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,