( 390 } 



the coefficients in the above expression heeome infinite, all tlie terms 



d'p , . . 



vanisli and - — = 0. In (he critical i)oint llie pressure is ui sreneral 



not a niaximnni, Init the vapour branch of the saturation curve in 

 the p — X diagram {t = constant) has a point of' inflexion with a 

 tangent parallel to the .I'-axis. 



In a special case van dkr I.epVs conclusion drawn from the equa- 

 tion becomes valid, viz. when in the critical point the condition 

 .I'l = ,v^ is fulfilled ; for in that case the next differential coefficient 



d'ü dp d'^p> 



— — becomes 0, as well as — and . After substitution of tlie 



dx^^ dx^ dx/ 



/()•■= SA ^ d /ö^^A 



general conditions ( ^ — ^ 1 = and -— ( ^ — - I = the expression for 



\0x^ //» dx \Öx^ Jp 



d'p 



dx. 



is reduced to 



.«< 



■^v, d' /d% 



Iv' i'„, (/./;' V dx 



'21 



and this expression is equal to 0, if a\ = ,t:^, but not otherwise. 



Without using the equations the same conclusions may be drawn 

 geometrically from the properties of the saturation curve in the 

 p — X diagram ; if there are only one mininuim and one maximum 

 in the j) — .x'l curve, three points of intersection coincide in the critical 

 point and consequently there is a point of inflexion, if on the other 

 hand there is a minimum as well as two maxima, four points of 

 intersection coincide in the critical point and there will be a maximum 

 of the second order. 



The whole argument thus turns on the question, whether it is 

 legitimate to assume as self-evident, that the point, wiiere .?\ = ,v^^, 



remains between the two points, where ( — ^ ) :=i ; that this is 



not the case follows from the fact that the condition ^\ = ,i\^ is 

 totally independent of the condition of critical contact between the 

 two saturation curves : in fact there are cases, such as those referred 

 to above, where the point i\ = x^ lies at a far distance from the 

 critical point, and others where there is no maximum or minimum 

 at all, either outside or inside the three-phase triangle, such as for 

 mixtures of ethane with the lower alcohol ^). The question therefore 

 arises and has to be answered : how does the point where x^ =^ x\, 

 which is known in many cases to be inside the two other maximum 



1) KuENEN en RoBsoN, Phil. Mag. (5) 48, p. 192, foil. 



