Theory of Dynamo-electrical Machines. 125 



is, relatively to it, at rest, and induction can therefore only be 

 due to alterations in the current itself. Such changes do as a 

 matter of fact occur in certain positions, particularly in those 

 portions of the conductor which pass by the brushes, where 

 the direction of the current is reversed, and these continually 

 repeated inversions of the current must necessarily have an 

 inductive action on the core. 



But it can be easily shown, from considerations like those 

 in § 9, that the electromotive forces induced in the rotating 

 iron core, in the case in which the coil shares in the rotation 

 while at the same time those changes of direction occur in it, 

 must be the same as in the case in which the coil does not take 

 part in the rotation but when also changes of current do not take 

 place. In order to determine the induction, we may suppose 

 that the rotating core is under the simultaneous influence of 

 the fixed electromagnet and of an invariable current in the 

 fixed conductor. We thereby arrive at the result that the forces 

 which act inductively upon it are the same as those which act 

 magnetically upon it ; and we know with regard to the latter 

 that they have a resultant whose magnitude, apart from a 

 constant factor, may be represented by \/M 2 + N 2 , and whose 

 direction is given by the angle <j> defined in equation (15). 



By the electromotive forces induced in the iron core closed 

 currents may be formed which circulate in the iron core itself. 

 The formation of these currents may, however, be completely 

 hindered if the iron core is suitably split up into parts in such* 

 a manner that the electricity cannot circulate among them, 

 which in Gramme's machine is obtained by using a ring made 

 up of iron wire instead of a massive iron one. 



In the cases in which these currents occur to any appreciable 

 extent their action is a twofold one. In the first case these 

 currents have themselves a magnetic moment, which must be 

 taken into account like other magnetic moments ; and in the 

 second place they exert a magnetizing action upon iron, and 

 thereby alter the existing magnetism of the iron core. 



The strength of the currents induced in the iron core, and 

 thus also the magnitude of their magnetic moment, is propor- 

 tional on the one hand to the inducing force and therefore to 

 the magnitude \/M 2 + N 2 , and on the other hand to the velo- 

 city of rotation v. This moment can therefore be expressed 

 by the product 



in which tj is a small constant. In determining the moment 

 of the magnetism produced by these currents in the iron, it 

 must be remembered that the iron in which these currents 



