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TRANSACTIONS
OF THE
AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS
VOL. IX. NEw YORK CITY, JANUARY, 1892. No. 1.

REGIULAR MEETING, JAN. 19th, 1892.

The meeting was called to order at 8.15 P. M. by Vice President Thomas D. Lockwood.
The Secretary read the following list of Associate Members elected by Council, January 19th:

Name.

Address.

Endorsed by

BARBERIE, E. T.

Electrician, Safety Insulated Wire Wm. Maver, Jr.

Co., 234 W. 29th St., New Chas. Cuttriss.

York City.

G. A. Hamilton.

DESMOND, JERE. A.

Supt. and Electrician, Kingston Chas. J. Bogue.

Electric Light and Power Co. Rob't. J. Sheehy.

Kingston, N. Y.

H. A. Foster.

GRUNOW, WI1.LIAM JR. Expert Mechanician and Manu-

M. I. Pupin.

facturer of Special Machinery Francis B. Crocker.

and Instruments, 204 and 206 W. H. Freedman.

East 43d St., New York.

INRIG, ALEC GAVAN

Rue St. Gommaire, 23, Antwerp Belgium.

T. C. Martin. Joseph Wetzler. Ralph W. Pope.

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

New York City, 1053 Bedford Geo. H. Stockbridge.

Ave., Brooklyn, N. Y.

Wm. Maver, Jr.

MACFARLANE, ALEXANDER Professor of Physics, University of Texas, Austin, Texas.

E. L. Nichols. H. J. Ryan.
Ernest Merritt.

MOLERA, E. J.

Civil Engineer, 40 California St., San Francisco, Cal.

T. C. Martin. Joseph Wetzler. Ralph W. Pope.

PAGE, A. D.

Assistant Manager, Edison Gen-

F. R. Upton.

eral Electric Co. Lamp Works, John W. Howell.

Harrison, N. J.

H. Ward Leonard

READ, ROBERT H.

Patent Attorney, with Electrical

S. S. Wheeler.

Review, I3 Park Row, New Chas. S. Bradley.

York City.

Ralph W, Pope.

2

STEINMIETZ ON THE LA W OF HYSTERESIS, [Jan. 19,

WEBSTER, DR. ARTHUR G. Docent in Physics, Clark University, Worcester, Mass.

M. I. Pupin.
F. B. Crocker. Louis Bell.

WILLIAMS, WILLIAM PLUMB Electrical Engineer, Nicholson

T. C. Martin.

Electric Hoisting Company,

G. M. Phelps.

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.

ca, West Indies.

Thos. D. Lockwood.

Total, I2.

THE CHAIRMAN:-[Vice-President Lockwood.] The Institute has every reason to congratulate itself on the accessions to its mnembership which it is niow receiving. It is a matter to be lamented that the weather, which may be properly characterized by the same descriptioni that Shakespeare gave to the late
lamented Cleopatra, namely that " Age cannot wither, nor custom stale, its infinite variety," has prevented a large audience at
the beginning of our proceedings. But what we lack in quantity we must make up in intensity of hearing-if you will pardoni the use of the old terms. The subject that we have to-night before us, and which you will find so ably dealt with 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 peculiarly his own, that one might at first suppose there was nothing new to be known about it; but I am confident that after this paper is read, those of us who read it with Mr. Steinmetz will find that there is something new under the sun. We will now hear Mr. Steinmetz's paper.

A jpaj6er read at the sixty-third meeting of the A merican Institute of Electrical Engineers, New York, January Igth, I892. Vice-President Lockwood in the Chair.
ON THE LAW OF HYSTERESIS.
BY CHAS. PROTEUS STEINMETZ.
In the number 137, of December 17th, 1890, of the Electrical Engineer I puLblished a slhort article under the title " Note on the
Law of Hysteresis," where I showed that in a set of determinations
of the loss of energy due to hysteresis by reversals of magnetism, for different magnetizations, made by Ewing, this loss of energy
due to hysteresis can fairly well be expressed by the equation: A- - _B 1.6
where H: is the energy consumed by hysteresis during one magnetic cycle, in ergs per cubic centimetre, B the magnetization in lines of magnetic force per square centimuetre, and rj (1) a numerical coefficient, in this case = .002.
Considering that even the simple law of magnetism-that is, the dependence of the magnetization B upon the magneto-motive force F (for instance, in ampere turns per centimetre length of the magnetic circuit) has until now defied all attempts of mathematical formulation, it appeared a strange feature that the apparently much more intricate phenomenon of hysteresis, or rather of the consumption of energy by hysteresis, should yield to 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."

4

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

cal formulation in such a simple way, to be directly proportional to the 1.6th power of the magnetization. At the same time the coincidence of Ewinig's tests with the curve of the 1.6th power was near enough to be considered as something more than 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 very high saturation, without showing any kink at that point where the magnetic characteristic goes over the bend or " knee " and thereby entirely changes its shape, nor any marked tendency of deviation of the extremest observed values from the
calculated curve.

I13

I1i
I 't,00a - -_

'C2,000
2,004
I

4-

-

_

__ X-'I

~-I-- 80col <_/

_

2000

_

400C0

~

2000

=_ ,

2000 4000 6000 8000 O.COO 12000 14,1000 18,000 18,000
Fig. 1.

In Fig. 1 and Table I, I give from the article referred to, the calculated curve of hysteretic loss, as a drawni line, with Ewing's tests miarked as crosses, and in dotted line the curve of magnetomotive force I, corresponding to the different magnetizations, as
absciss-e. In the table, I:
F -theM. M. F., in absolute units, B the magnetization, in lines of magnetic force per square
centimetre,
H1 the observed values, and
obs

1892.] STEINMETZ ON THIE LAW OF HYSTERESIS.

5

IH - the calculated values of hysteretic loss, in ergs per cubic
calc
centimetre, TTI - H the difference between both, in ergs and in percent-
calc obs
ages.

TABLE I.

.F: F:
1.50 I1.95 1.56 3.01 3.76
4.96
6.62 7.04
26.5
75.2

BB::
2,974 3,830 5,950 7,I80 8,790
10,590
I1,480 11X960
13,700 I5,56o

H: obs
410 Iii6o
2190
2940 3990
5560
6I6o
6590
86go
10,040

Ii: calc
375 1082
2190
2956 4080
5510
6260
6690
831o
10,I90

H-fl: calc obs
+ 35 + 58
......
- i6 - 90
+ 50 -100
-I00 +380
-150
Av. + 98

%
+ 8.5
+ 5.0
......
-5 - 2.3
+ .9 - I.7
-.5 + 4-4
I.5
± 2.6

To study inore completely this phenomenon of hysteresis and of the energy consumption caused tlhereby, I enldeavored to make a number of determinations with different magnietic circuits and
at different magnetizations.
To be enabled to carry out these experimnents, I am highly obliged to AMr. Rudolph Eickemeyer, of Yonkers, N. Y., who, being greatly interested in the laws of the magnietic circuit and having donie considerable work himself in this branch of electri-
cal science, not only put the large facilities of his well-known factory at mny disposal, but also guided the experiments with his valuable advice. A part of the instruments used in the tests are of AMr. Eickemeyer's invention and covered by his patenlts.
To be able to deal not only with the small amounts of energy
which the reversal of magnetism in a tiny bit of iron wire sends
through the ballistic galvanometer, but to reduce the determinia-
tions to readings of considerable power-values, and where a much
greater exactness can be reached, and at the same time to deter-
mine the dependence of the hysteretic loss of energy uipon the
velocity of the magnetic cycles, I decided to use alternating currents, at least as far as this could be donie, whereby the determin-
ation of the energy consumed by hysteresis is reduced to a simultaneous wattmneter, voltmeter, ammneter and speed reading.
At the same timne this electro-dynamnometer method has the advantage that the mnagnetic cycle is comnpleted in a steady, continuous motion, while in thie ballistic mnetlhod the magnetic cycle i's

6

STEINMETZ ON THlE LAW OF HYSTERESIS. [Jan. 19,

completed by sudden changes in the magnetization, which jumps from point to point, to enable the produetion of the induced current. This feature introduces an error into the ballistic method, for if a magnetic cvele is gone through by sudden changes, a larger amount of energy may be consumed than if the magnetization varies steadily in harmonic vibration.
Suppose, around a magnetic circuit, an alternating current of iV complete periods per second is sent in n convolutions. Let C = the effective strength of the current,
E -the effective E. M. F. induced in the circulit by self-induction, after subtracting the E. M. F.'s induced by the self-induction of the instruinents,
IV = the energy consumed in the circuit, after subtracting the energy consumed by the electric resistance,
Then, I being the length and s the cross-section of the magnetic circuit, all in centimetres, amperes, volts, watts, etc.,
Let B the maximum magnetization in lines of magnetic force per square centimetre,
II the loss of energy by hysteresis, in ergs per cycle and cubic centimetre; it is
W_ lsNHX 0-0
hence
I ITY X 10+7

the hysteretic loss of energy, and

E-= / 2 sB Xn X 10-

hence

B

E_1 x 10+9 -2rsN

(1)

4/ 2 ;r s lTn

the maximum magnetism. For higher frequencies, 80 to 200 periods per second, the alter-

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

dyniamo. This was driven by a 3 H. P. Eickemeyer continuous current motor. By varying the excitation of the motor field 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 sinewaves. Besides, a deviation from the sine shape would not alter the results at
all, but only sligfhtly change the coefficient 97.

1892.1 STEINMETZ ON THE LA W OF HYSTERESIS.

7

varying the E. M. F. supplied to the motor, the speed and therefore the frequency of the alternating current could be varied in wide limiits. At the same time, supplied with constant E. M. F. and like all the Eickemeyer motors of unusually 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 of AMr. Stephen D. Field. On the continuous current commutator two sliding rings were mounted and conlnected with opposite commutator bars. In the ordinary continuous current brushes a continuious current was sent in, which set the 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 maximum E. M. F. to effective E. M. F. found = 1.415, while the sine-wave requires 1.414-that is, essentially the same.
To determine whether the change of the shape of the alterniating 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.
2. By running the Westinghouse dynaino fully excited, feeding 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, and taking current off from the secondaries of these converters, connected from one to six in series.
3. By changing the E. M. F. by means of a Westinghouse converter of variable ratio of tranisformnation.
4. By loading the dynanio when small currents were uised for the tests.
But after having found that all these different ways of varying the alternating F. M. F. gave no perceptible difference whatever in the readings, I afterwards used the most convenient way to
vary the excitation of the dynamo field and, where higher E. M.

8

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 carefully calibrated.
For the electric readings, instrumnents of the electro-dynamometer type were uised, zero-reading-that is, the movable coil was carried back by the torsion of a steel spring to zero position.
These instruments were specially built for alternating currents,
with very low self-induction and low internal resistance, using
bifilar gerinan silver wire as additional resistance.
In the ammeter the range of readings was from 3 to 40 amperes, the internal resistance .011 co.
The norrnal inductance (that is, E. M. F. of self-induction induced by one amnpere alternating current, flowing through the instrument with a frequency of C10 complete periods per second): - .045 w.
In the voltmeter the range of readings was from .5 volts upwards but to avoid the necessity of corrections for self-induction sufficient additional resistance was used to decrease the correction under 1 per cent., and then the lowest readings were from 3 to 6 volts.
The internal resistance of the voltmeter is -2. (co, its normal
inductanee = 4.12 (o. In the wattmeter the resistance of the coarse wire coil (fixed
coil) was -.026 co, its normal inductanice .073 (0.
The internal resistance of the fine wire coil was .25 t, its normal inductance .33 (o.
In most of the readings sufficient additional resistance was used to make the correction for self-induction of the fine wire coil negligible. Only in a few readings where it exceeded 1 per cent. it was taken in account.
For small currents an Eickemeyer ammeter was used, which, while reading from .7 to 3 amperes, though built originally for continuous currents, had already been used by me for alternating currents and had been checked for its constancey of readings several times, and always found to give no perceptible difference in its readings for continuous currents and for alternating currents up to over 200 complete periods per second, the highest frequency I could reach.

1892.] STEINMETZ ON THE LA W OF HYSTERESIS.

9

Its internal resistance is -1.1 o, its normal inductance
- 2.03 to. Several sets of readings for different frequencies were taken
on an old Westinghouse voltmeter converter. The fine wire coil and one of the 50 volt coils were left open. Into the other coarse wire coil an alternating 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.
Hence a correction had to be applied for the self-iinduction of amnmeter and coarse wire coil of the wattnieter and for the resistance 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 constants found to remain constant.
The speed indicator was calibrated carefully and its corrections added.
Each reading consisted of an ammeter reading, a voltmeter reading, a wattmeter reading and a speed readiing.
Before and after each set of readings the zero positions of the instruments were determined, and only those sets of readings used
where the zero position had remained constant. Before and after each set of alternating curreint readings a con-
tinuous current was sent into the circuit and a few readinigs for different currents tak-n. Voltmeter and ammeter readings combined gave the resistance of the circuit, and both combined with the wattmeter reading gave a check for the instruments, here being watts - volts X amperes. Only those sets were used again where an entire agreemient was found, and with the alternating current first readings with simall currenits, then with large currents, and then again with smnall currents taken, so that I believe every possible care was exercised to avoid any errors in the
tests.
As before said, the first sets of tests were made on the magnetic circuit of a small Westinghouse converter.
The constants of this converter, so far as they are of interest here, are:
Mean length of magnetic circuit, 21 cm. Mean cross-section of magnetic circuit, 43.67 cm.2 Ilence volume of iron, _ 917. cm3. Resistance of secoindary coil, .2 co.

