\ 289 ) 



dT, dT, 1 dh 



the value of — - =: O, and for 2\ = 1\ the value of —— = — - -— 



dx 1 ydx o hdx 



dï) • 

 so the well-known limits for mixtures for which — ~ can be equal to 0. 



p^dx 



For the initial direction of the section normal to the p-axis, the 



following equation holds : 



and 



H dpc 



1 fdT\ RT \x^ — xA _R^{,_ ~Rf~di 



T V dx^Jp r ( A-j \ r 



Both yield at the critical temperature of the components : 



1 dpc 

 dT\ RT u dpc u dpc pc dx 1 1 fdpc\ 



Tdxjp r R T dx r dx T dp '^ pc\ dxj ,, 



pn' 

 According to results obtained before, we may also write : 

 1 f dT\ 6 I dTk I I dh ] 



T \dx y. ) u 7 j Tydx / Q b dx y. 



Physics. — "I'he exact numerical values for the properties of the 

 plaifpoint line on the side of the components." By Prof, van 

 DER Waals. 



In my two previous communications, inserted in the proceedings 

 of this meeting, viz. I on the properties of the plaitpoint line on 

 the side of the components and II on the properties of the sections 

 of the surface of saturation on the side of the components, it has 

 again appeared, that the thermodynamic treatment of such problems 

 enables us to find a complete general solution — but also that if 

 we want to compute numerical values in special cases, the know- 

 ledge of the equation of state is indispensable. In some cases it will be 

 sufficient, if we make use of an approximate equation of state; but 

 as soon as the density of the substance is comparable to that in the 

 critical state, the numerical values calculated by means of the 

 approximate equation of state can deviate strongly from reality. 

 This is specially the case with quantities which either refer to the 

 volume, or are in close connection Avirh it. Thus it is known, 

 that already llie ciitical volume of a simple substance is not 



20 



Proceedings Royal Acad. Amsterdam. Vol VIII. 



