steinmetz cp on the law of hysteresis part 2

... I2[F2-47] 24 .683.185.06I24(3)(4)LdLrILdLr+6 .25 6 .23 6.I36.I86.oo6.II5.866. 02 5.7I5.895.575-735- 42 5-565 -27 5.305. 12 +4-95[F2=+ 28 .1i.96.06i88[Fi= 28 ]-4-575.0I4.685 .22 4.845-375.005.505-I95.6o5.365-705. 52 5.8o5.675.865.8o-5.90.665.06178(5)-LdLr+6 .25 6 .23 6.136.i86.oo6.1I5.876. 02 5- 72 5.895.9595.6I5-45+5 .25 [F2=+47.]1 .29 .50.06I97TABLEXXIII. HYSTERESIS OF TOOL-STEELOh..(I) (2) (3)FLdLrLdLrLdLr +26 0± 23 .25 +I3 .25 +I3 .25 &apos ;24 0I3 .22 I3 .29 13 .22 I3.19I3 .22 13.2I 22 0I3.1913,1013.1913.1013.1913.I7 20 013.15I3.0013.1513.0I13.1513. 12 i8o13.10 12. 88I3.10 12. 9013.I013.06I6013.05 12. 77I3.05 22 .8013.05I2.99I40I2.99 12. 66I3.00 12. 70I3.00I2. 92 120 I2.85 22 .40I2.87 12. 46 12. 88 12. 76I00i2.66 22 .03 12. 68I2 .22 I2.69 22 .508oI2. 42 II.50 22 .45ii. 62 I2.47 12. 156oII.95I0.30 12. 00 20 .50 12. 02 iI.6540II.007.00II .20 8.6oII .22 II.04+ 20 9.40-I.709.804.60+io.6oo+6.707 .20 -.30LF2=+30.1- 20 I.80-I.90-30+ 2 24H=i06 .20 44-78 2. 75L=I3 .25 7-7451. 325 ]=o695. 026 83. 027 78(6)LdL,[Fi=-47-]-4-935- 32 5.o85- 52 5 .23 5.635.385-735-535. 82 5.675.875. 82 -5.90 2. 22 *485.06Io318 92. ]649ÆTHERFORCE ... I2[F2-47] 24 .683.185.06I24(3)(4)LdLrILdLr+6 .25 6 .23 6.I36.I86.oo6.II5.866. 02 5.7I5.895.575-735- 42 5-565 -27 5.305. 12 +4-95[F2=+ 28 .1i.96.06i88[Fi= 28 ]-4-575.0I4.685 .22 4.845-375.005.505-I95.6o5.365-705. 52 5.8o5.675.865.8o-5.90.665.06178(5)-LdLr+6 .25 6 .23 6.136.i86.oo6.1I5.876. 02 5- 72 5.895.9595.6I5-45+5 .25 [F2=+47.]1 .29 .50.06I97TABLEXXIII. HYSTERESIS OF TOOL-STEELOh..(I) (2) (3)FLdLrLdLrLdLr +26 0± 23 .25 +I3 .25 +I3 .25 &apos ;24 0I3 .22 I3 .29 13 .22 I3.19I3 .22 13.2I 22 0I3.1913,1013.1913.1013.1913.I7 20 013.15I3.0013.1513.0I13.1513. 12 i8o13.10 12. 88I3.10 12. 9013.I013.06I6013.05 12. 77I3.05 22 .8013.05I2.99I40I2.99 12. 66I3.00 12. 70I3.00I2. 92 120 I2.85 22 .40I2.87 12. 46 12. 88 12. 76I00i2.66 22 .03 12. 68I2 .22 I2.69 22 .508oI2. 42 II.50 22 .45ii. 62 I2.47 12. 156oII.95I0.30 12. 00 20 .50 12. 02 iI.6540II.007.00II .20 8.6oII .22 II.04+ 20 9.40-I.709.804.60+io.6oo+6.707 .20 -.30LF2=+30.1- 20 I.80-I.90-30+ 2 24H=i06 .20 44-78 2. 75L=I3 .25 7-7451. 325 ]=o695. 026 83. 027 78(6)LdL,[Fi=-47-]-4-935- 32 5.o85- 52 5 .23 5.635.385-735-535. 82 5.675.875. 82 -5.90 2. 22 *485.06Io318 92. ]649ÆTHERFORCE ... 18 92. ] STEINMETZ ON HYSTERESIS. 647TableXIX.gives the magneticcharacteristics of the threesam-plesintheirtwostates.TABLEXIX.MAGNETICCHARACTERISTICS OF TOOL-STEEL.HhHOh0ShbFpLPLpoL,0LPLPL 20 9.0 2. 22 3.o6.6730 27 0 2. 25.85.I84.96 .22 3.87.903 .2 9-3740 23 .01-745.47.404-78.so4-010.003.6II.I050 23 .0 2. I7 20 .0 2. 505.68.945.0 20 .004-45I1 .24 12. 206o2I.0 2. 86i8.03.336.059. 92 5.3ir.345.0 12. 001 22 .8770I9-53.5817-34.046.6io.6oI2 .20 22 .681 23 .34Soi8-54 .25 17 .2 4.65II10T 12. 6013-05I3-759019.04-7417.55.15I1.541I3.00I3.371 24 .08I00|5.0005.47|| 12. 76I3 .25 I3.67+14-37 25 0 12 5.75756-41 2. 704 24 -25 5 24 -5015;I6 20 0X6 .22 ...

