( 240 ) 



perfect mixture alsd for the solid state. The two yy, ,/• 7'snrfaecs meant 

 ill the preceding statemeid, are that for tiie eoexistence of the two 

 ihiid phases with eacli other and that foi' tlie solid state and the 

 tlnid })hases. 



I shall })roeeed to uive a few mathematical observations, which 

 may serve to ,uain a better understanding of the whole phenomenon, 

 and wiiich are also re(pnred for the pi'oof of some properties, which 

 have been given above. 



First the assnmed deformation in the shape of the ^>, ,r cnrve (solid 

 and tliiid phase) for increase of temperature. 



From the equation : 



\}l>\f'J,,T I 



follows that for constant .i-f the ecpiation holds: 



M' 



T 



]\\f being negati\e, lln' numerator of this expression is negative 



^'^^ 

 outside the curve ïov which ^r — = 0, aiul posili\e inside this curve. 



The numerator is ihe same (juaulily as has been discussed before 

 (p. 235). From this follows that for constant .Vf the ciirxe yy,7' has 

 a tangent normal to the 7'-axis iu two |toints, and between them 

 two points, in Avhich a maximum and a minimum value of yy occurs 

 — jnst as was the case with the p, .v curve at constant temperature. 

 One cur\e might be snbstitiited for the other, but still, there is a 

 ditference. The ji, ./• curve has its maximum and minimum coinciding 

 in the plait[»oint. The [>, T curve has it, when it runs througii the 



point tor which — ^ has two coinciding values equal to zero; so in 



Ov' 



the point which would be the critical ])oint, when the binarv mixture 

 behaved as a simjile substance. ^) The consequence of this is, that if 

 we trace the two }),T cnr\es, (that for liquid and vapour and that 

 for solid and tluid), these two curves intersect in the plaitj)oint for 

 the value of ,/■ of a plaitpoint, and that they do not touch as is the 

 case with the j),.f cur^•es. Only for another value of .?■ (the maximum 



1) It has appealed to me that llie course of the p,T curve requires further 

 elucidation. I intend therefore to soon add some remarks on this subject to this 

 communication. 



