54 Prof. R. Clausius on the 





by the brushy and therefore does not belong to the whole cir- 

 cuit, while on the other side it is bounded by a portion of the 

 conductor which does so belong. Hence in this case the elec- 

 tromotive forces induced on each side do not neutralize each 

 other completely, but there is an excess of the electromotive 

 force induced on the last-named side which, like the electro- 

 motive force resulting from self-induction, is opposed to the 

 direction of the current. 



To determine this excess we must form the electrodynamic 

 potential of the portion in question on a branch circuit, con- 

 sidering the former to be traversed by the actual current and 

 the latter by the unit of current ; and to determine the elec- 

 tromotive force arising from self-induction, we must form the 

 electrodynamic potential of the portion in question on itself, 

 in considering it as traversed once by the actual current and 

 once by the unit of current. From the change in the poten- 

 tial, occasioned by this change in the strength of the current, 

 we get the induced electromotive force. In doing this we 

 must not take into account the whole change of current, but 

 only that portion of the change of current which takes place 

 after our portion of the current has entered the second half of 

 the rotating coil. It cannot be stated in general how great 

 the portion is, for this depends on the construction of the 

 machine and on the position of the brushes. We shall there- 

 fore content ourselves with giving an expression which con- 

 tains an undefined factor, and adding an explanatory remark. 



In any case the electromotive force, which may be called 

 E 2 , due to the inducing action of the moving conductor on 

 itself, is proportional to the current-strength, which in the 

 two halves is together equal to i. It must, moreover, be pro 

 portional to the number of turns v, for on this the number of 

 changes of direction depends. Hence, remarking at the same 

 time that the electromotive force is negative, we may put 



E,= -pw, (7) 



in which p is that undefined factor. 



This factor has a remarkable property by which a charac- 

 teristic difference arises between the magnitude E 2 and the 

 magnitude E 1? previously determined. We will imagine that 

 the number, n, of portions into which the rotating coil is 

 divided is changed, by which of course the length of the indi- 

 vidual portions is changed also, and indeed in the inverse 

 ratio, and we will ask ourselves the question, what influence 

 this has on the magnitudes E x and E 2 . 



In determining E, we are dealing with the potential of the 

 fixed current, and of the magnet, on a portion of the rotating 



