PNEUMATICS. 259 



strokes of the piston, the density of the external 

 air being 1; D~ 



Hence log D =nlog ; from which D may be 



Jj -}- -ft 



found when n is given, or n when D is given. 



It is evident that the exhaustion can never be com- 

 plete, as no more than a certain proportion of the 

 air that remains can be taken out by the next 

 stroke of the piston. There is even a limit which 

 it cannot exceed in the ordinary air-pump ; for the 

 spring of the remaining air, being the power which 

 opens the valves, when it becomes too weak to 

 overcome their stiifness and their weight, the ex- 

 haustion necessarily ceases. In air-pumps of the 

 most improved construction, the valves are opened 

 by a mechanical contrivance, so that this limit to 

 the perfection of the instrument is removed. 



350. When the end of a cylindric barrel con 

 stmcted as above, is either immersed in water, or 

 made to communicate with a reservoir of that 

 fluid, on the piston being drawn up, and the air 

 in the barrel rarefied, the water will ascend on ac- 

 count of the pressure of the external air. By re- 

 peated strokes of the piston, it may be made to 

 rise so high, as to pass through the valve in the 



R 2 piston, 



