V49 



öW=A,(fa, + ^,ff«,+ . . —C{.r, ,ö^) dr . . . (6) 



If we now introduce tlie free energy of the system, the following 

 well known relation holds for it 



W= E~T . H 



when E repi-esents the internal energy, H the entropy. For an 

 infinitely small variaton we get from this: 



ö^ = 6E- T . ÖH— H . ÖT. 



Further 



T.éHz=öQ = öE-^ ÓW, 



in which <fQ is the quantit}^ of heat added to the system. Making 

 use of (6) we get from this : 



ƒ(^c^'^). 



ÖW= — A,6h^ — A^öu^ + I (^P ' f^'^) • dx—H. ÖT. . (7) 



Let in a certain initial state, in which the variables *«i, «,.. . 

 have the values «i„, a^^ . . ., 33 being = 0, the system have the free 

 energy ¥*„. In the magnetic state, iii which ^ will have a certain 

 value everywhere, and the temperature and another quantity, e.g. 

 the external pressure have remained constant, the geometrical 

 variables will assume other values, which we shall denote by «j, «^ . . . 

 We can now make this transition take place in two steps. We first 

 give the geometrical variables the values «j, a,, ^ remaining = 0; 

 hence the free energy will increase by an amount Agf. 



Further, while a^, (t^ . . . remains unchanged, we can bring the 

 magnetic induction 33 from zero to the tinal value; then the free 

 energy will increase by Aj/V^. In this way the final state is reached, 

 in which the free energy will be: 



W=W, + A,W+ L^tW (8) 



Then according to (7) the follow^ing equation will hold : 



AmW= ff{S;>,d^).dT (9) 



3. Let us now return to the above discussed case, in which two 

 electrodes of the same metal are placed in the dilute solution of a 

 salt of this metal. The concentration of the solution can be different 

 at different places. We think the circuit closed by means of a wire 

 connecting the two electrodes. Let one electrode be in a magnetic 

 field, in consequence of which it is magnetized. We think the 

 magnetic field excited by an electromagnet, the leads of which 

 possess no resistance. 



