That will) respect to the /^-values just liquids .behave entirely- 

 according to the 'ordinary theory with b=f{v,T) — without quasi 

 association being taken into account — has appeared in mj recent 

 calculations wath respect to Argon. In IV p. 458 we saw namely 

 that the liquid values of h behave entirely according to the relation 

 h=f{v) derived by me (if namely /^^ = 60 : ï^/c is only raised from 

 the value 0,286 obtained by extrapolation to 0,305). That the vapour 

 values of h exhibit deviations, and even become impossible, is to be 

 ascribed to the way of determination of the vapour ^^olumes at 

 lower temperatures — since it is no longer by direct observation, 

 but by application of the law of Boyle, which is not yet quite valid 

 then, as I have shown in IV p. 457. 



3. Let us now proceed to examine the influence of the quasi 

 association in the very rarefied gas state, by which it will be proved 

 that the kinetic result I),, = éin can no longer be maintained. 



Abbreviated derivation. If in first approximation (this is permissible 

 for great v) we put the quantity b independent of the state of 

 (quasi) association (the quantity a is always independent of it), the 

 equation of state for ^reat y is: 



p{v-b) = {l-^/,,v)RT , (1) 



when a fraction .i' of one single molecule associates to double mole- 

 cules, so that there will be 1 — x single and V'2 ^^' double molecules, 

 together 1 — V2 '^'- With very large volume the nvmibers of triple, 

 quadruple etc. molecules can namely be neglected with respect to 

 that of the double molecules. 



In this .X' is given by an equation of the form (see for a justi- 

 fication of this and of som.e other assumptions the Appendix) 



e,"- _ (1 - .vY CT 



^3 "" ' A^ — '/u^^) P ' 

 as the concentration t\ of the single molecules = v'l — x) -. {l~'/,x), 

 and that of the double molecules c, = '/^.v : {l—'/^x). 



In this it is supposed that also the specific heat does not undergo 

 any change in the quasi association, and that moreover the energy 

 change may be put =:= 0. 



In the ideal gas state wehaver:p = (i — 6) : /?(1—V,a;), according 

 to (1), so that we caji also write: 



or also, as -i- will always be exceedingly slight with large volume, 

 and V may be written for v — b: 



