58 



These are accordingly the inevitable conclusions to which the 

 investigation of the preceding paragraphs has led us. 



5. lite reduced equation of state. Already in previous papers 

 (v. L. Ill, p. 568, IV, p. 719) I made use of the reduced form of the 

 equation of state, when b=:f{v) was assumed in consequence of 

 association. Van der Waals has, however, (see particularly v. d. W. II) 

 given such a form to the reduced equation of state, that the law of 

 corresponding states was brought forward in a new form. For this 

 purpose it was only necessary to divide the former reduced volume 



(expressed in vk) by - = 1/ '-—-. (The relation bk-b^ or bg-.h^ 



may be left out of consideration for the present; we shall return to 

 it in our concluding paper). 



Van derWaals's results are naturally more or less approximative; 

 tirst because the factors l^ and A, have been disregarded, and secondly 

 because not r=zvk-f>k, hut again r' = Vk-bg was introduced. 



There is now no longer any approximation, and we get — also 

 by a simpler way — the results found by van der Waals, perfectly 

 defined, when />,7^ and v are not expressed in the real critical 

 quantities jyk, Tk, and vk — but in the ideal critical quantities, i.e. 

 those which would hold for the ideal equation of state with a and 

 b constant. If we call the latter quantities i)'k, Tk, and v'k, then 



8a ,1a , o. 



Then from : 



V' 



P + -^{v-b) = RT 



follows the equation 



(^'P'k + -7^1 {n'v'k - ii'v'k) = m'RT'k, 

 \ n" v'ky 



when f ', n', b', and m' resp. represent p : p'k, v : v'k, h : v'k, T : T'k, 



just as formerly p : pk, v : vk, b : vk, T : Tk were represented by 



f, n, /?, and m. 



After substitution of the above given values of RTk,p'k, and v'k, 



we get therefore as before : 



f g' . _L A !_ ^ (n' . dbk — /?' . ^bk) = m' . — f , 



i.e. 



