( .^^21 ) 



Anothei' (luestioii is, at what values of .c and T does -^^-^ ürst 



ö.v 



become O, or where does the plait commence, independent of the 



taci wlielliei' we find ourselves on the meltinopoiul-line or not. which 



had just been investigated. 



We have only to combine the relations — - = and -r — = 



d.c d.r,' 



— - always becomes in oiie place onlv in consequence of x-i—x-^ becoming 0, 

 d.ii 



()'^C IT 



whilst on account of -^ becoming 0, - — always becomes in tivo places, oi- 

 o.r- ax 



in the limiting case in two coinciding places in a point of inflection with a hori- 

 zontal tangent. De Visser thinks he has found sucb a point of inflection with 

 mixtures of stearic and palmitic acids, i) It is, of course, not impossible, that we 

 are dealing here accidentally with a case, in which the quantity a possesses the 

 value indicated by {h). That the line of the c-nd-solidifyingpoints also shows in the 

 immediate neighbourhood a similar point of hiflection, points to the fact, that the 



conditions .- =0, s , = are fulfdied on both lines at about the same time, 



which renders it more accidental still, because y would then possess the value 

 required for this also in the solid phase. It should be pointed out, that as a rule 



()•■'? 0'^ . , , 



the conditions <^ , = 0, .-'- = for Jwth phases by no means mchide.Ci =%. r or 

 ó,v' ü,r' 



this requires ^ ^ = \ '^ • h is there ore a new accident, that both points of 



inflection appear to coincide. But for this a reason may be given here. From the 

 equation, from which (a) is found, namely r.c^ — 2 (1 + r).c+ 1 =0, it follows 

 that with r = 0, x — '^/o. De Visser now found both points of inflection to beat 

 X about Vs (— 0.525), so that the quantity r, both in the solid and liquid phase, 

 is about (/j^ = ög). And in that case the values of x at both points of inflection 

 must agree, namely both at x = Vs- 



The case, studied by de Visser, may therefore be an accidental coincidence of 



tlie two points of inflection. But then, on account of <—~ = and ^r-~ = 0, both 



the liquid and solid phases must have broken up into two layers, although of 

 identical composition. The smallest delay in solidification would however imme- 

 diately have carried the system within the plait, and then both phases would have 

 broken up into two layers of a somewhat differing composition. It is however 

 more probable, that both Unes nearly show a point of inflection with a horizontal 

 tangent, and that they appioach very near, but not touch each other. 



1) Rec. Trav. Chim. (2) T. 2, N». 2 and 4 (1898). 