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 of iron, 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 50 turns, very coarse wire (3 No. 10 in parallel), were wound 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 58 layers of sheet-iron of the thickness
s = .02577 (1) and the widthw 2.579.
The whole volumne of iron was 153 cm.
The sheet-iron pieces were first freed from scales by dipping into dilute sulphuric acid.
In one set of tests an open magnetic circuit was used, by leaving the short end pieces (3 in. X 1 in.) off, and using two piles each of 66 pieces (8 in. X 1 in.) of the same iron, the same pieces as used in the former closed circuit tests.
In these readings, for the determination of the hysteretic loss, only voltmeter and wattmeter, but no ainrneter, were used, and the conductivity curve determined separately by voltmeter and ammeter.
The calculation of the readings was done in the following way: After applying the corrections for self-induction of instruments, resistance and speed, the readings were reduced to lines of magnetic force per square centimetre B and consumption of energy by hysteresis per magnetic cycle H, in ergs. Then the results were plotted on cross-section paper and if any value was found to be very much out of the curve connecting the other values, it was stricken out as evidently erroneous, not considering it worth while to determine whether it was a wrong reading of any one of the instruments or a mistake in the calcu-
lation. Then from the other values of B and H, under the supposition
that 1 were proportional to any power x of B:
H=g Bx
this exponent x was determined.

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. Then, under the assumption

= 1.6

hence

Hq a B1.6

the coefficient ; was calculated, and now the equation

11= Br 6

plotted in a curve, as given in the figures, and the observed val-

ues of THdrawn in and marked.

From the curve were taken the calculated values of H, corre-

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

determined, and expressed in per cents. of IL

calc obs

calc

These values are given in the tables and shown in the

curves.

I. MAGNETIC CIRCUIT OF THE WESTINGHOUSE CONVERTER.
FIG. 2; TABLE II.
MAGNETIC CHARACTERISTIC.
F. _ M. M. F.) in ampere turns per centimetre length of magnetic
circuit. B. Magnetization, in lines of magnetic force per square
centimetre.
TABLE II. (1)

F. B.

F. B.

F. B.

2

2500

3

3400

4

68oo

5

9600

6 22,750

7 12,850 8 I3,600

9 24,i00

20 24,350

12 14,750
24 I5,o8o i6 25,370
x8 15,630 20 15,88o
25 i6,450 3o 16,950
35 27,370
40 27,780

45 18,150
50 I8,500 55 28,820
6o 19,I40 65 I9,440 70 19,740 75 20,020 8o 20,300
85 20,560
90 20,820

HYSTERESIS.
B. Magnetization, in lines of magnetic force per squiare centimetre.
IL. = Loss of energy by hysteresis, in ergs per cycle, and cubic centimetre, - 10 - watt-second.

12

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

TABLE II. (2)
Frequency: N. - 28 complete periods per second.

B.
3510
10,560 13,800
17,940

H.
obs.
rI78 6286 10,286
15,357

H.)
calc. i16o 6612 I0,180 I59,6oo
av:

H.-H==
calc. obs.

-18 +324 -io6 +243
±1 73

-i.6 +4-9
-1.0
i.6
± 2.3

Exponent of power, derived from tests: x 1.6111 , 1.6
Coefficient of hysteresis: § .002410
hence, theoretical ciirve: H .00241 16

TABLE I. (3)
Frequency: N1= 36 complete periods per second.

P3i. B.~~ ~oI Hbs.. LIcHale,.

Hg. .
calc. obs.

%

7090
10,250
13,41I °0
17,080 19,340

53636373
9694
14,417 i6,iii

3500
630
97.0 14,400 17,600
av:

+ I67
+643
+6
-17 +1489
±464

++140I.82
+I
+, I +8.4
±4.4

Exponent of power, derived from tests: x 1.6476 1.6
Coefficient of hysteresis: - .002315
hence, theoretical curve: H .002315 B'6
TABLE II. (4)
Frequency: N -137 complete periods per second:

B.

H.

H.

11.- H. _ %

obs.

calc.

calc. obs.

4000
4670
55I0 5760 5840 6690
68oo 686o
12,430
13,750

1490
i8i8 2358 2482 2540 3285 3358 3374 86
10,000

1410
I8oo 2350 2520 2580 3180 3290 3370 8io
10,100
av:

- 80 - I8 -8 + 38 + 40 -105 - 68
4
+ '274
+ 100
± 73.5

5.7 -1.0
.3 -1.5 +71.6 -3.3 -2.1 - .16
+3.6
+1.0
±2.0

1892.] STEINAMETZ ON THE LAW OF HYSTERESIS.

13

Exponent of power, derived from tests: -1.5887'1.6
Coefficient of hysteresis:
=.002438
hence, theoretical curve.
-=:.002438 -B'-

TA,BLE II. (5)
Frequency. 20 N= complete periods per second.

f

B.

H.

H.

H-H.

obs

calc.

calc-obs.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i

1790

376

400

I990

463

4mO0

2380

585

510

2620

735

720

3060

893

920

3390

1054

I100

366o

I297

240

424
3

+6.o
-*7

+35

+5-7

-I5

-2.1

+27
+46

t41-229

-57

4.6

37IO
4620

1288 I1822

1250 I800

-38 -22

-3.0
-1.2

5070

2024

2070

+46

+2.2

4990

2034

20IO

-24

-I.2

5910

2693

2620

6xoo

2844

2750

-73

-2.8

-96

-3.5

6550

3039

3080

+4I

+1.3

7290

3673

3640

-33

.9

8050

4341

4300

4I

8320

44IO

4530

+120

+2.7

8240

456I

4460

-2.2

av:

+ 47

=9 2.7

Exponent of power, derived from tests: x = 1.6012 1.6

Coefficient of hysteresis: § .002434

hence, theoretical curve. .002434 B16

From these 4 sets of readings, we get the results:

1.

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

2.

36 5

"

1.6476 .002315

3.

137 10 "

1.5887 .002438

4.

205 18 "

1.6012 .002434-

Therefrom we derive the average, by giving to each value as

weight the number of readings, where it is based upon: x 1.60513 , 1.6

Hence:

a .0024164

ES .0024164 B16 This curve is used for calculating the values given as -H, and is
calc
plotted in Fig. 2 in drawn line.

14

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

The observed values of IH are drawn in Fig. 2:

1. For N= 28 with the mark 0

2. " 36

"*

3. " 137 " " y

4. d 205

"+

r- .ft-

;r

20.000

--

18.000

-

16.000 rr14.000r r
12.000 11V.UVU

--

f

I
1 1T

180-
_--__
0
50 1 .1 I
v ~1~1 ~~~40~

400

__n_00e

I,2

20 zt

20009 49QQ QQQ Q i0 1,0.000 L2.000 g Q .900 18.-000 20.000

.Z~kti F?

Brad(e9 & P&atce Engr.AY.

The magnetic characteristic is drawn in dotted lines. From this curve of hysteretic loss
Hf= .0024164 B'6 we derive the values:

1892.] STEINMETZ ON THE LA W OF HYSTERESIS.

15

TABLE II. (6.)

B.

BI.

B.

H.

1000 2000 3000 4000 5000
6ooo
7000 8000 9000
I0,000 22,000 22,000

152
462
884 12400
2000
2680
3430
4240
5130 6070
7070
8130

I3,000
14,000
I5,000 I6,000
27,000
i8,ooo
19,000
20,000
25,000
30,000
35,000
40,000

9230
1I0,400
Il,6I0 12,880
24,180
25,550 16,970
18,400
26,290
35,210
45,o60 55,800

II.-MAGNETIC CIRCUIT BUILT UP OF WELL INSULATED LAYERS OF VERY THIN SHEET-IRON. FIG. 3; TABLES II I.
MAGNETIC CHARACTERISTIC.
F_ M. M. F. in ampere turns per centimetre length of magnetic circait.
B = magnetization in lines of magnetic force per square cen-timetre.
TABLE III. (1.)

F. B.

F. B.

F. B.

2

I700

3

4.200

4

7400

5

9200

6 10,400

7 8

Ii,i6o
lI,850

9 I2,470

10 13,070

12 13,750 14 14,260 i6 14,600 I8 14,900 20 25,200
25 25,700 30 I6,200 35 i6,68o
40 27,050

45 27,500 50 17,900 55 18,300
6o r8,65o 65 19,030
70 29,380 75 19,730 8o 20,o80 85 20,400
90 20,750

HYSTERESIS.
B = magnetization in lines of magnetic force per square cen-
timetre. IH = loss of energy by hysteresis, in ergs per cycle and cubic
centimetre, = 10-7 watt-seconds.
CLOSED MAGNETIC CIRCUIT.
Frequency: N = 85 complete periods per second.

16

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

..
II-~ L--

1892.] STEINMETZ ON THE LA W OF HYSTERESIS.

17

TABLE IIT. (2.)

1ob.oIbIss.. I

II caalle.

