398 D'ALEMBERT. 



of the body moving along a ruler parallel to one side, 

 while the ruler at the same time moves along a line 

 parallel to the other side. Indeed I should rather pre- 

 fer this demonstration to D'Alembert's. 



The 'Traite de Dynamique' appeared in 1743, and 

 in the following year its fundamental principle was 

 applied by the author to the important and difficult 

 subject of the equilibrium, and motion of fluids, the 

 portion of the ' Principia' which its illustrious author 

 had left in its least perfect state. Pressed by the dif- 

 ficulty of the inquiry, which is one of the most im- 

 portant in Hydrodynamics, the motion of a fluid through 

 an orifice in a given vessel, and despairing of the data 

 affording 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 unauthorized by the facts. The celebrated 

 Cataract is of this description. He supposes (' Prin- 

 cipia,' 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 investigation 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 controversy among 

 mathematicians. Daniel Bernouilli at first maintained 

 it to be erroneous against Kiccati 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 



