Thermodynamic Properties of Air. 3 



specific heats, as well as their difference, can be deduced from 

 the fundamental equation of the body, viz. v = F(p, t). 

 Although we do not possess a sufficiently accurate general 

 expression for the volume of atmospheric air in terms of the 

 pressure and temperature, yet some inferences as to the 

 thermodynamic behaviour of that body at different tempera- 

 tures, down to the critical, and under different pressures, may 

 be drawn from the numerical data which have been given in 

 the first part of the present paper, both in tabular and in 

 graphical form. These results can be obtained by means of 

 the graphical calculus. It is true that results arrived at in 

 this manner cannot be as accurate and convincing as those 

 obtained by direct experiment. Still I thought them worthy 

 of attention, the more so as direct calorimetric measurements at 

 very low temperatures would be attended by serious difficulties. 

 Another reason which induced, me to try the indirect method 

 was the desire to learn something more about the specific 

 heat of gases, which has been investigated usually only within 

 very restricted limits of temperature and pressure. Besides 

 the important work of Prof. Joly*, the object of which was 

 to determine the effects of increased pressure and temperature 

 on the specific heat at constant volume, I have to notice a 

 memoir by M. Margulest on the variations of the specific 

 heat of carbon dioxide, determined by calculations based on 

 Andrews's and Amagat's experiments. 



§ 3. Integrating (1) along the isothermal t y between the 

 limits of 1 and p atmospheres we obtain 



If we assume the thermal expansion to be known, this equa- 

 tion (Rankine's) may be used to calculate the values of c p 

 corresponding to different states of the gas. 



First of all, however, it is necessary to inquire how far the 

 quantity c, — a constant of integration with respect to p — 

 depends on the temperature ; C\ denotes evidently the specific 

 heat under the constant pressure of one atmosphere, at the 

 absolute temperature t. 



In order not to depart from the notation adopted in the 

 first part, I shall denote by p the pressure expressed in atmo- 

 spheres. The mass m of the gas may be chosen so as to have 

 v = l cubic centim. at the temperature of melting ice, under 



* " Specific Heats of Gases at Constant Volume," Phil. Trans, part i., 

 vol. clxxxii. (1891) ; part ii. vol. clxxxv. (1891); part iii. vol. clxxxv. 



(1S94). 



t " Spezifische Warme der comprimirten Kohlensaure," JJ ten, Sttzber. 



xcvii. Ila., 1888. 



B2 



