270 Mr Parker, On Contact- and Thermo- Electricity. [Nov. 23, 



charge is zero, let us suppose that by altering the relative positions 

 of its parts, every one of its charges becomes zero, and denote the 

 corresponding values of the energy and entropy by U and <£ . If 

 from any cause, such as the parts of the system not being sufficiently 

 numerous, this (or any other) operation cannot be directly per- 

 formed, we may always make use of subsidiary bodies; and the 

 final result being independent of the subsidiary bodies employed, 

 we may argue as if they were entirely unnecessary. 



For the energy U, we assume Helmholtz' expression 



U=U +e$ < ^ + Q A F A + Q«F B + 



= U +6{iQ A V A + %Q s V B + } + Q A F A +Q B F B + (1), 



where A,B,C, ... are the different homogeneous bodies of uniform 

 temperature which the system contains; Q A , Q B , Q c , ... their 

 charges; V A , V B , V c , ... their potentials; and F A , F B , F c , ... 

 quantities which depend respectively on these bodies but not on 

 their electric states. In what follows, the states of the different 

 bodies will be completely defined by their temperatures, so that 

 F will be a function of the temperature depending in form on the 

 nature of the metal. 



To obtain the value of <£, we make use of Joule's law that if a 

 steady current I be flowing in a homogeneous body of uniform 

 temperature and resistance R, the heat evolved is RP ergs per 

 second. From this we deduce that while a quantity Q is being 

 transmitted, the heat evolved is RIQ ; and therefore, since R is 

 independent of /, as / diminishes, the heat evolved when a given 

 finite quantity of electricity is transferred, diminishes in the same 

 ratio as /. Now the process becomes more and more nearly 

 reversible as / diminishes, but does not actually become reversible 

 until / vanishes. Hence if our given system be made to undergo 

 a reversible operation of any kind in which no part of it is com- 

 pressed or distorted, and no charge made to pass from one body to 

 a different body or to a body of the same kind but at a different 

 temperature, there will be no thermal effect produced and conse- 

 quently no change of entropy. So long therefore as the charges 

 are not made to leave the bodies on which they were at first, the 

 entropy of the system is unaltered by any change in the distribution 

 of the charges or in the relative positions of the bodies. We may 

 therefore put 



4> = ir A (Q A ) + ylr B (Q B ) + f c (Q c )+ , 



where ^r A (Q A ) only depends on the body A and its charge, ^jr B (Q £ ) 

 only on B and its charge, ...... 



