zotero-db/storage/LTETKYGC/.zotero-ft-cache

AMIERICAN INSTITUTE OF ELECTRICAL ENGINEERS.

:New York City, September 27th, 1892.
The sixty-ninth mneeting of the Institute was held this date. The meeting was called to order by President Sprague.
THE PRESIDENT :-We meet to-niglht for the first time after the suminer vacation. The paper that is going to be presented to
yoU is one of great interest. It embodies the results of investiga-
tions which have been imade by one of the ablest mathematicians
of this Iinstitute, carried on for months both day and night with resources which were practically unlimited in their experimnental character, and they have been enibodied in a paper which I think may fairly be said to be one of the mnost iinportant ever presented
here. Owing to the pressure of private duties whieh has borne
heavily on ie for some time, I shall not be able to preside at this ineeting and I will request Mr. Hammer to take my place. If there is any new business to present, the Secretary will do that in connection with the annouincement of the election of new members.
THE SECRETARY: At the meeting of the Council lheld this afternoon, the following associate members were elected:

Name.

Address.

Endorsed by

ALBRIGHT, H. FLEETWOOD, Electrical Engineer, Western

G. M. Phelps.

Electric Co., 227 So. Clinton St.,

E. M. Barton.

Chicago, 111.

Chas. A. Brown.

ARMSTRONG, CHAS. G. Electrical Expert and Electrical F. J. Sprague.

Architect, I301 Auditorium C. T. Hutchinson,

Tower, Chicago, Ill.

Louis Duncan.

CALLENDER, ROMAINE Electrician,

T. J. Smith.

Brantford Electrical Laboratory, F. Jarvis Patten.

Brantford, Canada. Ralph W. Pope.

CRANDALL, CHESTER D. Assistant Treasurer, Western Electric Co., 227 South Clinton St., Chicago, Ill.

E. M. Barton. Geo. M. Phelps. Chas. A. Brown.

FISHER, GEORGE E.

General Manager,

Elias E. Ries.

Commercial Electric Co.,

Ralph W. Pope.

55-57Gratiot Ave., Detroit, Mich. Fred'k Reckenzaun.

620

ASSOCIATE MEMBERS ELECTED.

FLESCH, CHARLES

Electrical Engineer, Melbourne, Australia.

Jos. Wetzler. T. C. Martin. Geo. W. Davenport.

JACKSON, J. P.

Assistant Professor of Electrical D. C. Jackson.

Engineering, Penn. State College, Gilbert Wilkes.

State College, Pa.

W. G. Whitmore.

KINSMAN, FRANK E.

Electrical Engineer,

Geo. A. Hamilton.

Plainfield, N. J. Ralph W. Pope.

H. C. Townsend.

MAGENIS, JAMES P.

Editor the Adfams Freeman,

Frank J. Sprague.

Adams, Mass.

P. B. Delany.

C. E. Dressler.

MACFADDEN, CARL K. Chief Electric Light Inspector, Chicago & Northwestern Ry. Co., 22 Fifth Ave., Chicago, Ill.

R. W. Pope. Fred DeLand. A. H. Bauer.

MCBRIDE, JANIES

Superintendent,

W. A. Rosenbaum.

N. Y. & Boston Dye Wood Co,

J. A. Seely.

146 Kent St., Brooklyn, N. Y. Ralph W. Pope.

NOLL, AUGUSTUS

New York Insulated Wire Co.,
I5 Cortlandt St., New York City.

Jos. Wetzler. T. C. Martin. F. J. Sprague.

RAY, WILLIAM D.

Electrician of Local Line of Northern Pacific R. R. Co , at Chicago, 308 Home Ave., Oak Park, Ill.

D. C. Jackson. Fred. DeLand.
Ralph W. Pope.

RODGERS, HOWARD S. Electrical Engineer,

Franklin Sheble.

Thomson-Houston Electric Co., Caryl D. Haskins.

624 Western Ave., Lynn, Mass.

H. G-. Reist.

Ross, ROBERT A.

Engineer in charge of Engineering John Langton.

Dept., Edison General Electric Wm. S. Andrews.

Co., Petersborough, Ont.

Samuel Insull.

SMITH, FRANK S TUART Supt. of Carbon Dept., Westing- Chas. A. Terry.

house Electric & Mfg. Co., 0. B. Shallenberger.

Pittsburg, Pa.

Chas. F. Scott.

Total, i6.

Probably at one of the following mneetings the Committee on Units anid Standards, which has been pursuing its work for the last year or two will bring up a report for consideration by the Institute at large, in accordance with the action of the Council. We have a few proof copies of this report which I will be glad to have any of the members who are interested in this subject take witlh them in view of discussion at some future date.
THE PRESIT)ENT:--It is good for the Institute that we lhave at each returning meeting such a list of niew mnembers. I am glad to notice that the number of members, who either under the pressure of personal business or for other reasons, have found it necessary to drop out of the Institute are few.
The paper this evening will be by Alr. Charles P. Steinmetz. It is the second paper "On the Law of Hysteresis, and other Phenomena of the Magnetic Circuit." His work in the past has been most important in its character and this paper will fully .support the reputation he has already earned.
The following paper was then read by the author.

A Iagfer read at the sixrty-ninth mneeting of the
A merican Institute of Electrical Engineers,
New York, SefStember 27th, 1892, Vice-President
Hammer in the Chair.

ON THE LAW OF HYSTERESIS (PART IL) AND OTHER PHENOMENA OF THE MAGNETIC CIRCUIT.

BY CHARLES PROTEUS STEINMETZ.

