of Thermo-electric Phenomena. 533 



The rate of radiation work of a button is 



w 1+ w 2 -1 



2t _2 



= tra vie. 



(13) 



the same as that given by equation (1) when no current was 

 passing. 



We have found, then, that each button exerts an average 

 force on the cord equal to ru ; hence, if there are n but- 

 tons in a row on each cord, and m cords lying side by side, 

 the electromotive force or difference of potential required to 

 drive a current of strength ma = G through a conductor of 

 sectional area represented by m, and length represented by n, is 



— =E=m^=— r.mu = RC, . . . (14) 

 mm v 



which merely shows that Ohm's law, if true for each button, 

 is true for the whole conductor if its temperature is kept con- 

 stant. The work done by this force in any time T will be equal 

 to the product of the force into the distance through which it 

 may have moved the cord in that time — that is, FVT ; hence 

 the rate of " frictional " generation of heat by the current is 



jmnru 2 =jHC 2 , (15) 



which is Joule's law that the amount of heat generated in a 

 given time is proportional to the resistance of the conductor 

 and to the square of the strength of the current. It is conve- 

 nient to use j for the number of units of heat contained in a 

 unit of work, i. e. for the reciprocal of J. 



Though I have here taken account of more cords than one, it 

 will not be necessary to do this hereafter, as what is true for 

 any one cord will be true for any number, so we will henceforth 

 consider m=l. 



§ 28. So far we have considered only homogeneous circuits, 

 in which all the buttons have the same amplitude, the same 

 period, and the same average velocities. In these cases the 

 cord is in equilibrium under the united and balanced action of 

 all the buttons on it, but it is perfectly free and capable of per- 

 manent displacement by the slightest force ; so that if even 

 one button were made to move forward always faster than it 

 returned, it would exert an electromotive force on the cord 

 and move it forward a little at each oscillation. On the other 

 hand, if any button be made to go forward more slowly than 

 it returns, it will exert less force on the cord than is expected 

 of it, and the cord will be moved backwards by the other but- 

 tons while the slow one is going forward. Hence if we con- 

 ceive a cord on which all the buttons but one are oscillating 

 regularly to and fro with the average velocity v, while this 



