steinmetz cp on the law of hysteresis part 1

In the number 137,ofDecember 17th, 1890, of the Electrical EngineerI puLblished aslhortarticle under the title "Noteonthe Law of Hysteresis," where I showed that ina setofdeterminations

OF THE

ELECTRICAL ENGINEERS

VOL IX NEw YORK CITY, JANUARY, 1892 No 1

The meeting was called to order at 8.15 P M by Vice

President Thomas D Lockwood

elected byCouncil, January 19th:

Supt and Electrician, Kingston Electric Light and Power Co.

Kingston, N Y.

Expert Mechanician and facturer of Special Machinery and Instruments, 204 and 206 East 43d St., New York.

Ralph W Pope.

MCCARTHY, LAWRENCE A Western Union Telegraph Co., Alfred S Brown.

New York City, 1053 Bedford Geo H Stockbridge.

MACFARLANE, ALEXANDER Professor of Physics, University E L Nichols.

Ernest Merritt.

Ralph W Pope.

eral Electric Co Lamp Works, John W Howell.

Review, I3 Park Row, New Chas S Bradley.

2 STEINMIETZ ON THE LA W OF HYSTERESIS,

Louis Bell.

WILLIAMS, WILLIAM PLUMB Electrical Engineer, Nicholson T C Martin.

Box I47, Cleveland, Ohio Franklin L, Pope.

WILSON, HARRY C Supt of P 0 Telegraph, with the T C Martin.

Government, Kingston, Jamai- Nikola Tesla.

Total, I2.

hasevery reason to congratulate itself on the accessions to its

by the same descriptioni that Shakespeare gave to the late

lamented Cleopatra, namely that "Age cannot wither, nor

cus-tom stale, itsinfinite variety," hasprevented alarge audience at

we mustmake up inintensity ofhearing-if you willpardoni the

use ofthe oldterms Thesubject that we have to-night before

us, and which you will find soably dealtwith by Mr Steiinmetz,

relates to that phenomienon of molecular friction, which Mr

Ewing has denominated "hysteresis." Mr Ewing,as we all

know, has made the subject so peculiarlyhis own, that one

it; but I am confidentthat after this paper is read, those of us

who read it with Mr Steinmetz will find that there is something

new underthe sun We will now hear Mr.Steinmetz's paper

[Jan 19,

A jpaj6er read at the sixty-third meeting of the

A merican Institute of Electrical Engineers,

New York, January Igth, I892

Vice-Presi-dent Lockwood in the Chair.

In the number 137,ofDecember 17th, 1890, of the Electrical

EngineerI puLblished aslhortarticle under the title "Noteonthe

Law of Hysteresis," where I showed that ina setofdeterminations

of the loss of energy due to hysteresisby reversals of magnetism,

for different magnetizations, madeby Ewing, this loss of energy

due to hysteresis can fairly well be expressed by the equation:

where H: is the energy consumed by hysteresis duringone

mag-netic cycle, in ergs per cubic centimetre, B the magnetization in

lines of magneticforceper square centimuetre, and rj (1) a

numer-icalcoefficient,in this case = 002

the dependenceof the magnetizationBuponthe magneto-motive

force F (for instance, in ampereturns percentimetre length of

the magnetic circuit)has untilnow defied all attempts of

mathe-maticalformulation, itappeared astrange feature that the

appar-ently muchmoreintricatephenomenon ofhysteresis,orrather of

theconsumption ofenergy byhysteresis, should yieldto

analyti-1 If any quantity has a right to be called " magnetic resistance," it is this

coefficient 2' ; for 2 is the coefcient of conversion of magnetic energy into heat,

while as " electric resistance " we define the coefficient of conversion of electric

energy into heat.

The term generally denoted "magnetic resistance "-that is, the inverse

value of magnetic conductivity, does not deserve this name at all, but is more

properly called " reluctance."