1910 6200
7690
10,470 IlI, I 10
14,030
14,89g
17,940

i 20
3N90
4220
7160
8370 12,600
13,730
17,o40 17,570

~~~3I40 3420
4700
7700
8464
I2,280
13,540 17,040
I8.240

i~~~~~~ar

II. -
caalc.

ooibbi,s..

- I80 - 270
+ 480 - 540 t 96
- 320
_190
+ .66770
± 312

- 5.7
- 7.9
+ 10.2
+ 7.0
- 2.6
- 1-4 -1- 3.7 ± 4.4

Expoinent of power, derived from tests: x - 1.6041 . 1.0
Coefficier-t of lbvster
H' _ .002S5Jl
h11ence, theoretical cmunvA. e
If - i.(02)85 L")1
TA&BUt III. .)
Freqyenicy, Yi 13S cotiplete periods per seconid.

B.
_1
5220
65574500
7070 8210 8520 9570 10,450 111,990 14,570
14,660 I6,770 I7,970 19,320

11. ob)s1.
3030
3620
4320 4830
5950 6090
7850
8780 II,o6o 15,840
i6,i6o 20,350 20,620 23,180

II.
eal c.
310I 3550
4355 48go 6i6o
6530 7840
9040
1230 I5,340 i1,280
19,260 21,440 24,120
av:

IJ. 1H. =
calc. obs.
- 15
70 4 35 + 6o
_-2IO
_ 44°)
- IO
+260
t 170
- 500
- 58o
-IO9O
+ 820 + 940
± 37I

Ar2ll
II.()
+ .8
+ 1.2
+3-34 +5.7 - '1I
+2.9 +1.5 -3-.3 -3-7
-5.6
+3.9
2.8

Exponent of power, derived from tests: x - 1.6044 1.6
Coefficient of lhysteresis: -_ .00335
hence theoretical curve: .151 .0033.5 BI6

18

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

TABLE III. (4.)
Frequenicy, NV- 205 comuplete periods per second:

H.

H.

il-il.

ob. .

calc.

calc -obs.

630o
7340
I0,030
Io,86o
02,230
I4,600 14,700
15s750 ,6,700

4440 5380
Q500 9980
13.700
I7,390
I7,830
19,700 20,990

4660
5780
9300
I0,670
r2,940
I7,060
17,340 19,360
21,300
l av:

+220 +400
+690 760
-230
-490 340
690
+t 425

+4 8
+6.9
+6.5 -5-9
-I.3 _2.8 --0.7
3.2
±3-7

Exponent of power, derived from tests:
x- 1.697 1.6
Coefficient of hysteresis: .00373
hence theoretical curve: II .00373 B'-6

OPEN MAGNETIC CIRCLTIT.
Two gaps of , 4 cm. lenigth.
TABLE IIL. (.1.)
Frequency, Z - 138 complete periods per second.

B.
3I50 3640
46go 5490 6270
10,250 o,o000
12,280

H.
obs.
0570 20I r10 2930
3510 4380
10,450 ii,8to
14,250

H.
calc.
I56o 2020 2950
3780 4690 I0,290
01,520 13,740
av:

1 1%.-=f.
calc. obs.
-0 - 90
+ 20 + 270 + 310 - I60 - 290 - 510
+ 208

.6
-4-4
+ .7
+7-2 +6.6
-i.6 -2.5 -3.7
± 3.4

Exponient of power derived from tests: x - 1.6040 , 1.6
Coefficienit of hysteresis:
- .00394
hence theoretical curve: H = .00394 B"f

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

19

From these four sets of readings we get the results:

CLOSED MAGNETIC CIRCUITr.

- 5. 9 readings: x- 1.6041 -q .00285

138 14 "

1.6044 .0033"

205 9 "

1 6'97

.00373

OPEN MAGNETIC CIRCUIT.

NA 138 8 readings: x 1.6040 ri .00393

Hterefroin it seems that the conisumption of energy by hysteresis per imagnietic cycle iniereases with increasing frequency-
that is, with increasing velocity of the magnetic change. The three 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 frequencies, in Fig. 3 tlhe curve of hysteretic loss for N -100 complete periods per second is plotted, giving:

.003

lience

ff- .003 BI-6

and the observed values of .11 are not directly drawn in, but the observed values of I/multiplied witli the factor:

obs.
to compare the different frequencies with each other. These va-lues are plotted for: N' 85 with the mark y 138 " " + L Closed magnetic circulit. 205 c " * J
N 138 with the mark o; Open inagnietic cir'cuit.
From this curve of hysteretic loss,
II .003 b'-
we derive the values, for the frequency of IN 100 complete periods per second.

20

I[Jan. ASTEINMETZ ON TIIE LA W OF HYS TERESIS.

19,

TABLE III. (6.)

1,.
1000 2000
4000
5000
6000 700o 8000
9000
I0,000
11,000
12,C00

II.
I90 570
I [00 I740
2490
3330 4260
5280
6360 7530
8790 10,080

B.
13,000
I4,000
15,000
I6,ooo
27,000
18,000
9,00 20,000 25,000 30,000 35,000 40,000

II.
II.460
I2,900 14.430 15,990
I7,6I0
19,290 2 I,o60
22,830
32,640
43,68o
55)950
69,270

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 eniergy in the iron is sniialler in the
open magnetic eircuit than in the closed eireuit.
For the coefficient of hysteresis observed on- openI milagnletic cir-
cuit
^I-.00393
is even greater tlhani that for closed inm,ignetic cireuit,
Ti ,(3P35
Blut this discrepancy is easily exphlaiied bv the fact that in the
closed mnagnietic circeulit the mnagnetization is iiearlv uniformi throughout the whlole iron. Blut in the open magnietic cireuit the magnetic field initensity differs conisiderablv froml point to poilt,
being a maxiunnm in the imiddle of the magnetizingr coils, a miniunLtin at the elnds of the iron sheets. Now, the values of B given
in the table, are the average values of the milagnietizationi, and the values JT, the average values of lhysteretic loss. But the average
value of the 1.6th powers of different quantities IB is larger than the 1.6th power of the average value of 1B.
Fot instance, in a cubic ciii. of iron mnagnietized to B1 = 12,004) is I1 10,080; in a cubic crr[. of ironi miagnetized to B -000) is H _ 3330; henlce of these 2 cubic cenitimetres the average magnetizationi is
1, -_ 9000), and the average 1f 6,i705 ergs
but to 12 - 9000 corresponds 11 6360 ergs; that is, abouit 3 per cent. less, and the difference becomes still greater, if the values B differ still more.
Taking this into account, it seemis that the loss of energy due to hysteresis depends only upon the intensity of inagnetization, and perhaps upon the frequenicy, but is independent of open or closed magnetic eircuit, as is to be expected.

1892.] STEINMETZ ON THE LA WV OF HYSTERESIS.121
III.--IG. 4. TABLES IV. A third set of determinations of the lhysteretic loss of 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 pieces of 7.61 cm. length and 2.54 cm. width, of the thickness o .0686 cmn., that is, of considerably greater thickness than in the former set of tests.

22

SYEINMETZ ON THE LAW OF HYSTERESIS. [Jan. 19,

Here evident proof of 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 frequency was left acting upon the iron. This decrease inust be attributed to the increase of the electric resistalnce of the iron,
caused by its inereasing 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 was sent through the magnetizing coils and left on for ten to fifteeni mninutes, and thel fnrst readings witlh low imagiietization, then witlh high, and theni again with low mnag-
netization were takeni. But, nevertheless, as was to be expected,
in these tests the observed values agreed less with each other thain in the 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 at the same time. In calculating these
tests, the law of the 1.6th power was assumed as true, and the loss of energy in the iron expressed by the equation,
11 -- BL6+-ATB2
where
1-1 -^-§ ;1B11.6
is the true hysteretic loss pei cycle and cm3., which is independent of the frequiency, and
1J2 e AX I
is the loss of energy by eddy-currents per cycle which is propor-
tional to the frequency N.
From this expression
ll-fH +J/2
the coefficients ^ and e were calculated and the agreenment or disagreement of these coefficients § and s allow now to check the correctness or incorrectness of the law of the 1.6th power.
Thesetests gave the following results:
MAGNETIC CHARACTERlSTICS.
C IM. M. F., in ampere turns per centimetre length of mag-
netic circuit.
B - magnetization, in lines of magnetic force per square centimetre.

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

23

TABLE IV. (1.)

F. B.

F. B.

F. B.

1.5 29700 2 4,350
3 7,100
4 8,850
5 10,000 6 10,800

7

1 J ,700

8

12,200

9

r2.700

10

13,1000

12

23,900

14 24t500

i6

15,000

IS

15,450

20 I5,800

25 i6,400
30 xI6,8oo

35 17,200

40 17,500

HYSTERESIS.

B magnetization, in Iiiues of magnetic force per squiare centimetre.

Hf loss of energy by hysteresis, in ergs per cycle and cm'. ( 10-7 joules) - t + H3
EIA _ ;y B'6 loss of energy by hysteresis proper, in ergs per
cycle and cmin. (- 10- joules).

ll, e N 12 -loss of energy by eddy-currents,.in ergs per cycle
and cm'. (- 10-7 joules).

TABLE IV. (2.)

Frequency, 1N 78.

- = .00331

£.1l X 10-6

B. H,11 112 J1(I)i

calc.

obs.

4I71
5850 0520 13,I60 14,320
I6,05o

2,o60
3,540 7,740
22,960
24,880 17,280

I,o8o
2,120 5,600 I10,710 1I2,720 T5,900

3,140 5,66o
13 ,340 23,670
27,600 33,T80

3,060 5,640 I3,440 24,540 26,460 33.180
ax:

+ 8o + 20 - I00
- 870
+I"40
......

+ 2.6 + *3 - .8
- 3-7 + 4.0

6 ±9(+ I .9 (+ 4)

TABLE IV. (3.)

Frequency, N1- 140.

I= .00331

L

.730 X 10-6

B. H, H2 L(I) H. A = % calc. obs.

4980
678o
7720 I0,200
12,080
17,200

2,650
4,490 1,530 8,640 1,300
I9,860

2,720 5,270
6,830
II,940 I6 700
33 .840

5,300 9,760
I2,360 20,580
28,000
53,700

5,280
9,420
12,600o 20,400 29,100
53,000

+ So
+ 340
- 240 + i80 -1100
+ 700

+ I.. + 3-'
+ 4.-
+ I.

24

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

TABLE IV. (4.)

Frequency, AV 207

a .00336

-.757 X 10-

B. Hi H2 He I
caic. obs.

%

2710
4720 7540 12,380
13,200

1,030
2,510 5,320 1I,700 13,000

1,290
3.910
9,970 26,800 30,400

2320
6,430 15,290
38,500
43,400

2,340
6,480 I5,960
38,500 42,600

- 20
- 50 - 670
+ 800

- .8 - .8 - 4.4
+ i.8

av:

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

Therefrom we get the results:

N=V 78, 6 readings, rq .00331 e .751 X 10-s

140, 6 "

.00331 .730 X 10-6

207, 5 "'

.00336 .757 X 10-8

The values found for C are so nearly alike that we can consider them as constaint, and take their mean value

- .00333

as the coefficient of hysteresis. Even the values found for s are not much different froin eaclh
other, not more than was to be expected from the unavoidable differences in the temperature of the iron, which because of the high electric temperature coefficient of iron makes - rather variable.
Taking the average of e, we derive

= .746 X 10-6

and as formula of iron loss,

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

In Fig. 4 are drawn the four curves,

1. True hysteretic loss, H.- .00333 B'-6

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

3. "

"

140

.0001022 B2

4. "

" 209

.000156T B2

The observed values are plotted by crosses, +

1. H is calculated by using for I the 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.

25

I.-FiGS. 5 AND 6; TABLES V AND VI.
Two otlher sets of determinations of the Iysteretic loss of en-
ergy, for the frequency 170 coinplete periods per seconid, were made on two laminated hlorse shoe mnagnets, witlh laininated
keeper or armatuire.
The inethod of observation and of calculation was the same as in IfL., and the same precautions MTere taken.
The dimensions of the horse shoe mnagnets were:
Mean length of myagnetic circuit: 38 cin. cross-section: T7 cm.2
" voluine of iron: 2660 cm..3 distance of keeper from miagnet, in the first case: .15 cmu.
distance of keeper froin miagnet, in the second case:
.08 cm.
-each magnet consisting of 300 sheets well insulated iron, of the thickness.0405 cm.
In the first set of readinigs, considerable eddy-culrreints were found; in the second set, only a small amount of eddies.
The mnagnetic conduietivity of the iron was nof determined,
because the reluetance of the mnagnietic circuit mainly consisted of that of the air gap between magnet and keeper.
The results were,
B _ magnetization, in lines per cn..2
HF observed loss of enerigyg tIme iron, in ergs per cycle and
obs.
cnm.3 for N7 -170.
Hi - true hysteretic loss of energy. RJ2 loss of energy by eddy-currents.
I whiole calculated loss of energy, II, + In2
calc.

26

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

TABLE V.

Frequency, Y - I pT)0.

- .0045

e 1.16 X 10-6

B. .1/1

342

51

410

68

546

io8

620

670

I50

746

178

b30

2}0

I020

293

I100

345

12 00

392

1310

436

539

2930

820

2600

1310

H2 H. calc.

H. jH. -1.H. =
obs. calc. obs.

23

74

70

+4

+5.3

34

I102

102

59

i66

I66

+

I

+ .6

78

210

219

9

-4.3

go

240

234

+6

+ 2.5

III

289

300

- II

- 3.7

238

348

333

+ I5

+ 4.3

208

502I

524

- 23

- 4-5

234

579

549

+ 30

+ 5-3

290

682

695

I3

- 2.0

34

779

795 -

- 2.1

445

984

o85

-I

- .1

742

1562

1547

±+ 15

+ 2.0

1280

-90

2670

-80.

3.2

+ 7'
153

+ 19.0
19.8

av:

+ 16

±2.8

Therefore we get the for mula fol the loss in the ironi, _ .0045 _B16 + 1.1 6 2N X 1 0-B
In Fig. 15 are showin

Fig. 5.
1. The curve of true hysteretic loss, H1 .0045 Bl'6
2. The curve of the whole loss in the iron, ffI-1, +112
with the observed values marked by crosses +

1892.1

TLV-I EYZ ON TIlE LA T OF HYSTERESITS

TABLE VI.

Frequency, A-' 170(

- .00421

e - .2083 X 10 '

B.
85 182
211
560
670 685 775
8oo 1000
1070 1130 1250
1383
24200
2420

11,
5.2 17-3 22.0
105
140 '45
176 i86 265 296 322
379 445 940
1090

I"2 f.
cale.

.3
13 1.7
II
I5
I6I
'2r 22
35
41
47
56 69
170 208

5
I8.6 23.7
'55 i6I '97
208
300 337
369
435
514
1293

1/. 11.-H.
obs. calc. obs.

5.6
i6.9
23.5 122 I46
'57
202 200
300
353 386
430
5I4
1130
1268

-

I

+ I.7

+ .2 -6

-I9
+4 -5
+8

- I6 - I7
+5 - 26 -+20
+ 30

+ 38 - 90

- I.8
+I10.0
+ *9
5.0
+ 6.I
+ 2.6
2.4
t 4.0
- 4.t - 4.3 +Ir .2 -4.7 i- I .8 + 2.4
_I _
+27.2 -24.6

av-

+ 1O

+ 3.4

Therefore we get the forrnula for the loss in the iron, I1I- .00421 B'-' + .2083 x 10- N B2
In Fig. 6 are shown,

28

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

1. The curve of true lIysteretic loss,
JTL .00421 B1 ;
2. The curve of the whiole loss in the iron,
Ifi + 14
witlh the observed values inarked by crosses +
Especially interesting are these two sets of readinigs in so faI
as they cover (quite a different range of magnetizatioln as the 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, that is, for mnediuim mnagnietization up to high saturation, while the tests in IV. 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,
II aB16 + N- 1B2
and herewith proved for the full range from 83 lines per CuE2 up to 19,340 lines, a ratio from 1 . 230.
This seems not to agree with Ewing's tlheory of the iimolecuilar magnets. According to this theory, for very small mnagnietization the hysteresis slhould be expected to disappear, or almost disappear, and the cycle b-e reversible. Then for mtiediumn mlgnetization, where the clhains of miolecular mnagnets b)reak up and rearrange, hysteresis should increase very rapidly, and slowlyv again for saturation. Nothinig of this is the case, but hysteresis seems to follow the same law over the wlhole range of niagnetization, and is certainly not zero for even suchl a low itiaginetization as 85 lines pei Cm.'

