on the Formula for measuring Heights hy the Barometer. S55 
more satisfactory, as the absolute quantities of moisture in the 
air, were in the two cases exceedingly different. 
Now, if it be kept in vieV that the density of air is reduced 
one-half by an ascent of about 18,000 feet, while that of vapour 
undergoes the same degree of attenuation at the height of about 
4,500 feet, it follows, that the varying humidity of the atmo- 
sphere must, at different timeSj. affect, in different degreesj the 
law of the density of the aerial columns, and give rise to devia- 
tions from the geometrical progression, however strictly it might 
apply to the diminution of the density of dry air^ or even to that 
of the atmospheric vapour, when they are taken separately. For, 
if a, nr, &c. represent the density of successive strata of dry 
air, and &c. that of corresponding strata of vapour, 
at the heights &c. the sums of the terms representing 
the densities produced by the joint pressure of air and moisture, 
will be a ar -p &e. a series of terms no longer 
in geometrical progression. In conformity with these views, 
and the actual constitution of the atmosphere, it might be in- 
ferred, at first sight, that the difference of elevation deduced by 
the common formula, ought to exceed the true height so much 
the more as the air is charged with moisture in the state of va- 
pour ; the elasticity of the vapour at the lower station produ- 
cing a greater relative effect upon the height of the mercurial co- 
lumn, than at the upper station. This conclusion, however, is 
by no means supported by experience, but directly contradicted 
by it; as I have found, by numerous observations, that the 
heights computed by the common formula always turn out less 
than the truth, in proportion as the air is warm and damp. The 
cause of this is to be ascribed to the dilatation of air by mois- 
ture, already alluded to; which, acting in opposition to the in- 
fluence of the pressure of vapour, frequently neutralizes its ef- 
fects, and renders the mechanical constitution of the atmosphere, 
so far at least as the law of its density at different heights is in- 
volved, nearly the same ns would result from dry air alone. 
Hence a new coefficient, a function of the dilatation of air by 
moisture, depending partly upon the absolute humidity of the 
air, at the two stations, and partly upon the temperature of the 
intermediate column, must be applied to the formula, in a way 
analogous to that in which the correction for the excess or de- 