... 26 STEINMETZ ON THE LAW OF HYSTERESIS. [Jan.19,TABLEV.Frequency,Y-IpT)0.e1.16X10-6H.jH.-1.H.=obs.calc.obs.70+4+5.31 02 I66+I+.6 21 99-4.3 23 4+6+ 2. 5300-II-3.7333+I5+4.3 524 - 23 -4-5549+30+5-3695I3- 2. 0795-- 2. 1o85-I-.11547±+15+ 2. 0 26 70.-803 .2 +7'+19.015319.8av:+16 2. 8Thereforeweget the formulafol the lossin the ironi,_.0045_B16+1.162NX10-BInFig.15areshowinFig.5.1. The curve of truehystereticloss,H1.0045Bl'6 2. The curve of the wholelossin the iron,ffI-1,+1 12 with the observedvaluesmarkedbycrosses+-.0045H2H.calc.B.3 42 410546 620 670746b30I 020 I100 12 001310 29 30 26 00.1/15168io8I50178 2} 0 29 33453 92 436539 820 1310 23 345978goIII 23 8 20 8 23 4 29 0344457 42 128 074I1 02 i66 21 0 24 0 28 934850I 2 5796 82 77998415 62 -90ÆTHERFORCE 18 92. 1TTLVI-EYZ ON TIlELAT OF HYSTERESITS-.00 421 TABLEVI.Frequency,A-'170(e- .20 83X10'B.11," ;2 If.1/.11 ... 3-3-7-5.6+3.9 2. 8Exponent of power,derivedfromtests:x-1.60441.6Coefficient of lhysteresis:-_.00335hencetheoreticalcurve:.151.0033.5BI61711.II.ob)s1.ealc.3030310I3 620 35504 320 4355483048go59506i6o609065307850784087809040II,o6o 123 015,840I5,340i6,i6oi1 ,28 0 20 ,35019 ,26 0 20 , 620 21 ,440 23 ,180 24 , 120 av:r2lAlÆTHERFORCE 18 STEINMETZ ON THE LAW OF HYSTERESIS. [Jan.19,TABLEIII.(4.)Frequenicy,NV- 20 5comupleteperiodspersecond:H.H.il-il.ob..calc.calc-obs.630o44404660 +22 0+48734053805780+400+6.9I0,030Q5009300Io,86o9980I0,670+690+6.5 02, 23013.700r2,940760-5-9I4,600I7,390I7,060 -23 0-I.314,700I7,83017,340-490 _2. 815s75019,70019,360340 ... 18 92. ]STEINAMETZ ON THE LAW OF HYSTERESIS. Exponent of power,derivedfromtests:-1.5887'1.6Coefficient of hysteresis: hence,theoreticalcurve.-=TAFrequency.N= 20 B.1790I990 23 80 26 2030603390366o37IO4 620 5070499059106xoo6550 729 080508 320 824 0H.obs3764635857358931054I297 128 8I1 822 20 24 20 34 26 93 28 4430393673434144IO456I=.0 024 38:.0 024 38-B'-,BLEII.(5)completeperiodspersecond.H.calc.4004mO0510 720 920 I100 24 0 125 0I800 20 70 20 IO 26 20 27 5030803640430045304460av:H-H.calc-obs. 424 3+35-I5 +27 +46-57-38 -22 +46 -24 -73-96+4I-334I+ 120 +47+6.o-*7+5-7 -2. 1 129 t4 -2 4.6-3.0-1 .2 +2. 2-I .2 -2. 8-3.5+1.3.9 +2. 7 -2. 2=9 2. 7Exponent of power,derivedfromtests:x=1.60 12 1.6Coefficient of hysteresis: §.0 024 34hence,theoreticalcurve..0 024 34B16Fromthese4sets of readings,weget the results:1. 28 4readings:x_1.6111=j...

