[ 262 J 
the quickfilver to a common temperature, if the 
temperatures of the quickfilver, as well as the air, 
have been different, at the different times of ob- 
lervation. Find the fubtangent for each tempera- 
ture of the air (by problem 3d) 3 divide the cor- 
rected heights of the quickfilver by the fubtangents 
correfponding to the obferved temperatures of the 
air. The quotients are as the denfities in thefe 
temperatures refpeCtively 3 that is, calling the heights 
of the mercury reduced, P, n ; the temperatures, 
T, 0 3 the fubtangents, S, £ 3 and the denfities, 
p n 
D, A, D : A — ? '• “• For the denfities are as the 
compreffive forces direClly, and the abfolute elafti- 
cities inverfely (by fedtion 4th) 3 and the abfolute 
eladicities are as the fubtangents (by feCtion 4th) 3 
whence the truth of the rule is manifeff. 
The mod convenient method, however, for practice 
will be, to make the denlity of the air, in fome given 
date of the barometer and thermometer, a dandard, 
with which to compare the denfities in all other dates 
of thefe indruments. Suppofe, for inftance, at the 
level of the fea, 30 inches be taken for the dandard 
height of the barometer, and -(- 4° for that of 
the thermometer. Let D be the denfity of the 
air, at the level of the fea, when the barometer 
is 30 inches, and the thermometer -\- 40. Put 
P = 30 inches, and S — the fubtangent of the lo- 
gidic correfponding to the temperature -j- 4°* Now 
in another temperature 40 -4- n, let the fubtan- 
gent be S -4- - S. And let the height of the baro- 
meter P be changed into P -4- - P 3 and let A be 
the 
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