280 Professor Arpsoun on the Theory 
charged with the amount of vapour which belongs to the existing dew-point ; and as 
the specific heats of air and vapour are different, this mixed atmosphere, in cooling 
through @ —?¢°, will evidently not give out the same quantity of caloric, and can 
therefore not convert into vapour the same quantity of water that would be cooled 
and vaporized by the same weight of dry air alone. In fact, for .267, the specific 
heat of air, we should in strictness use the specific heat of the mixture of air and 
vapour ; or, what will answer the same purpose, multiply by the ratio of these, the 
value of the quantity to be deducted from f’, already obtained. Now, to determine 
the specific heat of the mixture, the relative weights of its constituents should be mul- 
tiplied by their respective capacities, and the sum of the products divided by the sum 
of the weights. But the weights, being obviously as the specific gravities, are to each 
wr 
other as 1 : .625 ce Also, the specific heat of air being .267, and that of vapour 
.847, the former is to the latter as 1: 3.172. Hence, according to the rule given 
above, we will have 
14 6254" 3.172 
(AS ees 
1 + 625 
P 
for the specific heat of the mixture of air and vapour referred to that of dry air taken 
as unity ; and, applying the correction as already explained, we will have an equation 
in which f” is the only unknown quantity, and from which, therefore, its value may 
be found. ‘The equation, however, being a quadratic, and the unknown quantity in 
its first dimension having a coefficient of three terms, its solution would involve 
tedious arithmetical operations, and can therefore not be recommended as a ready 
means of making the correction in question. Nor is such course at all necessary, for 
the same object may be achieved, and with a sufficient precision, by either assigning 
to f” an average value, or by deducing approximately the tension of vapour at the 
dew-point by the formula f"”= f’ — & x = (.0223 p + .3312), and using the 
value of f” thus obtained, in order to determine that of 
1+ .625 Sx 3.172 
P 
1 + 625 £ 
P 
the specific heat of the mixture of air and vapour. The latter method is decidedly 
the best ; and though not mathematically accurate, will not I believe exhibit a devia- 
tion from the truth until the calculation is pushed to the seventh or eighth decimal 
place. 