STEINMETZ ON THE LAW OF HYSTERESIS, [- Jai 19,

cal formulationin such a simple way, to be directly proportional

to the 1.6th power of themagnetization At the same time the

was near enough to be considered as something morethan a mere

incident, but at least as a clue to a law of hysteresis, the more as

this law held not only for low and mnedium magnetization, but

even for veryhigh saturation, without showing any kink at that

"knee" and thereby entirely changes its shape, nor any marked

tendency of deviation ofthe extremest observed values from the

InFig 1 and Table I, Igive from the article referred to,the

calculated curve ofhysteretic loss, as adrawniline, withEwing's

tests miarked as crosses, and in dotted line the curve of

magneto-motiveforce I, corresponding to the different magnetizations, as

absciss-e

In thetable, I:

F -theM M F., in absolute units,

B themagnetization, in lines of magnetic force per square

centimetre,

obs

4

1892.] STEINMETZ ON THIE LAW OF HYSTERESIS.

IH - the calculated values of hysteretic loss, in ergs per cubic

Tostudy inore completely this phenomenon of hysteresisand

of the energy consumption causedtlhereby,Ienldeavored to make

a number of determinations with different magnietic circuits and

atdifferent magnetizations

To be enabled to carry out these experimnents, I am highly

obliged to AMr Rudolph Eickemeyer, of Yonkers, N Y., who,

being greatlyinterested in the laws of the magnieticcircuit and

havingdonie considerable work himselfin this branch of

electri-cal science, notonly put the large facilities of his well-known

factory at mnydisposal, but alsoguidedthe experiments with his

valuable advice A part oftheinstruments used in thetests are

of AMr. Eickemeyer's inventionand covered by his patenlts.

To be able to deal not only with the small amounts of energy

which the reversal ofmagnetism in atinybit of iron wire sends

throughthe ballistic galvanometer, but to reduce the

determinia-tions to readingsofconsiderable power-values,andwhere a much

greater exactness can be reached, and at the same time to

velocity of the magnetic cycles, I decided to use alternating

cur-rents, at least as far as this could bedonie, whereby the

determin-ation of the energy consumed by hysteresis is reducedto a

simul-taneous wattmneter, voltmeter, ammneter and speed reading.

At the same timne thiselectro-dynamnometermethodhas the

ad-vantage that the mnagnetic cycle is comnpletedina steady,

contin-uous motion,while in thie ballistic mnetlhod the magnetic cycle i's

5

STEINMETZ ON THlE LAW OF HYSTERESIS [Jan 19,

from pointtopoint, to enable the produetion of the induced

cur-rent This feature introduces an error into the ballistic method,

for if a magnetic cvele is gone through by sudden changes, a

largeramount of energy may be consumed than if the

magnetiza-tionvaries steadily in harmonic vibration

Suppose, around a magnetic circuit, an alternating current of

iV complete periods persecond is sentin n convolutions

Let C= the effective strength of the current,

E-the effective E M F induced in the circulit by

self-in-duction, after subtracting the E.M.F.'sinduced bythe

self-induction of the instruinents,

IV= the energy consumed in the circuit, after subtracting

the energy consumed by the electric resistance,

Then, Ibeingthelength and s thecross-section ofthe magnetic

circuit, all in centimetres, amperes, volts, watts, etc.,

Let B themaximummagnetization in lines of magnetic force

per square centimetre,

II theloss of energy byhysteresis, in ergs per cycle and

Forhigher frequencies,80to 200 periods persecond,the

alter-nating current was derived from a 1 H P 5.0 volt Westinghouse

currentmotor. By varyingthe excitation of the motorfield and

1 This formula holds rigidly only for the sine-wave, but as shown in tl e

following, the currents used in the tests were at least very near

sine-waves Besides, a deviation from the sine shape would not alter the results at

all, but only sligfhtly change the coefficient 97.

