[ 37S ] 



in the defcending feries by the ratio of the rec to the cylr, 

 or the quotient of the former divided by the latter ; and in 



the 



tent of the gage to that of any part of the ftem^ mud be known, and it is thus 

 found. 



Let the whole of the iiariow part only of the flem be filled with merc>', and 

 this carefully fliaken out again, and weighed by the niceft balance ; let the fame be 

 again filled together With the wider part of the ftem, as far as it is cylindrical, 

 and the contents weighed as before ; then let the whole veflel be quite filled, and the 

 weight of the mere' it holds be found: fince the capacity of the whole gage is to 

 that of the ftem, or any part of if, as the quantities or the weights of mercy each 

 contains ; and the content of each half of the ftem is thus known, and the ratio of 

 the fame to the whole, and fince each half of the ftem is in itfelf cylindrical, equal 

 parts of the length of each feparate fegment, will be equiil poitions of the content 

 of that fegment ; i. e. the contents are as the lengths ; but the contents, and there- 

 fore the lengths, will be inverfcly as the rarefaftion, when the refidual air in the 

 gage is contained within them ; fo that if the whole length be graduated from 

 the upper end to the lower in any Nr of equal divifions, and the rarefatlion be known, 

 when the mercy ftands at the loweft divifion or greateft N' (which rarefaftion 

 is exprelfed by the quotient of the weight of the mercy filling the whoie ga"e, di- 

 vided by that contained in the whole fegment) then, as the whole N' of divifions, 

 is to that correfponding rarefaction, fo is inverfely any other lefler Nr of divifions, 

 to the rarefaftion, when the mercy will ftand at fuch divifion. This method muft 

 be taken to graduate each half of the ftem feparately, as they are of different dia- 

 meters ; but in eftimating the length of the wider half, as tlie content of the nar- 

 rower half muft be added to it, fo the wider part muft be computed to be fo nnich 

 longer than it is, as the addition of the content of the, narrower part would make 

 it, if' this were reduced to the fame diameter as that of the wider part. 



But if the ftem were to be thus graduated by an arbitrary Nr of divifions marked 

 ton it, the rarefaftion anfwering to each of them would be exprefled by odd or 

 broken N'* unfit for meafuring it; and it would be difficult, when the merCy ftands 

 not at any divifion, but between two, to find what may be neridy the rarcfaflion 



