[ 266 J 
the denfities of the fluids are the denfities of the air 
at A and B. Therefoft'the compreffive forces are as 
the denfities; that is, P:Q= R:S. Therefore 
GHxR:MNx3r?R:S. Therefore G H and - 
MN are equal. Therefore E F :GH = EFrMN; 
but it hath been fhewn, that EF : MN =TB 2 : TA\ 
Therefore E F : G H = T B- : T AV But A B being 
given, • TB is given, and the proportion of the 
iquareof TB to the fquareof TA is given. There- 
fore the proportion of EF- to G H is given. And 
GH, is given as hath been fliewn. Therefore EF 
is given, and the proportion of the given line EF to 
the given line CD, or of the deafity of the quick- 
filver to thedenfity of the air, at B, is given. QJE, h • 
COMPOSITION^- 
Find the fiibtangent GH competent to the given 
temperature; find a line, EF, to which that fub- 
tangent fhall bear the duplicate proportion of T A 
JO TB; that is, of the earth’s femi-diameter to the 
earth’s femi-diameter increafed by the given eleva- 
tion of the place of obfervation, above the level of 
the fea. As that line EF to the obferved height'of 
the Quickfilver, fo is the denfity of the quick ft lver, 
in the barometer actually employed, to that of the 
air, at the time and place of obfervation. 
Thus the fpecific gravity of air may be found, com- 
paring it with quickfilver, and by means of quick- 
filver with other fluids. Though- it is only the moflT" 
fimpie cafe of this problem that can ever come into 
practice, I chofe to difcufs it in its moft general ex- 
tent v 