6

1892.1 STEINMETZ ON THE LA W OF HYSTERESIS.

varying the E M F supplied tothe motor, the speed and

there-fore the frequency of thealternating current could be varied in

wide limiits At the same time, supplied with constant E M F

andlikeall the Eickemeyer motors ofunusually small armature

reaction,this electromotor kept almost absolutely constant speed

under varying load, the more as it never ran with full load

For low frequencies, this bipolar continuous current motor

was used as a bipolar alternating dynamo, as shown in a patent

commu-tator two sliding rings were mounted and conlnected with

op-posite commutator bars In the ordinary continuous current

ma-chine in motion as an electromotor, while from the sliding

rings by two separate brushes, alternating currents were taken

off By varying the E M F suipplied to the motor, the E ir

F of the alternating current was varied, while a variation of

the motor field gave the variations of the frequency The

curve of E Al F was very nearly a sine-wave, the ratio of

the sine-wave requires 1.414-that is, essentially the same

To determine whether the change of the shape of the

alter-niating current by varying load and varying excitation had any

influence upon the readings, the variations of the alternating

E M F were produced:

1 By varying the excitation of the field of the Westinghouse

dynamo

feed-ing the secondaries of a bank of converters, feeding fronm

the fine wire coils of these converters the fine wire coils

of another bank of converters, andtaking current off from

the secondaries of these converters, connected from one to

six in series

con-verter of variable ratio oftranisformnation

4 By loadingthe dynaniowhen small currents were uised forthe

tests

But afterhavingfound that all these differentways ofvarying

the alternating F M F gaveno perceptible difference whatever

inthereadings, I afterwards used the most convenient way to

varythe excitation of the dynamo field and, where higher E M.

7

STEINMETZ OV THE LA W OF HYSTERESIS [Jan 19,

Fis were needed, to increase the E M F by an interchangeable

converter, which gave the ratios: 1: 1, 2, 3, 4, 5

For the determinationi of the frequency, x direct-reading speed

indicator (horizontal ball governor, acting upon a spring) was

used, which was carefullycalibrated

Forthe electric readings, instrumnents of the

electro-dynamom-eter typewere uised, zero-reading-that is, the movable coil was

carried back by the torsion ofasteelspring to zero position

These instruments werespecially builtfor alternating currents,

with very low self-induction andlow internalresistance, using

bifilargerinan silver wire asadditionalresistance

Inthe ammeter the range of readings was from 3 to 40

am-peres, the internal resistance 011 co

The norrnal inductance (that is, E M F of self-induction

in-duced by one amnpere alternating current, flowing throughthe

in-strument with a frequency of C10 complete periodsper second):

- 045 w

Inthe voltmeter the range of readings was from 5 volts

up-wards buttoavoid thenecessity of corrections for self-induction

sufficient additional resistance was usedto decrease the correction

under 1per cent., and then the lowest readings were from 3 to 6

volts

Theinternal resistance of the voltmeter is -2 (co, its normal

inductanee = 4.12 (o

In the wattmeter the resistance of the coarsewire coil (fixed

coil)was -.026co, its normal inductanice 073(0.

The internal resistance of the fine wire coil was 25t, its

In most ofthe readings sufficient additionalresistance was used

to make the correction for self-induction of the fine wire coil

neg-ligible Only in a few readings where it exceeded 1 per cent it

wastaken inaccount

For small currents an Eickemeyer ammeter was used, which,

whilereadingfrom 7to 3 amperes, though built originally for

continuous currents, had alreadybeen used byme foralternating

currents andhad been checked for its constanceyof readings

sev-eral times, andalways found to give no perceptible difference in

itsreadings forcontinuous currents and for alternating currents

upto over 200complete periods persecond, the highest

frequen-cy I could reach

8

1892.] STEINMETZ ON THE LA W OF HYSTERESIS.

