Atom and the Charge of Electricity carried by it. 531 



ducting circuit. Let us take the case of zinc immersed 

 in acid, suppose we have a rod of zinc immersed in a 

 solution of zinc chloride. We may suppose that in the 

 solution we have positively charged zinc atoms, negatively 

 charged chlorine ones, and molecules of zinc chloride, con- 

 siting of a positive zinc atom combined with a negative 

 chlorine one. When a stick of zinc is immersed in the solution, 

 some of its positively charged zinc atoms combine with the 

 negative chlorine ones in the solution and form neutral zinc 

 chloride. This leaves on the zinc rod an excess of negative 

 electricity, while in the solution there will be an excess of 

 positive electricity carried by the zinc atoms. These atoms 

 approach the rod and form one plate of a condenser, the other 

 plate of which consists of the negatively electrified zinc atoms 

 in the rod, the charge in this condenser will be proportional 

 to the number of molecules of zinc chloride formed. 



We can find the potential difference between the plates of 

 this condenser when equilibrium is reached in the following 

 way : — When equilibrium is reached the mean Lagrangian 

 function of the system will be stationary. 



Now the Lagrangian function consists (1) of a part due to 

 the solvent; as this does not change during the process of 

 chemical combination we may leave it out of account. (2) A 

 part due to the zinc rod ; this will be of the form m 1 Z 1 where 

 mi is ^ ne mass of the zinc in the rod, and Z x a quantity inde- 

 pendent of m lt (3) A part due to the zinc chloride in solution; 

 if m 2 is the mass of ZnCl 2 , then this part of the mean La- 

 grangian function is equal to 



— m 2 R 2 log m 2 + m 2 w 2 



(see l Applications of Dynamics to Physics and Chemistry,' p. 

 154) : here 6 represents the absolute temperature, w 2 a quantity 

 independent of m 2 , while R 2 # is equal to the pressure exerted 

 by a number of molecules of ZnCl 2 in the gaseous state and 

 obeying Boyle's law divided by the density of the gas in this 

 state. (4) A part due to the zinc atoms in the solution; if ra 3 

 is the mass of these atoms, this part of the Lagrangian function 

 is equal to 



— m 3 Rj0 log w 3 -f m z w 3 . 



(5) A part due to the CI atoms in the solution ; if m A is the 

 mass of these atoms, this part is equal to 



— m^R ± 6 log m A + w 4 u' 4 . 



(6) A part due to the condenser formed at the junction of 

 the zinc and the solution ; if C is the capacity of this condenser 