At the sixty-third meeting of this InstituLte, on January 19th,

1892, in a paper, "On the Law of Hysteresis," 1 I have shown
that the energy converted into heat during a complete cycle of

nagnetization can be expressed by the empirical formula

HT = B-l6,

where ± B is the maximum magnetic induction reached during
the eycylic process, and § a " coefficient of hysteresis."
I have given the numerical values of this coefficient, ^q, for dif-

ferent materials, varying for

Wrought-iron, between .002 and 0045

Cast-iron Annealed steel

.016 .008 to .012 and up to

Hardened steel

.025 to .082 in manganese steel

AMagnetite

.020

I have slhown that this " coefficient of hysteresis," ~, is appar-
ently independent of the speed of reversals in practical limits, being the samne for slow reversals as for rapid alternations up to

somewhat over 200 comnplete periods per second. The tests pub-

lished there, covered tlhe whole range, from very low magnetiza-

tion, B- 80 lines of magnetic force per cm.2 up to saturations as hiigh as B ± 19,000 lines of magnetic force per cm.2 giving fair agreement with the law of the 1.6th power.

Under conditions where eddy or Foucault currents were induced

1. TRANSACTIONS, VO1. ix, p. 1,

622

STEINMETZ ON HYSTERESIS.

[Sept. 27,

in the iron, the loss of energy followed the more general formula,
H =- r B"6 + E N BI,
where N is the frequency, H the whole loss per cycle and cm.' in ergs or absolute units, and
_H,= ^q Bi6 represents the loss by mnolecular hysteresis,
HI- £ 1N B2 represents the loss by eddy-currents.
In an appendix I have shown that when the hysteretic loss lI is represented as function of the M. M. F. F,
If f (F),
we derive a curve of that shape which we would expect on the hand of the theorv of molecular magnets, as formnulated by Ewing.
The next question which offered itself was, to determine the conversion of energy into heat during a magnetic cycle completed between any two limits, eitlher of opposite or of equal sign; for instance during a cyclic variation of B between B, + 1 0,O(, and B -- 2000, or between B, _ + 18,000 and B + 6000.
In the latter case Ewing, I believe on the hand of theoretical
reasoning rather, contended the, hysteretic loss to be very small or, in the limits of saturation, even nil.
To determine the loss of energy in a muagnetic cycle between
any two lirmits, BR1 and B2, I have made a numnber of tests:
1. By the electro-dynamometer method, by einploying pulws-
ting cuirrents for the excitation of the imagnetizing helices; that is,
currents which were derived by the superposition of an alternating and a continuous E. M. F.
2. By means of the Eickemever differenitial magnetometer, described in the former paper.

CIHAPTER I. ELECTRO-DYNAMOMETER TESTS.
In the samne manner as described in the former paper, a magnetic circuit of rectangular form was built up of 41 layers of sheet-iron, each layer consisting of two pieces of 20 cm. length and 2.62 cmi. widtlh, and twco pieces of 7.5 cmI. length and 2.62 cm. width. of the thickness o = .042 cm. (calculated from weight, specific gravity = 7.7).
Length of mnagnetic circuit, 41 'cm. Cross-section ............ 4.512 cm.'
Between the different layers, two sheets of thin paper were laid to give thorough insulation against eddy-currents. On the long

1892.]

STEINMETZ OS HYSTERESIS.

6i23

sides of the rectangle forming the magnetic circuit, two magnetizing coils were wound, and connected in series, each consisting of 5U turns of three wires, No. 1O B. and S. gauge, wound simultaneous]y. Connecting the three wires, No. 10, in parallel gave 100 exciting turns of a resistance of .048 (o.
The instruments emiployed were the same as used in the former
experiments, of which the constants are there given. The alternating E. M. F. was derived from the same Westinghouse 1 ir. P. dynamo, varied in frequency and E. M. F., and driven in the same manner as before. In the same circuit with the Westinghouse
dynamo and exciting helices, were connected in series three cells of an Eickemeyer storage battery and a rheostat.
To determinie whether the superposition of the alternating E. M. F. affected the E. M. F. of the storage battery, the fixed coil of an electro-dynamometer was excited from a separate source, and the current of the storage battery sent through the movable coil, the armnature of the Westinghouse dynamo and the rheostat. Then the Westinghouse dynamo was started, and it was found that the deflection of the electro-dynamometer was not changed perceptibly, thereby showing the absence of any perceptible interference between the alternating and the continuous E. M. F.'S.
The method of determination had to be changed somewhat to
make it applicable to tests with pulsating current. If the fine wire coil of the wattmeter is connected in shunt to
the magnetizing helices, across the main circuit, the wattmeter measures the whole energy expended in the magnetizing helices, which consists of the energy consumed by the iron, and the energy consumed by the electric resistance of the magnetizing helices.
For low and mediiin imagnetization, the magnetizing current, and therefore the energy consumaed in the electric resistance, constitutes only a small percentage of the whole wattmeter reading, and correction, therefore, can be easilvy made. But if a higher rate of satuiration is reached, the magnetizing current becomes very large and the energy consumed by the electric resistance becomles a great or eveni the greater part of the whole expenditure of energy. At the samie time, the temperature of the magnetizing helices rises somiewhat, and consequently, the electric temperature coefficient
of copper being very large, its electric resistance increases and the
energy expended tlhereby can not be determined exactly. This
imipairs the exactness of the readings at higher saturation considerably.

624

84STEINMETZ OV HYLSTERESIS.

[ept. 27,

Now. if upon the alternating E. M. F. a continuouLtS E. M. F. iS superposed, the current inereases greatly, while the magnetic
fluetuationi and consequently the energy consumed by the iron
decreases, because now the magnetic cycle is performed entirely
or greatly within the linmits of saturation. For instance, while an altern,atin. E. M. F. of 15.S volts effect-
ive, at the frequency 170, sends only 1.6 amperes through the magnetic circuit described above, apal&tting E. M. F. of 15.8 volts effective, produced by the superposition of six volts storage bat-
tery upon an alternating E. Ar. F., sends not less thanl 14.5 aimperes

FIG. 1.-Diagram of Connections.
effective through the same magnietic circuit at the same frequency.
Hence I devised another method whereby I was enabled entirely to eliminate the loss of energy caused by the electric resistance of the magnetizing helices (and of ammeter, etc.) and directly to measure the energy given off to the iron.
Of the three wires, No. 10, which were wound simultaneously on the magnetizing helices, only two were joined in parallel and con-
nected into the imiain circuit, in series to ammeter, coarse wire coil
of wattmeter, alternator, storage battery and rheostat. Voltmeter and fine wire coil of wattmeter, with their additional resistances,

1892.]

