20 A. W. Witkowski on the 



Indeed, we shall see later on that the influence of pressure on 

 the specific heat at very low temperatures is very considerable; 

 for instance, at a temperature of — 144° a doubling of the 

 atmospheric pressure brings about an increase of specific heat_ 

 by 0*03. Now the air on entering the heater is clearly under 

 a pressure exceeding the atmospheric by an amount indicated 

 by the mercury manometer. In the liquid-oxygen series of . 

 my experiments this was about 70 centims. of mercury. Part 

 of this pressure-head is absorbed by the resistance of the 

 heater ; but on entering the cooler there remained still an 

 additional pressure of about 48 centims. This is amply 

 sufficient to account for the observed small increase of the 

 specific heat. 



In what follows I shall therefore consider the specific heat of 

 air under atmospheric pressure as a constant (0-2372) from 

 4- 100° down to -170°. 



§ 11. We are now prepared to take up the more general 

 problem proposed in § 2, to determine the dependence of the 

 specific heat c on pressure, at different temperatures. That 

 a dependence of this kind does really exist may be inferred 

 from the fact that the values of the second differential 



coefficient ^— g (§ 2, equation 1) are in general different from 



"d L2 v 

 zero. The values of — can be obtained from the results 



recorded in the first part of the present memoir. Denoting 

 by v the volume, under the pressure p, at 6 degrees, of a mass 

 of air which occupies the volume 1 at 0°, under atmospheric 

 pressure, we have 



"=J(l + ^)» (6) 



a. denotes here the mean coefficient of expansion under the 

 pressure p, between 0° and 6°, r) the coefficient of com- 

 pressibility at 0°, depending on p only. The values of a. 

 have been given in a table in § 15, those of rj will be found 

 in the table of compressibility (§ 17, vol. xli. p. 309) in the 

 column headed " 0." 



In what follows I shall assume 



£ = 273 + 0. 

 In order to obtain ^- I chose the graphical method of cal- 

 culation, which seemed more direct and reliable than the use 

 of empirical formulas such as those of Clausius, van der 



