170 AIR-PUMP. 



expansion, the air which, at first, was in R and t, now fills 

 R, t y and C. When the piston is pushed down, v closes, v 

 opens, and the air in C escapes from the apparatus. 



(a.} The lower valve v is sometimes supported, as shown in Fig 

 102, by a metal rod which passes through the piston. This rod 

 works tightly in the piston, and is thus raised when the piston is 

 raised, and lowered when the piston is lowered. A button near the 

 upper end of this rod confines its motion within very narrow limits, 

 allows v to be raised only a little, and compels the piston, during 

 most of the journeys to and fro, to slide upon the rod instead of 

 carrying the rod with it. 



289. Degrees and Limits of Exhaustion. 



Suppose that the capacity of R is four times as great as 

 that of C. (The capacity of t may he disregarded.) Sup- 

 pose that R contains 200 parts of air (e. g., 200 grains), 

 and 6 Y , 50 parts. After lifting the piston the first time, 

 there will be 160 grains (= 200 x f) of air in R, and 40 

 grains (200 x -J-) in C. After the second stroke there will 

 be 128 grains [= 1GO x f = 200 x -fr x f = 200 x (|) 2 ] 

 of air in R, and 32 grains in C. After n upward strokes, 

 200 x ($)" grains of air will remain in the receiver. Evi- 

 dently, therefore, ive never can, by this means, re- 

 move all the air which R contains, although we 

 might continually approach a perfect vacuum, if this were 

 the only obstacle. It requires an exceedingly good air- 

 pump to reduce the tension of the residual air to -^ inch 

 of mercury. This limit is due to several causes, among 

 which may be mentioned the leakage at different parts of 

 the apparatus, the air given out by the oil used for lubri- 

 cating the piston, and the fact that there is a space at the 

 bottom of the cylinder untraversed by the piston. 



290. SprengePs Air-Pump. This instrument is 

 used to apply the principles set forth in 259 to the ex- 



