189 



vation of course remind of the ordinary gas pressure, (law of Boyle, 

 or for non-diluled solutions the formula of van der Waals), but which 

 are to be called inaccurate in the most absolute sense. 

 Fontnnivent suv Clarens, April, 1915. 



AppendLc durimj the correction. 



In a correspondence on tins subject with Prof. Ehrenfest (Prof. 

 LoRENTZ was namely so kind as to send him my article) it iuis 

 become still clearer to me to what E.'s result, whicii in my opinion 

 is erroneous, is to be ascrilied. 



In his considerations he namely assumes (this had not api)earcd 

 to me from his paper) that the molecules of tlie substances do not 

 exert any action on each other, i.e. that all the forces and actions, 

 also those in the collisions, are neglected, (that the attractive forces 

 are neglected, does not affect the correctness or incorrectness of the 

 calculations). Prof. E. e.^presses this by saying: The water is quite 

 unaffected by the sugar present, and vice versa. 



This is the very core of the problem. When the water is not 

 affected by the sugar present, then i>iv) = fi(0), and no longer 

 f*(,r) --:= fi(0) -|- RT log (1 — .r). In other words: E. works with substances 

 for which Gibbs's paradox lias disappeared, and which have therefore 

 become entirely free from Iherniodynamics. Hence he could not 

 possibly find the expression — log [\ — .r) corresponding to it. 



Such extra-stellary, thermodynamic-free substances have of course 

 lost all diffusion tendency - which just causes the phenomenon of 

 the osmotic pressure. For if the water is quite unaffected by the 

 sugar present, there exists no impetus any longer for the water to 

 be displaced, so that the disturbed equilibrium (between concentrations 

 X and 0, or ,i\ and ,*'j) is reestablished. 



As so many before him. Prof. E. has in my opinion allowed 

 himself be carried away (see e.g. p. 1241 of his paper) by the striking 

 analogij, which was already mentioned in Thesis IV above. That 

 we can only speak of analogy here, is no doubt clear after all that 

 was remarked above. The aiuilogy pressure of E. and others acts 

 namely precisely in the opposite sense from the real osmotic pressure. 

 In the limiting case it is not ,c that is found instead of —/('</ (1 — ,r), 

 but — ,(■'. This mistaken opposite |)ressnre is of course the conse- 

 quence of the perfect freedom of the sugar molecules assumed by 

 E. and others, which molecules now begin to exert a pressure of 

 24 atms. per gr. mol. on the semi-permeable wall — a pressure 

 which of course is not e.xerted for ordinary solutions as we know 



