Air-Pump. 405 



a certain part of the remaining air, which is in proportion to the 

 quantity before the stroke, as the capacity of the barrel to the 

 sum of the capacities of the barrel, receiver, and communicating 

 pipe. 



508. Now if we suppose no vapour from moisture, &c,, to 

 rise in the receiver, the degree of exhaustion after any number 

 of strokes of the piston may be determined by knowing the res- 

 pective capacities of the barrel and of the receiver, including the 

 pipe of communication &c. For, as we have seen above, that 

 every stroke diminishes the density in a constant proportion, 

 namely, as much as the whole capacity exceeds that of the cylin- 

 der or barrel ; the exhaustion will go on in a geometrical pro- 

 gression, the ratio of which is the same as that which the sum 

 of the capacities of the receiver and barrel bears to that of the 

 receiver; and this ratio of exhaustion will continue until the 

 elasticity of the included air is so far diminished by its rarefac- 

 tion as to render it too feeble to push up the valve of the piston. 



Let then the capacity of the barrel, receiver, and pipe of 

 communication together be expressed by 6 -}- r, and that of the 

 barrel alone by 6, and let 1 represent the primitive density of 

 the air in the pump ; we shall have 



& + r : r : : 1 : - = the density after 1 stroke of the piston. 



method suggested itself to Dr. Prince much more perfect and more 

 simple. It dispenses with the valve entirely by extending the bar- 

 rel downward so as to admit of the piston's descending below the 

 opening which communicates with the receiver, and thus allowing a 

 free introduction of air into the barrel. The air in this case is ex- 

 pelled through a valve at the top of the barrel, opening upward. 

 There will still be a limit however to the exhaustion ; for the air 

 cannot be forced through the valve at the top of the barrel, unless 

 its elasticity, and consequently its density, produced by the motion of 

 the piston, exceeds the density of the external air. To remove this 

 difficulty Dr. Prince enclosed the valve in question in a vessel fur- 

 nished with a small exhausting apparatus, by which the valve was 

 relieved from the pressure of the atmosphere. This appendage is 

 not necessary, except for purposes of very accurate exhaustion. 



