295 On. the Principles of Pump-TFork* 



something analogous to this will always be the case of a 

 single pump, where the stroke of the piston is large, and 

 its velocity nearly equal to that of the rising water. 



70. But it is quite otherwise with the pump which has 

 two pistons upon one pipe, and where the rismg water is 

 constantly in a uniform motion ; for there the whole force 

 is employed to continue that motion only, and the velocity of 

 the water will always be as the square root of the difference 

 between 36 and the height of the pump, or in the present 

 case of fig. 6, as ^fio. 



71. The piston playing at the bottom of the pipe or the 

 top, makes no difference in the power to work the pump ; 

 since in both cases the same column of water AG is moved 

 by the piston, the pressure of air on the column at G and 

 A being equal. 



72. The force of anv column of a fluid to resist motion, 

 is compounded of its quantity of matter and velocity; there- 

 tore while the force remains the same, the quantity of the 

 fluid may be varied as you please, since the velocity will 

 ever compensate any deficiency or redundancy of force thai 

 may happefi on that account. 



Fig. 7. 

 7v3. Thus suppose EKLI be the cistern of the head of a 

 pump, in which the piston MN works, then the pipe 

 ABCDmaybe in bore in anv proportion less, and still 

 the watpr shall be supplied to the cistern when the piston 

 rises, with the same force and in the same time as it would 

 be if the bore of the pipe were all the way the same with 

 thai of the head, or equal to KFHL. 



74. In this latter case the velocity of the water will be 

 the same with that of the piston, but in the former the ve- 

 locity of the u ater will be to that of the piston as the square 

 of MN to the square of BC, because the quantity of fluid 

 in EFHI is to that in the contracted pipe ABCD in the 

 same proportion. 



75. If the pump be required to raise water 26 feet (as in 

 fig. 7.) J then since the height AG = 26 is «- of 39 = AX, 

 the jet GX will be 13 feet j and since the air at a mean 

 gravity is equal to a column of water 34 feet high, we have 

 34 — 26 = 8 ; therefore the maximum force will produce 

 a uniform velwcitv of near 29 fcct per second j and the pres- 

 sure of the air only a velocity of '22-6 feet per second, if the 

 piston move, m a pipe ABCD of an equal bore through- 

 out. 



76. In this case the water would be wire-drawn, since 



th« 



