44 



Physics. — ''Some difficulties and contradictions met with in the 

 draioing up of the equation of state." By J. J. van Laar. 

 (Communicated b}^ Prof. H. A. Lorentz). 



(Communicated in the meeting of April 25, 1913). 



1. The latest papers by van der Waals on the equation of state ^) 

 - also ill connection with my own recent investigations ^) — induce 

 me to publish the following remarks, vvhicli may not be entirely 

 devoid of interest at the present stage of the question. 



When we start from van der Waals's fundamental equation, viz. 



i22' a 

 P = T--^' 0) 



and for the present disregard association or quasi-association, there 

 ^Ye — the chosen form of the equation of state being retained — 

 only two possibilities for the explanation of the found deviations 

 from the. above equation : 



The quantity h is still a function of v (and possibly of T). 

 a „ „ „ „ „ V, or of T. 



If at lirst we still disregard the variability with the temperature, 

 we shall in the first place ascertain the consequences of the varia- 

 bility of b with V. 



If h=^f{v), the above equation of state gives at the critical point: 



\dv)t 



RT , 2a ^ 



{v-by v^ 



^>\ 2i^T(l_,-). + ^_,"_^ 



dv'Jt {v-by' ' {v—bY 



db d'b 



where b' is written for — , and b" for — -. 



dv «y 



Hence it follows from this that 



2a{vk — bicY 



Rl\ (1 - b'k) rz: 

 RTjc 



]6a {vk — bkY 

 "k 



1) These Proc. Vol. XV, 903-910; XV, p. 971—981; XV, p. 1131—1145. 

 (To be cited as v. d. W. I, II, and III). 



2) These Proc. Vol. XIV, p. 278-298; XIV, p. 428-442; XIV, p. 563-579 ; 

 XIV, p. 711—724. (To be cited as v. L. 1, II, III and IV). Further XIV, p. 771-781; 

 XIV, p. 1091—1107. (To be cited as v. L. A and B.) 



