56 Prof. R. Clausius on the 



traversed in each of the halves by the current — , then, assu- 

 ming that the system does not change its position, and that all 

 current-strengths are constant, the work of this ponderomo- 

 tive force in the time dt is expressed by 



idW' + 



From this we get for the time of half a rotation the work 



|(W"-W); 



rr 



and as the duration of half a rotation is equal to ~, we have for 

 the work referred to the unit of time the expression 



£(W"-w);j 



or, what is the same thing, 



i(W"-W f )v. 



Since there are n such portions of the conductor, the work 

 T for unit time of the whole ponderomotive force of the rota- 

 ting coil is defined by the equation 



T=w(W"-W)m> (10) 



If this work is compared with the work of the electromotive 

 force expressed in (9), we see that it only differs from that by 

 the sign, and by the expression — pi 2 v, which represents the 

 work of that electromotive force which is induced in the rota- 

 ting coil by the current itself on it. We can thus write, 



Ei= — T— pv*v (11) 



§ 7. Determination of the Magnetism in the Electromagnets 

 in Dynamo-electrical Machines. 



In order to give the results hitherto obtained in a form 

 more suited for further calculations, we must obtain an ex- 

 pression for the strength of the electromagnets in dynamo- 

 electrical machines. 



First of all we have to deal with the fixed electromagnet. 

 Its magnetic moment, on which depends the force which it 

 exerts in the space between its poles, is not proportional to the 

 strength of the current which traverses its coil, but follows 

 another law. For a small strength it increases approximately 

 in the ratio of the current-strength ; but as the strength of the 

 current increases it increases also, but more slowly, and with 



