... 1894.]STEINMETZONHYSTERESIS.593orE1.6V10tiy3103P=aNfwhere:a=8-<8St.6fl65or,substituLting.0033:a191.45l6'or,substitutinigV=S1l,whereI=length of mnagneticcircuit:L01._58VL1031914/28r16S6A1.6-S6165.6n1.6and58E16L103191A4El6INAT65.6n16AT=5.6n1.6Asseen,thlehystereticlossisproportionalto the 1.6thpower of the E.M.F.,inverseproportionalto the 1.6thpower of the number of turnls,and,inverseproportionalto the .6thpower of frequency,and of cross-section.Ifo=equivalentconductance, the energycoinponent of cur-rentisC'=Ep,and the energyconsumedinconductancepis:P=CE='p.Since,however,E:1.6p=CCF1-6itis:p16aE2pN,6or,a58VL103L11.P-51t4sEAr6Zn64191.4Elj17.]94A'21.6S.6n1.6EF4j1.65.6n1.6Thatis:"TCheewivvalentconductctnceduetomagnetichysteresis,ispro-portionalto the coejfieient of hysteresis,i,andto the tengtht of the ?maqneticctrcut,I,andinverseproportionalto the .4thpower of the E.3.F-E,to the .6thpower of the frequency,-Y,andopf the cross-seetion of the magneticcirauit,5,andto the 1.6thpower of the number of turns,n."Hence, the equivalenthystereticconductanceincreaseswithde-creasingE.M.F.,anddecreaseswithincreasingE.M.F.;itvaries,however,muchslowerthan the E.M.F.,SOthat,if the hystereticconductancerepresentsonlyapart of the totalenergyconsumnp-ÆTHERFORCE ... 602STEINMETZONHYSTERESIS[May18,x-frequiency,r=electricconductivity of iron.,C=coefficient of eddy-currents. The loss of energypercm.3inergspercycle,isA=tyN1VB2,hence, the totalloss of powerbyeddy-currentsis:w=VrVN2B210-watts,and the equivalentconductanceduetoeddy-currents:o_VF10I.507I_--O_O-B22278,n2$X2where:I-length of magneticcircuit,Sesection of magneticcircuit,Annumber of turns of electriccircuit. The coefficienit of eddycurrents,a,dependsmerelyupontheAshape of the constituentparts of the magneticeireuit,thatis,whetherironplatesorwire,andthiekness of, platesordiameter of wire,etc. The twomostimportanitcasesare:(a),laminiatediron,(b)ironwire.a.LaminatedIron.Let,inFig.14,d=thickness of the ironplates,B=maximum.magneticinduction,N=frequieney,=electricconductivity of the iron.Then,ifxis the distance of azone,d?,frorn. the center of the sheet, the conductance of azone of thickness,dx,anidonecm.lengthandwidthis,dx;and the magneticfluxecutby-thiszoneis,Bx.Hence, the E.M.F.iniducedinthiszoneis:8E=7-2NWBx(c.G.S.)UDitS.ThisE.M.F.produces the current:dC=aE;,dx4/2N7AfBrxdx(C.G.S.)Units,if the thickness of the plateisnegligiblecomparedwith the length,sothat the currentcanbeassumedasflowinigparallelto the sheet,in the onedirectionat the one,in the otherdirectionat the otherside.ÆTHERFORCE ... 602STEINMETZONHYSTERESIS[May18,x-frequiency,r=electricconductivity of iron.,C=coefficient of eddy-currents. The loss of energypercm.3inergspercycle,isA=tyN1VB2,hence, the totalloss of powerbyeddy-currentsis:w=VrVN2B210-watts,and the equivalentconductanceduetoeddy-currents:o_VF10I.507I_--O_O-B22278,n2$X2where:I-length of magneticcircuit,Sesection of magneticcircuit,Annumber of turns of electriccircuit. The coefficienit of eddycurrents,a,dependsmerelyupontheAshape of the constituentparts of the magneticeireuit,thatis,whetherironplatesorwire,andthiekness of, platesordiameter of wire,etc. The twomostimportanitcasesare:(a),laminiatediron,(b)ironwire.a.LaminatedIron.Let,inFig.14,d=thickness of the ironplates,B=maximum.magneticinduction,N=frequieney,=electricconductivity of the iron.Then,ifxis the distance of azone,d?,frorn. the center of the sheet, the conductance of azone of thickness,dx,anidonecm.lengthandwidthis,dx;and the magneticfluxecutby-thiszoneis,Bx.Hence, the E.M.F.iniducedinthiszoneis:8E=7-2NWBx(c.G.S.)UDitS.ThisE.M.F.produces the current:dC=aE;,dx4/2N7AfBrxdx(C.G.S.)Units,if the thickness of the plateisnegligiblecomparedwith the length,sothat the currentcanbeassumedasflowinigparallelto the sheet,in the onedirectionat the one,in the otherdirectionat the otherside.ÆTHERFORCE...