STEINMETZ OIV HYSTERESIS.

625

were connected into the third wire of the magnetizing helix in a separate secondary circuit, as shown in the diagram Fig. 1.
As seen, in this connectioni the voltmeter directly measures the E. M. F. induced by the fluctuation of the inagnetism, that is, measures these fluctuationis, while the wattmeter measures the time integral of the product of instantaneous values of main current into variation of magnetism,

1T

0

that is, the energy given off to the iron. It was necessary to
correct only for the small amount of energy transferred from the
irorn to the secondary circuit, and possible thereby to measure exactly even small magnetic fluctuations taking place at high
values of saturation. The precautions taken, the method of de-
termination anld calculation of the readings, etc., were essentially the same as in the former tests, so that I need not dwell upon them.
The magnetic characteristic B = (F) derived from these tests,
was checked by means of the differential magnetometer. Tests were made at the frequencies of

170 complete periods per second,

110 "

"

67

''

'

first with alternating current, using only the alternator, then with pulsating current, having three cells of storage battery in series to the alternator, and then with pulsating currents with three cells of storage battery and rheostat in series to alternator.
The magnetic eharacteri8tic is given in Table I. in the usual imanner, that
F = Mi. M. F. in ampere-turns per cm. length of magnetic circuit, B magnetic induction in thousands of lines of magnetic force
per cm.2,
,o mietallic reluctivity in thousandths, that is:
If we subtract from the magnetic induction B the miagnetic field

intensity ii 410 _ 4 F, and thereby derive the "mmetallic
induction, 1 I _ B - H, this metallic induction is

1. Kennelly on Magnetic Inductance, TRANSACTIONS, vol. viii, p. 485,
October, 1891.

626

STEINMEIZ ON HEYSTERESIS.

[Sept, 27,

TABLE I.
MAGNETIC CHARACTERISTIC OF SHEET-IRON IN KILOLINES.
p 3.16 e-.2F+ .275 + .058 F, in mils.

F.

B.

p.

0

F.

B.

p).

obs. calc. obs.

I.

.54

I.85

1.5

1.00

I.50

+.02 .o6

i6

13. 32

I8

13.67

2 2.5

I.70
2.60

1.18
.952

--..o0i48

20

13.95

25

14.52

3

3.65

.822

-.009

3,v5

4-74

.738

-.oo6

4

5.86

.683

+-oor

4.5

6.8.

.658

+.002

5

7.77

.644

+-007

5.5

8-55

.644

+.oi6

6

9.27

.648

65

9.85

.66I

+.020

30

14.94

35

15.23

11

40

15.47

N

45

I5.65

Ut

50

i5.8o

6o

I6.o6

T

70

I6.24

O

80

I6,38

o

10.28

.682

+ .oI8

go

16.49

";

8

0o.83

.739

+.OIO

100

I6.57

9

II.30

.797

TO

II*71

.855

[120 150

I6.7I i6.86

I2

12.37

.97 1

14

12.90

I.087

200 I 000

17.09
18.-41]

Absolute saturation, (B-

17.24.

L F,
p
where p is the " metallic reluctivity" (referred to ainpere-turns as
unit); indeed, referring to maaneti,/field intensity as unit, we
get

wh-re

pO

47w

5

Po10P 4 P

Or, in. the usual manner of writing, calling tlhe " permeability" , and the susceptibility " x, we have

B TH = (4 z x + 1) Al,

and Ibeing the " intensity of magnetization," or "magnetic mo-
ment,"

I-x HL, and

B = 4 I+ 1,

so that the "metallic induction" is

I 471,

and the "' metallic reluctivitv"

2

Po° 4x

25 x

1892.]

STFIAMETZ ON HYSTERESIS.

62,7

In the following I shall, as in my former comilunication, ex-
clusively uise as unit of M. M. F., F, the " ampere-turn per cm.,"
since this is the unit directly derived by the tests and, at the same time, the value needed in electrical design, so that by this the

factor

47r 10

is

avoided.

The absolute units Hand po can casily be

derived herefronm by the equations given above, H - 10 F, anid
f'14;0-rP

In Table I . this rmnetallic reluctivity " in thousandths can, over the whole range of magnietization, be expressed witlh fair approx-

imation by the equation

p

-
3.16 e

.72

F
+

.27-5+0

.81, 8F

About at F 7 the first termi, 3.16 e .72 F vanishes and the

reluctivity assumes the simpler form

p .275 + .0a8 F,

given by Kennelly, in his paper already cited.
The " inetallic induction" is, then,

and the whole induction

BR

F 0

+

4'F
10

where, in the range used in dynamo building, etc., the last term

can usually be neglected, and instead of B using 1,.

This iron reaches " absolute sat-uration " at tlhe " m-etallic induc-

tiou" Io 17.24 kilolines.

TABLE II.

Frequeney, NV 170 complete periods per second.

ALTERNATING MAGNETISM.

i B.

K.

obs.

H.

H.-II

calc.

obs. calc.

2.74

1.17

III

3.59

1.62

1.70

3.89

1.97

1.94

5.50

3 41

3.38

7.52

5.6i

5.57

.00

5

+.o0

+5

-03

-2

-.c3

.04

-r

Av.0 +5

+3

Av. dev

-.02

-1

628

STEIYNMETZ ON HYSTEREkSIS.

[Sept, 27,.