... 1894.] STEINMETZ ON HYSTERESIS, 59%Asconclusionswederivefromthischapter:1.Inanalternatingcurrentcircuitsurroundedbyiron, the currentproducedbyasine-wave of E.M.F.isnotatruesine-wave,,butisdistortedby hysteresis. 2. Thisdistortioniisexcessiveonlywithaclosedmagneticcir-cuittranisferringnoenergyintoasecondarycircuitbymutualinductance.3. The distortedwave of currentcanbereplacedby the equiv-alentsine-wave,thatis,asine-wave of equaleffectiveintensityandequalpower,and the superposedhigherharmonic,consistingnainly of aterm of triplefrequency,canbeneglectedexceptinresonatingcircuits.4.Belowsatur-ation, the distortedcurve of currentanditsequivalentsine-wavehaveapproximately the samemaximumvaluLe.5. The angle of hystereticadvance,thatis, the phasedifferencebetweenmagnetismandequivalentsine-wave of M.M.F.isa,maximumfor the closedmagneticcircuit,anddependsthenonlyupon the magneticconstants of the iron: the permeability,aand the coefficient of hysteresis r,andupon the maximummagnetieinduction,by the equation:sinaB-6. The effect of hysteresis canberepresentedbyanadmnit-tance:Ya+j,oranimpedance:Ur-js.7. The hystereticadmittance,orimpedance,varieswith the 'magneticinduction,thatis,with the E.M.F.?etc.8. The hystereticconductancepisproportionalto the coeffici-ent of hysteresis Candto the length of the magneticcircuit1,inverseproportionalto the .4thpower of the E..F.,Lto the .6thpower of frequeneyNand of cross-section of the magnetiecircuitS,andto the 1.6thpower of the number of turns of the electriccircuitnthusexpressedby the equation:s58L,103EL4jV.6AS16qib9.Tlleabsolutevalue of hystereticadmittanceev4/pt+a2ig:proportionalto the magneticreluctanee:P=Pi+Pa,andin-verseproportionaltotllefrequencyNandto ... 596STEILNETZ ON HYSTEREIST[May18,therefore,all the ironcladmagneticcircuitsconstructed of the samequality of iron,andusing the samemagneticdensity,give the sameangle of hystereticadvanee."" ;The angle of hystereticadvance,a,inaclosedcircuittrans-former,dependsupon the quality of the iron,and the mnagnleticdensityonly."" ;The sine of the angle of hystereticadvaanceequalsfourtimes the product of permeabilityandcoefficient of hysteresis, dividedby the .4thpower of the magneticdensity:sina-44u'_BAIf the magneticcircuitisnotentirelyironclad,but the mag-neticstructurecontainsair-gaps, the totalreluctanceis the sum of the ironreluctanceand the airreluctance:p=Pi+i'ahence,tlheadmittanceis:P+ 62 b(PPVor:"Inacircuitcontainiingiron, the admnittanceis the sum of the adiimittancedueto the iron part of the circuit:ViXPi,and the admittancedueto the air part of the circuit:QJa~ Vpalif the ironandtlleairareinseriesin the magneticcircuit." The conductance,o,represents the loss of energyin the iron,and,siniceairhasnoimagnetic hysteresis, isnotchangedby the introductionl of anair-gap.Hence, the angle of hystereticadvance of plhaseis:sinaP=P,opv-Xvi+Va-VIP1+faanidisainaximnunm=°Ifor the ironceladcircuit,butdecreaseswithincreasingwidth of ... 1894.]STEINETZ ON HYSTERESIS. 581ceptance the reciprocal of reactance;otherwise the susceptancedependsuponreactanceanduponresistance.From the definition of the admnittance:Y=p+ja.as the reciprocal of the impedance:U=r-j8wegetY1or1P+jq=-aor,multiplying on the rightsidenumeratoranddenominatorby!(r+js):+j(r-j8)(r+j8)'hence,since(rjs)(P+j8)=r2+ 82 = 2: r8.Sr+SY/+8S2u2+u78or,P 2 r+-gandinversely:t_P -2+ 2 v2C_CS= 2 +ve 2 Bytheseequations,fromresistaneeandreactanee, the conduct-aneandsusceptancecanbecalculated,andinversely.Multiplying the equationsforpandr,weget:?rpPrt2 2, 1lavhence, ,2 2(r2+ 82) (p2+?)=1and11;U=-ÆTHERFORCE...

