[ 233 3 
curve DE^ of that fyftem, can be afcertained, in fome 
known meafure, as English fathoms, or Paris toifes. 
The eafieft method of doing this, that theory 
fuggefts, is to compare barometers at two ftations, 
fappofe B and b , each of a known elevation AB 
and Ab, above the level of the fea. For the 
logarithms of any given ratio, in different fyftems, 
are proportional to the fubtangents; and the differ- 
ence of elevation, B b, diminifhed in the proportion 
of CB, (the diftance of the higher Ration from the 
earth’s center) to C£, (a third proportional to Cb, 
the diftance of the lower Ration from the earth’s 
center, and CA, the earth’s femi-diameter) is the loga- 
rithm of the ratio of the denfity at B, to the denfitv at 
b (that is, of the columns of quickfilver fuftained in 
the barometer at B and b ) in the atmofpherical fyftem. 
Therefore, as the difference of the tabular loga- 
rithms, of thefe columns, to the fubtangent of the 
tabular fyftem, fo fhould B^, diminifhed as hath 
been faid, (that is, fo fhould (3£) be to the fub- 
tangent of the atmofpherical logarithmic. The 
utmoft height, to which we can afcend, above the 
level of the fea, is fo final], that the reduction of 
B b may, even in this inveftigation, always be neg- 
lected. For, if AB were four Englifh miles, which 
exceeds the greateft acceffible heights, even of the 
Peruvian mountains, and AS three, /3S would be 
lcarce one part in 500 lefs than B b. So that, by 
comparing barometers at different elevations, within 
a mile above the level of the fea, the fubtangent of 
the atmofpherical curve might be determined, as 
it fhould feem, without fenfible error, by taking 
limply the difference of elevation, without redue- 
Vol. LXIV. H.h tion, 
