FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 53 
suggests a method of measuring heights by the thermometer that requires little or no 
computation. 
Let ST on the chart of vapours, which there represents the sixth root of the 
density of steam at 212 °, be also taken to represent the whole height of the 
atmosphere above a point where the water boils at the temperature of 212 °. Then 
from or, the ordinate to the steam line at 200 °, draw zsq parallel to QS, the line 
of one atmosphere pressure, or rather, it ought to be converging to the point where 
the cord QS produced meets the axis. It is evident that SQ represents very nearly 
the height where water boils at 200 °. Now, if such lines are drawn at each degree 
between 200 ° and 212 °, they will divide S(/ into parts that are sensibly equal. 
The value of each of these parts depends on the value given to ST, which, 
according to our theory, is in feet 318 times the absolute temperature of the air at 
the station where water boils at the temperature corresponding to the square of the 
abscissa of the ordinate ST. 
The following is the accurate formula by the theory for any vapour of which the 
constant G (see Note B) is known :— 
317-6 
/ y/r + 461 - G \ 
Wt + 461 - Gj 
/t + 461V 
\y + 461/ 
(T + 461) = h, 
in which T is the temperature of the air at the lower station, t = temperature at 
which the liquid boils at the lower station, r = temperature at which the liquid boils 
at the upper station (all expressed in degrees on Fahr. scale), G the first constant of 
the vapour (see Note B), and h the difference of height between the stations in feet. 
By boiling temperature is meant the temperature at which the tension of the vapour 
is the same as that of the external atmosphere. 
Let us apply the formula to the vapour of water, in which G is 19’4923, and let us 
take an example where T is 60°, t — 212°, and r = 211° ; the value of h is 528'6 feet. 
It will be found, by taking other values for T and r, that this elevation for 1° 
difference in the boiling point increases about |ths of a foot for each degree that r 
diminishes, and increases exactly 1 foot for every degree that T increases, and vice 
versd. 
Professor Forbes, who has discussed this subject fully in a recent paper, finds that 
his observations indicate a number between 540 and 550 feet. The accordance is 
thus satisfactory ; by the formula, 550 feet per 1° is the mean value for T = 75°, 
t — 212°, r = 202°, which corresponds with Professor Forbes’ mean ; and what it 
wants of uniformity is too small to be discovered in practice. 
Suppose that we wished to employ the vapour of sulphuric ether for this purpose. 
It boils at 96° under a pressure of 30 in. Dalton’s observation on this ether gives a 
line of vapour which has G = 16-86. Compute the above equation with this value of 
G, and t = 96°, r = 95°, T = 60°. The result is h = 568, being y^-th greater than in 
the former case of steam. 