... 2 United Nations Convention on the Law of the Sea and the polar marine environment  The 19 82 United Nations Convention on the Law of the Sea (LOSConvention) was conceived ... reflected in the 19 82 United Nations Convention on the Law of the Sea. 2 341 The LOS Convention was negotiated through eleven sessions of the Third United NationsConference on the Law of the Sea (UNCLOS ... answer on how its provisions relate to other international norms.First, one of the Final Provisions (Part XVI) of the Convention deals gener-ally with the relation of the Convention to ‘other conventions...

... which the writer will bring the flesh and the blood. The more clearly the writer perceives the shape, the better are the chances of success. 13. Make the paragraph the unit of composition. The ... a paragraph on the dramatists of the Restoration, the second in a paragraph on the tastes of modern readers. The need to make a particular 28 For more material and information, please visit ... relationship between statements is one of the most useful devices of composition. The relationship, as above, is commonly one of cause and consequence. Note that if the second clause is preceded by...

... depend on γ. The same argument as inProposition 2 with the exponent γ>0 instead of 1 2 gives: ON THE NONNEGATIVITY OF L(1 2 ,π) FOR SO 2 n+1913Proposition 3. If γ>0 then Iπ1⊗ π 2 ,1 2 ,γadmits ... irreducible.Annals of Mathematics On the nonnegativity of L(1 /2, π) for SO2n+1 By Erez Lapid and Stephen Rallis* ON THE NONNEGATIVITY OF L(1 2 ,π) FOR SO 2 n+1909Proof. In the case ... SO(2n+1,).Then LS1 2 ,σ≥ 0. The L-function is the one pertaining to the imbedding of Sp(n,), the L-group of SO(2n + 1), in GL(2n,). By the work of Jiang-Soudry ([JS])Theorem 2 applies...

