16 PROCEEDINGS OF THE AMERICAN ACADEMY. 



7 my 



The constancy of the quantity, R T— — or a, we have only proved 



in the cases of the gases which were experimented ujion by Joule and 

 Thomson, and through limited range of j^ressure. However, since the 

 constancy of this term was established for all the gases tried, we may 

 assume that the same result would have been obtained with any other 

 gases through the same limits of pressure. It cannot be taken for 

 granted that this constancy will hold at all pressures. In fact, the inter- 

 pretation given by van der Waals for the quantity a, as the interraolec- 

 ular attraction, would lead to the idea that it must be a function of the 

 volume. Otherwise the attraction between two molecules would be 

 independent of their distance apart. The variation of a with the vol- 

 ume will be mentioned later. 



Van der Waals considered a priori that a would not depend upon the 

 temperature. But it is evident from page 14 that it is a constant only if 



-~ = 0. Although the change of specific heat with moderate change of 



volume is negligible, the change through wide limits of volume is proba- 

 bly always a measurable quantity, as will be shown later. 



Since the quantity a has been defined as equal to — M T—-~ , we 



dp 



should be able to determine its value from the data of Joule and 



Thomson. A calculation which is in effect the same as this has already 



been made by van der Waals,* who calculated from the values of a and 



b, given by experiment, the cooling effect that should be observed in free 



expansion. This cooling effect, in Centigrade degrees, for a change of 



one atmosphere in pressure is given below, as calculated by van der 



Waals and as determined by the averages of Joule and Thomson's 



results : — 



The agreement, although not close, is very satisfactory considering the 

 uncertainty of the experimental results. 



2. Liquids. — The experimental proof of the continuity between the 

 liquid and gaseous states shows that we must regard them as identical, 



* Kontinuitat der F. und G. Zustand, p. 116. 



