 ticles of these being related to one another by a cohesion 



