ON THE THEORY OF HYDRAULICS. 211 



motion, contained in any one transverse section of the vessels or pipes 

 'through which it runs, must always move with equal velocities ; thus, if 

 water be descending through a vessel of any form, either regular or irre- 

 gular, he supposes the particles at the same height to move with the same 

 velocity ; so that the velocity of every particle in every part of a cylindrical 

 vessel 10 inches in diameter, through which a fluid is moving, must be one 

 hundredth part as great as in passing through a circular orifice, an inch in 

 diameter, made in its bottom. It is evident that this cannot possibly be 

 true of the portions of the fluid nearest the bottom of the vessel, since the 

 particles most distant from the orifice must be nearly at rest, while those 

 which are immediately over the orifice are in rapid motion ; but still the 

 calculations founded on the hypothesis agree tolerably well with experi- 

 ments. In this case the actual descent, in any instant, may be estimated 

 by the removal of the quantity discharged, from the surface of the fluid to 

 the orifice, since the intermediate space remains always occupied. The 

 ascending force thus obtained is to be distributed throughout the fluid, 

 according to the respective velocities of its different portions ; and it may 

 easily be shown, that when the orifice is small, the part which belongs to 

 the fluid in the vessel is wholly 'inconsiderable in comparison with the 

 ascending force required for the escape of the small portion which is flow- 

 ing through the orifice, and the whole ascending force may, therefore, be 

 supposed to be employed in the motion of this portion ; so that it will 

 acquire the velocity of a body falling from the whole height of the surface 

 of the reservoir, or the velocity due to that height. It appears, also, that 

 very nearly the same velocity is acquired by almost the first particles that 

 escape from the orifice, so that no sensible time elapses before the jet flows 

 with its utmost velocity. 



This velocity may be found, as we have already seen, by multiplying 

 the square root of the height of the reservoir, expressed in feet, by 8, or 

 more correctly, by 8^ ; thus, if the height be 4 feet, the velocity will be 

 sixteen feet in a second ; if the height be 9 feet, the velocity will be 24, 

 the squares of 2 and 3 being 4 and 9 ; and if the height were 14 feet, the 

 velocity would be 80 feet in a second, and a circular orifice an inch in 

 diameter would discharge exactly an ale gallon in a second. In the same 

 manner, the pressure of the atmosphere being equal to that which would be 

 produced by a column of air of uniform density 28,000 feet high, the air 

 would rush into a vacuum with a velocity of more than 1800 feet in a 

 second. 



The velocity is also equal, whatever may be the direction of the stream ; 

 for since the pressure of fluids acts equally in all directions at equal depths, 

 the cause being the same, the effect must also be the same. And if the 

 motion be occasioned by a pressure derived from a force of any other kind, 

 the effect may be found by calculating the height of a column of the fluid, 

 which would be capable of producing an equal pressure. When also the 

 force arises from the difference of two pressures, the velocity may be deter- 

 mined in a similar manner. Thus, the pressure of a column of water 1 foot 

 in height, would force the air through a small orifice with a velocity of 230 

 feet in a second, corresponding to the height of 830 feet ; a column of mer- 