Its internal resistance is -1.1 o, its normal inductance

- 2.03 to

Several sets of readings for different frequencies were taken

on anold Westinghouse voltmeter converter The fine wire coil

and one of the 50 volt coils were leftopen Into the other coarse

wirecoil analternating current was sent, in series to ammeter and

coarse wire coil of wattmneter, while the voltnmeter and the fine

wire coil of the wattmeter were connected in shunt around the

whole circuit

Hencea correction hadto beapplied for the self-iinduction of

amnmeter and coarse wire coil of the wattnieter and for the

resist-ance of the circuit Only in very few readings this correction

amounted to somewhat more than 10 per cent Generally it was

much smaller

The instruments were calibrated several times and their

con-stants found to remain constant

The speed indicator was calibrated carefully and its

correc-tionsadded

Each reading consisted of an ammeter reading, a voltmeter

reading, a wattmeter reading anda speed readiing

Before and after each setofreadingsthe zero positions of the

instruments were determined,andonly those sets of readings used

where the zero position had remained constant

Before and after each set of alternating curreint readingsa

con-tinuous current was sent into the circuit and a few readinigsfor

different currents tak-n Voltmeter and ammeter readings

com-bined gave the resistance of the circuit, and both comcom-bined with

the wattmeter readinggave a checkfor the instruments, here

be-ing watts - volts X amperes Only those sets were used

again wherean entire agreemient was found, and with the

alter-nating currentfirst readings withsimall currenits, then with large

currents, and then again with smnall currents taken, so that I

be-lieve every possible care was exercised to avoid any errors in the

tests

As beforesaid, the first sets of tests were made on the

mag-netic circuit of a small Westinghouse converter

The constants of this converter, so far as they are of interest

here, are:

Mean length ofmagnetic circuit, 21cm

Ilence volume ofiron, _ 917 cm3

Resistance of secoindary coil, 2 co

9

10 STEINMETZ ON T'HE LAW OF HYSTERESIS [Jan. 19,

Further sets of readings were taken on a magnetic circuit,

built up of very thin sheets ofiron, alternately 8 in X 1 in and

3 in X 1 in., in rectangular shape very carefully insulated

against eddy currents with layers of thin paper between the

sheets On the two long sides two coils of each 50turns, very

coarsewire (3 No 10 inparallel), werewound and eonnected in

series, thereby giving n 100 turns of an internal resistance of

.048

Here the mean length of the magnetic circuit was I 41 cm

The cross-section, 8 _ 3.784 cm.2

The circuit consisted of 58layers ofsheet-iron of the thickness

The sheet-iron pieces were first freed from scales bydipping

intodilute sulphuricacid

In one set oftests an openmagnetic circuit was used, by

leav-ing the short end pieces (3 in X 1 in.) off, and using two piles

pieces asused in the formerclosed circuittests

In thesereadings, for the determination of thehysteretic loss,

only voltmeter and wattmeter, butno ainrneter, wereused, and

ammeter

The calculationof thereadings was done in the followingway:

After applying the corrections for self-induction of

instru-ments, resistance andspeed, the readings were reduced to lines

energy by hysteresispermagnetic cycle H, in ergs

Then the results were plotted oncross-section paperand if any

valuewasfound tobe very much outof the curve connectingthe

other values, it wasstricken out as evidently erroneous,not

reading of anyone of the instrumentsor a mistakein the

calcu-lation

Then from the othervaluesof B and H,underthe supposition

that 1 wereproportionalto any powerxof B:

this exponentx wasdetermined

1 Calculated from the weight.

1892.1 STEINMETZ ON THE LAW OF HYSTERESIS 11

This value x will be seen always to be so near to 1.6 that 1.6

can be considered at least as first approximation to x

plotted in a curve, as given in the figures, andthe observed

val-ues of THdrawnin and marked

Fromthe curve were taken the calculated values of H,

corre-sponding to the observed values of B, the difference H - B

I MAGNETIC CIRCUIT OF THE WESTINGHOUSE CONVERTER

FIG 2; TABLE II.

12 STEINfETZ ON THE LA W OF HYSTERESIS [Jan 19,

TABLE II (2)

obs calc calc obs.

P3i. B.~~ ~obs.H.ILIcale.H , Hg.calc. obs.. %

1892.] STEINAMETZ ON THE LAW OF HYSTERESIS.

Exponent of power, derived from tests:

-1.5887'1.6Coefficient of hysteresis:

hence,theoretical curve.

1288

2024

2034

2693 3039 3673

+2.2 -I.2

-2.8 -3.5 9

.002434 B16From these4sets of readings, we get the results:

1. 28 4 readings: x _ 1.6111 =j-.002410

.002434-Therefrom we derive the average, by giving toeach value as

weightthe number of readings, where it is basedupon:

x 1.60513 , 1.6

a 0024164Hence:

14 STEINMEIT'Z ON THE LAW OF HYSTERESIS [Jan 19,

The observed values of IH aredrawn inFig 2:

1 For N= 28 with the mark 0

v 11

.Z~kti F? Brad(e9 & P&atce Engr AY.

