278 HAWKSBEE'S AIR-PUMP. 



Suppose P at its lowest and P' at its highest position, 

 and turn the wheel so that P ascends and P' descends. 

 When P' descends, the valve v closes and the air in B' flows 

 through V, while the valve V is closed by the pressure of 

 the external air, and air from R, by its elastic force, opens 

 the valve v and fills the cylinder B. When P descends, the 

 valve v closes, and the air in B being compressed flows 

 through the valve V, while the valve V closes, and. air from 

 the receiver flows through v' into B'. At every stroke of 

 the piston, a portion of the air in the receiver is withdrawn ; 

 and after a considerable number of strokes a degree of rare- 

 faction is attained, which is limited only by the weight of 

 the valves which must be lifted by the pressure of the air 

 beneath. 



Let A denote the volume of the receiver, and B that of 

 either cylinder ; p the density of atmospheric air, and p lf 



p 8 , p n the densities in the receiver after 1, 2, n 



descents of the pistons. Then after the first stroke the air 

 which occupied the space A will occupy the space A -f B, 

 and therefore we have 



Pl (A+B) = pA. 

 Similarly, p g (A + B) = p^A ; 



.-. p 2 (A + B? = pA\ 

 and after n strokes we have 



Pn (A + B)* = pA n , 



the volume of the connecting pipe AC being neglected. 



Hence, calling rr n and TT the pressures of the air in the 

 receiver after n strokes and of the atmospheric air respect- 

 ively, we have 



rrn_p n _( A \ , 



TT --7-- trr*/ 



Thus, suppose that A is four times B, and we were re- 



