( J04 ) 



to elements of" (lie pi-iiicipal rliagoiial l)e('oine hut also all other 

 minors of degree 5 ^). 



Then however it is clear Ihal for mixtures with H and more 

 components the determinants o]i the />'s disappeai- identically. 



Berthelot and before him (Iat-itzink have made about the quantity 

 a^jrj the simple supposition ^/-^„^ ^ ((f, «f,/. x\lthouuli this formula may 

 not be strictly true, as has already been clearly pl•()^ed by exj)eriments 

 on binary mixtures, it is worth while to cojisider lo what conclu- 

 sions the afore mentioned rule leads us for multiple mixtures. 



For af,q ■=y^a/, riq all minors of deg-ree 2 and higher of the deter- 

 minant on the as become 0. tVoui which ensues that the equation 

 An = can be reduced t(t 



p=n <i—n 

 /«-^ y^ ^ B^„l a,,^ — /" A/, =r 0, 

 P^ 7=1 



where when develojjing the determinant hi, the coefficient of b^^j 

 is Jjjj(/. So there is an (»— 1) fold root P.— 0, which cannot of course 

 indicate an attainable maximum ov minimum, not even another 

 stationary point. 



Let us now consider the different mixtures assumijig the rule 

 of Galitzine-Berthelot. 

 n = 2. 

 Beside the root ). = a secoiul root appears which can certainly 



not point to a maximum, for from "' > aiul ^ ' would ensue 

 ^'^ "> - -* and in comiectioii with fr ,., ^ h, b.,, certainlv 



1) So we find lor tlio asymmetric determinrml 



b.2i h^ J).2:i ^^ii ^h-> 



D 



bn h-2 h^ ^i ho 



hi ^KhA^c^ihi I 



44 



55 



X{V:i^)*Q(ri - r.2)-0\ - r.>)Hr. - r.^r-ir^ - r.-;)(/-i— r,/)(r. - r-)(r2 - r,^{r,^ - r-){r:. - >•«)+ 

 — (V3t)*9(>-i - r.)Hri - r:j)2(>-. - r.)Hi-\ - ryni\ - r,-,)(/-. - r^M.r. - r-Mr,, - r^'^^r.. - rrj>: 



-0, 



