30 SECTIONAL ADDRESSES. 



Copper-f-E. Eacli has a vapour pressure for electrons. When equi- 

 librium exists between the metals the vapour pressure must be the same 

 for both. 



Now there is a theorem which deals with such cases of equilibrium. 

 This is Margules' theorem. If [i^ is the molar fraction of the volatile 

 component and p the vapour pressure, 



(i.1— -log j9=a symmetrical function of iXi and 1— pt,. 



This theorem is not quite exact, but at temperatures remote from 

 the critical value the error is one part in a million or less, and may be dis- 

 regarded. A simple case is that for which the right-hand side can be 

 written aH-2P(j,,(l— [j.,), and when integrated it gives 



log ^=a log (x,+p(l— (Xjf . 



Po 



An equation of this kind fits exceedingly well many binary mixtures 

 (even when both components are volatile), the value of p varying in 

 difierent cases from plus three or four to minus six, and a being often 

 equal to one. The form of the equation indicates that [3 is the coefficient 

 of mutual action between the components. Its value varies neajly 

 inversely as the absolute temperature, and since the equation may be 

 written 



p=Poliie T 



it is seen to have a close connexion witFBoltzmann's equation. But the 

 general form of Margules' equation has, I believe, much wider validity 

 than Boltzmann's equation. 



Now when copper and zinc with their electrons are in contact-equi- 

 librium with each other they must have the same vapour pressure for 

 electrons— i.e. p is the same for both. Hence 



This is an equation for determining the concentrations ([x) of the free 

 electrons in copper and zinc respectively. 



Our present knowledge about the numbers of free electrons in metals 

 requires that [i^ and [i. be small. Hence approximately 



or 3i-P'=log&. 



Now ^^ — p,. is certainly proportional to the work done in the escape of 

 an electron, but we do not know enough about the concentrations (fx) of 

 the free electrons in the metals to make any use of this equation, which 

 is of such importance in connexion with the properties of ordinary 

 solutions. I give it in order to call attention to it as an equation which 

 may some day be of use in elucidating the Volta effect. 



More hopeful in giving information is the equation for the latent 



