The following table expresses very nearly the elevation in feet corresponding to a fall of 1° in the temperature of boiling water:—
| Boiling Temperatures between. | Elevation in Feet for each Degree. | |
| 214° and 210— | 520 | |
| 210 and 200— | 530 | |
| 200 and 190 | 550 | |
| 190 and 180 | 570 |
These numbers agree very well with the results of theory and actual observation. The assumption is that the boiling-point will be diminished 1° for each 520 feet of ascent until the temperature becomes 210°, then 530 feet of elevation will lower it one degree until the water boils at 200°, and so on; the air being at 32°.
Let H represent the vertical height in feet between two stations; B and b, the boiling-points of water at the lower and upper stations respectively; f, the factor found in the above table. Then
H = f (B - b)
Further, let m be the mean temperature of the stratum of air between the stations. Now, if the mean temperature is less than 32°, the column of air will be shorter; and if greater, longer than at 32°. According to Regnault, air expands 1⁄491·13 or ·002036 of its volume at 32°, for each degree increase of heat. Calling the correction due to the mean temperature of air C, its value will be found from the equation,
C = H (m - 32) ·002036
Calling the corrected height H′, it will be found from the formula,
H′ = H + H (m - 32) ·002036
that is,