( 106 ) 



Case I. 

 There is a positive root ;. making A., = 0, whicli can however 



ilL. 



dl 



never indicate a possible al)Sohite niaxiniinn or niininnini. for 



is positive tliere, denoting a negative vahic of the minors of degree 

 2 and these mnst he (see inequalities (7\) and (7'.,)) positive for a 

 maximum as well as for a minimum. 



Case II. 



One root making A, = () is negative, the other 0, so neither of the 

 two can indicate a possible mixlure. 



So for a ternarv mixlure ilic rule of (i.u-iTZiNK-BKKTUKi.oT caimot 

 be united with the ap|)earance of a maximum oi- a uuninmm. A 

 stationary point, however, being lu'illier maximum nor miuinmm. 

 is nol excluded in case I. 



A„ =z has tor y/, = 4 a threefold root / :=:^ 0. 

 So the series of signs becomes : 



or 



II 



In case 1 the simple i-oot ;. belongs lo a negalive value of 



, so it cannot repi-esent a possible mixture. 



ÖA 

 In table II -^ is positive for the simple root; thus the minors of 



degree 3 must be negative in case the mixture is to be possible. So it is 

 evident, that as soon as we put r/^^^' equal to a^ a^ quaternary 



mixtures cannot show a minimum in - - . A maximum is excliided, as 



b 



this would lead to maxima in at least 2 binary mixtures to be 



formed out of the components and these are not possible if a^„^' is 



put equal to ap dq. 



Foi- mixtures where v^/>4 a mixture for which j is stationary is 



