384 NEWTON S PRINCIPIA. 



q = -62 . a . t . JTgTi. 



But the efflux is very much influenced by the nature of 

 the orifice. If a small vertical cylinder, or adjutage, be 

 applied to the exterior of the orifice, the discharge is 

 greatly increased, and will be nearly 



q = -8 at 



if, on the contrary, the cylinder be placed on the interior 

 of the orifice, the discharge is decreased, and will be 

 nearly 



q = -5 a t V2 oh. 



Venturi found an adjutage, consisting of two conical 

 portions having their smaller ends united at the com 

 mencement of the vena contracta, to give a very large 

 discharge. 



(5.) An attempt has also been made to determine the 

 velocity of efflux of an elastic fluid rushing out of a small 

 orifice. The problem is a very difficult one, and no satis 

 factory solution has been found. 



Let a quantity of any gas be compressed at density D 

 and pressure P, in any vessel A ; let it be allowed to run 

 out by a small orifice into a vessel A , filled with the same 

 kind of gas at density D and pressure P . It is required to 

 determine the rate at which the gas runs from the first 

 vessel into the second. 



Draw a line of motion from the interior of the vessel 

 A to the interior of A , so that at any instant all the par 

 ticles in this curve are moving along tangents to the curve. 

 The motion of the particles at the two extremities of this 

 line will be infinitesimal when the aperture is very small 

 compared with the size of the vessels. Since the aper 

 ture is very small, the motion may be considered for any 

 short time steady ; hence the equation 



