a c'liange of volume. Then, however, a reaction occiu'S. at which 

 the quantities of some phases increase, those of other phases decrease, 

 and onl_y after disappearance of one of the phases, pressure, tempe- 

 rature and composition of the phases can change. 



May the composition of a piiase F^ be given by the quantities 



('«i)i (*',)i (■'•j), • • ■ {■>-„-i)i and 1 or 1 — (.«,), — {.v,), . . . {j'„-\), 

 that of a phase 7*"", by : 



(.I',), (.«J, {.V,), . . . (.i'„- i), and 1 or 1 — (,«,), — G^'J^ • • ■ (.''„--O^ 

 of the n components. We express in the same way the compositions 

 of the phases F„ F„ . . . Fi,j^i. Let occur between these ?« + 2 phases 

 the reaction : 



.'/,^, + .'/.^; + y,^', + . ■ • + y»+2^'„+2 = Ü . . . (1) 



t/iF^ means //, quantities of the phase F,, each of which has the 

 composition given above ; i/^F, etc. have tiie same meaning. It is 

 evident that these reaction-coeflicients v/, . . . i/,.^2 cannot have all tlie 

 same sign, in order to know reaction (1) it is not necessary to know 

 tiie n-\-2 reactioncoefticients //j . . . ii/,._|.o tliemselves, tlie reaction is 

 viz. determined by their ii -\- 1 relations. 



From the condition, that at tiie reaction the tola! quantity of 

 each of the n components rests unchanged, the n relations follow : 



.'/l + 2/2 + .'/» + ••■ + J/"+2 = 



.'71 (■'^1)1 + .'/» (■'-■l). + .'/, (■'■l), 4 • • + .'/n+2 i'",)n+-i = 



,'/, (•«,), 4- .'/, {■r:X + .'/, (■<^.), 4- • • 4 y>,+2 (.'•,)„+2 = I . . (2) 



.'/, (.»,,-l), 4- .'/. (■'■•«-1). + ,'/3 (•'•«-!)« • • ^ ,'/«+2 (.r„_l),,-|-2 = ' 



As we have only 11 conditions for the determination of the«-|-l 

 ratios, (2) and therefore also (1) may be satisfied in infinitely many 

 ways, or in other words: the reaction between the n -{- 2 phases 

 of an invariant equilibrium can take place in intinitely many ways. 



Now we put the condition that the totalvolume remains the 

 same at the reaction ; the reaction is then : "isovolumetiical". When 

 we represent the voluraina of the above-mentioned quantities of the 

 phases F^ , F, etc. by t\ , v^ etc. then it follows: 



Hx^i 4- 'J^v^ -f y^v^ 4- • • ■ 4- 2/«+2U„+2 = . . . . (3) 



Now we have n -\- J equations [viz. the 11 equations (2) and 

 equation (3)J ; the n-\-l ratios of the reaction-coefficients are conse- 

 quently determined and therefore also the proceeding of the reaction 

 (J). Consequently we find that an isovolumetrical reaction between the 

 a -\-2 phases of an invariant equilibrium is completelj- determined. 



