260 NEWTON 7 S PRINCIPIA. 



mean velocity perpendicular to the orifice is nearly 



the orifice being at the side of the vessel : thus the mean 

 perpendicular velocity at the orifice is that due to half the 



T&amp;gt; 



depth below the surface. This ratio pp however, depends 



on the nature of the orifice and the thickness of its sides ; 

 accordingly different experimentalists have given different 

 values. Thus for the ratio* of the diameters (the square 



21 11 



root of the above ratio), Newton found , Poleni , 



Bernouilli ^, Du Buat ^ Bossut -=--, Michelotti ^, Ven- 

 / y ou o 



. 4 _. , 33 ,, , . 32 



turi -, Bidone ^-~, li/ytelwein . 



5 50 50 



The velocity of efflux will be the same whether the hole 

 be at the centre or the side of the vessel ; for though a 

 heavy particle of water will take a longer time in descend 

 ing to the same depth by an oblique curve than by a 

 straight line, yet in both cases it acquires in its descent the 

 same velocity. The velocity also is independent of the 

 form of the hole, for it merely depends on the depth below 

 the surface. And if the orifice be immersed in water the 

 velocity of efflux is that due to the height of the water in 

 the vessel above that of the surrounding fluid. 



2. Newton proceeds to deduce as a corollary from this 

 theory the law of resistance of a fluid to the motion of a 

 body in it. The case of a discontinuous fluid has already 

 been discussed, and it has been shown that if v be the 



* Encyc. Brit., Hydrodynamics. 