TABLE III.
Frequency, N = 110 complete periods per second.
ALTERNATING MAGNETISM.

± B.

H.. H. -H.-

obs.

calc.

calc. obs.

1.91

.68

.62

-.o6

-I

2.54

.93

.98

+.05

+5

2.80
3.1I85

3.21184.-115.405

1.I5

+.0

+I

I1.-441T

--o.09

-6

4.12

2.19

2.13

-.o6

-3

4.77

2.56

5.82

3.75

6.48

4.25

7.12

4.72

7.72

95.46

8.48

6.98

2.68

+.12

-4

3.69

-.o6

-2

4.39

+. 4

+3

5.10

+-38

+7

5.80

+-34

+6

6.75

.23

-4

9.74

8.50

8.43

-- 07

-I

11.70

ii.65

11.29

-.36

-3

I4.65

I6.30

16.19

-.21

-I

16.64

19.83

I9.85

+.02

+0

Av

±14

±4

Av. dev.

+0

-0

TABLE IV.
Frequency, V - 67 complete periods per second.
ALTERNATING MAGNETISM.

! B.

H.

H. H.-HL.- %

obs.

calc.

cal c. obs.

2.50

.93

.95

7.22

j

5.40

5.22

8.I8

6.07

6-37

+--3

+2

8

-3

+-30

+5

Av. Av.

dev

i.
....

+±0127

+±I3

In Tables II. 1II. and IV. are given the tests made with tlternating currents.
±B = maximum value of trmagnetic induction in kilolines of magnetic force per cm.2 The corresponding M. M. F. ± F can be taken from Table 1.
if = the observed value of the energy consumed byhysteresis
obs.
during one complete cycle of magnetization, in kiloergs or thousands of ergs per cm.3 iron. if = the value of the energy consumed by hysteresis, calc-
cale. lated by means of the "coefficient of hysteresis"
; = .003497.

1892.]

STETNMETZ 0IV HYSTERESIS.

629

H - H gives the difference between these two values in ergs
calc. obs.
and in percentages of RI. calc.
The tests cover the range of magnetization from B = 1910 up
to B = 16,640, for frequencies of 170, 110 and 67 complete peri-
ods per second. As seeni, at these speeds the " coefficient of hysteresis " is con-
8tant, and therefore the consumption of energy by hysteresis is still independent of the frequency.
As average of these 23 values, as coefficient of hysteresis, is derived the value
= .003497,
.0035

TABLE V.
Frequency, 1V= 178 complete periods per second.
PULSATING MAGNETISM.
Constant E. M. F., T -- 6 volts.
Constant m. M. F., F, 22.93 ampere turns per cm.
Maagnetism induced thereby, B_i 14.3 kilolines per cm.2

B ~~~~~.F.

B2_ obs. H. H. ;H-H. =% Volts tAumrnps.' B1 B25

_

obs. ca!c. calc.obs

eff eect-

2

1e. iv .

2-4I
3. I2

*93 .90 -.03 -3 8.4

I.35 I-36

+.oi +I

II.I

3340

|II5S.-54

fio.6
9.2

4.o8 2.07 2.09 +.02 +I 14,6 37 +I5.5 + 7-4

7.00 5.0o 4.96 -.07 -2 24 I 44 +!25.6 + I.6 7.70 5.46 5.78 +-32 +6 26.3 47 +I5.7 + .3

+B2
I13,0
12
11.4 8.6 8.o

Av... ± 09 2.6
Av.dlv +-05 +.61

1. In the appendix to the paper of January 19th, 1892, a curve of hysteresis is already given, constructed by means of a part of these tests, giving
^q = .003507,
.0035.

630

STEINMETZ ON BYSTERESIS.

[Sept. 27,

TABLE VI.
Frequency, N 115 complete periods per second.
PULSATING MAGNETISM.
Constant E. M. F., Vc = 6 volts and less. Constant M. M. F., F, 22.2 to 17.8 ampere turns per cm.
Magnetism induced thereby, B_ - 14.15 to 13.70 kiloliiles per cm.2

B=

vF.

1 B, obs.

H. H.- I. 1. =,(VVolltssturns

Bj-B2 obs. calc. calc obs

effect- effect-

2

ive. ive.

B.,

Bj+B2
2

1i.63
2.80
5.40
5-75 * 135

.50 .481 -.02

5

3.7

22

+15.0 +II.8

I. I5 4+Oi +I1 6.5 26 +15.2 + 9.6

3.30 3.28 -.02 j 1 12 I

33

+153 + 4.5

3.68 3.63 10.55 10.76

-.5
+.21

+21 2I53-.I8

38 2

+I5-3 + 3-7
+I15*5 7.2

I3.4 I2.4
9,9 9.5
4.15

Av

+ .o6 + 2

Av.dv + 03

TABLE VII.
Frequency, = 175 coiuplete periods per second.
PULSATING MAGNETISM.
Constant E. M. F., V = 6 volts. Constant M. M. F.I F 3.415 ainpere turns per cmn.
Mlagnetism induced thereby, B, 4.6 kilolines per cm.2

B

F.

. H.