MIAGNETOMETER TESTS.

The imethod used in the foregoing has the great advantage
that
1. It allows the taking of a greater miumber of readings, over a wide range of magnetization, in a short time, by mere simultaneous instrumenit readings, and tlhereby reduces the probable error by increasinig tie niumnber- of observations.
2. It allows the use of electro-dynamoneters, as the 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 tme hyvsteresis iiider the inifliience of an liarinoiii(-ally, anid niot suddenfly varying m. M. F., that is uder the

30

STEINJE7TZ ON THE LAW OF HYSTERESIS. [Jaii. 19,

samne conditioins, wlhere it becoines of iiniportance for practi-
cal engineeriing. But it has the great disadvantage that it can be used only for
testing sheet-iron or other thoroughly lanminated iron, where ed-
dies ale either inappreciable or can be calculated also. For testing solid iron and steel pieces, this method cannot be used, because of the tremendouis amount of eddies which wouild flow in a
solid piece of iron. To determine the hysteretic loss of energy in steel and cast-ironi
the Eickemeyer differential magnetometer was used. Complete description of this instrument and its use is to be found in the
Klecirtical Fitg1neer, March 25thl 1891, wherefrom is taken a
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 is interested in it. In Fligs. 8 and 9 are diagrams of its action.
The principle of this instrument resembles somewhat the priniciple of the well-known differential galvanometer. applied to the magnietic circuit. In Fig. 8, suppose F1 and FY were two E. 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 a and b of equal resistance, which influences a galvanometer needle G in opposite directions but with equal strengtlh.
Then the zero position of the needle G ShOWS that the electric current (a, flowing in a, is equal to the current cb in b. But let the current in x be c'1, and in y, ey ; then we imiust have
0a + Cy Cb + C.
because the currents ca and c are the two branches of the saine initegral current as Cb and cx
Therefore, if ea- Cb, then

But if Ca Cb, and a - b, the difference of potential at the ends of a (or, what is the same thing, y) is equal to the difference of potential at the ends of b or d and, therefore, the current in x and y, and the potential differences being the same, it follows that x y.
That is, this method of connection allows us to compare an unknown resistance x with a standard resistance y.
Now, instead of " electric current," say " magnetic current"

1892.] STEINAMETZ ON THFE LAW OF HYSTERESIS.

31

or "iinumber of lines of miagnetic force; " instead of " electiromotive force" or " potential difference," say "magneto-motive force;" and instead of "1 electric resistance," say " reluctance,"
and we have tile priniciple of this instrume-nt.

FIG. 8
Its imagnetic circuit consiSts of two pieces of best Norway ironi,
ULJ shaped, shown in the illulstiation of the complete instrti-
ment, Fig. 7, and in the diagramn Fig. 9, at F, and Fv. The middle portion is surrounded by a inagnetizing coil c. Therefore if -coil c is traversed by an electric current, the front part vq of the left iron piece becomes southl. anid tlhe back part Ye northt polarity.

172
FIG. 9
The froint part of the right iron piece n becomnes north, and tl,e back part south; and the lines of magnetic force travel in the -front from the right to the left, from n2 to 81; in the back the op posite way, from the left to the right, or from ii1 to 82, either

32

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

through the air or, wlheni m2 and 81, or n, and s2, are connected by
a piece of magnetizable metal, through this and tlirough the air. In the middle of the coil c stands a small soft iron needle with
an aluminiium indicator, whicl plays over a scale K, and is held in a vertical position by the lines of magnetic force of the coil c it-
self, deflected to the left by the lines of magnetic force traversing
the fronlt part of the inistruimen-t from n2, to si, deflected to the
riglt by tlhe lines traversing tthe back fromn ii. to s,. This nleedle slhows by its zero position that the imagiietic flow through the air in f"ronlt fro]m ii2 to lhas the same strengtlh as the mnagnetic flow in
the back fr ito1, to tlhrough the air.
Now we put a piece of soft iron x oni the fronit of time instriimient. A large number of lines go throughl x, less through the air fromt i, to bl-)ut all these lines go fromn n1 to , tlruolgh the air at the back part of the muagmietouieter, the fro;nt part and back part of the instrutment being connected in series in the magnietic
circuit. Thlerefore the needle is deflected to the riglit by the inignetic flow in the back of tlhe inistrum-Lent
N ow we put aniothier piece of iron, y, oni tlhe back part of the instrumient. Theni eq:uilibrium woulld be restored as soon as tlle same m1un1Il)er of lines of inagnetic force go through ii, as throllgh 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 takes the
place of the resistanees a( and 1b, influencing the galvanometer
nleedle (n, as in the diagrami, Fig. S.
The operation of the instrumneut is exceedingly simlple and is as
follows : Into the coil cz ani electric eurrent is sent whichl is
mlleasured by the aimmeter A, amid regulated by the resistaneeswitcli R. Tlihen tlhe nee(dle wliel before lhad no fixed position,
points to zero.
Now the magnetic standard, consistinig of a cylindrical piece of Norway iron of 4 cin.2 cross-section and 20 cm. lengtlh is laid againist the back of the instrument,with both ends fitted into holes in large blocks of Norway iron, A3, A4, whieh are laid against the poles S1 V of the mnagnetometer, so that the transienit resistance from pole-face to iron is elinminated.
The sanmple of iromi tlhat we wislh to exainine is turned off to eaetly the saime size, 4 cm.2 cross-section and 2() cm. length, and
fitted into blocks A, A2 in frotnt of the magnetometer. Then-
so iany fractional standard-pieces of Norway iron are added in. front, that the needle of the instrumrnent points to zero. This

1892.] STWIN2IETZ ON THIIE LA W OF HYSTERESIS`.
mneans that the 4 cmn.2 Norway iron in the back, carry under the same differeice of mnagnetic potential, the saine magnetism as the 4 Cm.2 of tlhe examined sample plus the x cm.2 of fractional standard, added in the front. Hence, 4 cm.2 of the exanmined sample are equal in miiagnetic conductivity to (4 -a) cm.2 of Norway
4-
iron, an(d the magnetic conductivity of this sample is 4 X
100 per cent of that of Norway iron for that differenice of mag-
netic potenitial, viz., mnagnetization, that corresponds to the
magnetometer current.
To get absolute values, the instrument has been calibrated in tihe following way: In the front and in the back the magnetic
cireuit of the instrument hlas been closed by 4 cM.2 Norway iron.
Then aniother pieee of iron, anid of any desired size, has been
added in the front. This piece, y, carr-ying sone magnetism also, equilibriumLn was disturbed. Then tlhrough a coil of exactly 110 turns, surrounding this piece y, aii electric current i was sent
anid regulated so tlhat equilibrium was restored. In this case no m:ragnetism-ri passed tbmrough y, or in otlher words, the M. M. F. of
the curreient i 1 101 ampere tuLrns, is equal to the differences of miag,netic potenitial between the pole-faces of the instrumlent. In this way, for any strength of current in the main coil C of the
magnetometer, the differeiiee of magnetic potential produced
thereby between tlhe pole-faces of the instrument, was deter-
mined and plotted in a culrve, for convenience in amupere turns per cm. lenigthi.
Now, the Norway ioion standard was compared on the milagnetomneter witli sheet-iron, of wrhich, from tests witlh low frequency alternatinog currents, the mnagnetization corresponiding to any mI. Ai. F. was known, and tlherefroin derived the miagnetic clharacteristic of the Norway ironi standard, amid plotted in a curve also.
In the way explained before, the iron sample that was to be determined, was balanced by the imagnetometer bv Norway iron, thereby giving its magnetic conductivity in per cent. of that of the Norway ironi standard, the magnetometer current read, from the carves taking the M. M. F. corresponding thereto-denoted with F- and the magnetization of the Norway irol, corresponding to this xl. M. F, F, amid fro-n thle determined per centage of conductivity of the examined sample, the magnetization B of this sample corresponding to the M. M. F. F.

34

STEIVYMETZ ON THE LA W OF HYSTERESIS. [Jan. 19,

With this instrumeiit a number of magnetic cycles of different samples of steel and cast-iron were determined.
First, a powerful alternating cuirrent was sent through the magnetometer and arounid all the iron pieces used, to destroy any trace of permanent or remanent magnetisrn.
Then the examined sample was laid against the front, the
standard against the back of the magnetomreter, balanced, and a larger number of magnetic cycles completed between given limnits, for instance, + 95 and -95 ainpere turns M1. -M. F. per cm. length. Then readings were taken from imaxinmumn M. M. F. + 95 down to zero, and again up to the miaximum- 95, downi over zero and up to + 9(5, thereby completing a whole magnetic cycle, and then of a second magnetic cycle, a few readings were
taken as check for the first one.
In this way for different AM. M. F.'S the curve of hysteresis was found, and by measuring its area the loss by hysteresis determined.
The furthier calculation was done in a somewlhat different way. Generally the number of cycles was not large enough to determine conveniently the exponent by analytical methods.
Therefore the law of the 1.6 M. power:
1.1 '§ B 1
was assumed as true, and for each cycle froimi the kniown values of ff and B determined the co-efficient i.
If for different cycles the values of qi agreed, this would prove the assumption, the correctness of the law of 1.6th power, while a disagreement would disprove it.
In the following for a niumber of samples the iiiagnetic cveles are given:
F = M. M. F., in ampere turns per cm. length. Br and Bd - the intenisity of magnietization, in kilolines, corresponding to M. M. F. F, for the rising and the decreasing branch of the magnetic curve.
The area of the looped curve, representing the loss of energy by hysteresis is derived by adding the values of Bd, and subtracting therefrom the sum of the values Br, Bd and Br, being given from 5 to 5 ampere turns, or .5 absolute units, the difference of the sums of Bd - Br just gives the loss by hysteresis, in ergs per cycle.

1892.] STEINMETZ ON YIHE LAW OF hlYSTERESIS.

35

CAST-STEEL, ANNEALED ANI) HARDENED. FIG. 10; TABLE VII.

Of one kind of steel, two test pieces were cast, at the saime
casting, tuirined off to standard size and, by comparing tlhem in the

magnetometer, found to be exactly alike. Then the one piece was hardened, the other left annealed. Magnetometer tests gave the following magnetic cycles:

36

STEISMIETZ ON THE LAW OF HYSTERESIS. [Jan. 19,

TABLE VII.

Hardened.

Annealed.

F. Br Bd Br Bd B, Bd Br Bd Br Bd

L 5.0

4.4 +5.6

I5!
'0

-3.7 2.7 0

6.I 6.5 6.9

25 +3-9 7.3

432o0

5.- 7.6

35

6.7 8.o

7.7 8.3

8.,

50 (44-5.)

.3t655o7

I467500D

i75

48,300

I55

go 95
1!055

IIO.
48,300

± 7.0

± 7.8

-6.4 + 7-5 7-3 + 8.2

5.6 7.9 - 6.8 8.6
4-4 8.2 - 5.6 8.g

-'.9 8.6- 2-3 9.2

+ I.9 9.0 _- .4 9.5

4.2 9.3

2.5 9.8

6.2 9.6

4.2 10.I

7.6 9.9

5.8 20.4

8.7 9.6 10.4

20.2
10.2 io.8

7.2 10.7 8.4 II.0 9.6 II.2

I0.9 I1.1

IO.4 11.5

11.4
(64.5.)

IO.9 II.8 II.4 I2.0

1 I.9 12.3

12.2 I2.5

12.5 I2.7
I2.8 I2.9

I3.0 I3.I

I3.2 13.3

I2.4 13.4

13-5
(Io8 o.)

± 6.6
- '.4 +10.7
+ 3-4 II.9 8.4 12.5
IO.9 I2.8
I2 2 I3.I 13.0 I3.4 13.5 I3.7
13-9 I4.0 I4.1
(44.5.)

± 8.6 2.6 +11.3
+ 3-7 I2.3 8.4 I2.7
io.8 I3.0
12.0 23-3
12.7 13.0
13.2 I3. 9
I3.5 14.2
13.8 I4.D
14. I 14.7
I4-4 25.0
14.7 I5.2
15.0 I5.4
15.3 15.6
I5.6 I5.8 I5.8 i6.0
i6.o I6. I I6.2 I6.3 I6.4 i6.5
I 6.6
(IOI .O.)

77,800

101,10 34,800

45,000

Herefrom as coefficient of hysteresis, was found -- .02494 .02eo12 .02490 .007997 .007962

Average,

^r - .024987 - .025

S -.007980 .0080

Hence, when antnealed, the hysteretic loss is

II .008 1-.6

when hculde ned

ff- .025, B'6

and calculated by means of these formulas, we derive

II- 4S,400
calc.

and

II-
calc. obs.

+ 100

- per cent. of

77,500 -300

101,500
+ 400

34,730
- 70

45,100
4- 100

LIf

+.2 -.4 +.4 -.2 +.2

calc.

In Fig. 10 are drawn some of the magnetic curves for both

samples.

1892.] STLEKLYIETZ 0X- 771E LA TF OF H YSTERESTIS.

37

It is especially interesting to note that though the ch0nical constituition of both samples is exactly the saiyme, their imagnetic
behavior is entirel, different, so that the magnetic properties of iron seein to l)e deteriiniied mucli mnore by- its -A)y/mc8al thlan its
cehenweal constitutioni.

ANOTHER SAMPLE OF CAST-STEEL OF Low MAGNETIC CONDUCTIVITY. FIC. 11.
TABLE VIII.

F. BrJ,d

5 5
IO
I5
20
25
30 35 40 45
50
.55
6o 65 70 75 80 8,: 190 95

+ 2.5
-'.5 +3.4 + .6 4.I
2.7 4.6 3-9 5-I 4-7 5.6 5.5 6.o 6.2 6.3
6.38 (37.0.)

If-
obs.

14,600
.02I9

R'9 II'dI
B+2 .R8

-i± 2.8

1' .9 +3.6

-.4 4-3

+2.7 4.9

44..90

5-5 6.o

5.6 6.4
6.2 67 6.6 7.0

7-0

7-3

7.4 7.3

7.64

(52.0.)

Br L'd

3.I 2.2 +3-9

.6 4.6

+2.2

5.2

4.2

5.8

5.2

6.2

5.7

6.6

6.i 6.9

6.6

7.2

7.0

7-5

7.4

7.8

7.8

8.i

8.I

8.4

8.4 8.6

8.7 8.8

8.95

(75-0.)

29,900

25.000 .0I29

B, Rld

-2.7
I.3
+2.3
3.8 4.8 5.5 6.o 6.5

3.4 +4.2 4.8
5-4
5.9 64 6,7 7.2I
7.4

7-0

7-7

7-4

7.9

7.8

8.2

8. I

8.5

8.4

8.8

8.7

9.0

9.0

9.2

9.3

9.5

9.5

9.6

9.8

9.8

IO.O

(95.0.)

29,600

.01118

38

STEINMETZ ON T'IIE LA W OF HYSTERESIS. [Jan. 19,

Average, v =.001195 .012

Herefroin,

IH = .012 B'6

if

14,620 19I,520 25,140

calc.

I-Il
calc. obs.

+ 20 - 380 + 140

_ per cent. of

-+.1 - 1.9 +.6
calc.

30,020
+ 420
+ 1.4

#r

Fig. 12.

1892.] ST'EINMETZ ON THE LA W OF HYSTERESIS.

39

