and the Properties of Liquids. 581 



Other Relations. 



The equations (3), (4), (5), (6), and (7) are the funda- 

 mental equations giving the relations between the quantities 

 which they contain, and it should therefore be possible to 

 reduce all other empirical relations between these quantities 

 to one of these equations. We will illustrate this by some 

 examples. 



Walden * has shown that the expression — =- is equal to 



. . Pl * v . 

 the same constant for all liquids at their boiling-points, where 



%o is the sum of the maximum valencies of the atoms of a 

 molecule. Substituting for X in this expression from equa- 

 tion (3), and % \Zm x for 2«, since these quantities are 

 approximately equal to one another f, we obtain, since the 

 boiling-points are approximately corresponding points, that 



^ l X x/m, is a constant. This, it will be seen, is Traube's 



law. t 



Walden also showed that — v is constant at the boiling;- 



point, where L is the (total) heat of evaporation. Now the 

 work done during evaporation is the same fraction of the 

 internal heat of evaporation for all liquids at corresponding 

 temperatures (see "Heat of Evaporation," this paper), and we 

 may therefore substitute for L from equation (4), and sub- 



(P \ 1//3 

 — I . Now 



this is approximately constant as — does not vary much with 



the nature of the liquid. To conform to equations (3) and 



Lp 2/3 

 (4) the above expression should be written H \ /3 , when it 



will at once reduce to a constant on substituting for \ and L. 



T 



Walden states in his paper that ,=r- is equal to the same 



constant for all liquids at their boiling-points. But this 

 happens to apply only to the liquids mentioned in his paper. 

 The quantity is found to be by no means constant when all 

 the available data are considered. Its properties have been 

 discussed in a paper by the writer J, in which a meaning of 

 its constancy in the case of some liquids will be found. 



* Zeit. fiirphys. Chemie, vol. lxv. 1908-1909, pp. 257-261. 



t Phys. Zeit. Oct. 1909, p. 667 ; Phil. Mao-. May 1910, pp. 784-788. 



% Phil. Mag. Dec. 1910, p. 905. 



Phil. Mag. S. 6. Vol. 22. No. 130. Oct. 1911. 2 Q 