The magneticcharacteristic is drawn in dottedlines

From this curve ofhystereticloss

Hf= 0024164 B'6

wederive the values:

1892.] STEINMETZ ON THE LA W OF HYSTERESIS 15

16 STEINMETZ ON THE LAW OF HYSTERESIS. [Jan 19,

L 1892.] STEINMETZ ON THE LA W OF HYSTERESIS.

TABLE IIT (2.)

1ob.obs.sI cale.al calc.a ob,obs.

- IO +260

± 37I

I.() I

18 STEINMETZ ON THE LAW OF HYSTERESIS [Jan 19,

II 00373 B'-6

OPEN MAGNETIC CIRCLTIT.

Two gaps of , 4 cm.lenigth.

- 00394

hence theoreticalcurve:

H = 00394B"f

1892.] STEINA-IETZ ON 1THE LA TV OF HYSTERESIJr.

From thesefour setsof readings we get the results:

Hterefroin it seems that the conisumption ofenergy by

hyster-esis per imagnietic cycle iniereases with increasing

frequency-that is, with increasing velocity of the magnetic change

Thethree values of tltree coefficients of hysteresis for closed

circuit in their dependence upon the frequency N,can be

ex-pliessed by the einpii-ical forni-ula:

^ (0017 + 000016 - 00000003 !V)

To compare the valuies of hysteretic loss for different

frequen-cies, in Fig.3 tlhe curve ofhysteretic loss forN -100 complete

periods per secondisplotted, giving:

.003

lience

ff- 003 BI-6and the observed valuesof 11 are not directly drawn in, but the

observed values ofI/multiplied witlithe factor:

obs.

to compare thedifferent frequencieswith each other

These va-luesare plotted for:

N' 85 with the mark y

138 " " + L Closed magneticcirculit.

N 138 with the mark o; Open inagnietic cir'cuit.

From this curve of hystereticloss,

II 003

b'-we derive the values, for the frequency of IN 100 complete

periodsper second

1 9

20 ASTEINMETZ ON TIIE LA W OF HYS TERESIS.

Especially noteworthy is the last set of readings, on open

mag-netic cireinit, in so far as it proves the fallacy of the gener-al

opin-ion that the hysteretic loss ol eniergyin the iron is sniialler in the

open magnetic eircuit than in the closedeireuit

For the coefficient ofhysteresis observed on- openI milagnletic

cir-cuit

^I-.00393

iseven greater tlhani that for closedinm,ignetic cireuit,

Ti ,335(P

Blut thisdiscrepancy is easily exphlaiied bvthe fact that in the

closed mnagnietic circeulit the mnagnetization is iiearlv uniformi

throughoutthewhlole iron Blut in theopen magnietic cireuitthe

magnetic field initensity differs conisiderablv froml point to poilt,

being a maxiunnm in theimiddle of the magnetizingr coils, a

min-iunLtin at the elnds ofthe iron sheets Now,the values of B given

in the table, are the average values ofthe milagnietizationi, and the

values JT,the average values of lhystereticloss Butthe average

value ofthe 1.6th powers of different quantities IBis larger than

the 1.6th power of the average value of 1B

Fot instance, in acubic ciii.of iron mnagnietized to B1 = 12,004)

is H _ 3330; henlce of these 2 cubic cenitimetres the average

magnetizationi is

1, -_ 9000), and theaverage 1f 6,7i05 ergs

per cent less,and the difference becomes still greater, if the

values Bdiffer still more

Takingthis into account, it seemisthat the loss of energy due to

hysteresis depends only upon theintensity of inagnetization, and

closedmagnetic eircuit,asis to be expected

I[Jan. 19,

1892.] STEINMETZ ON THE LA WV OF HYSTERESIS.1

A third set of determinations of the lhystereticlossof energy is

given in the following:

Again a inagnetic circuLit was built inp of 17 layers of a soft

2';00 4000 b)O0 8000 10 000 12,000 14,000 10,000 IY k)0 20.000

Fig 4.

