On the Gas-equation. 869 



side. Case (ii.) is thus deducible from case (i.) by the 

 application o£ a smoothing process to C and S, whereby 

 fluctuations o£ small length are removed. 



We may sum up by saying that a smoothing of <j>(n) 

 annuls C and S for large values of u, while a smoothing of 

 C and S (as functions of u) annuls $(V) for values of x 

 which are numerically great. 



Terling Place, Witham, 

 October 1912. 



XCIII. On the Gas-equation. 

 By S. D. Wicksell, Lund, Sweden *. 



TN the famous gas-equation of van der Waals : 



(p+ j)(«-6)=B* (1) 



a and b are small constants depending, a on the mutual 

 attraction of the molecules, and b on the volume of the 

 molecules. 



P is the pressure of the gas, v its volume, and 6 denotes 

 the absolute temperature. R is the gas-constant. 



In reality, however, the quantities a and b are not constant. 

 They vary both with temperature and pressure. 



In the following I will regard a and b as functions of the 

 temperature only; thus getting a gas-equation that covers 

 the case of Clausius and several others. 



It is the object of this paper to transform the gas-equation 

 into a more convenient form by means of series, and to study 

 the quantities a and b, expressing them in known and 

 measurable quantities. 



The equation (1) can be transformed into 



We express P in atmospheres; 



v in the volume of one gram-molecule of the 

 ideal gas at one atmosphere and 0° centigrade ; 



6 in degrees centigrade. 



By index zero I mean the value at 0° C. 



* Communicated by the Author. 



