8-1 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY l'Jo4 



line, that marked ip in the figure. At vahies of (^ above this minimum, 

 the reluctance increases at an increasing rate, indicating an upper limit 

 to the value of ^p approached as Nl becomes verj^ large. The observed 

 \-alue of (/?' may be interpreted as that for which the core density cor- 

 responds to maximum permeability, while the indicated upper limit may 

 be interpreted as the saturation flux ip" . 



The observations plotted in Figs. 1 and 3 were obtained with the 

 sample initially demagnetized, a convenient reference condition for 

 measurement. In actual use, relays and other electromagnets have been 

 previously operated, and the applicable <p versus iP relation is that for 

 repeated magnetization. In this case there is little or no increase in re- 

 luctance below <p . For engineering purposes, the reluctance below ip may 

 be taken as constant at the value observed at ip in measurements made 

 from an initially demagnetized condition. This assumption is eciuivalent 

 to taking the ^p versus 3^ relation as linear up to the "knee" of the curve, 

 the point of tangency with a line through the origin. 



It follows that expressions for the magnetization relations ma}' take 

 (R as a function of x only, independent of (^, in the low density region, 

 (p < (p', while for (p > <p', modified expressions must be employed which 

 show (R increasing with (p, and approaching 3^/V". 



Magnetic Circuit Schematics 



The reluctance expressions for the magnetization relations can be con- 

 veniently defuied by the magnetic circuit schematics shown in Figs. 4, 

 5, and 6. In these the reluctance (R, or ^/(p, is represented by a network 

 of component reluctances, analogous to a network of electrical resist- 

 ances, with flux analogous to current, and magnetic potential analogous 

 to voltage. Thus the reluctance corresponding to Fig. 4 is given by: 



(R = — ^ ^ . (3) 



(Rl + (Ro + 2 



The interpretation of the parameters (Ro , cRz, , and A in terms of the 

 magnetic circuit concept is discussed in the companion article cited 

 above. ^ In the analysis of experimental results they are parameters 

 which summarize measurements in which the observed values of (R con- 

 form to (3). From this viewpoint Fig. 4 indicates only that the total flux 

 (p is the sum of a flux (Pl for which the reluctance is constant, and a flux 

 <Pg for which the reluctance varies directlj^ with x. 



