ESTIMATION AND CONTROL OF Ol'KllATE TIME OF RELAYS 115 



the flux incromciil ])i-o(Iu('(m1 by each shell is ,<ii\-eii l)y: 



f/(Z) = Itt/V (Ir ,—— . 



Oil subs! il III iiiji; Ihe pi'ecethiij;' expression for the current (leiisit\' /, 

 and evahiatini;- the int(>^ral / (l>p, the total flux ipE prochiccd by the 

 eddy currents is found to he: 



t dip 



This is identical in form with the expression for one of the linkiii,<>; 

 circuits assumed in derivino; equation (2), with (JV^ equal to ;Ta- , and 

 AttGe given by (/ (2p). Thus to the extent that the assumption of a uni- 

 form flux distribution is \alid, Ge is given by: 



This expression applies to a round core. A parallel approximation may 

 be obtained for a reet angular rod by considering it as made up of rec- 

 tangular shells of differential thickness, having their sides in the same 

 ratio as the rod. By treating the perimeter of each shell as corresponding 

 to the circumference of the circular shell in the cylinder case, with the 

 area enclosed corresponding to that enclosed by the circular shell, the 

 following expression is obtained for the conductance of a rectangular 

 rod whose sides are in the ratio Ir. 



This shows that the effect of using a rectangular section is equivalent 

 to increasing the resistivity of the material. A similar effect is obtained 

 by subdividing the core section, as in laminated construction. If the 

 core, for example, were made of two similar round rods, equation (6) 

 would apply to each, and the effective mmf acting on both would be the 

 vahie of (pKpj? given by this expression, with tp in d^p'dt eciual to half the 

 total flux, so that the resulting expression for Ge would be half that gi\-en 

 by (6). This argument can be generalized to show that, aside from the 

 effect of changes in .section sha])e, the etTect of subdivision is to reduce 

 Ge in proportion to the iiuinbcr of siil)di\-isions. 



The approximate \-alidity of these expressions for Ge rests on the 

 as.sumption that the eddy current magnetomotive force is minor com- 



