47 



Also the value of r, viz. 2,11 on an average, remains in the 

 neighbourhood of 2,1, the value found foi' it experimentall}'. 



I calculated all these vahies then not from those of s and r, but 

 from those of s and ƒ, viz. s :^ 3,774, ƒ =: 7. 



It is seen that th? assumption of possible association docs not 

 bring a real change in the values of the critical quantities (deter- 

 mined by r, Aj, and AJ ~ and may therefore be left out of account 

 in their determination. 



Another Remark. We put vi-:l)/c = r in the above, and notvk-.b,, 

 (v. D. W. 1. c). In the expressions for the critical quantities namely 

 bk occurs, and 7iot brj — and tlierefore to get more certainty in the 

 formuhie, and to remain independent of the tlieoretically and expe- 

 rimentally somewhat nnwieldy relation b^, : bk, I have thought I ought 

 to introduce bt and not /;,, into the formulae (cf. v. L. A., p. 772). 

 [According to the association theory, see v. L. II, p. 422 and 431, 

 bg'.bk is resp. =1,03 or =1,015 according as partial association 

 (to an amount of on an average only about l^j^ 7o> see above) to 

 double or to triple molecules is assumed]. 



There is another advantage in putting Vk : bt = r, namely this that 

 now the factors X^ and X^ in the formulae (3) and (4) for RTk and 

 2)k are much nearer unit}" than when /),/ is introduced. For both 

 for RT/c and for pi; (leaving the faclor r — 1 out of account) 

 r = Vk : bk occurs to the third power, so that the deviation of the 

 ratio b(j : bk from unity will be found in Aj and )..^ at least tliree 

 times enlarged. If therefore according to van der Waals b,, : bk = 1,04 

 a 1,05, or according to the above 1,015 a 1,03 '), hence on an 

 average about 1,03, A. and /^ can differ about 10 7o from unity 

 when 1"' = Vk : bfi is assumed instead of r = Vk ■ bk, and the relations 

 drawn up by van dkr Waals between r, s, and f will be valid 

 onlg by appro.rimafion, whereas they may be considered as almost 

 entirehj accurate when r = vk • bk is introduced. 



1) As rs = 8 yi , bg : bi, may be determined from : 



bk r' r's A J 



when r' = vt : b,j is known from experiment. 



r—1 s f 8\ 



As = — 7 or r 1 -— — = 1 follows from (G) — see § 2 — also 



r'\ 1 T |=— = r~, from which tlie relation b,, : bk may also be determined. 



\ } ) '^ ^'J 

 [When association is taken into account, the factor -j.k is added to s]. 