kind of sheet-iron, each layer consisting of two pieces of 20 cm

length, 2.54 cm.widtl, and two piecesof 7.61 cm.length and 2.54

cm.width,ofthe thickness o 0686 cmn.,thatis,ofconsiderably

greater thickness than in the formerset of tests

21

22 SYEINMETZ ON THE LAW OF HYSTERESIS [Jan 19,

Here evident proofof the induction of eddy-currents in the

iron was found Especially perceptible was a decrease in the

watts consumed by the iroil, when a larger M M F of high

attributed to the increase of the electric resistalnce of the iron,

caused byitsinereasing temperature

To eliminate this source of error as far as possible, before each

set of tests an alternating current of high frequency (N - 20(0)

and considerable strength wassent through the magnetizing coils

andleft on for ten to fifteeni mninutes,andthel fnrstreadingswitlh

lowimagiietization, then witlh high, and theni againwith low

mnag-netization were takeni But, nevertheless, as was to be expected,

in these tests the observed values agreed less with each other

thain inthe former readings

The method of determinationi, the apparatus, etc., were the

saine as in the second set of tests, oiily that animeter, voltineter,

and wattmeter were used atthe sametime In calculatingthese

tests, the law of the 1.6th power was assumed as true, and the

loss of energy in the iron expressed by theequation,

11 BL6+-ATB2

where

- ;11.6

1-1 -^§ B1

isthe true hysteretic loss pei cycle and cm3., which is

independ-ent ofthe frequiency, and

1J2 e AX I

isthe loss of energy by eddy-currents per cycle which is

propor-tional to the frequency N

From thisexpression

the coefficients ^and e were calculated and the agreenment or

dis-agreement of these coefficients § and s allow now to check the

correctness orincorrectness of the lawofthe 1.6th power

Thesetests gave the following results:

1892.] STEIN-METZ ON THE LA W OF HYSTERESIS.

EIA _ ;y B'6 loss of energy by hysteresis proper, in ergs per

cycle and cmin (- 10- joules)

ll,eN 12-loss of energy by eddy-currents,.in ergs per cycle

1,530 8,640 1,300

24 STEINMETZ ON THE LAW OF HYSTERESIS [Jan 19,

av: 6.o + i.6 (- 8)

Therefrom wegetthe results:

207, 5 "' 00336 757 X 10-8

The values found for C are so nearlyalike that we can consider

them as constaint, and take their mean value

- 00333

as thecoefficientofhysteresis

Even the values found for s are not much different froin eaclh

other, notmore than was to be expected from the unavoidable

differences in the temperature of the iron, which because of the

high electric temperaturecoefficient of iron makes - rather

vari-able

Taking the average of e,we derive

= 746 X 10-6andas formula of iron loss,

.H 00333 B'-6 + 746 X 10-6 _N B2

InFig 4are drawn thefour curves,

2 Iron loss for NV-78 00333 B1.6 + 00005856 B2

Theobserved valuesareplotted by crosses, +

1 H is calculated by using forIthe mean value 7 00333, but for e the

calc.

individual values, corresponding to the particular set of observations.

1892.1 TEIlNMIETZ ON TIlE LA W OF HYSTERESIS.

Two otlher sets of determinations of the Iysteretic loss of

made on two laminated hlorse shoe mnagnets, witlh laininated

keeper orarmatuire

The inethod of observationand of calculation was the same as

inIfL., and the same precautionsMTere taken

The dimensions of the horse shoe mnagnetswere:

Mean length of myagnetic circuit: 38 cin

In thefirst set of readinigs, considerable eddy-culrreints were

found; in thesecond set,only a small amount of eddies

becausethereluetance of the mnagnietic circuitmainlyconsistedof

that of the air gap between magnet and keeper

The results were,

B _ magnetization, inlines per cn 2

HF observed loss of energyig tIme iron, in ergs per cycle and

obs.

cnm.3 for N7 -170

Hi - true hystereticloss ofenergy

RJ2 loss of energy by eddy-currents.

calc.

