f = 0.00106 e / (1 + 0.00367 t)
in which e is the vapor pressure in millimeters of mercury, and t is the common Centigrade reading. As an illustration of the actual values of the pressure, temperature and density of saturated water vapor, for various conditions, the following table is presented:
TABLE III
Temperature, Pressure and Density of Aqueous Vapor, in Metric Measures.
| Temperature, Centigrade. | Pressure, Millimeters. | Density Kilos. per cubic meter. |
|---|---|---|
| −25 | 0.61 | .557 |
| −20 | 0.94 | .892 |
| −15 | 1.44 | 1.395 |
| −10 | 2.15 | 2.154 |
| − 5 | 3.16 | 3.244 |
| 0 | 4.57 | 4.835 |
| + 5 | 6.51 | 6.761 |
| 10 | 9.14 | 9.329 |
| 15 | 12.67 | 12.712 |
| 20 | 17.36 | 17.117 |
| 25 | 23.52 | 22.795 |
| 30 | 31.51 | 30.036 |
| 35 | 41.78 | 39.183 |
| 40 | 54.87 | |
| 45 | 71.36 |
Now by Dalton’s law, each gas or vapor in a mixture of several behaves as if it were alone. Thus if the foregoing experiment be conducted in a bottle containing various gases chemically inert to water, the same mass of water will be evaporated, and exert the same uniform pressure, in addition to those exerted by the gases. Now the density of each gas or vapor present, will equal its mass divided by its volume, and the density of the mixture will equal the total mass divided by the volume. Furthermore, it is well known that aqueous vapor is less dense than dry air at the same temperature and pressure. From this it is at once evident that moist air, which is merely a mixture of dry air and aqueous vapor, must be lighter than dry air at the same temperature and pressure. This is true whether the two fluids compared be in closed vessels or in the free atmosphere.
Accordingly in all precise dealing with the free air, whether involving its buoyancy, its resistance, its energy or any other mass function, its density as affected by the humidity must be taken into account. This can be computed from the observed pressure, temperature and relative humidity as revealed by well known instruments, the barometer, thermometer and hygrometer. Thus from the observed temperature and relative humidity, the mass of vapor present per cubic meter is read from Table III, the reader, of course, multiplying the given tabulated mass by the observed percentage of humidity. To this aqueous mass must be added the mass of dry air present. Then the total mass per cubic meter is the density.
Various formulæ are available for computing the density of moist air from the readings of the three instruments mentioned above. Also, tables have been worked out giving the density without further calculation. Moreover, the density of free air may be directly measured, accurately enough for most purposes, by means of a densimeter. A simple formula for finding the density of moist air is as follows:
ρ = 0.465 (b−e)/T
in which b, e, are the pressures in millimeters mercury respectively of the moist air and its vapor, as revealed by the barometer and hygrometer.