With regard to hysteresis, this kind of cast-steel is 50 per cent. worse than the annealed cast-steel No. 1, but still twice as good
as the hardened sample. But, magnetically, it is poor-that is,
of low conductivity, giving for 40 ampere turns M. M. F. per centimetre leingth only - 6600 lines of magnetic force per square centimnetre. while the annealed steel gives , 14,000-that is, more than twice as many, and even the hardened steel gives more,
8000.

SOFT MACHINE STEEL. FIG. 12.
TABLE IX.

F
0
5
10
I5
20 25
30 35 40 45
obs

I.

IL

III.

Br Bd Br Bd F Br Bd

± 8.3

9.6

50

5.7 -+-I0.2 - 7-5 +11.2 55

+ I.2

II 6

- 20

12.4

6o

7-4 12.6 + 7.2 13.5 65

1I.0

I1.4

10.9

14.2

70

12.6 I3.8

12.4 14.8 75

13.5 14.2

13.3

15.3

8o

14.2

14-5

14.8

I4.0 15.7 85 I4.7 i6.o 90

(39-0.)

I5-3 I6.4

I5.9

i6.8

I6.4

I7.0

i6.9

17.4

I7.3

I7.7

17.7

I8.0

I8.0 I8.2

I8.3

I8.4

i8.6

I8.7

I8.8

(90.0.)

44,400

64,ooo

.00944 !00928

Average, ;q- .00936

hence

H

44,000

calc.

A

-400

64,600 + 600 ± 1.0 per cent.

40

SBTINMETZ ON TIHE LA TV OF HYSTERES]J>K. [Jan. 19,

CAST-TRON. FIG. 13.

Fig. 13. TABLE X.
I~~~~~~~1.~~~~~~~~~~~~~~~1~1~. ~~~~~~~~

F Br B,i Br Bd F

5

+ 2.5

± 3-5

50

-I.7

+3.2 -2.7

+4.I

55

-.6

3-9 -I-7

4-7

6o

I5 + -9

4 4 - .2

5.2

65

20

2.6

4.9 +I.6

5-7

70

25

3-8

5-4

3.0

6.i

75

30

4.6

5.8

4-0

6.5

80

35

5.2

6.i

4.9

6.8

85

40

5.8

6.4 5-5

7.2

90

45

6.3

6.6

6.Ii

7.6

95

50

6.8

(50.O.)

H=
obs.

22,300 ergs

7/ -I0i647

42,ooo ergs .01589

11.

Br Bd

6.8 7.9

7-3

8.2

7.8

8.6

82 8.9

8.6

9.2

9.0

9-4

9-4 9.7

9.7 9.9

20.0

2O. I

10.3
(95.0.)

Average,
H-
calc.
H- Il-
calc. obs.
- per cent.,

Ti .01616 22,000

42,800

-300

+ o800

1.54+ 1.9

1892.] STbTINMETZ OX THE LAW OF If YSTI?RESI.S.

41

MAGNETIC IRON ORE. FIG. 14; TABLE XI.
In the following are given the inagnetic curves of a piece of
magnetic iron ore, apparently pure Fe,)4, of the dimensions,
Iin. X 1 in. X 22in.

42

STE1NMETZ ON THE LAW OF HYSTERESIS. [Jan. 19,

TABLE XI.
MAGNETIC CHARACTERISTIC.
F M. M. F.. in ampere turns per centimetre length of magnetic circuit.
B magnetization, in lines of magnetic force per square centimetre.

F

B

F

fB

F

B

10

750

20

15I0

30

2000

40

2220

50

2560

6o

2760

r---r-

70

2930

8o

3080

90

3220

I00

3350

10

3470

I20

3580

-

140

3770

i6o

3930

i8o

4070

200

4200

220

431I0

240

4400

Fi.q. 1J.

1892.1 STFIAYMEZ OIV TIlE LA W OF HYSTERESIS.

43

TABLE XII.
CYCLIC MAGNETIZATION.

; ~~I.

II.

F Br Bd

0 10 20 30 40 50 6o 70 80 90 I 100 I20 120

± g900

0 ±1520

+1200
I 800 2260

1920 2230 2500

2450 2700

2670 2850
2850 3000

3020 3120

3I90 3250

3340 3360

3440
(To6.)

Br Bd

1020 - 200 +I66o

+I000 2750

2020
2280

2250 2520

2390 2720

26I0
2800

2880

2980 3I50

3I40 3280

3280 3420

34I0 3530

3530
3640

II.

F Br Bd

I30

3640 3740

140

3730 3820

150

3820

390

I 6o

4910 3980

270

3990 4050

r8o

4050 4210

I90

4120 4I70

200

4290 4230

210

4250

4280,.

220

4320 4340

230

4360 4370

240

4400

(240-)

oH. 9,340 ergs

13,780 ergs

-.02049

.02041

Average. i_ .02045

Ciurve of hysteresis,

I- .02045 B1.6

1- 9,320 ergs
calc.

13,810 ergs

-1 LI - 20) ergs
calc. obs.

+ 30 ergs

.2 per cent. + .2 per cent.

As seen, the coefficient of hysteresis of magnetic iron ore,
.020, rainges between that of cast-iron, r .016, and of
hardened steel, --.025.
The magnetic condictivitv is approximnately 20 per cent. of that of wronght-iron.

In Fig. 15 is given a comnparison of the hysteretic curves of

11 ardened steel, Annealed steel, Cast-iron, Magnetic iron ore, in the same size.

This figure shows well the three characteristic forms of hysteretic curves:

44 ¢

I *~ STEINMETZ OX THE LA Wlf OF HIYSTERESIhS.

K
CL

0H

CL)

0.

.jc

(N C)

+- 'r) t\0 Icoo3 0 0 0
H O . H H Co

M IY)N 10 N s O M L)1 C

Nm

.H- _ .

O~ O O
C~O

OO

C

O

0 0

cL
ct
=;C&
ct c3
ct-

[Jan. 19,

0

_

(-)

I~

CL

0

.C

0 CL

C))

CL

-.

II

.K

C G5 O_; 'b ^

ur_o0o0Ifc)sD

_
N

U) "r

0w II
u t-C C,. t, u

0 ! ct CLO

ct

>

(N

0

CL

4I

C0Lv

+I

.

C C r._
bk tt~
C)
0_,

O C. C OO0C t,o _0 )In + t1-s th
F . r!

:

OO O oO0

O0+-O O OCCC

O rl

"t-r'SO 00 CN

.4F

O O C0 OOOC oo "l - w

0C0

O0

D 3

O C

C O

LOn

+o oo O 'D N t-

* +++cgO

C N 0oo N OL o CmLN UO O N O L

0O

0 3 3 3c

oe

CL

-0

I

.

CL CL
4 SH -; 0

0

to'
Ql

X XX

I I C= 0 0

1-

-, r.

*ClL 11 II 11

(N)

'^

1892.] STE1INMETZ ON lJHE LA W OF ITYSTERESISS.

45

1. The lhardened steel curve, of higlh coercitive force, has the
bend or " knee " on the regyatixe side, so that for zero AI. M.
F. the "remanenlt" magnetis[ni is still in the saturation part of the curve-thlat is, in stable equilibrium; therefore permrlainently mnagnietizable.
2. The soft iron curve, with the bend on the_posUive side, so that
for zero M. M. F. the "'remanent" magnietismr. though still very high, is already below the raTnge of saturation, on the branchl of unstable equilibre Therefore the remanent
mnagnetismn is very unistable and easily destr'o-yed, the more
as the coereitive force is very small.
3. The cast-iron curve, wlhilch lhas no rnarked knee at all, but a steady eurvature of low remanen-t myiagnetization, but with regard Io coercitive force ranging between 1 and 2.
The curve of the mnagnetic iron ore shows all the characteristics of a cast-iron ecurve.
Having, deiived. inow, a larger numiber of values of tlhe hyster-
etic coefficient ^z forl diferetlt kinds of ironi and other inaterial, we shall puLtthlemii togetlher for cornparison in Table XI.
It is reiniarkable, in these results, that for several samnples of
each set the quiotient C gives almiost exactly the same value,

while other values disagree therefrom. From this average value
of C ar-e calculated the values of the coercitive force Cof sheet-
iron, given in the brackets. For conivenience, in the followinig table are given the values IV
of consumnption of energy in watts per cubic inch, for toO coinpiete periods (nagnetic cycles) per second, and for the nmagnetization of If lines of force per square ineh, giving as coefficient of hysteresis the value y- 8.3 X 10'6
In Table XII., I have given a nuimber of experimnental values of the consumption of energy by hysteresis and believe to have shown that this consumption of energy can fairly well be expressed by the emipirical forinula,
11 -j Bx
where the exponenit x is equal, or at least very inearly, to 1.6,
and the coefficient C a constant of the material, which ranges from .002 up to .025 and more, and may possil)ly have a slight

6

STEINMIETZ N THE LA W OF H YSTERESIS. [Jan. 19

-

6'
n

t4 '40 - N0..

'0

aD

on

4.

0

NO

4

v

NO0

0n N 0

6'

NNe

M

NO co ooN
0

o

n0

N

6

N

O

NO

0
8 N

C)

en O '0

N

8

£

s u U) vC °

bt

CC2

C!.

F-

4-

0'4N

¢f

4*

0

0.

O

*

4-

N

O

a'0

CL

CL

6'

00

t >0

CqNf

6

4.4

(5,

o

nQV

*

*O

IO N

H

Ns

Z ' 4-o Nt rB o

!4.)

0

Q ct

6
1)

K:20 X C>

U)

E

NN

00

-

6'

m -.0

o

oo,

,,

o .,4

0 0

C.-

0

m

0 0
C.
0 ci

8
0

-4- c,-,C ~

0

I-4.-'

C.

LO ON'

c.

C,

N N *n

I-

tO No a

t-

0

C

OC

C

°

Nl

Qo

~

Qce

0p;

4

4._

S-l

ii

O CL

11

41,

O

O

0
4)
0 t
aN)'InmK). >

4° 4v0 >

dd

>

;:

o *4.* h0v

_cn
L)

U

*.

.

4.

*

V*

1892.] STFINMETZ ON THE LAW OF HYSTERESIS.

47

dependence upon the velocity wherewith the mnagnetic cycle is performed, as the second set of alternate-current readings seems
to indicate. In the following table, I give the values of tlhe hysteretic re-
sistance ri for some ironi samples, subjected to a nmagnetic cycle between F - + 190 and - 190 ampere turns per centimetre, calculated from Tlopkinson's tests' by the assumption of the law of hysteresis.
= the coefficient of hysteresis. B _ the maximLm magnetization in lines of magnetic force per
square centimetre.
R the rernanent inagnetization in lines of magnetic force per square centimetre.

TABLE XIII.

Mlaterial.

Condition.

BR

Wrought-iron.
Soft Bessemer steel.

Annealed ........

.00202

.o45percent. C. annealed .00262

Soft Wittworth steel .09

.00257

.32

.005os8

.89

.00786

.32 .89
Silicon steel ........ 3.44 3.44 13.44
Manganese steel .... 4 73 8.74

oil-hard. .00952g

oi844

Si., wrought .00937

"

annealed .00784

" " oil-hard. .01282

Mn.,wrought .o0563

12 36

48.773a ose' annealed |..80I4I8446

4.73

oil-hard. .o6706

8.74 Chrome-steel ....... .62

Cr. ,wrought OII79

I.2

"

i85I

.62 " an"nealed .oo897

1.

OI638

.62

oil-hard. .03958

I.2

Tungsten steel

4.65

Wo. wroughtl

4.65
3-44

annealed
oil-hard.!

2 -35 very hard

Grey cast-iron...... White cast-iron ....

3 45 P- C - C 1C 7P.C.Mn. 2.04 C; *34

.4.5 C.;8o " "

*04442
.10O1I54i365
.04776 .05778
.01826
.oi6i6

18,250 I8,200 I9,840 I8,740 I6,I20 I8,8oo
I6, I20
I5,1I50 14,700 I4,700
4,620
747
310
io,58o I ,985 4,770
733
15,780 24,680 I4,850 13,230
I3,96o
I 2,870 I5,720 i6,500 24,480 12,130
9,I50
9,340 385

7,250
7.860 7,080
9,840
I0,740 I1,040 8,740 1 I,070
8.150
8,o8o
220
5,850 540
2,I60
9,320 7o570 7,570 6,490 8,6oo 7,890 10,140 11,010 8,640
6,820 3, i6o 5i,50
77

These values of the hysteretic resistaince vary from .002 up to
.082, 41 times the first value. But especially marked is, that C depends inuclh less upon the
chemical constitution of the iron sample, than upon its physical
1. From "Kalender fur Electrotechiniker," by Uppenborn, Berlin, Ger-
many.

48

SITELYMETZ7 ON THE LAW OF HIYSTERESIS. [Jan. 19,

condition, anneaH1ftyg doects'iin, and harden ing increasimg the
lhysteresis v-ery considerably.
So far as the chenmical conistitution is concerned, the purer the
iron the lower is its lhysteresis, while any kind of foreign matter increases the hysteresis. Especiallv m-anganese increases the
hysteretic loss enortmously, much less wolfram and chromiunm,
least silicon and carbon. Connected with the increase of hyster-
esis is alwaays a decrease iniimagnietic coniductivity.
I wish to add a few remnarks on two alleged plheniomena.
connected with hysteresis, whiclh lhave been talked about considerablv, withouit yet being miadle clear; the decrease of lhyster--
esis for open nmagnetic circuit, and the dec ease of lhvsteresis of
a transformer wvith increasing load. With regard to the first, as showvn, actual tests do lnot show a
smaller value of hysteresis for opeii tlhani for closed inagnetic
circuit. And it can niot be understood how that could be.
For conisider an iron mnolecule of tl-e magnetic circuit exposed
to the hlarmonically, varying -M. mI. F. and performying a magnetic
cycle, Evidentlv it cani make no differemice for this iron iuoleciile, whletlher some trillion of imolecules distant the magnietic circuit enlds in air, or is closed entirely in ironi, sUpposinlg that the M. M. F. and the mnagnetism, anid therefore also the mnagnetic reliuetivity, are the saiime in both cases.
Neitlher can it make aniy difference whietlher the M. M. F. iS ciused only by one sine-wave of electric current, or is the resultant of several AI M. F.'s, as in the loaded transformer. It is the same as with the electric current, wlhere the energy coniverted into heat in each miolecule of the conductor does not depenid
either, whetlher the material of the conductor on some other point changes, or whether onie or more E. Mn. F.'s are acting ulpon
the cireuit.
HIencie, until absolutely exact and undoubtable determinationis
of the hysteretic loss for ftully loaded transformers are at hand, the asstumption of a decrease of hiysteresis with increasing load umust be rejected.
That an apparent decrease with increasing load has been observed several times inay be conceded, for besides the exceedingly great liability to errors in these tests, where the hysteretic loss comes out as the small difference of two large values, prim-
ary energy and secondary energy, and tlherefore is very much

1892.]

STKELNMETZ ON THE LA W OF HYSTEREVSTh

49

affected by the slighitest error in any one of the comnponents, it must be understood that the inain possible errors in tbe deter-
rminiationis on fully loaded transforiners all point this wav. Neglect of secondaryv self-induction, decrease of magnetization with increasing load, slowing down of the dynaimo-alternator, etc., all caLise an apparent decrease in the hvsteretic loss for
inereasinig load. At least in one set of tests, those made -by Prof.
Ryan, at Cornell University, on a small Westinghouse converter, 1 was able to show in mny Elemnentary Geometrical Theory of
the Alternate Current Transformier" tthat the observed decrease of the hysteretic loss disappears by reducing the different readings to the satne inagnetization and the same frequency.2
if, indeed, the shape of th-e wave of Ai. 3I. F. varies, then a
certaini differenice in the value of the hysteretic loss can be iminagfinied. Comnpare it withi a meehamtical or elastic cycle. A moving1 pendullull, or an oscillating spring,, for instanice, continuously converts potential energy into kinetic energy and back;
in each oscillation consumninz, that is, coniverting into lheat, a part of the energly by internal and external frictioni. Now, if this inotion of sprin-lg or pendulmtn is truly hiartmoic, less energy is
converted inlto heat than if the motion varies abruptly, is jerking, etc. So, in -a unagletic cycle, between the saine limnits of mnagnitetization the lhysteretic loss iniglht be smallest, when the evele is etitirely harmonical, but mnight be larger if the M. M. F. varies abruptly; for instance, wlhen cauised by an initermittent current.
Now, in a transformner witlh open secondary the At. M. F. acting ulponi the iron is that of the primt-ary current, and this current is rigidly determined in its shape by tlle E. M. F. of the dynamo anid the E. NM. F. of self-induction. But in a fully loaded transformer the secondary current is proportional to the changes of time inagrnetism, therefore iniereases very considerably in the inonent of a sudden ehange of magnetism. Hence, if a sudden and abrupt clhange in the pritmary current occurs, just as suddenly the secondary current increases in the opposite direction, and thereby mnakes a sudden change of resulting M. Al. F. and magnet-
