330 BELL SYSTEM TECHNICAL JOURNAL 



frequency component must have one of its maxima very near each 

 maximum of the lower one so that a maximum value practically equal 

 to the sum of the amplitudes of the two components is reached every 

 cycle of the lower one; likewise for the minima. Between these two 

 extremes other reversals in the magnetizing force would be expected 

 to cause the hysteresis loop to comprise additional small loops not 

 necessarily closed. Experiments confirm this conjecture and indicate 

 that not only for weak fields but even for fields near saturation the 

 small loops nearly close and the paths between them are traced nearly 

 the same as portions of a large loop. 



If the amplitude of the higher frequency component is considerably 

 the larger, all the loops composing the characteristic are virtually the 

 same size and shifted slightly with respect to each other on account 

 of the lower frequency component. The characteristic will be that 

 depicted in Fig. \c. 



When the amplitudes of the two components are not grossly unequal, 

 the hysteresis loop is of the type represented by Fig. \d. Small loops 

 formed when the magnetizing force is near an extreme value are 

 longer than those formed when it is near zero, aside from any elTects 

 of superposition, because of its different rates of change in the two 

 positions. In general these loops will not occur in the same place for 

 different cycles and the distances between them will be lessened by 

 increasing the higher frequency. By considering the complex loop 

 to consist of a major loop, such as a single frequency would generate, 

 encompassing a number of minor loops, the induction may be derived 

 from the magnetizing force since the form of the minor loops is known. 

 When these are not too widely spaced, each may be assigned a mean 

 position in a loop fixed for all time and the induction calculated there- 

 from. It is evident that such an undertaking is vastly more com- 

 plicated than the ones suggested heretofore and that unlike them it 

 requires information in addition to that obtained from single-frequency 

 measurements performed with no superposed field. 



By decreasing the amplitude of the higher frequency component of 

 the magnetizing force, the amplitudes of the minor loops may be 

 reduced until those in the neighborhood of zero magnetizing force 

 vanish entirely. Further decrease of the same component causes more 

 and more of the minor loops to disappear, so that finally only a few 

 small ones remain at eeich end of the major loop. This condition is 

 shown in Fig. \e. As the wave form of the induction is only slightly 

 affected by the presence of these loops, they may safely be omitted 

 and the characteristic simply taken as the major loop, determined from 

 single-frequency results alone. 



