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Physics. — ''Contribution to the theory of corresponding states'' 

 By Mrs. T. Ehreïsfest-Afanassjewa. D. Sc. (Communicated by 

 Prof. H, A. LoRENTz). 



(Communicated in the meeting of September 26, 1914). 



^ J . Meslin ^) has tried to demonstrate that every equation of 

 state which contains the same number of material constants as 

 variables, is to be reduced to a universal shape (i. e. to such a form 

 that no parameters occur any more which vary with the substance), 

 if the variables are replaced by their relations to suitable special 

 values, which may be designated as "corresponding" for different 

 substances. 



On closer investigation it appears, however, that the equality of 

 the number of the parameters and that of the variables is neither 

 necessary nor sufficient for the existence of corresponding states. 



A method will be given here to decide whether a given equation 

 allows the existence of corresponding states. This method furnishes 

 at the same time the possibility to calculate the eventually corre- 

 sponding values of the variables for different substances. 



§ 2. In the first place we shall define the term "corresponding 

 states" in a somewhat more general form. Let an equation be given 

 between a system of n variables: x^,.i\,...Xn and a number m of 

 such parameters: C\, C^, . . . Cm that they can vary with change of 

 definite circumstances {for example of the substance). 



Let an arbitrary system of special values: x\' , ,i\' , . . . x,,' (we shall 

 briefly denote it by xi') of the variables .iv be known, which satisfies 

 this equation for definite special values d' of the parameters Ci. 



Let us introduce the following new variables: 



lh=—, ' 3/2 =—'••• ^« =—, • • • • (1) 



All the constants Sj of the thus transformed equation can be 

 calculated as functions of the former constant coefficients, of the 

 values Ci' and of the values Xh'. 



When the parameters d assume other special values Ci", other 

 systems of special values of the variables will satisfy the original 

 equation. 



The case may occur that there is among them such a system of 

 values ; 



^) Meslin: Sur l'équation de van der Waals et la demonstration du theorema 

 des états correspondants CR. 1893, p. 135. 



