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XV. On the Theory of Dynamo-electrical Machines. 

 By R. Clausius. 



[Concluded from p. 59.] 



§ 8. Work of 'the Ponder vmotive and Electromotive Force for the 

 Case in which the Iron Core of the Rotating Coil is at rest. 



AFTER having expressed the magnetic moments, we may 

 determine the work done by the ponderomotive force 

 when the machine is in action. 



We will make an assumption, which is not indeed realized 

 in the machines of ordinary construction, but the results of 

 which may be readily transferred to these machines, and which 

 facilitates the investigation. We will assume that the iron 

 core of the rotating coil does not share the rotation of the 

 latter, but is fixed, and that therewith the rotating coil rotates 

 alone, in which it is subject to a double force, the force of the 

 magnet acting from without, and the force of the magnetic 

 iron core acting inwards^. 



The ponderomotive force which the fixed electromagnet 

 exerts on the rotating coil, is proportional, on the one hand, 

 to the magnetic moment M of the fixed electromagnet, and, 

 on the other hand, it must be proportional to the magnetic 

 moment of the current in the coil, and therewith be propor- 

 tional to the above-mentioned magnitude N. We can there- 

 fore represent the work done by this force in unit time, which, 

 moreover, is proportional to the number of turns v, by the pro- 

 duct of the value MNv into a constant factor. But in the direc- 

 tion of that rotation which we must impart to the machine in 

 order to produce a current, and which we will assume to be 

 the positive direction of rotation, the work of the pondero- 

 motive force is negative; for it acts in opposition to such a 

 motion, and must be overcome by an extraneous force. It is 

 therefore convenient to express this by affixing the minus sign 

 to the constant factor, and it may accordingly be denoted by 

 —A. The expression which thus determines this work is then 



-IM^v. 



The other ponderomotive force which the rotating coil expe- 

 riences from the magnetic iron core in it is, like the former, 

 proportional to the magnitude N. It depends, moreover, on 



* Strictly speaking, two forces must be distinguished in reference to 

 the fixed electromagnet — that is to say, first, the force exerted by the 

 magnetic iron mass of the fixed electromagnet, and, second, the force 

 directly exerted by the current which traverses the coil of the fixed elec- 

 tromagnet. But since in the dynamo' machines at present constructed 

 the latter force is very small in comparison with the first, we will neglect 

 this difference, and only consider the total force of the fixed electromagnet. 



