on the Formula for measuring Heights by the Barometer. 25S- 
its present state, when the common logarithms are employed, 
becomes 
A= 10,000r 1 + -00244. ^ Sii'i "llog. . =-") 
L V ^ / J ® Vl +-000102T— T')-®/ 
In addition to the corrections which have been described, two 
others have indeed been proposed ; one for the change produced 
by temperature upon the substance of the scale, which measures 
the lengths of the mercurial columns, and the other for the in- 
fluence of gravity upon the aerial particles, by a change of geo- 
graphical position. The first of these corrections, however, is 
too minute for the ordinary range of temperature, within which 
barometrical observations are made, to deserve the slightest atten- 
tion ; and the last is a refinement in calculation, carried, perhaps, 
beyond the limits of exactness which are furnished by the grosser 
and more palpable data of the problem. The corrections which 
I mean to apply, in order to adapt the formula to the actual 
state of the air, with respect to humidity, are, I conceive, of a 
far more important character, as they appear calculated to ac- 
count for the difference in the results of barometrical measure- 
ments, which have been obtained by different individuals, in 
determining the same heights, or by the same individuals in dif- 
ferent states of the air, with regard to moisture. 
If ^the density of the atmospheric vapour at different heights 
above the surface of the earth, were regulated by the same law 
as that of the aerial medium in which it floats, it is evident, 
that the presence of a greater or less quantity of vapour would 
not render any correction necessary upon the present formula ; 
so far at least as the result depends upon mere pressure. For 
if b and /B denote, as before, the lengths of the mercurial 
columns, produced by the weight of dry air alone ; and ify'and ' 
f represent the elasticity of vapour, at the lower and upper 
stations, we should have 
Therefore, b:b+f=./3:^-i-f' 
And, - = 
/ 3 +/' 
Hence also, Log. 0) ^log.(J-^) 
