52 Prof. R. Clausius on the 



motive force e, induced at the time t in the stationary con- 

 ductor, by the following equation, which corresponds to (2): — 



da 



e ~ dt' 

 In order to deduce from this the mean electromotive force, 

 we must again perform an integration in respect of the time, 

 and divide the integral by the time. As the positive direction 

 of the electromotive force does not alter in the stationary 

 conductor, we may in this case extend the integration over 

 the entire time of rotation t (i. e. from any given time if to 

 the time t' + t), and thus obtain the equation 

 1 rt'+r 1 /»/'+T r /o i 



it e<ft=-i( ^<^=i(0'--X2"); 



rj t , T J t , dt r v 



in which I2' represents the initial value, and fl // the final value 

 after a complete turn. But after a complete revolution, both 

 the position of the portion of the conductor and the direc- 

 tion of the current, which has changed twice during this time, 

 are again the same as at the outset; from which it follows 

 that il f/ is again equal to O', and thus the preceding expression 

 is equal to null. This holds also for all portions of the con- 

 ductor, and we arrive therefore at the conclusion that in the 

 stationary conductor no electromotive force is induced ; that is to 

 say, that the electromotive force induced by the motion and 

 that by the reversal of the current mutually neutralize each 

 other. 



§ 5. Inductive Action of the moving Conductor, in which a 

 current is circulating, on itself. 



It remains to consider the inductive action which the cur- 

 rent in the moving conductor exerts on the moving conductor 

 itself. 



In this respect we must first of all observe that the conductor 

 in question (that is, the rotating coil) only moves as a whole, 

 so that any two portions of it retain their relative positions. 

 It follows from this that the motion can produce no reciprocal 

 action. 



Hence we need only consider the change of current (that is 

 to say, the change of direction which takes place twice in each 

 revolution) to decide whether an effective induction can result 

 from this. The subject has already been discussed by Max- 

 well* and by Joubertfj and I can assent to the principle 

 applied by these authors in their explanations, if not to the 

 special execution of the calculations. 



* Phil. Mag. 4th series, vol. xxxiii. p. 474 (1867). 

 t Comptes Rendus, vol. xcvi. p. 641 (1883). 