- .I-'

turns

obs. calc. calc.obs

effect-I effect-

2

~~~V~&~ .

I-5I

.44 .43 -1 -2 5.3 5-I + 6.i +3.I

4.6

I.75

.59

54! -.,5 i-Q

6.o

3 + 6.4 +2.9

4.6

3.3I

1.54

1.-50

-.04 |3

II.5

6.I + 8.I +1 5

4.8

3.88

1.92 .193

+-OI +1

I3.6

7-I

+ 8.7

.9

4.8

5.24

3.18 3.I2

-.o6 -2

I8.4

9.1 +10.3 - .2

5.I

'Av.d;_034 ±3.4
Av.dv -.03 -3

1892.1

STEINfMElZ ON HYSTERESIS.

631

TABLE VIII.
Frequency, N1 111 complete periods per second.
PULSATING MAGNETISM.
Constant E. M. F., V-, 6 volts. Constant M. M. F., F,, 3.49 ampere turns per cm.
Magnetism induced thereby, B0 4.7 kilolines per cml.2

B

-.

obs. H. I. H-H.

B1-B2 obs. calc. calc.obs

2

Volts tAumrpn-s B1
effect- effect- 2
lV* ive.

B2 B1jB

.92

.193 .193 -

-O0 2.1 3 8 +5 6 +3.8 4.7

I.86

.62 .6o -.02

3 4.1 i-7 +6.o +2.8

4-7

i.q6 .64 .65 +.-I +2 4.3 5.7 +6.7 +2.7 4.7

2.2 .00107 Av.03 -3 5.5 6. +7.3 +23 4.8

Av**
Av.'dv'

±015
ox

4-2
i

In tables V., VI., VII. and VIII. aile giveni tests made with pul-
satiing currents at the frequencies 178 and 115, and 175 and 111.
B1 and B2 are the two limiting values of magnetic induction between which the cycle was performed.
Since in the alternating current tests B t-he amnplitude of magnetic fluctuation, here as B is given lhalf the difference between B1 and B2, that is, again the amplitude of mnagnetic variation.
B PT- 2 2
The continuous E. M. F. consisted of three cells of storage battery, giving approxiinately V0 - 6 volts.
The M. Al. F. Of the continuous part of the current is given as
F,, and amounted to 22.93, 22.2 to 17.8, 3.415 anid 3.488 ampere-
turns per cm. respectively. The magnetic induction excited by
this Mvl. M F., F,, if no alternating M. M. F. is superposed, is given by B., and amounted to 14.30, 14.1l5 13.70, 4.60 and4.70 kilo-
ines of magmietic force per cmi.t respectively. In the second set of tests the E. M. F. of the storage battery fell
off somewhat.
V gives tlhe E. M. F. of the alternrbator, which was superposed
upoli the VT 6 volts, in volts efective.
F gives the M. M. F. of the alterlnatinq part of the current, in

632

ST'EINMETZ ON HYSTERESIS.

LSept. 27,

efective ampere-turns per cm. (so that thie maximumii alternating
M. M. F. iS- 2 X F)
B1 and B, give approxirn tte values of the two limiting values
of magnetization, and B + B2 their mean, calculated by means

of the observed values B -B 2 B2

,1700°°

_

/|

19,000

52000-

:<

3600000

5T_

7B0-000C;e0t0 _-0---,

_4
_ _ f < 10
0

FIG. '.-Sheet-Iron. Curve of htysteresis.
byJ dal- toJebsIe. i,ftiumne obsyertvsedsvwaliuhe aofternaerigyn0counrsunmsed hysteresis
ring thle magnetic pulsation with time amplitude 2 BN, that is, between the values B1 and B2, in kulo-ergs per cycle and ciii.tm
H[ the energy calculated by the formula
calc.

;i where B Bt- B2, and .003497 is the coefficient of hys-

te0s0

20c

.1892.]

STEIJVMETZ ON HYSTERESIS.

633

H - Hgives again the difference in ergs and in per cents.
cale. obs.
Fig 2 gives the curve of hysteresis, with the values observed
by means of alternating currents mnarked by crosses +, the values
observed by pulsating currents marked by circles 0. The aver-

age~ valu~ e of~ magn netizat~ion~,~B~, 2+ B2, is written in the figure in
kilolinies. The dotted curve is the magnetic characteristic.
These tests prove that the energy dissipated by hysteresis depends only upon the diiference of the limiting values of magnetic itnduction, between which the magnetic cycle is performed, but not
upon their absolute values, so that the energy dissipated by hys-
teresis is the same as long as the amplitude of the magnetic cycle
.is the same, no matter whether the cycle is perforrmedfor instance
between the values of magnetization,

B =+ 4000 and B2 4000,

or Bi=+ 6000 and B2 = 2000,

or B, = + 8000 and B2

0,

or B, + 14000 and B2 + 6000.

In either case the hysteretic loss is the sa,me, since the magnetic variation is the same, B - B2 800().
H/ence the generalform of this empirical law! pf hysterestis is

JI<_§(B1, B2>§

wlhere B, and B2 are the values between which the mnagnetisim
varies, ^ a constant of the material, in our case .0035. Includivg the energy dissipated by eddy-currents, we derive

I C (Bi + AB2)'16 + (Bi - B2)

wlhere N is the frequecyv, s a coefficient of eddy-currents. Ilerewitlh I conclude the first part, the results of the tests made
by nmeans of the electro dynainometer method with alternating and with pulsating current. A large number of further tests
made bly the samne mnethod proved these results, but cannot be
given here, since I lhave had no time to reduce them to absolute
units.
For further tests made with alternating currents by means of tile electro-dynamoineter method, see Chapter IV.

