20 PROCEEDINGS OF THE AMERICAN ACADEMY, 



the molecules, we cannot say a priori how it will change with the dis- 

 tance between the molecules. In fact it is not necessary to suppose that 



a or — r — must always have a positive value. Joule and Thomson 



found in the case of hydrogen a rise of temperature instead of the usual 

 cooling effect on free expansion. This would indicate a small negative 

 value of a, corresponding to a preponderance of repulsive force between 

 the molecules. Tlie unreliability of the experimental data, however, 

 precludes certainty on this point. 

 In place of the equation 



RT dm. RT 



a 



.■2 ' 



-f{v) dv ' ^ v — b 



the equation of van der Waals, can be applied to liquids with the under- 

 standing that a and b are not constants but volume functions to be deter- 

 mined. In all liquids p is small compared with the other two terms. 

 When p = 0, if we represent the volume by Vq, 



^ = ~,; (32) 



but since the volume of liquids is only slightly changed by changing the 

 external pressure, Vq — b will not differ materially from v — b at 

 atmospheric pressure. We may write, then, as the equation for liquids at 

 atmospheric pressure, 



(oo) 



V — b 



,2 



From this equation may be found the values of a and b when the vol- 

 ume of a liquid is known at two different temperatures. From the 

 values thus found it should be theoretically possible to calculate the com- 

 pressibility of the liquid at constant temperature. Thus by differentiating 

 the van der Waals equation we obtain the reciprocal of the compressi- 



bi%' dp RT ^a 



dv {c-by^ v^' 



practically this method fails on account of the fact that the difference 

 between the last two terms is very small compared with their total val- 

 ues, and therefore any error in either of these terms is multiplied euor- 



d 7) 

 mouslv ill the determination of ~— . 



•' do 



The values of a and h obtained from equation (33) will be of service 



