88 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



lar, when (Ra is a constant, the reluctance (Rp , or '^e/^a , represented by 

 the series parallel path of (Pa in Fig. 6(a), may be represented by the 

 simple parallel path of ipA in Fig. 6(b). By analogy with equations (7) 

 the constants applying are related by: 



(7A) 



where 



The circuit of Fig. 6(b) is identical with that of Fig. 5 with 1/(Rl2 equal 

 to the sum of 1/(Rlc and 1/(Rlp ■ Thus the circuit of Fig. 6(a) may be 

 reduced to that of Fig. 5 when (R^ is constant. The resulting circuit may 

 be reduced in turn to the equivalent circuit of Fig. 4 when (Re is constant. 

 Thus the equivalent circuit may be used to represent all cases in the low 

 density region, where the component reluctances are independent of tp, 

 provided the gap reluctance varies linearly with x. 



3 ANALYSIS OF MAGNETIZATION MEASUREMENTS 



In analysing the observed magnetization relations, it is convenient to 

 treat the low density and high density relations in separate and successive 

 steps. For the former, the analysis is based on the equivalent magnetic 

 circuit of Fig. 4. 



EVALUATION OF EQUIVALENT MAGNETIC CIRCUIT CONSTANTS 



For a given value of x, the total reluctance in the low density region is 

 taken as constant at the minimum value (R' (x) observed in measurements 

 made from the demagnetized condition. If the observations are plotted 

 as reluctance curves, as in Fig. 3, these values of (R' (x) may be read di- 

 rectly. When the recording fluxmeter is used, (R' (x) can be obtained 

 from the (p versus fF curve as the slope J7/v? of the line through the origin 

 tangent to the curve. The reciprocals P(x) of the values of (R' (x) thus 

 evaluated may be plotted against x. Values of P(x) corresponding to the 

 minimum reluctance values of Fig. 3 are plotted in this way in Fig. 7. 

 The origin of x is taken as for a gap of 0.025 cm., corresponding to the 

 operated position of the actuating card for maximum stop pin height. 



