[ 3/6 ] 



the afcending feries by the reciprocal of the fame, or by the 

 ratio of the cyl'^ to the reC. For the air intruded, &c. at each 



ftroke, 



that experiment ; it is therefore neceflary to graduate the ftem by a decimal divifion, 

 exprell'ing the rarefaiTbion or refidunl air by looths or loooths ; which may be thus 

 done : 



Let, as above, the weiglit of the whole content of the gage be divided by that of 

 the whole content of that fegmcnt of the ftem, which is to be graduated ; the quo- 

 tient will expiefs the rarefaflion when the mercy ftands at the loweft divifion or end 

 of the fegment ; then fay, as that quotient or rarefaction, is to the whole length of 

 the fegment, meafured by and exprefled in equal parts, fuppofe hundredth parts of 

 an inch; fo is inverfely the decimal, centefimal, or millefimal N'' neareft to and above 

 the faid quotient, to the Nr of hundredth parts of an inch (to be meafured from the 

 top of the fegment) at which the (loweft) divifion fhould be marked on it, anfwer- 

 ing to f\ich decimal, centefimal, &c. N' exprefl!ing the rarefaftion, when the mercy 

 will ftand at that divifion : and as the faid quotient (of the weight of the content 

 of the whole gage, by that of the whole fegment) to the faid length of the fegment; 

 fo is the fecond decimal, centefimal or millefimal N'' inverfely, the fecond divifion 

 to be marked ; and fo on until the whole is graduated. 



Example. Let the weight of the mercy contained in the narrower or upper feg- 

 ment, be two grains, and that in the whole gage be 1970 grains (which v/ere the 

 meafures of my gage) : the quotient of the latter divided by the former is 985 ; fo 

 that when the merO ftood at the loweft divifion, the rarcfaftion was 985 ; the neareft 

 millefimal N'' to which is 1000 : alfo the length from the top of the ftem which two 

 Grains weight of mercy filled, was 141 hundredth parts of an inch : as therefore 985 

 is to 141, fo is inverfely 1000 to 138, 88 hundredth parts of an inch; which is 

 the length from the top of the ftem, at which the divifion (hould be made, where 

 the mercy, when ftationary, would fiiew a rarefaflion of 1000. In like manner as 

 98c : 141 : ■• inverfely 2O00 : 69, 44 hundredth parts of an inch, the lengtli from 

 ■the ton, at which the divifion anfwering to a rarefaftion of 20 3o fliould be made ; 

 which will be half the former length : and tlius may the reft of the fegment be 



graduated 



i 



