y "Ppa 
Tae 

TRANSACTIONS OF THE SECTIONS. 21 
respective pressures at the upper and lower stations, as measured by the barometer, or 
in any other way. ‘The conditions, however, which lead to this simple expression, are 
in nature never fulfilled; for it will seldom happen that the temperature of either sta- 
tion is 32°, and the atmosphere always includes a greater or less amount of aqueous 
vapour. A correction for temperature has been long applied, by augmenting or di- 
minishing the approximate height, or m x log - by the amount that a column of 
air of this length would expand or contract, if its temperature were changed from 

32° to p us 4 t being the temperature of the lower, and 4 that of the upper extremity 
of the aérial column, by which the expression becomes 
$*—82) 
9 
a 
D=m x log Al (+ 553 3 
Such is, I believe, a correct account of the present form of the barometric formula; at 
least, when we neglect the correction for variation of gravity, which is, however, so 
minute as to be in general safely negligible. The presence of moisture in the air 
must obviously exercise some disturbing effect upon this formula; but though this has 
been generally admitted by those who have turned their attention to the subject, I am 
not aware that any attempt at estimating its exact amount has been as yet made; and 
as the correction for moisture is frequently of considerable magnitude, and may, in 
my opinion, be applied with as much accuracy as that for temperature, I have taken 
the liberty of occupying for a few moments the time of the Section with an explana- 
tion of the method which it has occurred to me to devise, and with which, from some 
trials I have made of it, I feel every reason to be satisfied. Let p be the pressure, 
and ¢ the temperature of the air at the lower station, z!’ the dew-point of the air, and 
J" the force of the included vapour; and let p!, 6, 6” and F" represent the correspond- 
ing quantities at the upper station. This being understood, a little consideration will 
suffice to show that the presence of the aqueous vapour produces upon the formula a 
twofold deranging effect. It augments the values of p and p! beyond what they would 
be in dry air; and it produces an alteration in the length of the column of air be- 
tween the two stations, additional to that which results from the difference between 
its mean temperature and 32°, or the freezing point. The first of these is obviated, 
or, in other words, the correction for it is made, by substituting for p and p’ in the 
approximate formula, p—f" and p'—F", by which it becomes 
D=™m x log ae 
Having thus eliminated the effects of the tension of aqueous vapour upon the pressures, 
we have next to estimate the conjoint influence of it and temperature in elongating 
the pillar of air between the two stations. The theory of mixed gases and vapours 
enables us to do this, provided we can assign proper mean values to the temperature, 
the pressure, and the force of vapour of the aérial column in question. The mean 

e and this must be very nearly its true value. 
A t 
temperature is usually taken as. 
" " 
a and 
For the same reason the mean force of the vapour may be set down as 
let us assume the mean value belonging to the pressure as VW (p—f") X (p!—p”. 
Now volume », of dry air at 32°, under a pressure p, if raised to a temperature ¢”, 
" 
each ; and if saturated with vapour at this temperature, the tension 
493 461 +2" p ie 
of such vapour being f”, will become v X ey pay This is the volume of 
becomes v x 

the air when raised to ¢", and saturated at this temperature with vapour. And if this 
volume of air have its temperature further raised, we shall say to ¢, then its bulk will 
be represented by the expression 
46142"  p 4614+ ¢ _ 
461 +2 p 
0X aos * p— fi * 461 
0% —g93° X por 