... 1906]DISCUSSIONATNEWYORK.707physicalrelationtoarationalbasis.Idiscussthispointratherfully on page 28 5 of Vol.XX of the InstituteTRANSACTIONS.(b)InconnectionwithDr. Steinmetz& apos;sreferenceto the influence of vibration on the BandHcurve,Icalledattentiontoapaper of mine*inwhichvibrationswere,usedin the determilnation of whatIcallanormalcurve of BandH.C.P. Steinmetz (byletter):(1)Regarding the ... 710ALTERNATING-CURRENTWAVE-FORM.[Sept. 28 the sampleundertest.Infact,evenwhen the utmostprecau-tionsaretakentokeep the impedance of the circuitexteriorto the magnetizingcoilassmallaspossible,thisexternalim-pedancemaybe the controllingfactorin the circuit,particularlyforhighvalues of the flux-density,andcorrespondinglowvalues of the permeability.Asthisexternalimpedanceispracticallyconstantundersuchconditions, the currentin the magnetizingcoilmayhaveverynearlyasineform,andconsequentlyproduceamuchdistortedwave of inducedelectromotiveforcein the sample. The accompanyingoscillographrecordsgive the pressure-wavesundervariousconditionsinducedinasecondarywinding on asample of ironweighingabout6lb. The samplewasbuiltup of punchingsin the form of ahollowsquare5in.outside,3in.inside,eachsheet0.14-in.thick. The magnetizingcoilhad 20 turns. The totalresistance of the circuitbetweengeneratorandsamplewasabout0.75ohm, of which0.3ohmwasin the instrumentsin the circuitand0.45in the step-downtransfomer(one-halfakilowatt, 20 to1ratio). The magnetizingcoilit-selfhadpracticallynoresistance. The source of pressurewasasmall110-voltmotor-generator,givingasine-waveelectro-motiveforce.Curve1isfor 25 cyclesandamaximumflux-density of 6,850lines of inductionpersquarecentimeter.Curve 2 isfor 25 cyclesandamaximumflux-density of 11,300Curve3isfor 25 cyclesandamaximumflux-density of 12, 800.Asine-wave of pressureat the terminals of the magnetizingcoilwouldhavegivenflux-densities of 7,000, 12, 000and15,-000linesrespectivelv. The followingtablegivesforanothersample the flux-densitiescalculated on the basis of asinewaveelectromotiveforceand the trueflux-densitiesdeterminedfrom the averagevalues of the electromotiveforcewave:BTrueBRatio of TrueBtoCasldc-Calculated on basislatedB. of sinewave.60Cycles. 25 Cycles.60Cycles. 25 Cycles.4,0004,0004,0001.001.007,0006,8006,5000.970.9310,0009,4009,1000.940.91 12, 00011,00010,6000. 92 0.8815,000 12, 2000.8117,50013 ,20 00.76 20 ,00014,1000.71A.HenryPikler(byletter):ProfessorBedell'spapergives the impressionthat the hysteresis loopis the onlycause of the dis-tortion of alternating-currentwave-forms.Thisisnotso. The ÆTHERFORCE 6 92 ALTERNATING-CURRENTWAVE-FORM.[Sept. 28 DISCUSSION ON " THE EFFECT OF IRONINDISTORTINGALTER-NATING-CURRENTWAVE-FORM"ATNEWYORK,SEPTEMBER 28 ,1906.CharlesProteus Steinmetz: Thispaperdealswith the wave-shapedistortionproducedinalternating-currentcir-cuitsby the introduction of iron.Itisatheoreticalpaper,andwhile of scientificinterestappearsatfirst of ratherlittlepracticalvalueto the electricalengineer.Thereis,however,to-dayonlyaveryshortstepbetweenpurescientificinvestiga-tionandengineeringpractice;andIhopetoshowyouithat the phenomenadealtwithinthispaper,andsimilarphenomena,are of verygreatpracticalimportanceinalternating-currentdis-__.LjL__ ... 1906]DLICUSSIONATNEWYORK.695zerovalue.Thatis, the harmonicssymmetricalwithregardto the electromotiveforcearenoticeableonlyat the zeropoint,asaflatteningout. The magnetismcurveatthispointishorizontal,sothat the resultantcurrentcurvemustbehorizontalalso.Thiscouldbeexpressedbystatingthat the distortion of the wave of the excitingcurrentisdue,notto the energylostin the iron,butto the magneticcharacteristicor the bending of the satura-tioncurve,andthereforeitisthiscurvewhichweshouldendeavortoconstruct, the magneticcharacteristicasitwouldbegivenbyamagneticcycle,in the absence of hysteresis loss.Thiswouldprobablygiveapproximately the higherharmonicsin the ex-citingcurvewave.Sometimein1881or18 82 Dr.Froehlichnoticedthat the magneticcharacteristic of the dynamomachinecouldbeap-proximatelyvrepresentedbyaparaboliccurve.Dr.Kennellyshowed,in`1891*,that the BHcurve,ormagneticcharacteristic of iron,for the highervalues,couldbeexpressedbyaparaboliccurve,an~equation of the seconddegree.Usingthisequation of aparabolafor the relationbetweenBandH,therecouldbefoundastrictlymathematicalcurve,aboutlikeBinFig.5,.whichcombinedwithasinewaverepresenting the hysteresis loss,wouldfairlycloselyrepresent the distortedwave of excitingcurrent.Indealingwith hysteresis wehavetokeepinmind the differencebetweenmagnetic hysteresis and the energylostin the iron.Ifironisexposedtoanalternatingmagneticfield, the loss of energythattakesplacein the iron,bysomeform of magnetic*MagneticReluctance,byA.E.Kennelly,TRANSACTIONSA.I.E.E.Vol.8,page485.ÆTHERFORCE...

... Appendix 1: QUESTIONNAIRE The following questionnaire is conducted to investigate issues relating to the pronunciation of the first year students at the English Department, College of Foreign Languages, ... secondary school?a. Yes b. No Part 2: Pronunciation learning at secondary schools5. How often did you listen to authentic English at your secondary school?a. No time b. < 20 mins/week c. 20 - ... but the teacher taught the pronunciation of new words and corrected students’ pronunciation mistakes during the lesson. (If yes, how long approximately? )8. When you look up new words in the...

... classified in terms of: (1) The height of the bulk of the tongue in the mouth (2) The front/back position of the tongue in the mouth(3) The degree of lip-rounding(4) The length of vowels (Roach, 1998: ... attention to when teaching pronunciation. 2. 2.1 Aspects of pronunciation The question of “What is pronunciation?” has been answered by a number of different definitions. Generally speaking, pronunciation ... affixation. Many learners have the habit of pronounce a new-formed word according to the pronunciation of the root one. For example, they tend to pronounce the sounds of Exhibition like the sound...