isin imnpossible, so that the fully loaded transformer compares with the elastic spring whlich oscillates freely, while the open-
1. Dec. 1891, Electrical Eagineer, New York. 2. The latest tests of Ewing prove that, in a fully-loaded transformer the loss by hysteresis is n9t smaller than for open secondary circuit.

50

SY'EINMETZ ON THE LAW OF HYSTERESIS [Jan. 19,

circuited transformer compares with a spring, where the m-otion

is determined by a rigidly-acting outside force.

Hence, if the shape of the alternating primary current

differs considerably from the sine law, a certain decrease

of the hysteretic loss for increasing load can be expected, though

certainly not such an enormous decrease as some former tests

seemed to point out. These tests must undoubtedly have given

erroneous results, perhaps caused by the neglect of the

secondary self-induction, which, even if very small and causing

only a slight error in the secondary energy, must cause an

enormous error in the hysteretic loss, the small difference between

the two large valuies-primary anid seconidary energy

That an electro-magnet witlhout keeper loses its inagnetism

quicker than a mnagnet with keeper, or a closed magnetized iron

ring, is a plhenomenon. wlhich has nothing whatever to do witlh

this loss of energy by hysteresis, but is merely due to the

demagnetizing, force of the remianent magnetism. For the

remanent magiletism in an open imagnetic circuit causes between

its poles a certain differeniee of mnagnetic potential, whieh in the

moment of breaking the electric circuit acts as demagnetizinog

AI. M. F., and, if the coercitive force is small, as in wrouglht-ironl

or annealed steel, alm:nost entirely destrovs the rernanent magnet-

ism, while in an iron of large coercitive force it affects the

permanent magnetismn very little. In the closed magnetic

circuit the reiaineint magnetism. causes nio or very little differ-

ence of magnetic potential, and therefore no destruction of the

remanent myiagnetism by its own demagnetizing M. M. F. takes

place. But witlh the hysteretic loss of energy this phenomenon

has nothing to do.

To combine the results, what I believe to have proved is that

loss of energy in iron caused by reversals of magnetism can be

expressed by the analvtical formula:

where

-r B'-6 + eN2

W = the co-efficient of hysteresis,

e the co-efficient of eddy currents,

N the frequency of the alternations of maginetism,

; B"6 = the loss of energy by hysteresis proper, or by molecatlar

friction, and

N, B2 - the loss of energy by eddy currents, per magnetic

cycle and per cm.', proportional to the frequency N.

1892.]

DISCUSSIO-N.

51

TABLE XIV.

B v BBl'6 Bl; ,, >

11,U8e6 B

B' 6

500
m000
_500
2000>

. .0 02 20 088
.0631 .1206 .1913

42 goo
0503 IO,OOo
1424 I6 10,500

2.122 2.313 2.5II 2.716

378 37

17,OC0

17,500 ,8.o..40

I'I8,500

5.870

5
_55

6.148

6-434

57

6.722

59

2500

.2732 183000 2.925

2 19,000

7.017

3000

.3659

I 11,500

3.I4I

43

9,500

7.12

3500
4000

I021 .4684
.58oo

223

000 12,500

3-363 3.589

46

2202,.000000

78.668883

63

4500

.7000 2348

13.000

3.821 4

24,000

I0. 193

70

5000

.828Ji

I3 0

4.o6o

4

26,ooo II.59

5500
6ooo

55.90 660 2 1.I

275
202 22

143000
14,500

44 .303
4-580

48 28,000 13.05

30,000

14.57

7
8

6500

I

30

1>000

4 807

50

35,000

I8.65

89

7000

I-420

324

15,500

5.o62

40,000 23.09

7500

353398(3

8000 .I-758 3 6 I6'500o 5.598

b500 I*936 3066

45,000 50,000

33-00

For conveniernce, I give in Table XIV., the values of the 1.6th power of the numbers, from 500 to 050,000 with the parts proportional, or the increase of B'6 for 10() lines of magnetic force.
Yonkers, N. Y., December 7th, 1891.

DISCUSSION.1 THE CHAIRMAN: Gentlemen, the poet has informed us thiat "better fifty years of Europe than a cycle of Cathay." What le would lhave done hadl he rmet a cycle of mnagnetism, we cani but conjecture. The Instituite has therefore good reason, I conceive, to cong,ratulate itself that one of its m-lembers does not shrink frolm sueh a conflict. I am suiie I slhall but express the sentiiments of every menberpresent, when I say that we are mruch obliged to Mr. Steinmetz for hiis very elegant and exhaustive treatument of a subject whose title, to say the least, hias a mnost unproi-mising and uninteresting sound-- a subject dealing with the cauises of those indispositions of iron to clhange its magnetic condition which in our old telegrapl-ic days we were wont to suin up by the unscientific termn of " residual inagnetism." Before calling for general discussion, I would like to ask AMr. Steinmetz whetlher, in his experiments and tests, he had determined whether orInot there was any real foundation in fact for the distinction which Professor Ewing has drawn between the inolecular friction, which he calls "static hvsteresis," and the real time-lag, which he denominated "viscous hysteresis." MR. STEINMETZ:-l really am not yet prepared to answer the questioni whether viscous or tiine hysteresis exists or not. My tests in only one set of determinations gave me an increase of hysteretic loss with increasing frequency, which seems to point to
1. Discussion by Messrs. Bradley, Kennelly, Lockwood and Pupin.

5o2

STEINMETZ ON TIIE LA TV OF IIYSTERESIS., [Jan. 19,

the existenee of a viscouls hysteresis. For if a viscoUs hysteresis exists, it would show by ani apparent iinerease of the coefficient of
hysteresis, witlh iniereasing frequency. But nmost of the tests do
niot show this, but give the same coefficient of hysteresis for different frequencies.
At any rate, if there exists such a tinie-liysteresis whielh I shall
try to fiind out-it follows the law-T of the 1.6th power also. But I think, oiily at mueh higlher frequencies than those I have
used in iny tests, caln we hope to meet witlh viscouts Ihysteresis. I hope to be able at a fuiture mneeting to give mnore detailed infor-
ination on this and sonie other phenomnena connected witlh tlle
magnetic hyTsteresis. THE CHAIRMANN:-Gentlermen,the subject is before vou. Wlhile
a few of us were in the parlor, prior to the reading of the paper, I lheard Mr. Steiinretz conidoling with himuself in r-elation to the weather and expressing the hlope that there would still be a very considerable discussion. It is therefore to be hoped tlhat any of us who may feel able to grapple with suclh a subject will not hesitate to do so.
MR. CHARLES S. BRADLEY: I do not feel able to discuss this paper, but I know it will prove very valuable to us. Our work of late has beeniupon transformners. I aim connected witlh the Fort Wayne Electric Company, wvlhose transformers now use about 2,001) linies of force to tlhe square centimnetre, and we have been trying to increase the lines of force. We encountered the very phenoomena treated in this paper, and therefore it is very interesting to me, and I think that we ought to congratulate ouirselves upon having a ineimber who can tackle such a subjeet. It
is very seldom that in Amierica, anTything of this kind is taken up. We see it very often in Europe, but our commercial age will
hardlv permit us to devote ouLr time to such experiments and carry them out as they should be.
MR. JOSEPH WETZLER :-A gentlen1an wh1o is present but wvho is not a mnember, has asked me to inquire of the author whether he made any experiments oni mitis iron and, if so, what his restilts were.
AIR. STEINMIETZ: -I never made any experimnents with regard to hysteresis, on mitis iron-only on different kinds of castiron.
MiNR. A. E. KENNELLY :-Mlr. President and genitlemen, I think that we have to congratulate ourselves upon a magnetic and physical treat in the paper that we have just listened to. Mr. Steinmetz has been, I think, the first to point out this renmarkable law of hysteresis-the variation of the energy consumed per cycle, with the total flux per square centirnetre that passes through it. I think that it is perhaps preferable to express the exponent in the equation as a vulgar fraction instead of as a decimal-not that it alters the facts in any way, but merely because it gives us a little more hope of being able to understand what

1892.]

DISCUSSION.

53

the equationi means, if not now, at least let us say in the
future. If, instead of writing the energy Mr. Steinmiletz calls
it Hf, as B I-, we write it ^ B", it gives us some lhope of being able to tranisform that in a simnple manner,
whieh will give us the fundamtental law concerned I think there is very little dooubt that the law AMr. Steinmnetz gives is the true onie. It is, first of all, as he showed uls some timne ago,
in accordance witl-h the values observed by Professor Ewing, and
so far as my owvn knowledge goes I am able to corroborate it, for I have observed the same law in the case of one sample of
wrought-ironi takemi bv a ballistic methlod, and another sam-le of wrouglht-iron taken by wattrneter metlhod, both giviing the < power, altlhough I do n:ot know wlhat the exact value of time coefiicieint - was in those particular instanices. It is verv puizzlinlg to understand wlhat that peculiar fractioin i neans. It is rather too high and uniwieldy a fraction to be understood at a glance. But whlatever its inniier meaning may be, its outward and visible indications are elear enough, beoause if vou double thle flux densitv in a piece of iron you. Will treb)le the energy whliich is coiisiimed
iu it per cycle, by lfy_steresis, independlent o'f th-le energy that is
conisumed in it lbv ecldy currenits. Of coiirse, if you hlave any culrve whlichl starts froin the zer'o poinlt a,nd riSt s Up in. that way, and if von take arbitrary distances like this in the formn of rt, 2, a3
and so on, tlhen if yvon want to finid ouit whietlher that curve follows any+ suelh law as

you lhave onlv got to mark off the ordinates corresponding to those absciss&u, and to see if with the powelrs of ar along Xyou
have a constant ratio from one to another in the ordinates. If von (to[ that ratio will be a n. In this case, if a is 2, an is almnost exactly 3). For the 1.6th power of 2 is 3.03, whichl ineanis that if vou double tlhe maxim-umI imagnetization in a piece of wrought-
iron, you will lhave 3.03 times the lhysteresis loss, and this is a simple way of stating thie results whielh AMr. Steinmetz has poinited
out.
AIR. STEINMIETZ: As pointed out by AMr. Kennelly, this law of lhysteresis gives a very sinm ple numerical meanin1g. It meanis that by doubling the magnetization you approximatelv treble the hys-
teretic loss and quadruple the eddy loss. So if you-i make but two tests therefrom, you can find out the amount of energy consumed by eddies and the amount consumed by hysteresis for any magnetization.
And, in general, you will see at once whetlher the ratio of the iron loss for doubled mnagnetization is nearer to three, or rather 3.031, or to four, that is, whletlher hysteresis or eddies consume
more eniergy in the iron.
I would like to add a few remarks regarding the results of the tests given in the paper. This law of hysteresis is of interest from another point of view:

54

STEIN3IETZ ON TIlE LAWIV OF II YS7'ERESIS. [Jan. 19,

We all know, now, that energy is always the samne and indestructible, and merely chanoes its form and appearance, so that a certain quantity of any kind of energy converted into any other kind of energy always gives an exactly determined amount of the other form of energy, which we call the law of conservation
of energy. But this law of conservationi of energy needs a certain restric-
tion or, rather, addition, because every conversion of ole form of energy into another is not possible, but only those wlhere the value of a certain integral, called by Clausius the "entropy," is
positive or more correctly, is not negyatibe, tlhough the case, that
tlhe integral of entropy equals zero, hardly exists in nature otherwise bat as iitlttheinatical fiction, or, in plain English. only tlhose conversionsyswhereby the sum of the latent heat of the universe
increases. According to this law of entropy, if the complete con-version
of one form of eniercry into another is possible, the opp-osite coniversion is not conmpletely possible. Or if we coonvert a certain
amoLiunt of one forni of energy into another form of energvy and this back agyaini inito the first formn of energy, whichl we call a cyelic conversion of energy-we do not get back the originTal
amount of eniergv, but less, anid a part of thIe energvy has beeni lost;
that means, converted into and dissipated as heat.
Thler-efore n1o comiplete cycvlic comnersion of eniergy exists, buit
by any sluCh cycle the amount of available energy hlas decrealsed bv that fractioni tl-hat wxvis conveerted inlto lheat.
ow, these cyclic coniversioins of energy are of great impor-
tance in niature. For instance, a mi-oving pendulum. an oscillating sprhig, a dis-
charging condeenser conmpletes cyclic pwocesses. In the mloving
pendtlulum, continiuously kinetic in echianical energy is converted
into potenltial inechanical energy, wlihen it moves from the vertical positioni into its greatest eloni-ation, whlile when inovingfroml
elongation into vertical position its potential energy is reconiverted
inlto kinietic energr,therebv completing a evyle, so that in vertical
positioli all the energy is kinetic, in elongation all the eniergy po-
tential.
In the same way, in the oscillating spring, a cycle is perfornnecl between potential energy of elasticity and kinetic enervoy of mnotion, in the diseharging condenser betweeni electrostatic and eleetrodynamic energy, anid that the pendulum and the spring conie to rest, anid the conidenser discharges! is due to the continuous loss of energ-y by dissipation as heat, caused by the law of en-
tro)y. Now, in none of these cyclic conversionIs of energy, so far as I
know, was the law known which determuines and analytically formulates the loss of energy by conversion into heat. The electro-. magnetic cycle is the first one where in the law of hvsteresis, this law of dissipation of energy by heat, finds an analytical formnulation.-

1892.]

DISCUSSION.

