532 Mr. 0. J. Lodo;0 on a Mechanical Illustration 



r- 



fchese faces would become equalized by surface leakage or 

 otherwise; but any quickening of the motions of the molecules 

 (rise of temperature) will increase the electric displacement 

 and strain, and will restore a certain amount of difference of 

 potential to the faces. On the other hand, a lowering of the 

 temperature of the crystal will give the elasticity an advantage 

 over the friction ; some of the previously displaced cord will 

 return, and the potentials of the faces will change sign. 



§ 27. Return now to the consideration of a simple metallic 

 conductor with its buttons all executing isochronous simple 

 harmonic motions on the cord. Apply a force to the cord so 

 as to make it move continuously forward with a velocity u ; 

 that is, generate a current of strength proportional to u in the 

 conductor by means of external electromotive force. We will 

 not suppose that u is great enough at all to interfere with the 

 motion of the buttons ; in other words, we will assume that u 

 is incomparably less than Y; nevertheless the vibrations of the 

 buttons, though unaltered in space, are no longer symmetrical 

 right and left with respect to the cord : in one direction their 

 relative velocity is the sum, in the other the difference of their 

 respective velocities ; hence the motion of the cord is resisted, 

 and work must be done to drive it. If the buttons were sta- 

 tionary, the force opposing the motion of the cord in each 

 button would be ru by Ohm's law ; and this force is unaltered 

 by the motion of the buttons so long as u is small. For con- 

 sider the work done by a button in one excursion ; properly 

 speaking it would be 



W=l (v±u)rdx, .... (11) 



the signs to be taken according as the excursion is against or 

 with the cord; but as this expression is unmanageably long, I 

 will be content with the simpler one, true when u is small, 



Wi = \ (v + u)rdx = ^ ra 2 s/ k + 2aru 



for the work clone by a button in an excursion against the cord, 

 and 



W 2 = 1 (v — u)rdx = ^ to? sf k — 2aru 



for the work done in an excursion with it. The balance of 

 work done against the cord in a double excursion (that is, 

 while the button travels over a distance 4a) is 



W 1 -W 2 =Aaru$ (12) 



hence the average force exerted must be equal to ru. 



