FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 61 
the reading of the scale marked off. Heat is then applied to the shut glass bottle, 
SS, that encloses Q, until the capsule, C, shows the equilibrium ; the air in Q, of 
course, has the same temperature, and has expanded accordingly against the constant 
pressure of the external atmosphere; the reading of the mercury in the scale, n, will 
now show the amount of expansion, and, therefore, the ratio of the constant density 
of the air enclosed in SS to the density of the atmosphere at the station. Thus, we 
ascertain the absolute temperature and absolute density of the atmosphere at every 
station from scales with as large a reading as we please. 
To obtain the law of tension of a vapour by three experiments made upon it at 
different temperatures when mixed with an unknown quantity of air, let t Q , t, t x be the 
three absolute temperatures found by adding 461 to the reading of Fahr. scale, and 
e 0 , e, e x the corresponding tensions. Also, let G and H represent the two unknown 
constants of the vapour, and F 6 the constant that represents the quantity of the 
enclosed air, or number of gaseous molecules, which is the same at all temperatures, 
while the number of vaporous molecules 
y/t ~ G\° 
H 
changes with the temperature t. 
These expressions mean the number of molecules in a constant volume, so that the 
experiments require to be made with the enclosed volume over the liquid constant. 
The general expression for the observed tension is 
e =. t F 6 + t 
V* - a y 
H / 
. ( 1 ). 
By eliminating F 6 from each of the three experiments, we have 
JTG _ _ 
y Ap - Ct \ 6 « 
H j t 
vA — G \ c h AAi ~_G\ G 
H 
H 
. ( 2 ). 
From the first and second of these, we have 
H6 ( r -?) = (^“ G ) 6 “(^“ G ) 6 
• ( 3 ). 
From the second and third, we have 
H6 (!-*) = (^-G) 6 -(^o-G)" 
( 4 )- 
Dividing (3) by (4), we obtain a known ratio R, 
5 _ GA - G) 6 - GA - G) 6 
R = 
GA — G ) 6 — GA 0 — ^-) 6 
(5). 