684

STEINMETZ ON NYSTERESIS.

[Sept. 27,

CHAPTER II.-MAGNETOMVETER TESTS.
A large number of tests have been made by means of the Eickemeyer differential magnetometer, of which description and illustration is found in the forrmer paper.
To increase the sensitivity of the instrument and reach down to lower values of magnetization where the directing force of the inagnetizing coil is weak enough to allow a perceptible influence of outside magnetism, the terrestrial magnetisnm was balanced by mieans of two permanent steel bar magnets of 10" length and i' cross-section.
In the tests, the direct method was uised exelusively, and the tested piece balanced against standard iron of known miagnetic characteristic, because the method of overbalancing the test piece by anl integer number of cm.2 of Norway ironi and then adding to the test piece as muchl standard iron as will restore equilibrium, is for low inagnetization and test pieces of higlh coercitive force liable to an error introduced by the fact that the test piece is the seat of an independent At. MA. F., that of the remanent magnietism, as will best be understood by comuparing it with the differential
galvanometer.
In determining the imagnetic characteristic, before each test the magnetizing current, and thierefore the magnetismn, was reversed repeatedly to destroy the remanent magnetism left from formier readings, and alwaysfirst readings with lower, than with higher magnetization, were taken to make sure that the remnanent magnetisri of the former test could be destroyed by the reversal
of mnaynetismn in thefollo-wting test.
The hysteretic curves were taken by varying the magnetizing
current cyclic and taking readings at every step. Ul sually two or
three complete cycles were taken, plotted on cross-section paper, and the values of the imagnetization from 5 to 5 taken froin the plotted curve, or from 10 to 10 amnpere tuirns per cm., and these values added together, which gave the value of II. Before the readings a larger number of cycles were performed to make sure that durinig thie readings the cyclic process lhad become stationary already.
In somne cases a differential method was used, oy balancing the test piece against another piece of simiilar magnetic characteristic, which had been tested before, and was in this way used as an auxiliary stanldard.

1892.]

STEINMETZ ON HYSTERESIS.

635

TABLE IX.
MAGNETIC CHARACTERISTIC OF THIN TIN-PLATE.
30 pieces = 2.05 cm.2

C. .8+

L.=

P.- (.-

F. S. A. = LM. obsJ calc. calc -

S_s+Aa

M.2.05F.L..

.192 +~F0.5464

p.
obs.

H. B.

.45 I+i6 8 I3.30 540 2I.94 IO.70 .748
.55 2-21 IO.5 I4.20 595 27.o6 I3.I9 .798

.80 2--I16 14 I5. IO 645 29.92 14-59 .960

1-15 2-16 20 i6.o 695 31.96 15.58 1.284

2+Y8 I.40

26 I6.47 730 33.02 i6.io i.6i6

I-70 2+176 34 I6.90 758 34.I6 I6.65 2.04

2.20 2+'2 47 17.30 78I 34.98 I7.05 2.76

2.90 2+'2 62 17.57 802 3.5-54 I7.33 3.58

4.4 2+Y8 85 I7.78 8I8 36.o8 17.59 4.84

2++ 5.6

97 I7.83 821 36.22 I7 66 5.49

7.5 2+Y 11I1O 7.89 825 36.40 I7.74 6.20

IO.5 2+Y4 224 17.94 829 36.50 I 7.79 6.97

18 2+34 I43 28.02 832 36.66 17.87 8.oo

(.629)
(.766)
.957
1.285
1.6I3 2.05
2.76 3.58
4.84
5.49
6.20
6.97 8.01

.. ..

..OI IO.7T

.. .... ..0.,.2I3.20

-.003 -3 .02 T4.61

+.OOI +.1 .03 i5.6i

-.003 +01

-.2 .03 16.13 +-5 .04 i6.69

0

0 .o6 17.TI

0

0 .o8 I7.41

0

0 .11 17.70

0

0 .I2 17.78

0
0
+OI

0 .I4 17.88
.i6 27.95
+ 1 i8 Is05

Av.

± 0025 ±21

F> 14. p = .192 + .05464 F
As an example, I give in Table IX. a set of tests made for determining the inagnetic characteristic of a sample of thin tin-plate,of which 30 pieces were used, of 2.55 cm. width and.0268 cm.thickness, giving 2.05 cm.2 cross-section.
C = current in the mnagnietizing coil of the magnetometer. s + a _ number of cm.2 Norway iron (s) and of pieces of soft
sheet-iron (a), of 2'S cm.. cross-section, necessary to balance the test piece. F M. M. F. in ampere turns per cm., corresponding to current C and reluctance s + a, taken from the char-
acteristic curves of the instrument. S and A are the number of lines of inagnetic force which a cn.2
Norway iron (8) or 218 cm.2 sheet-iron (a) carry re-
spectively at the M. M. F., F.
=f 8 S + a A is consequently the number of lines of magnetic force carried by s + a and therefore by the
test piece. Hence

I-221.1055 - 8s-2aFA3+5 A is the (metallic) magnetic induction in the

test piece.

p=
obs.

F-e.iiss
I

the

metallic reluctivity of the test piece

which

for

636

STEINMETZ ON HYSTERESIS.

[Sept, 27,.

F> 14

can be expressed by the equation, derived from these tests,
p .192 + .05464 F

cp is the value of metallic reluctivity calculated from this equa-
alc.
