o99 



The quantitj a appeared to luive been left uneljanged by the 

 association, viz. =a, — the value for the ease that all the molecules 

 are single — everytiiing i-eforring to a single ^) molecular quantity 

 (e.g. J 8 Or. of H,0, 46 Gr. of C,H,0, etc.). For we have evidently 

 (the index 2 now refers, in distinction with my Teyi.er article to 

 the double molecules, the index 1 to the single molecules) : 



^2 + 2 X —7-. IT «12 + 



2 y ' 2 2 '■' ' V2 



in which a^., = 2a^ and a^=:4:ai, so that we get: 



a = (1 - ,^y a, f 2 (1 I?) ,i a, + /? '^a,=a,. 

 Further : 



b = ^K + f ^ = ^ -(I - i^){- 'A ^>. + ^) = ^ -(1 - i?) A6 



or == V. ^. + ,:? (- V. ^. + ^) = V, ^-^ + /? Aè. 



The equation of state used by van der Waals (p. 1078) is identical 

 with ours, as vats der Waals starts from 1 — x single molecules 

 and .1' double molecules, together 'J mol., while we started from ,? 

 single molecules and (1 — (3) -. 2 double molecules, together Va (1 -J- /3) 

 molecules. Accordingly we left the quantity of substance (viz. a 

 single molecular quantity, e.g. 18 gr. of water etc.) constant, and 

 varied the number of molecules on association from 1 to V2 (1 + 1^) — 

 and VAN DER Waals left the number of molecules constant =1, 

 while he increased quantity of the substance from 1 to 1 -[- .r. 



If this is borne in mind, van der Waals's v : {1 -{- ,v) now passes 

 into v' (now just as with us referring to a single molecular quantity 

 of substance), and we get : 



_RT:{i^.v) a, 

 P — '1 7 ^' 



in which therefore 1 : (l-f-t'j is identical with our (1 -\- ,i) : 2, v' 

 with our r. van der Waals putting Lh=zO. and therefore identi- 

 fying Ö with 0^. 



2. As f?. the degree of dissociation of the double molecules, is a 

 function of v, the dependence of the quantity /? on v will have to 

 be taken into account in order to find the values of the critical 



1) In the cited Teyler arlicle I made everything refer to a double molecular 

 quantity, but I think it more practical to continue to make the diiïerent quantities 

 refer to a single molecular quantity. Hence all the quantities have now been divided 

 by 2, resp. 4. 



