92 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



ip and 3^c , giving the corresponding values of core reluctance (Re = 5^c/<p- 

 Such values of JFc have been determined for two values of x (the smallest 

 and largest included in these figures), and are shown plotted against 

 3^o/(-47r) in the dashed curves included in Fig. 3. A^alues of (Re for inter- 

 mediate values of x are intermediate between these two curves, Avhose 

 similarity supports the assumption of Fig. 5 and equation (4) that (Re 

 is substantially independent of x. 



For ^ > <p' the plot of O^c versus Jc is substantially linear. In this it 

 conforms to (6) which, by substitution of JFc/(Rc for ^, may be written 

 in the form: 



(Rc = (R^' + ^ = (l-4VRc+^t (10) 



ip \ ip / ip 



Thus ip" may be evaluated from the slope of the plot of (Re versus 

 '5c , and (Re from the intercept of the dotted line extension, as indicated 

 in Fig. 3. The observed relation deviates from (10) in the vicinity of 

 (p', and the linear relation conforming to (10) does not intersect (Re at 

 ip', but at some higher value of (p. Thus (6) more nearly represents the 

 observed relation if ip' is taken as this higher value, rather than at the 

 flux for minimum (R previously taken as (p' and marked at such in Fig. 

 3. The error in using this latter value of tp' in (6), however, is minor, and 

 of little significance in engineering estimates. 



Alternative Method of Determining Core Reluctance Constants 



When magnetomotive force measurements are not made, the core 

 reluctance constants can be determined directly from the magnetization 

 curves as follows: 



As can be seen in Fig. 3, the line representing <p" can be directly identi- 

 fied as the apparent a.symptote of the reluctance curves: specifically by 

 determining the flux line parallel to the tangent to the upper portion of 

 the lowest reluctance curve. As (p' is the value of <p at which the reluctance 

 curves have their common minima, tp' and (p" can be readily evaluated, 

 and only (Re remains to be determined. 



On sul:)stituting 5/(R for tp in (6), and substituting this expression for 

 (Re in (4) the resulting equation can be solved to give: 



(R = i ((^K + («c + ^ + j/(^(R.. + (Re - ^Y + 4(Rc' % 

 Let 6{" be the particular value of (R for which 

 J? = (RV" = ((ftc + (^e)(p"- 



