of the Motion of Fluids, ^-c. 393 



city at the upper surface to the velocity of the issuing fluid, 

 where the pressure = P the atmospheric pressure ; and let z be 

 measured vertically from the surface. The equation for this 

 instance is, 



p-P^gZ-^{l-a') (/). 



Several inferences may be drawn from this equation, and com- 

 pared with experiment. 



(1) The velocity at every point of the issuing stream, which 

 is in immediate contact with the air, is very nearly the same, 

 and consequently, by reason of the contraction which experiment 

 makes known, greater than the velocity at any point in the 

 interior of the part of the stream between the orifice and vena 

 contractu. Hence in this part, the pressure will every where be 

 greater than the atmospheric pressure. Just at the contracted 

 vein there will be a transverse section of the stream, at every 

 point of which the velocity will be the same, and the pressure will 

 be P, because the section has no tendency to increase or dimi- 

 nish ; and if /* be its depth below the constant surface, the velocity 



= \/ '^Sh 



(2) Conceive the stream to descend vertically, and a tube 

 to be fitted to the orifice, its upper part having the form the 

 vein of fluid assumes on entering the air, as far as the vena 

 contractu, and its lower part being cylindrical. Let /* be the 

 distance of the lower extremity from the constant level of the 

 fluid, A' that of the vena contractu. Then it will be seen that 

 the expenditure is increased by the adjutage, by 



VT^.Cs/A-^/A'), 



3 E2 



