( 509 ) 



face, whereas in the second part the conditions are treated for the 

 appearance of a barotropic tangent-chord on the plait. 



A. On the conditions for the occurrence of a barotropic-plaitpoint 



§ 2. In a barotropic plaitpoint the isobar, which in a plaitpoint 

 always touches the plait, must run parallel to the .i'-axis. This gives 

 the condition : 



.3)=° (ia) 



Moreover a section v = v^i of the if'-surface with the limiting 

 position of the tangent-chord must then have a contact of the 3 rd 

 order. This furnishes : 



J)=° ■ (s?h° < 1W 



The two conditions (J h) and (1 c) follow also by applying (1 a) 

 to the general relations for the plaitpoint of Comm. N°. 75 (Dec. 

 1901) p. 294. 



The same may be obtained from the property of the barotropic 



/difA 

 points on the connodal curve that there — 1 along the connodal 



shows a maximum or minimum l ), so that the substitution-curve 



[ — j = const, (see for the substitution curves on the ifc-surface for the 

 \dej 



molecular quantity Comm. N°. 59"), touches the connodal line in 



these points. 



§ 3. For a first investigation we shall use van der Waals' equation 

 of state: 



Hrl Clr 



p=-V— ? (2) 



v — b x v' 

 with an a x and b x not depending on v and T for a definite x. 

 In this: 



*) This property for coexistence with r. 2 = i'j is analogous to the property that 



^— ) = — p along the connodal line is a minimum or a maximum for coexisting 

 Ov J 



phases with a^ = X\. In the same way the mean value of ( — J along an isome- 



ydxj 



trie line v = n, which joins two barotropic phases on the J. -surface, is equal to 



the value of I — — I for these phases. 

 \dw J 



34 



Proceedings Royal Acad. Amsterdam. Vol. VIII. 



