358 BELL SYSTEM TECHNICAL JOURNAL 



of 550 cycles per second, and / 475 cycles per second. Measured and 

 calculated values are plotted for comparison, with regions of appli- 

 cability of the special subcases indicated. Portions of calculated curves 

 falling in regions ^ or C were computed by the two sets of formulae for 

 subcases la and Ir, portions in the middle of region B by the formulae 

 for subcase lb. The trend of the quantities measured is accurately 

 portrayed by the calculations and agreement of the values is good. 



All the curves commence at those values of resistance or inductance 

 which would obtain in a single-frequency case with a current having 

 the magnitude of the one here superposed in fixed amount. Upon 

 increasing the variable current the measured quantities show an 

 increase as it begins to preponderate, and eventually they approach 

 asymptotically the values they would have if it flowed alone. 



The measurements were made by L. R. Wrathall using a Maxwell 

 inductance bridge with two imputs and a tuned detector. Eddy 

 currents being of no consequence at the low frequencies employed, the 

 chief sources of possible error are calibrations of the standards used 

 and variation in the temperature of the coil during taking of the data. 

 Changes in winding resistance caused by the latter are of the same 

 order of magnitude as the changes in hysteretic resistance being 

 observed. Precautions against both possibilities were taken. 



Conclusion 



The multiplicity of forms of complex hysteresis loops makes their 

 analysis in general a complicated and difficult matter if indeed possible 

 at all. Extensive experiments with two frequencies must be completed 

 and the results classified according to the types of loops before an 

 acceptable method of taking their form into account can be formulated. 

 The parameters k and k seem to be effective quantities for denoting 

 concisely a particular form of loop in many instances. 



A way of representing the behavior of complex loops more exactly 

 than do Madelung's propositions is needed, and might be the fruit of 

 precise experiments designed to clear up also the early closure and 

 lack of closure which Lehde apparently found in minor loops. The 

 tracing of complex loops is not simply cyclic, and only when a nearly 

 complete magnetic cycle is executed between successive maxima in 

 the magnetizing force can conditions approaching a cyclic state be 

 expected to exist. Some experimental evidence of performance in 

 other conditions is a present need which can perhaps be met by a 

 thorough investigation of spiral characteristics. These seem to have 

 been ignored entirely in the past, the literature dealing with sub- 



