( 210 ) 



The factor of — is only =0 for x„ = - and negative for 



1— 2x g ' ■ 3 



every value of x g between -- and -, between which values it lies. 



For all values of T <[ T g the section of the two surfaces has the 



shape of tig. 24a (Contribution V, p. 134). For T= T g , -^=Q 



fdp\ A , 



has contracted to a single point, and the line — =0 nas tne 



\dxJ v T 



minimum volume exactly at that point. 



If we take k still larger than was calculated above the section of 



the two surfaces will pass round the top, and there is again question 



of a maximum temperature, which, of course, lies then again below 



T q . At this maximum temperature there is again contact between 



the two curves, but then the contact is such that ( — - J = lies 



\dtr JvT 



entirely in the region where [ — ) is positive, except in the point of 



\dxJvT 



contact, where — = 0. The point of contact lies then on the branch 

 dx 



of [ — j = 0, where — is negative. 

 \dxJoT dx 



This however, does not exhaust all possible cases for the inter- 

 section of the two surfaces. Some more remarks remain to be made. 



da . . 



We first observe that if — is negative, there are no points of the 



dx 



intersection for the values of x for which this is the case. For such 



points B + Cx is negative, which can only be the case for positive 



G if B is negative. 



v — b 

 In the quadratic equation in (v — b) the factor of — — has become 



dx 



positive on account of B -\- Cx being negative, and the third term 



C 



is also positive, because — — — - has both its numerator and its 



B-\-Cx 



denominator negative. So no positive value of v—b can satisfy this 

 equation. In the second place we observe that for the value of x 



7 



for which — = 0, the value of v—b is infinite, and the value of T 



