Theory of Dynamo-electrical Machines. 51 



rotating coil, we can easily get the corresponding expression 

 for the entire rotating coil, if we multiply by the total number 

 of such portions. In defining this number, it is to be observed 

 that the electromotive forces induced in the two halves of the 

 rotating coil must not be added, but only counted as single; 

 for the two halves are not in series in the whole circuit, but 

 form two branch circuits at rest. If therefore the total num- 

 ber of portions of the rotating coil is n y the average electromo- 



ft 

 tive force of one portion needs only to be multiplied by - to 



obtain the electromotive force of the entire rotating coil. If 

 we denote the latter by E 1; we get 



E^-CW'-W") (4) 



We shall introduce into this, instead of the time of rotation 

 t, the number of turns in unit time, which we are accustomed 

 briefly to call the number of turns. If this is called v, then 



•-=? '• (5) 



and (4) passes thereby into 



Ex^W-W")* (6) 



§ 4. Reaction of the Moving Conductor on the Stationary one. 



In the previous paragraphs we only dealt with the electro- 

 motive force which the current in the fixed conductor and the 

 magnetism of the masses of iron induces in the moving con- 

 ductor. The question now arises whether the current in the 

 moving conductor also induces an electromotive force in the 

 stationary conductor. 



We shall again select for consideration a separate portion of 

 the moving conductor (that is, of the rotating coil), which, as 

 above, shall be designated by a. Let the current traversing 

 it be denoted by j ; in reference to which it is to be observed 

 that, during each rotation of cr, it changes its direction twice. 

 Let us suppose the stationary conductor to be traversed by 

 unit current, and form under these circumstances the electro- 

 dynamic potential of a upon s, which we will call XI, and 

 which is represented by an expression of the same form as 

 that given in (1 ) ; that is to say, 



Q= CCj cos {** 



- ds da. 



With the help of this magnitude we may define the electro- 



E2 



