148 Mr. G. von Kaufmann on the Theory of Corresponding 



is a maximum, and using this as " unit point " obtains the- 

 reduced equation 



The experimental testing o£ the theory of corresponding- 

 states, undertaken chiefly by S. Young, depends in the first 

 place on the possibility of measuring p k , v k , T k , and the 

 comparison of the different functions at equal values of 

 tt' or 0' ' , for various substances. A still more simple method 

 is that first suggested by Amagat *, the principle of which 

 is most simply carried out by plotting curves with the 

 variables logp, logv, logT, &c. (Raveau f). It follows at 

 once from the theory of corresponding states that these 

 curves should be of identical shape (superimposable by 

 parallel shifting of the axes) for the different substances. 

 This method requires no knowledge of the critical values. 



Although in many cases a fairly approximate corre- 

 spondence of states has been found to exist, the theory in its 

 entirety has been proved without doubt inexact ; it has not 

 been found completely true for even a single pair of sub- 

 stances. There is therefore no general (p, v, T) -state- 

 equation with only three specific constants. Nevertheless, 

 a theory which is so far-reaching and fundamental as this, 

 and which over a large range of phenomena gives a good 

 first approximation to the facts, will not lightly be discarded ; 

 and in the present position attempts are being made to 

 modify it in such a way as to bring it more into agreement 

 with the truth. Thus, Kristine Meyer J has found that a 

 fairly accurate correspondence of states exists if the reduced 

 variables pfc («-«-,)/(•,— J, (T-T^-TJ are 

 chosen, where v , T have certain values for each substance, 

 being selected zero for fluorbenzene. Berthelot expresses 

 the same facts as a correspondence with respect to p/p k , 



(v-"»JK+ h -*vJ, ( T_T J/( T a~ T J> and suggests a physical 

 meaning for v ,T . 



The following contains a re-statement of the fundamental 

 principles of the theory of corresponding states, from a 

 rather different and more general point of view, and 

 a suggestion as to the direction in which the true nature 



Bo 



of the generalities here certainly existing is to be sought. 



* C. P. exxiii. pp. 30, 83 (1893). 



f Journ.de Phys. (8) vi. p. 432 (1897). 



t Zeit. Phys. Chem. xxxii. p. 1 (1900). 