tion, aind

p p the differeniee in absolute values and in pereentage of p.

cale. obs.

cale.

H=4-
10

F is

the

field

intensity,

corresponding

to

M.

M.

F.,

F,

and thus

B = JL+I

the whole magnetic induction in the test piece.

It must be understood that the differential magnetometer measures not the whole induction B, but the metallic induetion
_L = B -H=4 xHH.

In all the following tests, NOT the whole induction B, blut the metallic induction L is given. To determine, therefore, the whole induction B, the field intensity II 4r F has to be added.

For the value of hysteresis, the addition of H makes no difference, since space has no hysteresis.
Where the dimensions of the test piece are not given, they are
cylindrical pieces of 4 cm.2 cross-section and 20 cm. length, fitting
into the pole-blocks of the magnetometer.

1892.]

STEINMETZ ON HYSTERESIS.

637

TESTS. I. CAST-IRON. 1. Ordinary Cast-Iron. Table X. gives the magnietic characteristic in the first column.

TABLE X.
MAGNETIC CHARACTERISTICS OF GRAY CAST-IRON.

No. i.

No. 4. No 7. fA1. No.8. f% Al.

F. . L. 10. L. 10. L. 0. L.

7.5 6.20

1.22 3.98

1.92 6.8o

I.10 8.20

.92

I0

5.00

2.00

3.70

2.70

5.45

I.84 6.55

1.53

12.,5 4.20

2.98 3.58

3.49

4.50

2 78 5>40

2-31

I5 3.94 3.8I 3-59 4.17 4.13 3.63 4.80 3.12

17-5 4.05 4-33 3-72 4.73 4.i6 4.21 4.70 3.73

20

4.68

5.00

4.63

4.15

30

-

5.74

0.04 t

5.67 t

5.20

40

6.50

6.72

11

6 37 11

s.96

s0

N

7.05

7.23

N

6.9o0

6.52

60

°

7.46

°

7.60

.

7.30 s

6.97

80

8.o6

U.

8.13

W

7.87

7.6I

I00

t 8.47 + 8.50 + 8.25 +

8.07

250

o

9.I0

0

9.00

0

8.8i °

8.74

[200

o

09.42

9.31I

9I.04

90.14

300

9.81

S

9.60

9.48

0

9-57

400

10.00

9*77

.

9.66

99. 8o

500

I0.12

9.89

9.78

9-93]

Absolute satura-

tion .

I0.28 io.66 ........

.......

I0.25 ......1..I0.5

XF = M. M. F. i]n ampere turns per cm. -L metallic induction in thousands of lines of force per cm.2
p metallic reluctivity 1 in thousandths (10-3).
The values inclosed in brackets are extrapolated by means of the law
p = a + a F [Kennelly, paper before cited].
Tables XI. and XII. give 11 magnetic cycles of this cast-iron and Table XIII. the results of these cycles.

638

STEINMETZ OI HYSTERESIS.

[Sept. 27,

TABLE XI. HYSTERESIS OF ORDINARY GRAY CAST-IRON, No. 1.

(I)

(2)

(3)

(4)

(5)

F. Ld Lr Ld Lr Ld Lr Ld Lr Ld Lr

+44
40 35 30
25 20
I5
+5
0
-5 -g
H-
L=

± 3-40 2.92 i.6o 2.35 - .55
± i.6o
5.82 3-40
.01302

± 6.68
6.58 6-44
6 42 6. io
6 20 5.70
5-93 5,10 5.6o 4.35 5-17 3.00
4-58 .70 3-80 - I.40
± 2.80
I7.08 6.68
.OI297

+ 6.70
6.6o 6.52 6.46 6.22

6.28 5.9I

6.oi 5 45

5-70 5.00

5.30 4-35
4-80 3.40

4.20 I.00

3.10

0

i.6o - .25

- .32

+ 6.70 6.6o 6.54 6.46 6.25 6.28 5.93 6.oi 5.SI
5-70 5.26 5.30 5I3
+ 4.66
[F2 = + II.]

+ 6.70 6.6o 6.56 6.46 6.32
6.28 6.o3 6.oi 5.66
5-70 5.50
[F2+=5+-33i6.]

6. I3

.86

.48

3.5I

I.02

.685

.OI303

.02320 _ 01393

TABLE XII. HYSTERESIS OF ORDINARY GRAY CAST-IRON, No. 1.

(6)

(7)

(8)

(9)

(IO)

( I I)

F. Ld Lr Ld LLdr LdLr LaE Lr Ld Lr

140

+ 9.0I + 9.o6 + 9.o6

+ g.o6

130

8.92 8.88 8.97 8.94 8.97 8.96 8.97 8.96

120

8.8i 8.72 8.86 8.79 8.86 8.84 8.86 8.84

IIO

i 8.7I 8.70 8.56 8.75 8.65 8.75 8-72 8.75 8.72

IOO

8.54 8.5o 8.59 8-39 8.64 8.50 8.64 8.57 8.64 8.6o

90

8.37 8.28 8.50 8.24 8.55 8-35 8.55 8-44 8.56 8.49

80 [F'= ± 74.] 8.20 8.o5 8.34 8.04 8.39 8.II 8.39 8.23 8.42 8-30

70)

± 7.92 8.o5 7-76 8,i6 7-74 8.21 7-83 8.21 8.OI 8.26 8.ii

60 7.62 7-44 7.80 7.40 7-96 7.36 8.0I 7.5I 8.02 7.78 8.o8 7.92

50 7.38 6.93 7-55 6.9o 7.68 6.80 7.73 7.08 7-74 7-48 7.80 7.70

40
30

7.06
6.60

6.37
5.68

7.2o 6.35
6-75 5-65

7-34 6.36
6.86 5-70

7.-9 6.6I
6.96 6.OI

7.41 7.I6
7.oo 6.84

+ 7.26 [F2= + 40-.

20 5.95 4-32 6.Io 4.25 6.i6 4.5I 6,3I 5.21 + 6.og

20 4.90 .60 5.00 .40 4.95 I.20 5.17 3.50 [F2= + I7-]

0

± 3.03

± 3-15

i 3.30 3-40 .80

9

0

H=

22.46

26.34

27-54

9.I9

2-53

.72

L=

7.92

8-71

9.01

4-53

1-485

.90

= .OI298

.OI3o8

OI225 .0I299

.OI288

.01350

1892.]

STEIIVMETZ ON HYSTERESIS.

689

TABLE XIII.
HYSTERESIS OF ORDINARY GRAY CAST-IRON, No. 1-RESULTS.

o1X No. F1 F2 F1-F1 L1 L2 L,-L2 H a')

2

2

(I) a + 5 - I5 (2) a + 44 - 44
(3) JA + 44 - 9 (4) A + 44 + II (5) O + 44 + i6
(6) a + 74 - 74
(7) a +jIO -IIO (8) a +I40 -240 (9) P +140 - 9 (IO) 1+I40 + 27 (II) 3 +140 + 40

5 +3.40 -3.40

44 +6.68 -6.68

26.5 +6.70 - .32 I6.-5 6.70 +4.66

I4 116.70 +5*33

74

+7.92 -7.92

IIO +8.7I -8.71

240

+9.02 -9.02

74.5 +9.o6 o 6i.5 +9.o6 +6.og 50 +9.o6 +7.26

3.40
6.68 3.5I
1.02
.685
7.92
8.7I
9.0I
4.53
I.485
.90

5.82 .01302 - 2 - .2
17.08 .012971 + 3 + .2 6.13 OI303 - 3 - .2+ .8t OI320 -20 1.5-5 .48 OI393 -93 -7.I--_ 22.46 .01298 + 2 + .1
