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Physics. — - "The liquid state and the equation, of condition''' By 

 Prof. J. D. VAN DKR Waals. 



(Communicated in tiic meeting of May 30tli and June 27lli 1003). 



It has, been repeatedly pointed out that if we keep tiie vulnes of 

 the quantities a and h of the equation of state constant, this equation 

 indicates the course of the phenomena only qualitatively, hni in 

 many cases does not yield numerically accurate results. In par- 

 ticular Daniel Bkrthelot testing the equation of slate at the expe- 

 rimental investigations of Amagat, has shown that there occur some 

 curves in the net of isothermals, e. g. those indicating the points foi- 

 wdiich the value of the product pv is a minimum, and other curves 

 of the same kind, whose general course is correctly predicted by the 

 equation of state, but whose actual shape and position as determined 

 by the experiments of Amagat, shows considerable deviations from 

 the course of those curves as it may be derived from the equation 

 of state. 



In consequence of this circumstance the quantities a and h \\;\\q 

 been considered as functions of the temperature and volume. Already 

 Clausius proposed such a modification for the quantity a ; for car- 

 bonic acid he does not put a := constant, but he multiplies it with 



273 ^ 



—;-;-. Such a moditication seems to be required principally with a 



view to the course of the saturated vapour tension. 



From the beginning I myself have clearly pointed out that, though 

 a, may probably be constant, this cannot be the case with the quantity 

 h. One of the circumstances w^hich I was convinced that I had shown 

 with tiie highest degree of certainty as well in the theoretic way as 

 by means of the comparison of the experiments of Andrews, was 

 that the quantity h must decrease when the volume decreases. So 

 for carbonic acid I calculated for h m the gaseous state at 13°1 the 

 value 0,00242 and in the liquid state a value decreasing to 0,001 5(i5. 

 But the law of the variability of b not being known, I have been 

 often obliged to proceed as if h were constant. In the following 

 pages I will keep lo the suppositions assumed by me from 1 lie begin- 

 ning, namely that a. is constant and that h varies wilh the volume; 

 and I will show that if we do so, the considerable deviations dis- 

 appear for the greater part and that it is possible to assume already now 

 a law for the variai)ilily of h with the volume, from which we may 

 calcidate in many cases numerically accurate data even for the liquid 

 state at low temperatures. 



