Thermodynamic Properties of Air. 291 



racter, I preferred to measure both pressures and expansions 

 by the volumetric method. By this device, as 1 hope, the 

 exactness and homogeneity of the results were materially in- 

 creased. 



§ 3. The Coefficient.— hi order to determine the thermal 

 expansion of air at constant pressure (1 to 130 atmospheres), 

 I have applied the following arrangement : — Two vessels of 

 known capacity are filled simultaneously with gas, under any 

 desired pressure, by connecting them with a reservoir con- 

 taining a sufficient quantity of condensed gas. One of these 

 vessels is cooled or heated to any temperature 6; the other is 

 kept at the constant temperature of melting ice. Letp atmo- 

 spheres be the common ' pressure in both vessels ; s { and s 2 

 their capacities, at the respective temperatures 6° and 0°, under 

 the common pressure p. 



The quantities M, and M 2 of gas contained in the vessels 

 are then brought under atmospheric pressure and temperature : 

 having measured their volumes, we calculate M t and M 2 in 

 the usual way. As unit quantity of gas I take here, and in 

 the following pages, the mass contained in unit volume (cub. 

 mm.) at 0° Centigr. under the pressure of one atmosphere. 



The densities of the two masses, when compressed in the 

 vessels s 1 and s 2 , are unequal; the colder one is also the 

 denser. Let their densities be p 1 and p 2 , then we have 



But 



therefore 



Mi 

 Pi= — > P2 = 



_M 2 



*2 



p2 





Pi ~'l + « P ,e. 



,6' 



1M 2 5i 



1 



e 



(1) 



This formula may be employed to calculate a p>e ; i. e., the 

 mean coefficient of expansion of the gas between 0° and 6°, 

 when under the constant pressure of p atmospheres. It will 

 be remarked that the value of a p>e is made here to depend on two 



ratios,^ and — , and on the temperature 6. 

 Mi s 2 



In most of the experiments to be described the temperature 



of the vessel s% was not 0°, but t° (usually +16°). In this 



case we have 



= Mi = __Po_. M 2= Po 



