( 838 ) 



dx z - 



&=0 

 SP',- 



for '\> 2/ 3 the two curves will lie 



outside each other, as has been 



drawn in fig. 10, and already 



observed above. For all other cases in 



which a and b cannot be equal to 



zero, the value of the expression for 



x = and x = 1 will be positive 



infinite. If it can become negative, 



this will, accordingly, have to be 



the case for two values of x. Now 



very different relations may exist 



1 da 1 db 



between and — — . Thus 



1 da 



a iij' 



b dx 



for the plaitpoint 



a dx 

 1 db 

 b dx 

 circumstances of a mixture taken as 

 homogeneous. l ) With these values the form reduces to a quantity 

 which will certainly be positive, as even if a t a, ]> o^', the value of 



the mini- 



Fig. 10. 



4 1 



can probably never be larger than — — — — , 



in ii in value of which is 



16 



da 1 db 

 value of or - , 

 dw o dx 



If == — -—, the sign of the form under discussion, depends on the 



b da a dx 



1 db i /16 1 1 

 If ■ "> / — - — -- , a negative value ot the 

 b ,!,■ y 5 x(l-x)a' ö 



form is possible. So for mixtures, 

 in which the components differ 

 greatly in the size of the mole- 

 cules, the case of fig. 11 occurs for 

 minimum 7\-, and this minimum 

 value of Tk could not be rea- 

 lised. For mixtures, for which 



1 da 1 db /l db 



a dx b dx V b dx 



may be ne- 



9 



/l da\ 

 glected with respect to - ( - — , 



4 \a dxj 



which is even perfectly allowable 



in the limiting case, for which 



d*ty 



A z= b,, and - - will be negative, 

 dx' 



l . In all the above calculations the equation of state has been applied with 



