410 Hydrodynamics. 



power necessary to raise the water to any proposed height, 

 must at least be capable of sustaining in equilibrium the pres- 

 sure experienced by the base of the piston when it is kept at 

 rest, and the fluid has attained the required height. This pres- 

 sure, then, we proceed to estimate. 



In general the power must be, at least, capable of sustaining 

 the weight of a column of water which has for its base that of 

 the piston, and for its altitude the distance between the surface 

 Fig.246. RS of the water in the reservoir and the upper surface XY of that 

 in the pump. For when the base DC of the piston is below the 

 surface RS of the water in the reservoir, it is manifest that the 

 power has not to sustain the pressure of the water contained 

 between US and DC; because this pressure is counterbalanced 

 by that of the water surrounding the lower part of the pump, 

 and which is transmitted by means of the inferior orifice of the 

 pipe. The power, therefore, has only to sustain the pressure 

 exerted upon the surface DC by the fluid comprehended between 

 RS and XY; which pressure is equal to the weight of a column 

 of water whose base is CD and altitude the vertical distance be- 

 414. tween RS and XY. 



When the piston is above R'S', the surface of the water in 

 the reservoir, then it is evident the water contained between 

 DC and R'S' does not press the piston downwards. But, as in 

 this case it can only be sustained above R'S' by the pressure of 

 the air upon the water surrounding the pump, and as this pres- 

 sure is only capable of sustaining in equilibrium the contrary 

 pressure of the air upon the surface XY, it follows that the sur- 

 face DC is charged with a weight equivalent to the column which 

 has DC for its base and CR' for its altitude. And this pressure, 

 joined to that which is exerted upon DC by the superincumbent 

 fluid between DC and XY, makes the whole pressure upon the 

 piston, as before, equal to that of a column of water whose base 

 is DC, and height the distance between XY and R'S'. 



514. The sucking pump requires in its theory the aid of other 

 principles. We must enquire if under the proposed circumstan- 

 ces the water can possibly be raised to the piston, and made to 

 pass through the valve L ; for in some cases the water will never 

 pass a certain altitude, how many strokes soever we give to the 



