( 744 ) 



dv p — dr, j 



1 

 ^3 



d*v 



dx 1 



d'v 



d? 



the factor of dx* is negative, but at P 2 this factor is positive. If 

 the points P 1 and P 2 coincide, this factor = 0. With coincidence of 

 these plaitpoints, called 'heterogeneous plaitpoints by Korteweg, besides 



dv\ _ fdv_ 

 dx) p ~~ \das 



and 



d* 

 dx 





d°v 



dx' 



If P t and P 3 coincide, 





has contracted with rise of tem- 



perature. Also : - = contracts with rise of the temperature and 

 1 dx 2 



is displaced as a whole, as I hope to demonstrate further. But the 



contraction of — = 0, whose top moves to (he left, happens rela- 

 dv % 



tively quicker, so that e.g. the top falls within the region in which 



d^xb • (d v \ 



— — is negative. The existence of the point 1 , requires that — 



dx* b \ d *Jq 



is positive. The point P 3 lies on the right of — = and above — r = 0. 



d*tb d*ty 



If the top of — - = lies within the curve — - = 0, neither P t nor 

 dv* dx 



P can exist any longer. Before this relative position of the two 



curves they have, therefore, already disappeared in consequence of 



their coinciding. Also in this case the coincidence of heterogeneous 



plaitpoints holds. At 7 J 2 the factor 



of dx* was positive, and at P s 



this factor is negative. In case of 



. mj fdH\ fd*v\ _.. 



coincidence — - — — - . With 

 \dx*J p \dx*J q 



further rise of T, however, the 



d 2 \p 



top of = will have to get 



dv* 



again outside the region where 



d*ty _, d 2 xp 



— is negative. The curve 77 =U, 

 dx 2 & dx* 



namely, cannot extend to x = 0, 



and the curve - — = at T— (Tk), 

 dv* 



has its top at x = 0. We draw 



Fj 9< from this the conclusion, that 



