152 Mr. Gr. von Kaufmann on the Theory of Corresponding 



the purely thermodynamic relations of volume- and heat- 

 energies in chemical individuals, although no accurate corre- 

 spondence of states exists with respect to pressure, volume, 

 and temperature (except at great dilution), the theory is not 

 exhausted ; it remains to determine the thermodynamic 

 functions in which there is proportional correspondence, by 

 whose means corresponding thermodynamic states of sub- 

 stances can be defined. Such an attempt has already been 

 made, with some success, in the work of K. Meyer and 

 D. Berthelot cited above. 



In conclusion, some examples will be given of the extension 

 of the theory of corresponding states to the most diverse 

 phenomena in physics and chemistry. 



In the first place, there are a number of natural laws 

 expressed as a proportionality, by an equation containing 

 only one specific constant, the proportionality factor. These 

 all give non-specific reduced equations by the specific choice 

 of only one of the units involved, and the logarithmic curves 

 are superimposable by shifting only one of the axes. The 

 proportionality factor may in these cases be regarded as a 

 ratio of specific constants of certain dimensions, characteristic 

 of the different systems. Thus, in the equation E/C = R, the 

 resistance R can be looked on as the ratio of specific con- 

 stants e and i, of the dimensions of Potential and Current 

 respectively. Again, in the equation qq , /r 2 = ~Kf (Coulomb's 

 law), and in any other equations involving K, the dielectric 

 constant K can be regarded as a ratio of specific constants 

 9i) u ii h o£ dimensions of Electric Charge, Energy, and 

 Length respectively : 1 K = q i 2 /u 1 li. 



The value of the theory is, however, more immediately 

 evident when it is applied to rather more complicated rela- 

 tions. Thus, in a large number of the systems defined as 

 metallic thermo-couples in which the temperature of one 

 junction is kept constant at zero temperature, the E.M.F. is 

 related to the temperature of the other junction by the 

 equation 



E = a£ + /ft 2 . 



Here, introducing the constants £ = a 2 //3, c = a//3, of dimen- 

 sions of E and t respectively, and putting E/g=e, t/c = 0, we 

 obtain the reduced equation, common to all the thermo- 

 couples, 



e = 0+<9 2 . 



In this case, there is an obvious " critical point," the so-called 

 neutral point, the vertex of the parabola, with the coordinates 



