( 837 ) 



All these remarks seem essential to me for the following reason : 

 we shall, namely, soon have to draw the relative position of the 



d 2 i|> </ 2 if> 



curves — = and — - = 0, also in regions lying more to the right 



of fig. 1, in order to decide about the more or less complexity of 

 the plaits at the different temperatures. Then we shall have to make 

 assumptions as to this relative position, which otherwise might seem 

 quite unjustifiable. A great many more similar questions would even 

 have to be put and solved, before alle doubt as to the validity of 

 the assumptions would have been removed. And it remains the 

 question if for the present the imperfect knowledge of the equation 

 of state for small volumes does not prevent our ascertaining with 

 perfect certainty whether a phenomenon of mixing or non-mixing 

 is either normal or abnormal. So, before proceeding to the appli- 

 cations I shall subject only one more point to a closer investigation, 

 viz. the question whether in the critical point of a mixture taken 



as homogeneous, the quantity — is positive or negative, so the 



dx 2 



sign of the quantity: 



or of 



+ 



+ 



Sdb\* d*a 



\dxj 1 dx* 



46 2 j ~ 36" 



/db\* d a a 



\dx) 9 dx~* 



a{l — a) ' 46 



d?a (da\ 

 As 2« — - = (— - M-4( a i a a — « 12 2 ) } we ma y a i so write for the 

 ax \dxj 



last form 



/dby /day 



\dxj 9 \dxj 9 a l a s 



x{l—x) ' 46 2 16 a 2 4 a 2 



As a first special case we consider a substance mixed with a 

 perfect gas ; then b x = 0, a, = and a 18 = 0. Hence a = a 2 x'\ 

 è — 6 a .t\ With these values the above form becomes: 



1 2 3a;— 2 



x(l— x) x* as* (I— as) 



d*ip 

 su — is negative in the critical point for values of x < 2 / 8 ; for 



x = 7j the curve — = will pass through the critical point. But 



CviC 



