( 445 ) 



Physics. — "Plaltpo/'nf.s (ind ctirri's/to/K/ii/i/ p/tti/s /// f/n' neufhbour- 

 hood of tke ddes of the xY-sui-jarc of van dkk Waals." Hv 



Prof. D. J. KOUTEWEG. 



(Communicated in the Mooting ot Doconiboi- :i7, 1902). 



First Desckiptivk Pant. 



I. As in \\\\ ''Th<'orie </i'ncr<i/e dc.s jiUs'^) I wisli fo prccodc in 

 lliis j);i[)er llio (leiiioiistrating part by a short summary of llic 

 obtained results. 



As we know a plaitpoint may occur on the side ./; = of the 

 ip-surface of van dek Waals,') which is represented l)y the equation : 



rp= - MR T loq{ r — /> ,) — - + MRT [ x loci ,r. + ( I — -r) Ion ( 1 — ./•) 1.(1) 



V 



where : 



a,=a,{\-.ry^'l ^,,^ ,.(1_,,)4.«^ ,,'^„, _^2(,.(,-<r0.'.-f (", + ".-2 ,">% • • (2) 



A,=^(l-.r)H-2 ,/,^..(l-..) + /.,./^=^ + 2(,V/>0.;-f(^4-V2 />.>% . . (::})■ 



Tiiis occurs only in the case that the temperature T corresponds 

 with the critical Tk of the principal component ; but in that case it 

 occurs always. This plaitpoint coincides with the critical point of the 

 {)rincipal component for which v = 3 b^ and which in our tijiures we 

 shall always represent by the symbol K; the plaitpoint itself will 

 be represented by P. 



If the temperatnre varies, the plaitpoint and the correspondinp: 

 plait can in general behave in two quite different ways. It will 

 namely either, as is indicated by the yir.y^ four cases on tig. I of the 

 plate, on which the (/',./.') projections of the sides of the ip-sui-face are 

 represented, at increase of temperature leave tiie /--axis and move 

 to the inner side, therefore entering the surface, and disapjieai- 

 from the surface at decrease of tempei-ature, or it will as in the 

 last fonr cases of that figure, enter the surface at decrease and leave 

 it at increase of temperature. 



1) Archives Necflandaises, T. 24 (1891) p. 295—308: La llióoric générale des 

 plis et la surface '^ de van der Waals dans Ie cas de symétrie. Sec there 

 p. 320—368. 



~) We take here the equation of the i-surface as it has been originally derived 

 by VAN DER Waals, so without the empiric corrections which seem to be rciiuired 

 to make the results agree quantitatively better with the experimental data. So is, 

 for instance, ctj considered to be independent of tlie temperature, and all the results 

 and formulae mentioned are founded on this supposition. It would not have been 

 dilïicult to take such empiric corrections into account, as has really been done by 

 Versghaffelt and Keesom in their [)apers. to which we shall presently refer; but 

 then the results wore of course not so easily surveyed. Therefore I have preferred 

 to leave them out of account, at least for the present. 



