H′ = H {1 + (m - 32) ·002036}
and substituting the value of H,
H′ = f (B - b) {1 + (m - 32) ·002036}
Strictly, according to theoretical considerations, there is a correction due to latitude, as in the determination of heights by the barometer; but its value is so small that it is practically of no importance.
If a barometer be observed at one of the stations, the table of vapour tensions ([p. 62]) will be useful in converting the pressure into the corresponding boiling-point, or vice versa; so that the difference of height may be found either by the methods employed for the boiling-point thermometer or the barometer.
In conclusion, it may be remarked that observers who have good instruments at considerable elevations, as sites on mountains or plateaus, would confer a benefit to science, by registering for a length of time the barometer along with the boiling temperature of water, as accurately as possible. Such observations would serve to verify the accuracy of theoretical deductions, and fix with certainty the theoretical scale with the barometer indications.
Example, in calculating Heights from the Observations of the Boiling-point of Water.—1. At Geneva the observed boiling-point of water was 209°·335; on the Great St. Bernard it was 197°·64; the mean temperature of the intermediate air was 63°·5; required the height of the Great St. Bernard above Geneva.
Method by formula:—
H′ = f (B - b) {1 + (m - 32°) ·002036}
In this case f is between 530 and 550, or 540.