320 BELL SYSTEM TECHNICAL JOURNAL 



through the origin along the line of slope a (or /xo). For this reason, 

 the sensibly-linear part of the initial curve is often called the "re- 

 versible part." When it passes over into the perceptibly-upward- 

 turning part, the hysteresis-loop becomes perceptible. Over a certain 

 range its area varies as the cube of H^, and Weiss gives this formula, 

 in which the coefificient h is used with the same meaning as heretofore: 



Area of hysteresis-loop = fHdl = f&i/o^ 



In the second segment of the initial curve, the loop swells out to 

 its fullest amplitude. This forms one of the reasons for the division 

 of that curve into three parts; the middle one is sometimes called 

 the "irreversible portion " of the curve. There is no formula available 

 in this region, except the oddly though not universally effective one 

 discovered by Steinmetz, in which the area of the loop is related not 

 to Ho but to the maximum value Bo attained in the cycle. This 

 "law of Steinmetz" reads * 



area of loop = r]Bo'^. 



Values of the constant -q are frequently quoted in describing magnetic 

 materials. 



When Ho is carried far into the third stage of the initial curve, 

 so that in each cycle / approaches within a few per cent of /max., 

 the hysteresis- curve assumes the form of a wide loop prolonged at its 

 northeast and southwest corners (I use the analogy of a map) by 

 long slender projections which narrow down into mere lines. So 

 long as / is nearly equal to /max., the point tracing the /-vs.-// curve 

 passes back and forth along nearly the same path. The final stage 

 of the initial curve is therefore also called "reversible." The 

 Steinmetz formula here becomes invalid. 



The reason for laying so much stress on the areas is well known. 

 When a piece of magnetizable metal is carried through a cycle of 

 magnetization, for instance by varying the current through an en- 

 circling solenoid in a cyclic manner, the battery supplying the cur- 

 rent is found to have expended an amount of energy SHdl per 

 unit volume; and the metal is found to be warmed to a degree indi- 

 cating that an equal amount of heat energy has appeared within it. 



* The formula of Steinmetz is more general; it applies to hysteresis-loops executed 

 between any two (not overly great) values of induction Bi and ^2, and for these 

 assumes the form 



area of loop = n \ ^ ) • 



It is clear that 5i and B^ must be given opposite signs if directed in opposite senses. 



