SLOW KKLKASl'; KKLW DKSKIX 203 



required to operate this load is minimized. Thus maximum release time 

 is attained by providing maximum ampere turn sensitivity. 



.V general expression for the relation between F and fF may be ob- 

 tained }\\' substituting in (13) the expression for (JFc + 9^)/^ given b}^ 

 (10). A much simpler relation is gi\-en by the linear approximation to 

 the decreasing magnetization cur\'e in which (fFc + ^)/<p is taken as 

 e(iual to(R,-. This approximation has the same slope at (pa as the curve 

 given by (3) or (10). The release pull usually corresponds to values of ^ 

 much nearer ^o than ^p" , and the approximation is satisfactory in this 

 range if <^o/V" is small. Writing {^c + 5)/CR, for ^ in (13), there is obtained 

 the equation : 



„ 27r(iV/ + {ND cY d(Ra ,_, 



^ = ^ "^ ' ^^^'^ 



in which {NI)c is written for Jc/(-i7r). This approximation is used for 

 convenience and simplicity. The general expression, which is required 

 for higher values of 5, is obtained by substituting the right hand side of 

 (10) for (Ri in (16) and in the expressions derived from it. 



By comparison with (12), (R, may be taken as ec^ual to the gap and 

 joint reluctance o^g plus a modified and minor term for the iron reluc- 

 tance. For the present purpose, it is convenient to take (Sii as the sum of 

 the main gap reluctance (Rg , which varies with x, and (R^ , which includes 

 the iron reluctance and the constant reluctances of the heel gap and of 

 any joints in the magnetic structure. For a plane pole face, (Rg is given 

 b}^ x/A, where .4 is the effective pole face area, and (16) reduces to the 

 equation: 



^ 2iriNI + (ND cY 



^ ^ — 7 X 



A (^(R. -f J 



As shown in one of the companion articles, the pull F at travel x for 

 a given value of N^I is a maximum when the gap reluctance x/A is eciual 

 to the reluctance (Sip external to the gap. A similar relation applies for a 

 domed pole face gap, as can be shown from the expressions given above. 

 Taking the linear approximation to apply, (^c + ^)/((Rf + (R«) may 

 be substituted for ip in (15). Writing x/(R^ for .1 in the i-esulting e(iua- 

 tion, this may be written in the form: 



^ ^ 27r(A^/ + (NI)cY ^ 

 Xdip 



