182 On the Energy of Magnetized Iron. 



cycle is much greater in the case of AEC, corresponding to 

 the ellipsoid of moderate elongation. 



The coefficient N reaches its maximum when the ellipsoid 

 is very oblate. In this case 



^73=^3 + 2tt3 3 ; 



which is applicable to large plates magnetized perpendicularly 

 to their surfaces. This is the form to which the iron must be 

 reduced in order that a given magnetization of a given volume 

 may store* the largest amount of energy. In this case the 

 energy is nearly all recoverable; but we must remember that 

 no practicable field would carry the magnetization very far. 



In the theory of alternating currents the neighbourhood of 

 of iron is often treated as if its only effect were to increase 

 the self and mutual induction of the circuits. A writer con- 

 versant with experiment usually guards himself by a reference 

 to the currents induced in the iron considered as a conductor. 

 The latter effect may be in great measure eliminated by a 

 proper subdivision of the iron, with intervening non-conduct- 

 ing strata; but a glance at fig. 2 shows at once that, apart 

 altogether from internal currents, the influence of the iron is 

 of a more complicated character. If the curve connecting 3 

 (or 23) and § were a straight line, the same on the upward as 

 on the downward course, then the presence of iron would 

 simply increase the self-induction. When the iron constitutes 

 a closed magnetic circuit, this is very far from being true. 

 Indeed it would be nearer the mark to say that the iron in- 

 creases the apparent resistance of the electric circuit, leaving 

 the self-induction unchanged. In so far as the curve of fig. 2 

 can be identified with an ellipse, the reaction of the iron can 

 be represented as equivalent to a change in the apparent re- 

 sistance and self-induction of the circuit. Which of the two 

 is the more important depends somewhat upon the other cir- 

 cumstances of the case ; but with closed electromagnets the 

 magnetic work dissipated during the period (corresponding to 

 increased resistance) is always greater than \he work spent 

 during one part and recovered during the remainder of the 

 period (corresponding to increased self-induction). On this 

 account, the resistance of an iron wire to variable currents is 

 greater than to steady currents, even though the current be 

 constrained to be uniformly distributed over the section. In 

 the absence of such constraint, the resistance undergoes a 

 further increase in consequence of the tendency of the cur- 



* It is not meant here to imply that the energy is resident in the iron. 



