230 Mr Anderson’s Corrections for the Effects of Humidity 
tension of vapour at the same temperature ; then, if v' represent 
the enlarged volume (still at the pressure b), which the air ac- 
quires by the addition of the vapour ; the elasticity of the air, 
V 
being inversely as its bulk, will be expressed by h — . If to this 
there be added the elasticity of the vapour, we obtain 
h ~ -f-yfor the elasticity of the mixture ; but, since the mixture 
V 
is supposed to be at the pressure b, we have b +f= b, from 
V 7 b 
which we easily deduce ~= - j . 
Hence the enlarged bulk of air by the humidity, is to its ori- 
ginal bulk , when perfectly dry , as b to b<—f or as 1 -f j—j. 
to unity. From this result, it is obvious, that any portion of 
an atmospherical column, having in admixture with it a quanti- 
ty of vapour, whose elastic force is f must be increased in length, 
in the ratio of 1 to 1 + j/ f * ts or igi na l length in the dry state 
being unity ; and that, consequently, since the density of the 
air is inversely as its bulk, a coefficient of the form 1 + j~~y 
must be applied to the barometrical formula, to compensate for the 
dilatation of the atmospherical columns by moisture. In applying 
this correction, the most convenient mode will be to substitute, 
in place ofy*, the mean tension of the atmospheric vapour at the 
f _i_ fr 
upper and lower stations, namely, J —~ ; and, in like manner, 
to substitute for b the mean of the atmospheric pressures, name- 
* -t- 
We thus obtain 1 + 
2 
b+r> /+,/ 
2 2 
or 
simply 
As the quantities jfandy' are supposed 
b + — (f -h f) 
to have been determined, in the case of the correction formerly 
