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Physics. — "Contribution to the theory of binary mixtures." IX. 

 By Prof. J. D. van der Waals. 



The intersection of ( — =0 and 



dxj v 



\dx* J v 



\dxj 



(v — by dx dx u 5 



As in previous communications we shall write the equation of 



dp\ MRT db da 1 



— = in the form — — = , and the equation of 



ft™ I In /II-* il v rl i' ->i* 



dx* J 



d*a 

 1 'N fdbV 1 ) dx* 



1 = in the form : 



MRT 



+m i 



jb (1 — x)J \dxj (v — by \ v 



Then the locus of the poinls of intersection is given by the 

 equation : 



d*a 



(db\* „ dx~* db 



(v-b)* + - m (l-x) = x(\-x) — v - 



\dxj da dx 



dx 



or 



d*a 



dz* db 



(v-b)* - x(\-x) — -(v~b) + x(l-x) 



da dx 



dx 



d*a~\ 



db dx" 



b 



dx da 



dx 



= 0. 



The factor of the known term of this equation 



may be written in the form : 



db n — 1 



db da d*a 



dx dx dx* 



da 



dx 



dx B -f Cx ' 



if b = b l (I—a) + 6,a?, and a = A -f 2 Bx -f- Cx 2 be put, and the 

 equation itself may be given in the form : 



(v-by „ k c (v-b) . ~^I 



C (v-b) 

 dx 



B + Cx 



= 0. 



