on the Formula for measuring Heights hy the Barometer. 251 
in which m is a constant coefficient, to be determined either by 
experiment, or by means of the relation between the specific 
gravities of air and mercury, and the logarithm of — to be taken 
in any system of logarithms whatever. 
The diminution of temperature, however, as we ascend into 
the upper regions of the air, requires, that this generic expres- 
sion, for the difference of elevation between the two stations, so 
simple in its form, and easy in its application, should receive two 
corrections : the first of these being made upon the length of the 
mercurial column, at either of the two stations, in order to re- 
duce it to the same standard, in point of temperature, as the 
other ; and the second, upon the coefficient which, in conse- 
quence of the elongation or contraction of the aerial column by 
heat and cold, must be modified, so as to adapt it to the actual 
temperature of the atmosphere, when it is either above or below 
the temperature at which m was originally fixed. The lengths 
of the mercurial columns, at the two stations, must therefore be 
reduced to what they would be, on the supposition, that the 
mercury in the barometers, at both, were at the same tempera- 
ture, either by computing the length of the lower, in reference to 
the temperature of the higher, or that of the higher in reference 
to the temperature of the lower ; or even by reducing each of 
them to what they would have been, at some common tempera- 
ture, different from that of either. In short, the design of this 
correction being to estimate the pressure of the air at both sta- 
tions, by mercury of the same specific gravity, it is a matter of 
perfect indifference to what temperature the barometrical co- 
lumns may be brought, by calculation. If the length of the 
mercurial column, however, at the upper station, be reduced to 
what it would have been, on the supposition, that its tempera- 
ture had been the same as at the lower station, the expression 
for the height will become 
the coefficient q depending, partly upon the difference of tem- 
perature of the mercury in the barometer, at the two stations, 
and partly upon the rate of the expansion of mercury, by in- 
