252 IVIr Anderson's Corrections for the Effects of Humidity 
crease of temperature. If T denote the temperature of the 
mercury in the barometer, at the lower situation, and T' that at 
the upper, then =: 1 -{- *000102 (T — T') the expansion of 
mercury for l°,of Fahrenheit being about a ten thousandth part 
of its volume. 
The other correction to which I alluded, depending upon the 
expansion or contraction of the air, according as its temperature 
is above or below the standard temperature, to which the co- 
efficient m refers, reduces the formula to the form 
/^ = mrloff. f ^ 
The coefficient r has been so assumed as to apply to the ex- 
pansion of air, holding in admixture with it the usual propor- 
tion of humidity which exists in the atmosphere. As the quan- 
tity of aqueous vapour, however, which mingles itself with the 
different strata of the air is extremely various, at different times, 
as well as over different places, it must be obvious, that, when 
the hygrometric condition of the atmosphere departs far from 
the mean state at which r is supposed accurately to apply, cor- 
responding deviations from the real difference of altitude, be- 
tween the two stations, will be produced upon the height A. 
Without doing any thing more at present, than simply advert- 
ing to this fact, it will be sufficient, in giving a brief exposition 
of the corrections which have hitherto heen applied to the for- 
mula for barometrical measurements, to state that it was found 
by comparing the experiments and observations of Sir G. Shuck- 
burgh and General Hoy, that atmospheric air, in its ordinary 
condition with respect to humidity, expanded of its origi- 
nal bulk for each degree of Fahrenheit ; that when h was 
expressed in English fathoms and common logarithms employed, 
the coefficient m was 10,000, the mean temperature of the co- 
lumn of air between the two stations being the freezing point of 
water ; but that, when the mean temperature was different, the 
formula required the application of the coefficient r, which, in 
that case, became 1 -|- *00244 ^ ^ ^ symbols 
t and t' denoting the temperature of the air at the lower and 
upper situations, respectively. The whole formula, therefore, in 
