[ 37° ] ^ 



of the aggregate of the rec and cylr divided by the recr, 

 this quotient will be a whole or mixed No. exprefling the 

 No. of times the primitive air contains the refidual, i. e. ex- 

 preiling the rarefadlion ; and it will be the common term of 

 a feries reciprocal of the former one and encreaftng ; the value 

 of correfponding terms in each, being equally above and below 

 unity. This is the common theorem for determining the rare- 

 fadion after any N". of ftrokes * ; but it fuppofes a perfedl 



vacuum 



* By this tlieorem two things will e;irily be found, which the experimenter mufl 



know, viz. what is tlie raref:i6lion which ought to be produced by any N"^ of ftrokes, 



and, and what N' of llrokes are rcquifite to produce a certain degree of rarefnftion ; 



(for I have found that if the pump does not efteft this in a very few more (Irokes 



than the theory requires, it will generally be loft labour to continue to work it, unlefs 



in dry weather or a dry room, one has hopes of pumping moifture out of the rec'). 



Both particulars m,iy be beft found by the afcending feries ; viz. by multiplying the 



quotient, of the fum of the contents of the rcc' and cyl^ (in cubic.il inches) divided 



by that of the rec (which v.'ill be a whole or mi.ved Nr, the fraftional part of which 



latter, is to be reduced to a decimal) continually into itfelf, as many times as there 



are ftrokes, and throwing away from every product all the decimal figures to the 



right hand, except two or three, vs'hich will occafion no material error, and much 



abridge the v.'ork ; which is alfo farther abridged by multiplying any power, fo 



produced, by itfelf, or by any oth^r power thus before found ; for the product thus 



arifing, will be that power whofe exponent is the fum of thofe fo multiplied ; as the 



cube or third power drawn into itfelf produces the fixth power ; or drawn into the 



fifth power, produces the eighth power ; and fo in any other. Thus the rarefaiflion 



produced by any N'' of ftrokes will be found, being exprefled by that produft or 



power, whofe exponent is the N- of ftrokes; and it will alfo be feen in t!ie procefs, 



what Nr of ftrokes fliouM produce any given degree of rarefaction ; which may 



alfo be found by the converfe of this prpcefs, viz. by dividing any greater power 



found, by any lefler, for the quotient will be that power whofe exponent is the 



djfercnci 



