274 THE AIR-PUMP 



brought into position III., by turning it in the direction 

 of the arrow d. The receiver is thereby shut, while the 

 barrel communicates with the external air by the tube a, 

 and since the air in the barrel is rarefied, the external 

 air rushes into it with an audible sound, until the air 

 inside and outside the cylinder has the same density. 

 The air is now again removed from the cylinder by 

 working the handle until the piston is at the opposite 

 end at the bottom of the cylinder ; the stop-cock is, 

 by a turn in the direction of the arrow e, brought back 

 into the position II., and the whole operation is repeated. 

 At every withdrawal of the piston the air in the re- 

 ceiver expands so as to fill the barrel as well, and 

 the rarefaction proceeds according to the same pro- 

 portion at every stroke of the piston as that which 

 was determined at the first stroke by the relative 

 capacity of the receiver and the barrel. Thus, if both 

 have equal capacity, the density of the air in the 

 receiver after the second stroke of the piston is ^th of 

 its original density, after the third stroke it is reduced 

 to ^th, after the fourth to T Vth, and so on; for 

 example, after the tenth stroke it will be diminished 

 to ToW^h- If ^ e receiver has only half the capacity 

 of the barrel, the degree of rarefaction after the first 

 stroke is ^rd, after the second ^th, and after the seventh 

 it is already as much as ^j^th ; if, on the contrary, the 

 receiver is twice as capacious as the barrel, the density 

 of the air in the receiver after the first stroke is re- 

 duced to f rds, after the second to ^ths, and after the 



tenth to no more than ^VViiF? tnat ' ls i to near ty ^s^ 1 * 

 the original density. It will thus be seen that the 

 exhaustion proceeds the more rapidly, the larger the 