25

26 STEINMETZ ON THE LAW OF HYSTERESIS [Jan 19,

1310

23

34 59

34 445

289

348

50I 2

579 779 984

1562 -90

1892.1 TLVI T -EYZ ON TIlE LA T OF H YSTERESITS

'45

176 265

I6I

'2r

35

41 47

56

69

170 208

5

I8.6 23.7 '55

514

1293

5.6

i6.9 23.5 122 I46

'57

202 200

300

353

430

5I4 1130

+ *9

5.0 + 6.I + 2.6 2.4

_I _

+27.2 -24.6

28 STEINMETZ ON IlHE LA IV OF HYSTEREKSIL [Jan 19,

1 The curve oftrue lIystereticloss,

JTL 00421 B1 ;

2 The curve of the whioleloss in the iron,

witlh the observed values inarked bycrosses +

Especially interesting are these two sets of readinigs in so faI

as they cover (quiteadifferent range ofmagnetizatioln asthe tests

in I to Ilt

In I to III the tests cover the range from 179'1 to 19,340 lines

of magnetic force per cm.2, thatis, for mnediuim mnagnietizationup

tohighsaturation, while the tests inIV cover the rano'ge from 85

to 2600 lines per cm.2, that is, from medium dowvln to verv low

magnetization

The law is found exactly the samiie,

and herewith proved for the full range from 83 lines per CuE2

upto 19,340lines, a ratio from 1 . 230

This seems not to agree with Ewing's tlheory of the iimolecuilar

magnets According tothistheory, for very small

mnagnietiza-tion the hysteresis slhould be expected to disappear, or almost

disappear, and the cycle b-e reversible Then for mtiediumn

mlgnetization, where the clhains ofmiolecular mnagnets b)reak up

and rearrange, hysteresis shouldincrease very rapidly,andslowlyv

again for saturation Nothinig of this isthe case, but hysteresis

seems to follow the same law over the wlholerange of

niagnetiza-tion, and iscertainly not zero for even suchl a low itiaginetization

as 85lines pei Cm.'

MIAGNETOMETER TESTS.

that

1 It allows the taking of a greater miumber of readings, over a

wide range ofmagnetization, in a short time, bymere

probable error by increasinig tie niumnber-of observations.

2 Itallows the use ofelectro-dynamoneters,asthe most reliable

electric ilieasuring inistriuments.

1892.] STELNMET7 0N THE LA WV OF IlYSTERENJS 29

3 It deals witlh largeir amounts of energy, coiiitillg l)y watts or

even hliuidreds of watts, whereby a mluc(h greateir accuracy

can lbe reached thian )bv the lballistie (-alvanomlete

4 It ii-easinrce tmehyvsteresis iiider the inifliience ofan

liarinoiii-(-ally, anid niot suddenfly varying m. M F., that is uder the

29

30 STEINJE7TZ ON THE LAW OF HYSTERESIS [Jaii 19,

samne conditioins, wlhere it becoines ofiiniportance for

practi-calengineeriing

But it has the great disadvantage that it canbe used only for

testing sheet-iron or otherthoroughly lanminated iron, where

ed-dies aleeither inappreciable or can becalculated also For

test-ing solid iron and steel pieces, this method cannot be used,

be-causeofthe tremendouisamount of eddies whichwouild flowina

solid piece of iron

To determine thehysteretic lossof energy in steel andcast-ironi

description of this instrument and its use is to be found in the

part of the following description In Fig 7 is shown this

instru:-ment, whiclh I shall be glad to show in our factory to anybocly

wlho isinterested in it In Fligs 8 and 9 are diagrams of its

action

The principle of this instrument resemblessomewhatthe

prini-ciple ofthe well-known differential galvanometer applied to the

magnietic circuit In Fig 8,suppose F1 and FY weretwoE M F.'s

conniected in series; for instance, two cells of a battery, ze and y

the two resistances whieh we want to compare Either resistance

e and y is shunted respectively by a conductor aand b of equal

resistance, which influences a galvanometer needle G in opposite

directions but with equal strengtlh

Then the zero position of the needle GShOWS that the electric

current(a, flowing in a, is equal to the current cb in b But let

thecurrent inxbe c'1, and iny, ey ; then weimiust have

because the currents ca and c are the two branches of thesaine

initegral current as Cb and cx

Therefore,if ea- Cb, then

But if Ca Cb, and a - b, the difference of potential atthe

ends of a (or, what is the same thing, y) is equal to the

differ-ence of potential atthe ends of b or d and,therefore, the current

in x and y, and thepotential differences being the same, it

fol-lows thatx y

That is, this method of connectionallowsus to compare an

un-known resistance xwith a standard resistance y

Now, instead of "electric current," say " magnetic current"

