124 Prof. B. Clausius on the 



are higher than the first order, we get 



P/= P (cos <£— €v sin <£), 



P 2 / = P (sin <f> + €v cos <£) ; 



and if in this we also put for the products P cos <f> and P sin (/>, 

 their values given in equations (16), we get 



In that direction of working of the machine in which it 

 furnishes an electrical current when mechanical force is ap- 

 plied, the members affected by the factor e have, as a conse- 

 quence, an increase of work and diminution of the current ; 

 and in that direction in which it furnishes mechanical work 

 by the application of an electrical current, those members 

 have as a consequence an increase of the current and a dimi- 

 nution of the work. Hence under all circumstances the 

 magnetic inertia of the rotating iron core has a deleterious 

 influence on the duty of the machine. By altering the posi- 

 tion of the brushes, with a more rapid rotation, this influence 

 may be somewhat lessened, but it cannot be altogether elimi- 

 nated. 



Besides this action, which depends on the magnetic inertia 

 of the iron, another action may take place in the rotating iron 

 core which is also detrimental to the working of the machine 

 — that is to say, the induction of electrical currents in the iron 

 core itself. Such currents are now often called Foucault's 

 currents, for Foucault made an experiment which demon- 

 strated their existence in a most striking manner ; it must, 

 however, be mentioned that these currents had been known 

 long before Foucault's experiment, and had also been cor- 

 rectly interpreted*. 



If the iron core rotates under the influence of the fixed elec- 

 tromagnet, electromotive forces will be induced in it as in any 

 conductor which is in a state of motion relatively to a magnet. 



As the rotating iron core is also under the influence of the 

 current in its coil, the question further arises whether an 

 inductive action is exerted upon it also by this. The conduc- 

 tor of this current rotates in common with the iron core, and 



* In connexion with this I will mention that the rotating motion which 

 a magnetic needle acquires over a rotating metal disk, and the damping 

 action which a copper envelope exerts on the vibrations of a magnetic 

 needle, depend on the same currents ; and both these phenomena were 

 known at that time, and there was no doubt as to their cause. 



