From Regnault's table of vapour tension, we can obtain the pressure in inches of mercury at 32 deg., which corresponds to the observed boiling-point; or _vice versa_, if required. From the pressure, the height may be deduced by the method for finding heights by means of the barometer. The following table expresses very nearly the elevation in feet corresponding to a fall of 1 deg. in the temperature of boiling water:-- Boiling Temperatures Elevation in Feet between. for each Degree. 214 deg. 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 deg. for each 520 feet of ascent until the temperature becomes 210 deg., then 530 feet of elevation will lower it one degree until the water boils at 200 deg., and so on; the air being at 32 deg. 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 deg., the column of air will be shorter; and if greater, longer than at 32 deg. According to Regnault, air expands 1/491.13 or .002036 of its volume at 32 deg., 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, _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.