P U M 



the moving force of the system = 



L Q T ""/ l P X H, and accelerating force of Q = g X L Q ~ /PX JL 

 L * LJX P + Q 



which may be substituted as before. 



PUMP. Air Pump. 



1. If b represent the capacity of one of the barrels, and r that of the 

 receiver together with the pipes and gages connected with it j then the 

 quantity of air extracted after every turn : the quantity before that turn 

 C : b I 2 b + r. And the quantity left in : the quantity before : : b + r 



Cor. Hence if P represent the quantity of air in the machine before the 

 first turn, the quantity left in after n turns is 



And the quantity exhausted is P P. ( ^^) - 



P. 



2. The density of the air in the receiver at first : the density after t 

 turns :: (2i + r)* : (&+*)* 



3. When the density of the air is diminished in the ratio of n : I, the 



number of turns t = WLJ2. . 



log. 2b -f- r log. b -f. r 



4. As the air is exhausted, the mercury will rise in the gage, and the 

 defects of the mercury in the gage from the standard altitude, after each 

 successive turn, form a geometric series, the ratio of whose terms is 

 2 b + r I b + r. And the ascents of the mercury at each successive turn 

 form a geometric series, the ratio of whose terms is 2 b + r I b 4. r. 



PUMP condensing, or condenser. 



If b represent the capacity of the barrel of the syringe, and r that of 

 the receiver, then after t descents of the sucker, the density of the air 

 in the receiver, will be to the density at first in the ratio ofr+tblr. 



PUMP, common or sucking. 



1. In the common pump the force necessary to overcome the resistance 

 experienced by the piston, in ascending, is equal to the weight of a co- 



