534 Mr. 0. J. Lod^e on a Mechanical Illustration 



one is oscillating forwards with velocity v + x and backwards 

 with velocity r — a\ then the cord will be pushed forward both 

 by reason of the too rapid motion and by reason of the too 

 sluggish one; and the electromotive force urging it is 



(y + x)r — (v — x)r = 2xr (16) 



If the cord were allowed to move, the work done per second 

 by this force would be 2xru ; and j times this is therefore the 

 rate at which heat is absorbed at such a point by this force. 

 The heat so absorbed is evolved in other parts of the circuit, 

 because friction opposes the motion of the cord with a force 

 nur equal to 2xr. If we urge the cord at any rate u through 

 such a circuit by an external electromotive force E acting in 

 the same direction as the force of the ^-button , the work done 

 per second is E u = Q mr _ 2a , r )u 3 



or the heat generated is 



j(nu 2 r—2xru), (17) 



and the strenth of the current is 



E + 2o?r E + II 



u— = — ^ — (lb) 



nr It v ' 



Now (17) contains two terms, one depending on the square of 

 the current and being the irreversible frictional generation of 

 heat (15), and the other changing sign with the current and 

 representing the heat absorbed or generated at the ^-button 

 according as u is positive or negative, remembering that the 

 current has been considered positive when going the way the 

 button tends to drive it. 



Something analogous to the unsymmetrical action of this 

 .^-button is what I imagine to go on at a junction either of two 

 different metals at the same temperature, or of two parts of the 

 same metal at different temperatures; and accordingly 2jxru 

 will correspond either to the Peltier effect or to Thomson's 

 convection effect; and 2xr is analogous to the coefficient which 

 which is called II in the one case and may be called in the 

 other. 



§ 29. Let us now proceed to consider what kind of unsym- 

 metrical motions may reasonably be expected to actually occur 

 at a junction either of two different metals at the same tempe- 

 rature, or of two portions of the same metal at different tem- 

 peratures. In both cases the molecules on the two sides of 

 the junction are vibrating at different rates: — in the first case 

 so that 



m a vl = rn b vl, (19) 



m a and m b being the atomic weight of the two metals ; and in 



