398 



BELL SYSTEM TECHNICAL JOURNAL 



Fit of Demagnetization Curve by Hyperbola 

 It will be noted that the points on the demagnetization curves for 

 which the product {BII) is a maximum are given quite accurately 

 in each case by the intersection of the demagnetization curve with a 

 line through the origin having the slope Br/Hc. That this should be so 

 follows from the fact that any demagnetization curve for magnet steel 

 may be closely approximated by a rectangular hyperbola whose equa- 

 tion IS B = a — kJ(II -f b) in which a, b, and k are parameters of each 

 particular curve. It is a mathematical property of the foregoing 

 rectangular hyperbola that the coordinates whose product is a maxi- 

 mum are located by a line through the origin having a slope equal to 

 the ratio of the intercepts of the hyperbola. This property of the 



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Fig. 12 — -Curves showing approximation of actual demagnetization curves by points 

 on the general hyperbola, B = a — kl{II + b). 



hyperbola is a property of the demagnetization curves for magnet steel 

 in so far as these curves can be closely fitted by appropriate hyperbolas. 

 That the fit is quite good in all cases is shown by Fig. 12 in which 

 hyperbolas calculated for each demagnetization curve are shown by 

 dots and the observed points by a full line. The graphical method 

 of Fig. 10 for determining the point on each demagnetization curve the 

 product of whose coordinates is a maximum is more accurate than 

 the method of plotting the curve of (BH) vs. B, because the latter 

 curve is usually quite flat-topped and its maximum is hard to locate 

 exactly. The fact that the curve is flat-topped explains why many 

 methods of magnet design give good results. It is because about 

 equal efficiencies are obtained in any case over a fairly wide range of 



values of Brem- 



