PROCEEDINGS OF THE AMERICAN ACADEMY. 



v that the value of c t in a i r a~ does change considerably through wide 

 limits of volume. He baa been the first to Bucceed in measuring directly 

 the Bpecific heal of g constant volume. The values were deter- 



mined by means of bis differential Bteam calorimeter, u method which 



us tn give ven accurate and consistent results. The results Bhowed 

 that the Bpecific heat at constant volume could be ezp in the 



following formula?, 



For Air, c,. = .17151 -f .02788p, 



For CO . c .1650 • .2125 p - .3400 p\ 



where p is the density in grams per cubic centimeter. According to 

 these formulae the specific heat at constant volume at atmospheric pres- 

 sure differs from that at infinite volume by only two hundredths of one 

 per cent in the case of air, and by three tenths of one per cent in the c 

 of carbon dioxide. Between the Bpecific heats of the gasi - at atm 

 pheric pressure and in a highly compressed or liquid condition the 

 change is much greater. For example, the value given by the formula 

 for '■ in the case of carbon dioxide is about twice as great at the critical 

 volume and about three and one half times as great in the liquid at I 

 as the value for the gas at ordinary pressure. Further evidence of the 

 change of r, between the liquid and gaseous condition will be given later. 



In these variations in the specific heat we find the probable cau 

 many of the deviations from the equation of van der Waals that have Keen 

 noticed. It may be found necessary, therefore, in order to obtain a more 

 exact equation of condition, to return to the more general equation < E 



rt rn d Cv d% dm 



p = - + J I ,,. -, dl — T— — . 



1 ?( \ 



in which the value of ," ■ contains not only the function for volume 



,1 v 



correction, but also a term depending upon the value chosen for the lower 

 limit of integration, 7',. [f we write 



g-JW, twn 7'- /-v, r= - r _'-' M r-r.n r. 



where f{ v) denotes the Bame function of v that has been used in equations 

 < 27 ) and { 28 I, namely . the quantity b in the \ an der \\ aals formula, and 



/ another function of v. Now ' is practically independent of 



mperature and the equation may be written 



