( 426 ) 



opinion are older (e. g. ( '. nodifiora Forst, and C. sumatrana Jungh.) 

 still survive for instance, in Australia, in Sumatra, Borneo, Celebes, 

 and in the Molucca-, hut recent forms are now wanting in Java, 

 and fossil ones have not 3 et been found in Java. 



5. ( >f the two Javanese indigenous species of Casuarina, C. montana 

 Jungh. appear to be phylogenitically younger than ( '. equisetifolia 

 Forst.; the former species is probably a mutant, which has only 

 maintained itself within the region of the Malay Archipelago, and 

 which has arisen from the latter species. 



6. Probably C. montana var. validior Miq. is a mutant, which has 

 maintained itself in Java only and which has arisen from C. montana 

 var. tenuior Miq. 



Physics. — "Contribution /<> the theory of binary mixtures" XI. 

 (Continued). By Prof. J. D. van der Waals. 



Now we shall proceed to the investigation of some properties of 



(Pip (Pip 



the loci of the points ol intersection of =Oand — =0, in the 

 1 dx' dv* 



first place when this locus is a closed figure, lying wholly at volumes 



larger than b. Let us write. 



AMY c 



\a.rj a 



in the form : 



i-.''(i -*)j\ - 2vb + jv +-*(V— V)j =°- • (») 



The form of the third term in this equation appears only to depend 



fdb\ 

 on the first power of x, because b*-\-x (1 — x) I — 1 may be written 



db fdb\" fdb\ 



b* + 2xb 1 1- x* — and to this added x (1— x) — I . The 



dx \d<oJ \dxj 



db f db\ db 



third term then becomes b^ -f- — 2b 1 -\- — )>c, in which — = b^ — b . 



dx\ dxj dx 



If we put x(L — x) — = -4, the equation (<f) becomes 

 a 



v > (1 _ A) — 2vb -f &, s + x (ft, 8 - V) = • • • («>') 



Let us seek the points of this line in which the tangent is parallel 



dv 

 to the ,*'-axis, and so in which — = : then we find another equation 



dx 



