( llfi ) 



of lines, as Kortewkg has done in anolher diagram (the x, y-diagram) '). 



This investigation showed that the last of the eight cases distin- 

 guished by KoRTEWEG of which the inconsistency was demonstrated 

 by him for one special case only, did not exist iji general, at least 

 for all the equations of state which satisfy Die law of corresponding 

 states. Not to make the investigation too elaborate I have compared 

 the situation of the plaitpoint only with that of the critical stale of 

 the pure substance, that is to say I have considered the fields within 

 which Txpi^' or < 7 a-, />,/./> or <^ pk and Ucy;/>or <r/:. I have 

 also determined in wliich area tiie retrograde condensation is of the 

 first or the second kind; and lastly I have indicated in the diagram 

 what had been ol)served experimentally. 



The plaitpoint temperature. According to foi'in. (59) the plaitpoint 

 temperature of the mixture is higher or lower than the critical 

 temperature of the pure substance as the expression 



_ — ct = 



is positive or negative; and, l\^ being negative, T^iji — T^ has the 

 same sign as the numerator. 

 If for shortness we put 



_ dp _ d^^p _ ö%> _ d%> _ ö^'. 



Po: - Yt' ^'^V- dv5t' '"' '^ 'Mi ' ' ' ^''" " 0^' ^'^" "" d?' ''^''^ 

 and for convenience we leave out an index which refers to the 

 critical state, because only those values are used which refer to 

 the critical state, 



so that the area, where T^-ri^ Tt is separated from that where 

 Tjpi <^ Tf: by a line of which tiie equation is: 



This line, a parabola, represented on the annexed plate ") by 



1) Proc. Royal Acad., Jan. 31, 1903. The y. and y are connected in a simple 

 linear way with a. and (3 (comp. the previous communication p. GGG). 

 ") For we have (comp. form. (19): 



Pk 1 Pk 



vk 2 vk" 



Ipk 1 Pk 



b I'k 24 vk 



For the definition of C^ comp. Kamerlingh Onnes (Arch. Néerl. (2), 5,070, 1901; 

 Comm. no. 66). 



S) The figure is drawn hy using llie values of p, 4, Pn etc. whicli will he calculated 

 in the next section. For clearness 1 have represented the u's in a 5 times larger 

 scale than the (3's. 



