Theory of Dynamo-electrical Machines. 121 



the individual particles of iron, do nevertheless continually 

 change their position relatively to the poles. 



With slow rotation it may be assumed that the poles of the 

 iron core have the same position in space and the same strength 

 as in an iron core at rest. With more rapid rotation this is 

 no longer the case, but deviations result in respect of the 

 position and strength of the poles; these deviations, however, 

 we will neglect for the present, reserving their consideration 

 until later, when we shall also deal with another accessory 

 action which occurs with rapid rotation. We will for the 

 present assume that in the rotating iron core the poles have 

 the same position in space and the same strength as in an iron 

 core at rest. 



The induced electromotive force is due to the fact that the 

 windings of the rotating coil change their position relatively 

 to the poles, and accordingly, under the supposition we have 

 made as to the unchanged position in space, and strength of 

 the poles, it must also remain without change. Hence to 

 determine the work done by the electromotive force we may 

 apply the equations (18) and (20) above deduced for the case 

 of an iron core at rest, also for the case in which the iron core 

 rotates with the coil. 



But as regards the work done by the ponderomotive force, 

 the state of affairs is not quite so simple, for according as the 

 motion is different, different forces come into play in such a 

 manner as to produce mechanical work. The force which 

 the magnetic iron core exerts on the rotating coil through 

 which the current is passing, and which, when only the coil 

 moves, does the work we have previously determined ; this 

 force, when the iron core forms with the coil a rigidly con- 

 nected system, which can only move as a whole, is neutralized 

 by the equal but opposite force which the current in the coil 

 exerts upon the magnetic iron core. Another force, on the 

 contrary, that which is exerted by the stationary electromagnet 

 on that magnetic core, and which could do no work when the 

 iron core was fixed, will act so as to do work when the iron 

 core rotates. The question therefore is to compare the mag- 

 nitude of this work with that which we have previously 

 determined. 



This results from a simple consideration. For this purpose 

 we will temporarily assume that only the iron core rotates, 

 while the position of the coil as well as of the fixed electro- 

 magnet is not changed. If now the iron core is magnetized 

 by the combined action of the fixed electromagnet and of the 

 current in the coil, it is subject to moving forces from these 

 two, but does not move, as follows from the fact that it has the 



