ON HYDRAULICS AS A BRANCH OP ENGINEERING. 155 



form an equilibrium, as may be supposed to take place with 

 the different sections of a fluid in a pipe, each section being 

 animated with velocities acquired and lost at every instant of 

 time. 



The theory of Bernoulli had not been proposed by him until 

 long after the discovery of the indirect principle of vis viva by 

 Huygens. The same was the case with the problem of the mo- 

 tions of fluids issuing from vessels, and it is surprising that no 

 advantage had been taken of it earlier. Michelotti, in his experi- 

 mental researches de Separatione Fluidorum in Corpore Ani- 

 mali, in rejecting the theory of the Newtonian cataract, (which 

 had been advanced in Newton's Mathematical Principles, in 

 the year 1687, but afterwards corrected in the year 1714,) sup- 

 poses the water to escape from an orifice in the bottom of a 

 vessel kept constantly full, with a velocity produced by the 

 height of the superior surface ; and that if, immediately above 

 the lowest plate of water escaping from the orifice, the column 

 of water be frozen, the weight of the column will have no effect 

 on the velocity of the water issuing from the orifice ; and that 

 if this solid column be at once changed to its liquid state, the 

 effect will remain the same. The Marquis Poleni, in his work 

 De Castellis j)er quce derivantur Fliiviornm Aquce, published at 

 Padua in the year 1718, shows, from many experiments, that 

 if A be the orifice, and H the height of the column above it, 

 the quantity of water which issues in a given time is represented 



by 2 A H X fTTTjT^j whereas if it spouted out from the orifice 



with a velocity acquired by falling from the height H, it ought 

 to be exactly 2 A H, so that experiment only gives a little more 

 than half the quantity promised by the theory ; hence, if we 

 were to calculate from these experiments the velocity that the 

 water ought to have to furnish the necessary quantity, we 

 should find that it would hardly make it reascend ^rd of its 

 height. These experiments would have been quite contrary 

 to expectation, had not Sir Isaac Newton observed that water 

 issuing from an orifice f ths of an inch in diameter, was contracted 

 Ijths of the diameter of the orifice, so that the cylinder of water 

 which actually issued was less than it ought to have been, 

 according to the theory, in the ratio of 441 to Q9,^ ; and aug- 

 menting it in this proportion, the opening should have been 



~ A H jTqqq, or l^ths of the quantity which ought to have issued 



on the supposition that the velocity was in the ratio of the 

 square root of the height ; from which it was inferred that the 

 theory was correct, but that the discrepancy was owing to cer- 



