with a single Cylindei'. 299 



Haustiou ; then 



E"=E' + E(e-1) = ^ + E(e-1), . . (3) 



which expresses the limit of exhaustion for the receiver of the 

 common air-pump. The elasticity of the air in this case is 

 greater than the limiting elasticity of the air in the receiver of 

 the new pump by the fraction E(e — 1). 



Assuming « = ]08 cub. inch.; 6 = 13 cub. inch.; ^i^HnlH 

 cub. inch.; E = 30 inch.; e= y^ (which gives about a press- 

 ure of 10 grs. on a valve orifice of y^jjth of an inch in diameter) ; 

 and 71 = 60; then by formula (1) E6o = '095 ; that is to say, the 

 elasticity of the air in the receiver of the new pump at the end 

 of sixty singk strokes will be measured by about -j-V*^^ ^^ ^^ 

 inch of mercury. Again, by formula (2) we find the limit of ex- 

 haustion to be measured by '041 inch of mercury, or about ^'^th 

 of an inch of mercury. 



Now by formula (3) we have 



E"=04I + -25 = -291, or -3 nearly; 

 that is to say, the limit of exhaustion for a common pump in this 

 case will be measured by j^ths of an inch of mercury, being ^th 

 of an inch in excess of that derived for the new pump. 



This pump, therefore, not only exhausts the air more rapidly 

 than the common pump, but it also carries that exhaustion to a 

 much higher limit. 



These theoretical calculations have been fully confirmed by 

 actual experiment. 1 have had a pump made on this new prin- 

 ciple, with a stroke of 8 inches, and li inch in the section*, and 

 I have compared it with a superior pump on the old construc- 

 tion : the following is an exact statement of the results of my 

 experiments. 



Results of experiments ivith the new Pump. 



Capacity of the receiver 108 cubic inches. Common siphon 

 gauge. 



Elasticity of the air in the receiver at the end of sixty single 

 strokes =-13 inch of mercury. Limit of exhaustion =-05 inch 

 of mercury. 

 Results of experiments with a common double-barrelled Pump, 

 EACH PISTON having a stroke of 4< inches. 



Capacity of the receiver, &c. as before. 



Elasticity of the air in the receiver at the end of 120 strokes 

 of the two pistons =*6 inch of mercury. 



Limit of cxliaustion = -3 inch of mercury. 



* This iustrinnent may be seen at Messrs. Murray and Heath's, Philo- 

 sophical Instrument Makers, Piccadilly. 



X2 



