70 HISTORY OF MECHANICS. 



equal to the momentum which the column verti- 

 cally over the orifice would generate by its gravity. 

 But Torricelli's experiments, which had given the 

 velocity due to the whole depth, were confirmed 

 on repetition : how was this discrepancy to be ex- 

 plained ? 



Newton explained the discrepancy by observing 

 the contraction which the jet, or vein of water, 

 undergoes, just after it leaves the orifice, and which 

 he called the vena contracta. At the orifice, the 

 velocity is that due to half the height; at the 

 vena contracta it is that due to the whole height. 

 The former velocity regulates the quantity of the 

 discharge ; the latter, the path of the jet. 



This explanation was an important step in the 

 subject: but it made Newton's original proof ap- 

 pear very defective, to say the least. In the second 

 edition of the Principia (1714), Newton attacked 

 the problem in a manner altogether different from 

 his former investigation. He there assumed, that 

 when a round vessel, containing fluid, has a hole 

 in its bottom, the descending fluid may be con- 

 ceived to be a conoidal mass, which has its base 

 at the surface of the fluid, and its narrow end at 

 the orifice. This portion of the fluid he calls the 

 cataract; and supposes that while this part de- 

 scends, the surrounding parts remain immovable, 

 as if they were frozen; in this way he finds a 

 result agreeing with Torricelli's experiments on 

 the velocity of the efflux. 



