( 753 ) 



-L—L civ + - )dp = ( - d* + dp, 



a?,— ff, \dpjhet \dxjp \dpJkom 



and from this the former relation. 



f dv \ 



From the form for in general, so not only at the begin- 



V dp J hei 



ning or at the end of the condensation, we see thai the empiric 



isotherm can have an element in which it has an horizontal direction 



only when a nodal curve is intersected, al one or the oilier of 



whose ends — is infinitely large. Hut as neither the sides nor 

 \dpjbi» 



the nodal curve which runs parallel to the y-axis can be intersected, 



it would follow that the empiric isotherm can never run horizontally 



in one of its elements. There are, however, cases which form 



exceptions to this rule. First of all if we widen (he idea empiric 



isotherm, and understand by it the section of a surface // v-a.\is 



with the derived surface of the ifj-surface, also in the case of a 



complex plait. Then there are also nodal curves to points in which 



the binodal curve passes through the spinodal, and where therefore 



fdx\ 



I — = go. But as such equilibria arc hidden equilibria, they cannot 



\dpjbin 



be realised in spite of this. Instead of this w T e have rectilinear inter- 

 section of the surface // v-axis with the three phase triangle, and in 



fdv\ 

 this part — is, of course, again infinitely large. But second Iv, 



\dpjhet 



and this is a case which might, indeed, be realised, the binodal 



fdx \ 



curve has a point in which ( — =: oc, when this point is a plait- 



\dpjbin 



point which with increasing or decreasing temperature will become 

 a hidden plaitpoint. This is a limiting form of the lirsl mentioned 

 case, in which the three phase triangle was intersected. Then the 

 three phase triangle has contracted to a single line, and the above 

 mentioned straight line has contracted to a single point. Then there 

 is, of course, a point of inflection of the empiric isotherm in that 

 point. With larger volumes it is curved negatively, with smaller 

 volumes positively. 



