Theory of Dynamo-electrical Machines. 53 



The inversion of the current when one of the portions of the 

 conductors passes by a brush takes place as follows: — Up to a 

 certain time this division of the conductor belongs to one 

 half of the rotating coil. A short time then elapses, during 

 which both ends of that portion of the circuit are in contact 

 with the brush, and the portion of the conductor is thereby 

 momentarily closed. After the expiration of this time this 

 portion of the conductor belongs to the other half of the rota- 

 ting coil. From the circumstance that the division of the 

 conductor is closed, though for ever so short a time, it cannot 

 be assumed that it enters the second half of the rotating coil 

 with the same current which it had in the first half ; but it 

 must be remembered that one part of the change of current 

 takes place in the interval, and only the rest after its entrance 

 into the second half. 



Each of these two successive changes of current has, as a 

 consequence, a double induction — in the first place, the induc- 

 tion of the portion of the conductor in consideration, which 

 we will briefly call self-induction, and, secondly, the induction 

 upon the other portions of the rotating coil. 



We may first of all consider that part of the change of cur- 

 rent which takes place in the interval. The self-induction 

 which occurs in this time need not be taken into account; for 

 the portion of the conductor is closed in this interval, and 

 therefore does not belong to the entire circuit, for which we 

 have to determine the induced electromotive force. In regard 

 to the induction on the other portions of the rotating coil, it is 

 to be observed that these portions lie symmetrically on each 

 side of the portion of the conductor in question, so that on 

 each side equal electromotive forces are induced. But as the 

 positive direction is different in the halves on each side of the 

 rotating coil, the electromotive forces induced in them are of 

 opposite signs, and therefore neutralize each other as regards 

 the entire circuit. The change of current which takes place 

 in this interval produces no induction of electromotive force 

 effective for the whole circuit. 



We must now consider that portion of the change of cur- 

 rent which takes place after any portion of the conductor has 

 entered the second half of the rotating coil. 



The self-induction caused by this change of current must 

 be taken into account, for our portion of the conductor now 

 belongs to the entire circuit. And the induction on the other 

 portions of the rotating coil is now different from before. The 

 halves on each side formed of those portions are not quite like 

 each other ; for on the one side one portion of the conductor 

 is bounded by such a portion of the conductor as is just closed 