In the alternatinlg electromagnetism we have such a cyclic conversion of energy frorn electric into magnetic energy and back. Magnietism represents a certain amount of stored up or potential energy determined by the integral

fFd B

Now, as long as the magnetism increases, electric energy is tranisferred froin the electric currenit and converted into potential inagnetic energy. While the magnetism decreases, potential magnetic energy is reconverted into electric energy, and appears
in the electric cireuit as E. M. F. But the full amount of energy is not given back to the electric
circlit, but less. Less by that amount that lias been converted
into lheat by hysteresis.
Hence the law of hysteresis is the depenidenee of the integral of entropy in the electroniagnietie cycle, upon the intensity of
nag,netization, and therefore of interest. DPR Al. I. PTPIN:-t a('ree fullyv witlh Mtr. Steinmetz's last re-
inarlks that no pr-ocess in n]ature is perifeetly reveisible and that the phleTloinenoni of inagnetic hysteresis is onlly a speeial case of
the irreversibilitv of natuiral prucesses. It is only a special ease of the gfeneral law whichl wafs fir,st ainnloiunicee i by the late Professor Clausinis, the law namely that the enttropy of tlhe universe is tending(, toward a mnaximnulm, that is, that there is a certain func-
tionl of tlhe propelmties of matter of tlhe universe wlxhieh increases
as tlhe ainouint of heat eneroy inu-reases in the universe. Now, as
in every proeess tlhere is a certain aimiouniit of energy converted into lheat, the amHount of' heat in the universe is continually in-
creasing. Thlerefore tile enitropy is continually increasing and
th-eefel'ore steadily approachIi ing its niaxinmnin.IProfessor Rankine
imade a gutiess as to h1ow iulan-iv years wouldl elapse before the
wlhole energy of the unniverse will be coinverted in1to heat, whlen there will he nio life, nio natural plhenomrlena exceptinig lheat vii)ra-
tions. It is very far of yet
Closely, conniected with thlis magnetic liysteresis is, I think, the so called electro-static hysteresis. Of course experimiiental researchles in this field have not beein carried on far enough yet, to enable us to speak witlh any- definliteniess, buit still it is beyond all doubt thtat if you polarize a dielectric and depolarize it again, a certain amounlt of hieat is developed. I think one of the obstacles to the commnlercial introduction of the condeenser, is its getting hot. Now soine tlhink it gets hot on account of the coiivection currents wlichl are passing between the plates of the condeinser bv ineans of the air currents and the dust that is in the air; but if yoLu use paraffinie so that it will prevent those convectioni currelits, even then you will observe heat developed in the paraffine wlhichl mnust be attributed to the same cause which develops heat whlen ironi is magnetized and demagnetized; that is hysteresis.

56

`STEJNIETZ ON TlHE LAW IOFHY67iREBESS. LJan. 19,

Polarization aiid depolarization- of parafline, anid in fact any other dielectric, is not a perfeetly reversible process.
Allow ine now to coinmient upon a few points brought up ina Mr. Steinmetz's paper. I always believed tlhoroughly in Professor Ewing's views with regard to the followinig experiimentally well
supported assumption, namely that in very low magnetizations the act of miiagnetizing and demagnetizing is practicallv reversible,
and that wheni a high point of saturationi, say 24,(00 or 205,0 0 lines per sqtuare centimetre is reaclhed, that after that the loss due to
hysteresis does not increase. I do not see why it slhonld increase,
because after that the iron does not reeeive any stronger magnetization-. The additional lines of force after passing the saturation point are due to tlhe iinereased magn-etization of the air itself, and that magnletization is practically reversible.1 I see that MIr. Steininetz has found out an incerease. indepeindenit of the degree of saturation. There is a discrepaney, and I aml iniclined to side with Professor Ewing, until I am eonivinced b)y MAr. Steininetz that his method of measnrenmeint and observationl could not be objected to in any particular whiatever. UnfortunatJvyMv1r. Steihunetz lhas Inot (liscimssed hlis m-ethod so that onie cani examine it critically. Ile has giveni the general idea, the instruneniets em-
ployed, etc., bu-t tlhere is no discuLssioni of the theory of the mnetli-
od, and also of the prolable percen-itage of lhis errcrs of observation. I am sure that A1r. Steinrnetz will do that at sonie future
tinme. It woould be very initeresti ig and very imrportant indeed
to know wlhether that disagreeinent is in favor of Atr. Steinmnetz or of Professor Ewing.
There is on eag,e 49 a discussioni of the variation of tlhe hyvsteresis loss witht the load. In tlhat discuission AMr. Steini1netz says as loiig as tlhe secondarv current is open, the formli of the wave of the priimiary curren-t mnav not be a sinie curve; but that whleni the secondarv cuirrenit is started, the wave of tlhe iiagneto-imotive force is forced into the shape of tlie sine curve on acconimt of the reaction of the seconidary current. Now I would beg to disagree with Mr. Steimni1etz; I tlhinlk it is just the opposite. It dloes not make any differeice wlhat tIme electromnotive for-ce is, as long as there is a very large self-induction in the circuit, as there certainlv is in the prinmary circuit as long as the secondary is open, the wave of the p)rimary circuit is indepeident of the wave of the impressed electromnotive force and is practically a sinie wave. But wlieni the secondary circuit is closed, then the impressed electromnotive force, being assisted by time electromuotive forces in the secondary circuit, asserts itself and gives the primarv current its own shape, amid the stronger tlhe secondary currenlt, the larger assistance the primary impressed electromtotive force gets
from it. The secondary current aids the primary impressed

1. A. E. Kennelly, on " Magnetic Reluctance" TRANSACTIONS, vol. viii. Nol1, p. 500.

01892.]

DlSCUSSIOiN.

57

E. Al. F. to assert itself and( force the primarv currenit into its

shape, that is, the slhape of of the iimnpressed E. M. F. That can be

proved very easily b)oth from tlheoretical and practical stand-

points. So that I do not see the force of Mr. Stei-inmetz's

argumlent.

AIR. STEINMAIETZ The mnethiod used in imy tests -was the well-

known electro-dy-nainioiineter miietlhod, as explained in the paper,

witl-h somne sliglht modification)s to insure the greatest possible ex-

actness in tlhe results.

With regard to thie differ,ence between open eircuited and fully

loaded transforni ers, I thinki Professor Pupiin imiisunncderstood mne.

I (lid niot sav that thle vwave of the primary eCvaPcfl in the trans-

former nuider bidl7 Ioad resembles tlhe sine wave imore tlan witlh

open (H(a41, for that would have been wr'ong. WVhat I said was

that the wa-ve of thle rnaynet½u&Rn? anid of the Mestut,M. M. F. in

the transforiner u-nder f-ull load resembles mnor-e the sihe wave

tlhain it'does in the open cireuited transforni-ier.

Suppose the impressed . MI. F. at the term:inials of tlhe tranis-

foirner differs from the sine shiape, differs even considlerably.

Then the priinary curren-it, wlhielh at open cir'CUit represenlts the

resulting IM.AL F., will differ much less from-l the sinie shape tlhani

tvheeryimgYrlperaetsseexdteE.ntAl.byF.t, hbeeilnhoegavsym-sleoloftl-hiendidoucuttioanndof

roltnided off to a the openi cii(rcuit

transformer. For in tl-he inoment of any suddlen r-ise of the ilun-

pressed E. M. F., already a small rise of the priialary current and,

therefore, of the i-magnietismn, will induce suifficieint eounter E. Ar.

F. to imiake a rapid increase of the priimiary currenit impossible.

IHence, in the open eircuited transformer, the wave of the

inagnetisin will resemble tl-ie sine wave mnore tlhani the wave of

im-pressed E. iM. F. But, nevertheless, it imnust differ froni- the

sine wave if the impressed E. -I. F. differs fr-om-rl sine shape. For,

as before said, the resuiltingo or- curirent p)ro(lucinig F. M. F. and,

therefore, the currenit, is rigidly determined )by the smnall (lifier-

einee of imipressed and incduced E. Al. F., and tle induced E. n. F.

mInust tlherefore lhave a slhape very simtilar to the impressed E. N.

F., Ilence differinlg from sine slhape the miore tlhe impressed E. iN. F.

differs tlherefronm.

Now, the iindclued E. M. F. iS the differenitial quotien-t of the

inagnetism. Iellnce, if thte inagnetism is a sine wave its differen-

tial quotient, the induced E. N. F , has to b)e a sine waave also anid,

on the other lhand, tIme imore the inidueed E. 3. F. differs froni sine

shape, the more its integral function, the inagnetism, is forced to

differ. Iiideed, the inagnietismnmay apparently differ, in its abso-

lute value, less from1 sinTlsoidlal form thian the impressed :N. M. F.,

for it is nlot th-ie instant-mmneous valuies of tIme magnietism wh-iiel are

directly influenced by the slhape of impressed E. M. F., but the

greater steepness or flatness of the curve of iniagnetisii- which is

directly caused by the impressed E. Ml. F. Buit it is jiust this dif-

ference in the velocity of chlange that is, in the quicknes.s of rise

58

SIEINYIEYTZ O' T'UIE LAW OF HYSTERESIS. [Jan. 19,

or decrease of the magnetism, and not the magnetism itself.which would have to account for an increased loss by hysteresis. Hence, it is really not the difference of the curve of magnetism, from sine shape, but that of the curve of induced and, therefore of impressed F. M1. F., which may possibly cause an increase in the loss by hysteresis.
Quite different i-n the transformer at full load. Indeed, its apparent self-induction is essentially decreased and the primary current will therefore resemible the shape of the impressed F. M.
F., and differ from the sinusoidal form, much mnore than for open
circuit. But at full load the wave of uiagnetismn an-d of resulting Ai. mi.
F. iS MuCh iuiore independent of that of primary current and pri-
mary E. AIi. F. It is caused by the combined action of the instantaneous values of priminary and of seconidary current, and the sec-
ondary current, again, is induced by the magnetism. IHence the result will be, if a sudden change of imnpressed F. M. F. ocCurs and
produces a suidden change of prim-ary current, julst as suddenly as
the opposite change of tlhe secondary currents will take place, so that the resultant Al. M. F. of both combined currents will not change perceptibly, but practicallv inidependent of either current, will alternate freelyr in sinusoidal waves, in spite of any difference iii the wave shape of prinmary and secondarv c-urrent fron the siiie law.
Anid, indeed, a glance over the curves of inistantaneous values of the electric luantities in the transformer, as they lhave been determuined, for instance, by Professor Ryan, at Cornell Universitxy, ancd communulicated to this Institute some time ago', shows a considerable discrepaney at openl circuit between the primary currenit ancd the sinie wave, while in the loaded transformer the secontdary E. Mr. F. andc, thlerefore, the niagnetisni, almost universally resenhbles sine slhape.
Witlh regard to Ewing's theory of the imolecuilar mlagnets, I do
not say that I disbelieve in it, neither that I believe in it. At the
ftist view, this theory did not seem to agree with the results of m-v tests, as I said in my paper, but I did inot take the time to tlhink it over more comipletelv wlhether this theory could he made to agree with the tests; miy aim was to gather faetS, being con-
vinced that based upon a largye nutiber of facts, a theory will be
foi-und ili due tim:le to explain thenm. [See appendix, p. 64.] DRz. PUPiN: Magnetic force is certainlv a resultant of the
priimary and secondary currents. As long as the secondarv is open, the primary cnirrent will be a sine wave, practically. It
does not make any difference what the impressed electromotive force is of the alternator, and therefore the magneto-motive force will be a sine wave and the magnetic induction will vary like a sine wave If you close the secondary circuit, the self-induction

1. TRANSACTIONS, VOl. vii, p. 1 et seq.

1892.1

D-ISC USSIO-N.

59

in the primary is reduced, and therefore the back electromiiotive
force in the primary is smnaller and the impressed electromotive
force begins to assert itself more and mrlore and gives to the 1rimary culrrent its own shape. The shape of the secondary cur-
rent, as long as the secondary's resistance is very large and the secondary current is small-that, too, is practically a sine wave, the primnary current being also practically a, sine wave, the resultant of the two-that is, the magneto-motive foree-muLst also
be a siine wave. B3ut now, if you diminish the resistaniee in the
secondarv eirculit, that is, increase tl-e load, then the shape of the pritnary current begins to corresponid to the shape of the impressed electroimotive force, anid also the slhape of the seconidary currenit beg,ins to correspond to the impressed electromotive force, and tlhie resultant of thle two, the magnetizing current,
mnust also be Iiin to corresponcd miore and iiore in shape to the iinpressed electromotive force-that is, the niagueto-()otive force
begins to correspond to the shape of the iml)ressed electromrotive
force. The samie is true of the magnetie induietionr. We are inot to forget that the secoindary current does not depend on the rate of clhaige of the primary current on-ly. The relation is a little muore complicated. There is a dlifference in plhase 'between the
priinarv and secondary, vary ing anaywhere le)tx eeu 9(0 dlegrees anid 1 t degrees. When the difference in plhase is near1, ] degrees, that is, at full load, thIeln tlie primary cuirrent and the see-
aonnddahrayvec-tulh'eSeisitaicnoerrselhsappoendasttoheeacilinpoitlehsesiedalme)loescttre-xoamcottliyveinfosrlcaep.e,
MIR. STE1,JNME'rZ: I can not vet quiiite agree witlh Dr. Pupin. The resultant of two M. M. Fr.'s of equal shape, but different phase, need not lhave the saine shape, but can lhave an entirely different formii. So for instanee the resuiltant of two very raggedlookinig ws-aves can be a comiiplete sinie wave. Let us comle down to numiierical values. Take for inistaniee a 10()O volt alternator,
