326 BELL SYSTEM TECHNICAL JOURNAL 



posed fields to have no measurable effect upon the form of the loops for 

 the specimens he investigated. Based upon these results, the branches 

 of simple loops can be taken to be independent of their location in the 

 B-h plane, and in so far as the complex magnetizing force gives rise to 

 branches of simple loops, they have the same shape they would have 

 in such a loop centered at the origin. 



The formation of complex loops has been determined experimentally 

 by E. Madelung.^ He found that after reversing the magnetizing 

 force at any point along the branch of a hysteresis loop a new curve 

 is traced which, if continued, passes through the tip of the loop. A 

 second reversal before the tip is reached causes another new curve to 

 be traced back to the point of reversal on the original branch, which 

 is followed thenceforth as if the two reversals have not occurred. The 

 return to a reversal point makes all subsequent traces of the loop the 

 same as if no changes of magnetizing force intervened between the 

 two transits through that point. Any branch of the complex loop is 

 then, in accordance with Madelung's determinations, completely 

 specified by two points of reversal — the one from which it starts and 

 the one through which it must pass if continued far enough; after 

 passing the latter point it becomes the continuation of another branch 

 similarly specified by different points of reversal. 



The foregoing principles furnish sufficient information for deducing 

 the form of the branches of complex loops. If such a branch be 

 extended to one of the reversal points defining it and a trace then be 

 carried back to the other, the loop so formed will be retraced by 

 repeating the cycle. As these repetitions can be carried on indefinitely, 

 the path must comprise a simple loop, the branch of the complex loop 

 forming a portion of it. Every complex loop can therefore be con- 

 sidered as composed of adjoined sections of simple loops. Each 

 branch of the complex loop is representable on suitably transformed 

 axes by formula (1) with H taken as half the change in magnetizing 

 force between the reversal points which specify the branch. In 

 general, a different pair of axes will be required for each branch; they 

 can subsequently be referred to a common origin. 



The application of this analysis to the complex loop discloses the 

 requirement that the relation an = 2ao2 must be true if Madelung's 

 propositions are to hold, because the values of // differ for the two 

 branches of a subsidiary loop. If this equality is not satisfied, the 

 return to the original branch does not take place at the point of 

 departure. Madelung's observations do not include this possibility, 



« Annalen der Physik, Vol. 17, pp. 861-890, 1905. See also Ilandbtich der Physik, 

 Vol. 15, pp. 106-107, Berlin, 1927. 



