Internal Pressure of a Liquid. 197 



values obtained by applying van der Waals' equation to the 

 same substances. (Traube considers van der Waals' equation 

 applicable to the solid state. This is extremely doubtful, 

 though the calculated values of K thereby obtained appear to 

 be of the right order of magnitude.) Traube rewrites 

 Richards' relation in the form 



K= -— • 



3 dv 



(/) C. Benedicks (Zeitsch\ fur anoryan. Chemie, xlvii. 

 p. 455, 1905), in the course of an investigation as to whether 

 van der Waals' equation may be applied to the solid state, 

 and in which he points out that Traube's considerations are not 

 conclusive, has deduced the following expression for K, viz. 



K 



a R r 1 -\ R . . 



= -= = — 1-21 = ■- approximately. 



V 2, V L«l V«t ' r J 



(Benedicks writes 3/3 for the coefficient of expansion of the 

 liquid or solid with temperature, I have here denoted it 

 by a i-) v denotes volume in the liquid state. The equation 

 is based on that of van der Waals. It will be seen on com- 

 paring them that Richards' equation would only become 

 identical with Benedicks' if C were put equal to R. For 

 elementary bodies is the atomic heat, a constant having the 

 value 6 approx. (Dulong and Petit's law). The invalidity 

 of Richards' formula is thus apparent. The formula of 

 Benedicks is the most convenient one we have for calcu- 

 lating K — the values obtained being of course dependent upon 

 the assumptions underlying van der Waals' equation. 



It will be observed that the expressions for K rest on one 

 or other of the assumptions, (1) that K itself is independent 

 of temperature, or (2) that the a and b in van der Waals' 

 equation are independent of temperature. 



The relation 



k. ..Or 



-'-*($) 



is probably correct, but it does not allow calculation of K 

 unless some new assumption be made with respect to K and T. 



I take this opportunity to express my indebtedness to 

 Prof. A. W. Porter, F.R.S., for helpful criticism and 

 suggestions. 



