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Chemistry. — "On rclnxjiu'ssin' mcllliKj-poui.t lines.'' Hv Prof. 

 A. Smits cind J. 1'. Tkkuh. (Tliird foiniTniiiicjUioii). ((k)iinnn- 

 nicated l\y Prof. .1. 1). van dkr Waals). 



It has appeared from llie preceding coniirinnicatioTi on the {PT).r 

 liiies foi' the eqiiilihriiiin solid-thiid tlial in the system ether-anthra- 

 quinone not only the locus for ?'>/= 0, bnt also that for 10,,/:= 

 enters the stable region in the neighbourhood of the plait, which 

 involves the i)henomenon already predicted by one of us (Smits), 

 that when the melting-point lines under constant jn-essure are deter- 



mined, a point where —-1 = can occur twice. 



\dJ Jp 



From VAN uek Waals' differential equation 



vsf dp = {.vs—^cf) { ^ I ƒ%■ + Vsf dT 

 follows for constant pressure: 





dx'\ 



■fjrr 



or 



'd,t "N Waf 



T 



\d.r-jyrr 



Now it follows from this relation that when in the stable region 



two lines for solid-jiuul touch a plane for constant pressure projected 



in the 7-*, TjA'-figure of the system idher-Kut/waquimme, which contact 



must take place in its maximum for the line for snuill anthraipiinoiie- 



concentrations, and in its minimum for that for greater concenti-a- 



tions, the melting-point line will lia\e to possess two remarkable 



points, because in the said points of contact ?(),,/■ must be = 0, so 



fdx \ 

 7' — - =: 0, and so the tangent must be vertical. 

 \dTJ j> 



Now it follows from the shape of the found (7^7's/)-lines that the 

 melting-point line will not present this particularity for all pressures, 

 but that this phenomenon remains restricted to a certain region of 

 pressure, outside, which oidy the lower, resp. the upper point will 

 still possess a vertical tangent in the stable region for some time, 

 while for greater, resp. smaller pressure it will vanish from the 

 stable region. 



In the annexed 7-^'-iig. the projection of the liquid and the vapoui- 

 line uf the two parts of the intei-ru|)ted three-phase region, and 



\'3 



Proceedings P»oyal Acid. Amstordani. Vol. XIV. 



