[ 3% 1 



laft refidual air ; fo that the lefs the rec is, the lefs will be 

 the reliduum, and confequently the greater the rarefa&ion : but 

 this is after the pump has exhaufled as much as it can ; for 

 in every flroke from the commencement to the end, the air 

 in the rec'', whether left in it, or intruded, (or its denfity 

 which is the fame thing) is to that which remains in it after 

 any flroke (or its then denfity) as the fpace into which it is 

 difFufed on the elevation of the pifton, i. e. the aggregate or 

 fum of the capacities of the rec'' and cyl", is to the primitive 

 fpace in which it was confined, i. e. to the capacity of the 

 rec"^ alone : In which analogy, each of the confequents, divided 

 by its refpedlive antecedent, muft give the fame quotient, or 

 ratio, and vice verfa ; and fuch quotients muft be /;/ every 

 Jlroke conjiant quantities, becaufe the two laft terms of the ana- 

 logy are fuch : but the refidual air after any ftroke is the pri- 

 mitive air with refpedl to the fubfequent ftroke, hence if the 

 firft refidual be A of the primitive air, the fecond will be 

 the i of ^ (i. e. i) and the third, 4 of ^ of ;t (i. e. J) of the 

 primitive air ; and any refidual will be the laft term of a 

 gebm.etrical progrefTion, the N°. of whofe terms is the N''. of 

 ftrokes ; each term being fo often involved or multiplied into 

 itfelf : if the firft term be as here, the quotient of the rec' 

 divided by the fum of the capacities of the rec^" and cyb", it 

 will exprefs what fradlional part of the primitive air the next 

 refidual is ; and the progreflion or feries will be fractions and 

 decreafing; and if the firft term of the feries be the quotient 

 Vol. VI. 3 A of 