1892.] STEINAMETZ ON THFE LAW OF HYSTERESIS 31

or "iinumber of linesof miagnetic force;" instead of "

electiro-motive force" or "potential difference," say "magneto-motive

force;" and instead of "1electric resistance," say "reluctance,"

and we have tilepriniciple of this instrume-nt

FIG 8

Itsimagnetic circuitconsiSts of two pieces of best Norwayironi,

ULJ shaped, shown in the illulstiation of the complete

instrti-ment, Fig 7, and in the diagramn Fig 9, at F, and Fv The

mid-dle portion is surrounded by a inagnetizing coil c Therefore if

-coil cistraversed by an electric current, the front part vq of the

left iron piece becomes southl anidtlhe back partYe northt polarity

172 FIG 9

The froint part of theright iron piece n becomnes north, and tl,e

back part south; and the linesof magnetic force travel in the

-front from therightto the left, from n2to 81; in the back the op

posite way, fromthe left to the right, or from ii1 to 82, either

31

32 STEI-NMIETZ ON THE LA W OF HYSTERESIS [Jan 19,

through the air or, wlheni m2 and 81, orn,and s2, are connected by

apieceof magnetizable metal, through this and tlirough the air

In themiddle of the coilc stands asmall soft iron needle with

analuminiiumindicator, whicl plays over ascale K,and is heldin

avertical position by the lines of magnetic force of the coilc

it-self,deflected totheleft bythe lines of magnetic force traversing

the fronlt part of the inistruimen-t from n2,to si, deflected to the

rigltby tlhe linestraversing tthe back fromn ii. to s, This nleedle

slhowsby itszeroposition that the imagiietic flow through the air

inf"ronlt fro]m ii2to lhas the samestrengtlhas themnagnetic flowin

the backfrito1,,to tlhrough the air

Nowwe put a piece of soft iron x oni the fronit of time

instri-imient A large number of lines go throughl x, less through the

airfromt i, to b-l)ut all theselinesgofromn n1 to ,tlruolghtheair

at the back part of the muagmietouieter, the fro;nt part and back

part ofthe instrutment being connected in series in the magnietic

circuit Thlerefore the needle is deflected to the riglit by the

inigneticflow in the back of tlheinistrum-Lent

Now we put aniothier piece of iron,y, oni tlhe back part of the

instrumient Theni eq:uilibrium woulld be restored assoon as tlle

same m1un1Il)eroflines of inagneticforce go through ii,asthrollgh

y, because tlheni also the samne number of lines go through air in

the front as in the back As will b-e noted, tlhe air here takesthe

place of the resistanees a( and 1b, influencing the galvanometer

nleedle (n, as in the diagrami, Fig S

The operationoftheinstrumneut isexceedingly simlple and isas

follows: Into the coil cz ani electric eurrent is sent whichl is

mlleasured by the aimmeter A, amid regulated by the

resistanee-switcli R Tlihen tlhe nee(dle wliel before lhad no fixed position,

points tozero.

Now themagneticstandard, consistinig of acylindrical piece of

Norway iron of 4 cin.2 cross-section and 20 cm. lengtlh is laid

againistthebackoftheinstrument,withboth ends fitted into holes

in large blocks ofNorwayiron,A3,A4, whieh are laid againstthe

poles S1 V of the mnagnetometer, so thatthe transienit resistance

frompole-face to iron is elinminated.

Thesanmpleofiromi tlhat wewislhtoexainine is turned off to

e-aetly the saime size, 4 cm.2cross-section and 2() cm.length, and

Then-so ianyfractionalstandard-pieces of Norwayiron are added in

front, that the needle of the instrumrnent points to zero. This