>40 Mr. 0. J. Lodo-o on a Mechanical Illustration 



'is 



only assume that it is different in A and B, and shall call its 

 value in B, b. Putting the values of r into (22), we get 



n=A(h'-h'' a )(a»-l)-B(h' t -h" t )(V>-l). . (23) 



This is the electromotive force generated at a junction of two 

 metals A and B at the absolute temperature ; and therefore 

 it is the coefficient * of the Peltier effect ; and the heat absorbed 

 per second at such a junction by a current of strength u 

 is (§ 28) 



fllu (24) 



The roots of the equation 11 = will give temperatures at 

 which there is no electromotive force, or at which the two 

 metals are neutral to one another. There are only two posi- 

 tive roots : = is of course one ; for then all molecules are 

 standing still. The other will be the neutral temperature of 

 Cumming ; a first approximation to it is 



a A -2A(h' a -h" a ) logq + 2B(A',-A",) log b 



"°- A(A'.-A".)(loga)«-B(A',-A",)(log&)*- ^> 



§ 35. Leave this for the present, and proceed to find the 

 electromotive force generated at a junction of two parts of the 

 same metal A at different temperatures 1 and 2 — or rather the 

 electromotive force generated in a certain length of A, in which 

 the temperature is gradually falling from the value X at one 

 end to the value 2 at the other. Consider a small element 

 with temperature 0, resistance r, and out and in velocities of 

 the molecules v, v + civ at one end ; and at the other, tempera- 

 ture + d0, resistance r + dr, and velocities i\ and i\ + dv 1 : 

 then the force exerted on the positive cord in this element is, 

 just as in (21), 



A¥=r / dv — (/ + dr f )dv 1} 

 or in the limit 



which 



dF = dvdr', (2P) 



= A0dr f , 



since dv is proportional to (§ 29). 



Similarly, the force on the negative cord is 



dW = A0dr f, - i 



so the balance of electromotive force in the element is 



d<d=dF-dF'=A0(dr'-dr"). . . (26) 



* I find I have not used the symbol in quite its ordinary sense : Thom- 

 son calls JJu the heat absorbed, and Jn the electromotive force. I have 

 preferred my notation, however, as the J occurs more naturally in a quan- 

 tity of heat than it does in an electromotive force. 