feeding into the pliliary coil of a transformer. The internal resistanice of the primilary coil is 20 (o. The current flo\\iig
througlh the primary, at open secondair ceircuit, a sm-lall fractioll of an ampere. IHenee, wlhat I call the 'resulting F. Al. F.,t'tlat iS thle E. AT. F. 'WhiCh senlds the c'Urr'ent throun'1h thle resistance is only a few volts.
BIut this resuIltillg E. Mt. F., is the difference of this instanitaneouis values of primnarv imupressed, and primary inducedE . MI. F. The difference is onilv a few volts, the primary imnpressed . Ma. F. 1001 volts, lhence the primary indaced 1E. Al. F. lmullSt be almiiost like the imnpressed E. M. F., and mu11lst differ fromn sine-shape, therefore, if the imlpressed E. 3I. F. differs; amid if thle differential quotient of magnetism, the inducedEu. M. F., iS non0-Silnusoidal, the curve of mlagnetismn is non-sinusoidal also.
In the transformer at full.loald the current anid therefore the difference between induced and impressed E. Al. F. iS nm1uch greater, the induced E. MI. F. is therefore mnLch more indlpendent of the

80

StY'E)TEIhVTfETZ O-N TUE LA W OF HEYTEJESLJ$. r[Jan. 19,

impressed E. -I. F., the ilnlre, tlhe greater tlwe load is, lence the curve of miagnetism alternatti;.n freer tl-han at opeii cireuit, anid tlheiefore more approximating the htarmnoniie vibration of the sinie-wave
DR. PUPIN: It does not bv anyT imeans follow thiat at every momient the difference between the imlpressed E. A. F. and the back E. Mi. F. is sm-all when average value of the enurent is small,
and that is the point in your argument. Anid even if it is I do
not see how that can prove that tlhe shlape of the cuirrent and the
iinpressed :E. M. F. are the same.
MAR. STEINTZIETZ: -We lhave seent that the effective valule of the cnirrent, and tlherefore the effective or averagre value of the differeence of prinary imnpressed anid primary inlduced x. M. F. muilst be smnall. Trlhis indeed does not prove thiat somiie of tlte iristantanteous values of this difference mway niot be considerable. But first, this cotuld be only the case with very few values, because, if for any grealt length of time the cu-rrent wvere conisidlerable, this wvoukld slhow in the average or effective valuie, the muore, as this is
the average of time sqluar es of instantaneous values.
On thie otlher h-atnd, to make the cnirrenit eonsiderable onlv for a momenit, wlhile immlllediatelv before anid after it is smiiall, eitlher the indueed E. M. F. IImust Suddenly decrease enornuouslv, anid the
next momlent iierease just as sudtdenly-whichl implpossil)le,
becallse it is tlhe differential quiotienit of inacrnetisin or tlhe p)iiula-
rV E. Af. F. had to rise and decrease again very sll(ldeilv, and suel
a sudden rise, and inuinediately afterwards decrease of primiaarv
iml-nressed E. Al. F., ntot only is an electro dyllamic alternal-tor- una-
lle to produce, but no electric eircuit wouild peirluiit a culrrent of
sutelh enormously large value and short duiration to pass. Hlenee we can fr oin thle small value of effective primuary current, conelude tlhat also its instantanieouis valuies withonit exceptiont inust be smnall.
DR. PUPIN: I do not sUppose that a wave wlhiclh is niot a sine, in ust necessarily I)e a wave that goes ulp and down witth sudden-I variations. I think that every good coinimercial tlachine is constructed in suLelh a way that tlhe electromllotive force is a perfectly
smooth curve. There myiav be smnall corners, but even those corners are very nicely rounlded. Generally speaking it is a sign of good construetioni of the machlinie wlhen the im-lpressed electromnotive force is a smooth curve certainly not a curve that has kinks in it. Kinks in the curreint curve are produced by a har-
iuonically varying resistance. It wouild be almnost impossible to construct a machinse so badly as to give kihiks in the electromnotive
force curve. The current mayT run smoothly, but still be verv far from a sine wave. A sine wvave is not the only smoothlv running
wave. There are inany other waves that are nice ani( smnootlh. The only possibility of lhaving such a current as MNr. Steinmnetz described, would be simply to introduce into the circuit a harmonically variable resistance. An arc light circuit represents a

1892.]

D)ISC ZITi5SSON.

61

hiarnmonically variable resistanice, and introduces those complications, the kinks. Ani are light mnachline violates imost of the well establislhed rules in dynanmo conistruction, but it does the work of the arc light cireuit admirably, and it does it because it eneourages kinks anid otlher irregularities in the current wave.
MIR. STEINMETZ :-I entirely agree with Professor Pupin, that there is reallyT nowadays almost ino possibilitv of getting such slharp poirnted waves of alternatillg E. Al. F. that a differenee of thle hysteretieloss between open circuit and closed circuit could
be expected. Anid I did niot believe mnyself in this eause of
the discrepanev of forier tests on transforners under full load and witlh openi stconidary eireuit. I made this remalrk o*nly to be absoluitely just, and not enitirelv to reject as erroneous, determnina-
tions made by others, but at least to J)oint ouit a cause whichl
miglht produ-e, though not at all likely, a sliglht difference between- the values found under full load anld with open circuit.
Indeed, all our imiodern alternators produce waves very mluclh
resembling sine curi ves, and the onily wav to get froim tlhen suelh rapidlv changing 1X. i. I 's is, as Dr. Pupin pointed out, the introduction of variable resistances, as are lamps, into the circuit.
But somtie of the older types of alternators. as, for instanee, the Klimenko alternator at the Vienna exhibition, ISS221 gave evi-
dently slhar-p poinited E. M. F.'S, as I found by drawing the curve
of instantanieous values of E. M. F. of an alternator of a simnilartype, where induction was produced by making and breaking the magnetic circuit. As youi see, this is a very similar case to that referred to by Dr. Pupin, only that in tlhis case a variable magnetic reluctance and not a variable electrical resistanice was introduced into the circuit.
MR. KENNELLY :-It is uniifair, perlhaps, wlhen we lhave such a good paper, to offer criticisms upon it, but wheni it is as likely as this is to becom-e classical I think that in self defense we ought to try to keep it as free froin all imnperfections as possible. I am taking the liberty of making a criticismii on one term Mlr. Steininetz lhas used. He has spoken of the normial indnctanee of the coil of his ammeter as so mnanyv ohms, and I woutld suggest that it would be preferable to employ the word impedance, instead of inductance, because an inductance is a henry and an impedance is an ohm, and I think it is a pity to confuse the two ideas.
MIR. STEINMETZ:--I did not uise the term induictance as synonymous with coefficient of self-induction, where it would be expressed in henrys, but I used induietance in the very senise
that Mr. Kennelly means with iinpedantce.
I intentionally used the termi iniJdetance, following a proposition whieh I read once, I do not remember where. but which seemed to me so highly commendable, that I should like to see it introduced in practical engineering.
1. A remarkable feature was that it consumed 4 ii. P. when running under full load, but almost 6 H. P. when running fully excited but without taking current off, that is, without load.

62

ASTYIN2VTETZ ON THE LA TW OF IIYS1Ell I.S. [Jan. 19,

Indeed, the " coefficienlt of self-inductioii " gives all the infor-

nmation nleeded for determiniing the electric phenomena in induc-

tive circuits. But everybody will concede that it is a tedious,

cumbersome work, frolm tle "coefficient of self-induction" to

calculate. for instance, the instrument corrections for a whole set

of tests made with somnewhat differing frequencies. Besides, I

think it will be solne time before the " practical electrician" will

lhanidle the " coeflicient of self-induction"' just as easily as he now

does ohms and amnperes.

Let us consider som-iewhat closer the phenomena in an induc-

tive circuit. If a sine wave of alteinatinig currenit flows through

an inductive circuit, a certain E. M. F. is consuined by opposing E.

M. F.' S.

First, bv the electric resistance of the circuit, an E.Nu.F. El is con-

sutmled, whielh is proportional to the currenit C, with a coefficient

of proportionality, R, which is called the true or ohmic resist-

anee, or, in short, the Resistanee of the circuit.

TlhiS E. Mt. F. iS
a

of

equal

(but opposite) phase witlh the current

E1lRC
Tlhen by the action of the changing magnetic Iie]d of the circuit aii F. M. F., EL is conisumed, whiclh lags one-quarter of a phiase, or 90 degrees, belhind the currenit, and is proportional to the current C, with a coefficient of proportionalitv A, which I call the Jlndu?tan,ce of tl-he circuit:

E2 IC

This inductance, 1, is of equial diimension witlh the resistance II, hence measured in ohms also.
This inductance, I, is proportional also to the frequency of the alternating current. HIence, if I call the inductance for 100 com-
plete }eriods per second the Aormmal indetanehe 4., for any other firetliency 3V the iniductance is simply

I
I 0o
Now, the " nortnal inductance " is a constant of the circuit just as well as the " resistance" or the " coefficient of self-induction," and only depeinds upon the latter by the equation,
1 =20uXwI only that " iniductance " is mieasured in ohms also, therefore most easily combined with the resistance.
The combination of the resistance-which determi-nes the E MN1. F. of equal phase with the current--with the inductance? wlich deteriimines the E. M F. lagging one-quarter phase behind the current, is the " impedance," or " apparent resistance."
Hence,
Impedance -/ (Resistance)2 + (Inductance)2

-1892.]

DISCUUSSION.

63

The quotient of inductance and resistance is the angle of difference of phase between culrrent and impressed E. M. F.
Inductance
tan ~ Resistance You see, it is easy to make a person understand that lie has in an alternating current circuit two kinds of resistanees. a " resistance " which consumes energy and an " induetance " which does not consume energy, and make himn calculate the apparent resistance or " impedance " as the lhvpotlhenuse of a right-anlgled triangle, with resistance and iniductance as catlheti; wlhile the coefficient of self-inductiorn will frig,hten the " piractical iaan still for quite a while. On the other hand, inductance " is imiore convenienit tlhani "coefficient of self-induction," because expressed in the same
dimensions as resistance, in ohrmis. I used the ternii " normal inductanee," because in reducing tlhe
readings I founid it much iore conveniient thi-n the uise of the " coefficient of self-induction," and tlherefore reconunllend its use.
AIR. WETZLER: B1efore moving to adjourn, I wouild like to inove a vote of thaniks to AMr. Iteinunetz for Ihis admirable aind interestinig paper this evening.
THIE CHAIRMAN: Gentlemen it is with feelings of peculiar gratification that I put this motion. I was very glad inideed to hear MNLr. Bradley, in his initiatorv remlarks speak of the nmar ked
excellences of the papem we lhave lheardI read, anid I was pleasecd also to lhear hiim remark upon the raritv of suclh papers in Amnica. MIr. Bradley. I tlhink, did our sister societies of Europe
more thani justice, becanse it is in blut few of tlhe societies ox-er there, and I amn speaking of Englislh-speaki-ig countries of course, that we find suchl papers as tlhis-leavinig out tle Physical Society and that other in wlichl tlhe mnost distiniguiislhed mnember of our own pr ofession now presides so ably (I mean the Ro-val Soeie ty), there is none in whieh papers of tlhis character < re of h1igli frequeney.
[A vote of tlhanks was carried and the mneeting adjourniied.]
APPENDIX:
[COMMUNICATED BY MIR. STEINMETZ AFTER ADJOURNMNS[1T.] Having had time in the last few days to consider mtiore deeply the relation of this law of hysteresis to Ewing's theory- of magnletisi, I found that this law of hysteresis agrees very nicelv with Ewing's theory, giving just the phenomena this theory leads us
to expect.
According to Ewing's Theory, for very low M. MX1. F.S, forces
too small to affect the chains of mnolecular magnets, the magnetic cycle should be almnost reversible, that is, the hysteresis very small or almost nil.
For medium M. M. F.'S, that is M. M. F.'5 large enough to break up the clhains of molecular magnets, the magnetic cycles mnst become markedly irreversible, and the hysteresis as function of the M. M. F., must rapidly increase.

64

S TE1N-METZ ON TU'E LA W OF HYSTFRES;Iq. [Jan. 19.

For high M1. AT. F.'S, whlice the ehains of molecular mnagnets are mnostly brokenl by the superior outside M. A. F., the hysteretic loss, as funetioji of the lii. xi. F., slhould be expected to increase slower again- and always slower
Thlis is exactly the case, when the hysteretic loss, follows the
law of the 1.6tb. of the inayne6zafton -B, as shown best by the
affixed curve Fig. IC).
In Fig. IC) thedottU6d eturve gives the magnetization B, in lines
F, of magnetic force per em2, as fuinction of the M. AM. F. in am-
pere turns per cm.
The d1rawn (`UPQ(e? gives the hysteretic loss, in ergs per cm.3 and cVcle calculated by the equation:
.003507 BP 1

but not plotted, as in the former curves, with the magnetizations B as abscissoe, biut with the M. M. F.'S: F as abscisste, that is in the form:
JI f(F).
As seen, the hysteresis II for low :X1. NM. F.'S 0 1 is very low and almost nil, increases very rapidly for medium iL.D.I. F. F 2 5 and then increases slower again and always slower, just as Ewing's theory leads us to expect.
Yonkers, N. Y., February 7th, 1892.
1. This curve corresponds to a set of tests not contained in the paper, being made after its completion. I chose this particular set of tests, because it covers a larger range of magnetization than any set of tests given in the paper.