1891.] Mr Parker, On Contact- and Thermo- Electricity. 271 



Now take a second system identical with the first, forming 

 with it a compound system whose entropy is 2(f>. By a reversible 

 process, such as we have already described, let a charge be made to 

 pass from one metallic body A to the other body A, and suppose 

 that no other charge passes from one body to another. Then, since 

 by what precedes the entropy of the compound system is unchanged, 

 it follows that, if q be the final charge of one body A and 2Q A — q 

 of the other, yjr A (q) + ^ A (2Q A — q) is independent of q, whatever q 

 may be. We therefore infer that ty A {Q A ) = ^(0) + Q A H A , where 

 H A is independent of Q A . 



Next, let us take a system formed of the original system <p and 

 of a second system which also contains a metal body A at the same 

 temperature as the body A in the first system but different in 

 form and size and with any chai'ge Q A . Let H A be the quantity 

 corresponding to H A . Then, by supposing any charge to pass from 

 one metal A to the other metal A, without the passage of a charge 

 between any other bodies, we find H A = H A . Hence H A is inde- 

 pendent of the size and form of A as well as of its electric state. 



Thus finally 



<f> = f A (0) + ^ B (0)+...+Q A H A + Q B H B +... 



= <f>o + Q^ A + Q B H B + (2). 



To complete the expressions for IT and $, we require an im- 

 portant identical relation which holds between F and H. Let the 

 metal A and any other part which is at the same temperature 6 A 

 be slowly heated to 6 A + dd A , and let the parts of the system be at 

 the same time slowly moved about so that no charge passes from 

 one body to another. Then we have 



dU=dU +edX^- + Q A dF A +...) 



dcj> = d<f> + Q A dH A + ... J 



If dW be the work done on the system, dll — dW is the heat 

 absorbed, and since the operation is reversible, we have 



dU-dW=e A d<j>, 

 or dU -6 A dcf>- dW+ ed?,QQ-+ Q A dF A + ... 



-QJJH A -Q B A dH B -...=O. 



Now take a second system identical with the first except that 

 every charge is reversed in sign, and let it undergo a reversible 



