( 476 ) 



The possibility of jirodnciiifi- the theoretical curves in the />-^diagram 

 lijid (>sc;i|)('(l om- iKtIicc ' i. 



Ill llie first |tl;ic(' Prof', van dkr W.\ai,s ohsorvc^ tliat tliccoiiiplotod 

 liiiure is ill coiilradiclioii wilii llic law {n-e\i()iisly deduced hy liiiu') 

 that a mixtiiro of iioii associatiiiii' siihsjaiiccs may liaxc a maxiiiiiini 

 or iniiiiiiiiiiii critical teiiiporatiirc, Ixit not hotli. ']"o this |)oiiil one 

 of my oi)jeclioiis refers. The law depends entirely on the simple 

 characleristic e(|uatioii, hut a[>art from that it only refers to tlie 

 critical ])oiiit of the lioino,u,eiieous mixtures and it must he looked 

 upon as a possilnlity that the ciii'xe of the critical points - the 



|)lailpoiiits should liaxc Ixilh a maximum and a minimum. 



Prof. VAN I)i:r Waai.s replies to this ^} tiiat near a maximum or 

 minimum the two curves in (|uestion are so close to each other that 

 no sucli (liiference between them can be admitted. This ari>iiment 

 does n(»t satisfy me. The two cnrxes touch each other at points wIkm-c 

 a jnaximum or minimum niiionrjH-i/.^surc exists and the two jthases 

 liave the same composition, but points of that kind <lo not exist iii 

 the case under consideration, it is true that a maximum or minimum 

 occurs on the plait when the connodal cur\-e intersects the >piii<Hlal 

 curve, but the character of these points is entirely different IVom 

 that of the points referred to. 'i'lie three-phase pressure tor mixtures 

 of ethane and the alcohol is betwcM'u the xaponrpressures of the 

 components aiul there is thus no occasion tV)r assuming- the existence 

 of another maximum or minimum. That beinu' the case, there is 

 Jio reason for a close i-esemblance between the two cui\es nor any 



') Note added to lianshdinn. 



The above was written In- me in tiie couvieliuu wliicli I llieu lield llial I'rof. 

 VAN DER Waals's views of the formation of tlie new jilait — although arrived 

 at in a different way — still agreed essentially with ray own : indeed I do not 

 even now see, how else tlie phenomena could be interpreted, l-'rom tlie paper 

 contributed by liim in the October-meeting of Ibis society (critical phenomena of 

 partially miscible li({uids. Kon. Ak. van Wet. Amst. :25tb Oct. 190:2) it appears 

 that such was not the case and that I ought to have been more careful in accept- 

 ing tlie theoretical curve drawn by him as corresponding to llie clianges on tlie 

 4»-surface as understood by myself. Doubt never arose in my mind on this point 

 at all and I never considered the question. Still I ought tu have noticed that the 

 theoretical curve has no vertical tangent at its extreme points, but ends in cusps, 

 corresponding to the circumstance that the curvature of the connodal curve is the 

 same in both plaitpoims of the closed plait. This is the only respect in which I 

 think my paper requires emendation although some of my arguments would have 

 been presented in a different manner had I realised how coini)lelely his views 

 differed from mine. 



2) Arch. Néerl. ii p. 23. 



■^) Gonlinuilat II p. 188 1. 17. 



