NEWTON S PRTNCIPIA. 257 



CHAPTER VI. 



MOTION OP FLUIDS RUNNING OUT OF SMALL ORIFICES. 



1. Newton s solution of the question, without limiting the orifice. 



2. Newton s corollary to deduce the resistance made by a fluid to a 



body moving in it. 



3. The fallacy of Newton s reasoning How others attempted to pursue 



the investigation. Note vii. 



4. The velocity as given by the Equations of Motion. Note vii. 



5. The efflux of an elastic fluid through a small orifice strange conclu 



sions to be deduced from the formula St. Venant and &quot;Wantzels 

 experiments. Note vii. 



1. THE problem to determine the motion of water running 

 out of any vessel through a hole is so difficult that it 

 has not yet been completely solved. We cannot there 

 fore be surprised if Newton s solution of the question is 

 not very satisfactory. He begins by considering a case 

 in which he is able to give some account of the motion. 

 Let us suppose that we have a circular cylinder filled with 

 fluid, the surface of which is retained at a constant level 

 in such a manner that the velocity of descent of all its 

 parts is also uniform. In order to aid our conceptions, 

 ]S&quot;ewton supposes this effected by the descent of a cylinder 

 of ice APQB, of the same breadth with the cavity of the 

 vessel, and having the same axis. The motion is supposed 

 quite uniform, and its parts, as soon as they touch the su 

 perficies A B, are supposed to dissolve into water and flow 

 down by their weight into the vessel. Let u be the uni 

 form velocity of descent of the cylinder, and let k be the 



s 



