Atom and the Charge of Electricity carried by it. 521 



increase in the potential energy, while an increase in the 

 negative charge would diminish the potential energy ; if <x A 

 is negative the converse is true. Now a dynamical system 

 behaves so as to facilitate any change which causes a dimi- 

 nution in the potential energy. Thus those substances for 

 which a is negative will tend to acquire a charge of positive 

 electricity, while those for which <j is positive will tend to 

 get a charge of negative electricity. Thus the existence of 

 the property expressed by the coefficient a would produce the 

 same effect as von Helmholtz's specific attraction of the ele- 

 ments for the two electricities. 



Suppose, for example, that we have two metals A and B in 



' contact, and that a A , cr B are the values of the Volta coefficients 

 for A and B respectively; let a A be greater than <r B . Then if A 



1 acquires a negative charge equal to — Q, and B a positive 

 if charge equal to Q, the potential energy of the two metals will 

 be diminished by (o" A — cr B )Q. If this were the only source of 

 potential energy, the transference of positive electricity from 

 A to B, and of negative from B to A, would go on indefinitely, 

 as each transference would involve a diminution in the potential 

 energy. The separation of the electricities wdll, however, pro- 

 duce an electric field the potential energy due to which will 

 increase as Q increases, so that the diminution in energy due 

 to the Volta effect will be accompanied by an increase in the 

 energy due to the electrostatic field. Let us suppose, for 

 example, that the two metals form the plates of a condenser 

 whose capacity is C, then when A has a charge — Q and B a 

 charge + Q, the energy in the electrostatic field is equal to 



1Q 2 



2 C 



while the energy due to the Volta effect is 



-(°"a-°"b)Q- 



The flow of negative electricity into A and of positive into B 

 will go on until the increment in the energy of the electro- 

 static field due to an increase 8Q in the charge on B is equal 

 to the decrement of the energy due to the Volta effect pro- 

 duced by the same displacement of electricity. 

 Since the total energy is 



1} -Q —\.< r ±—< r B) t 'i> 