26.34 0OI308 - 8 - .6
27.54 01295 + 5 + .4
9.2I9 .0299 + I + .,+ I,53.OI288 +i2 + .9-4
.72 .OI350 -50 -3.8+

Av.. .01300

Here are

FP and F2, the maximuim and the minimum value of M. M. F. in
ampere turns per em.
L11 and 1:, the mnaximumn and the minimum value of mnagnetic in-
duction in kilolines of magnetic force per cm.2

F

F- F2_
2

the amplitude of variation of M. M. F.

L-

-
2

,the amplitude of variation of magnetic induction.

_H, the observed value of hysteretic dissipation of energy in kiloergs per cycle and cm.3
the coefficient of bysteresis calcutlated therefrom. A,the difference between this observed value of § and the aver-
age of ^ taken from the five largest cycles (since in small cycles the exactness is necessarily considerably smaller, the result being based upon a lesser number of readings, I deemed it advisable to use only the largest cycles for the calculation of the miean value of &).

The conclusion derived from these tests is the same as that derived from the electro-dynamometer tests, namely, that the loss of energy by hysteresis can be expressed by the equation

H- q (Li - 212)

Hfence the magnetic properties of this cast-4ron can be expressed by mea,ns of the equations

640

STEINMETZ ON HYSTERESIS.

[Sept, 27,

p- +ao F,
H- - 1_2)6

by three constants,
a, the "coefficient of magnetic hardness," }, the "coefficient of magnetic satulration," -, the "coefficient of magnetic hysteresis."
Only for values of F < 20 the value of o, if determined by reversals of magiietism, is larger and may necessitate the intro-

duction of a term, c e , or of similar shape.

The term au I call the " coefficient of magnetic hardness,'"

since the value of a determ-ines what is called " magnetically

hard." I shall still show in the following that a is smallest in

soft Norway iron, increases by hardening and reaches very large

values in glass-hard steel.

The term a I call the "coefficient of imagnetic saturation,"

because Lb

1is the value of absolute saturation of the

metallic induction, that is, the value wlich the metallic inductioni
reaches for infinitely large M. M. F'S that is, for values larger
than F 1000 to 20,000 (according to the value of magnetic
hardness a<).

2. Cast-lron with 8, viz., X AAltuinitm.'
(Here the tests were made by comparinig the two test pieces with the cast-ironi given in 1.)
Table X. gives the magnetic characteristic in the third column;
Table XIV. gives two magnetic cycles of the sample containing
per cent. aluminium. Table X. gives the magnetic characteristic in the fourth col-
umn; Table XV. gives two magnetic cycles of the sample containing I per cent. aluininium.

1. Derived from Cornell University; a sample containing no aluminium could not be tested, because it was too hard to be turned off to standard size.

1892.]

STEINMETZ ON HYSTERES1S.

641

TABLE XIV.
HYSTERESIS OF CAST-IRON CONTAINING 1 % ALUMINIUM.

(I)

(2)

F

Ld

Lr

F

Ld

Lr

44

± 6.49

40

6.40

6.26

35

6.25

5-93

30

6.03

25

5-78

5.54
4.95

20

5.46

4.I8

I5

5.04

2.80

4.48

.55

5

3.68

- 2.50

0

± 2.67

8.48

200

8.32

8.27

90

8.i6

8.o6

80

8.oo

7-84

70

7.86

7.56

6o

7.63

7.22

50

7.40

6.76

40

7.o8

6.23

30

6.65

5.5I

2C)

6.oi

4-04

IO

4.9I

.i8

O

2.90

17.07
6.49

26.50 8.48

.o1358

*0O 373

Av. ^q =.01365.

TABLE XV.
HYSTERESIS OF CAST-IRON CONTAINING 1 % ALUMINIUM.

Av. .01459. The denotations are the same as in the former set of tests (1).
3. -Diherent Sa,mples of Cast-Iron. In like manner, five other samples of common cast-iron, obtained from different foundries, were tested. They are marked

642

STEINMETZ ON HYSTERESIS.

[Sept. 27,

with 2, 3. 4, 5, 6, while the two samples of aluminium cast-iron were marked with 7 and 8. Only one cycle of each of these five samples was taken and the magnetic characteristic determined.
Of sample No. 4 the magnetic characteristic is given in the second column of Table X. Of the four other samples, Nos. 2, 3, 5 and 6, the magnietic reluctivity p is given in Table XVI.

TABLE XVI.
MAGNETIC RELUCTIVITY OF GRAY CAST-IRON.

No. 2.

No. 3.

No. 5.

No. 6.

F

p0

p

7.5

5.50

4.95

10.

5.I5

5.40

4.60

4.10

12.5

4.35

4.65

4.10

3.68

I5-

4.o8

4.32

4.00

3.57

27.5

4.I2

4.44

4.04

3.76

20.

11 .

[1

11~11~~P.

b~~~~4

+

+

+

+

O~

~

O1

W

~~~~~~~~b

~

~
tJ

~

~

~

~~N2O1~:~4t~~t~~~1O~~ ~o

The results of the cyelic tests of all the eight cast-iron samples are combined in Table XVII.
TABLE XVII.
MAGNETIC HYSTERESIS OF CAST-IRON-RESULTS.

±F ±Llj H

x No. ... Graded Cycles

No. 2 .

...

58

7.35

No. 3..,,,,,.

58

7.00

No. 4 ........O110

8.63

No. 5 II0 ...

8.6o

No. 6 .

110

8.62

Y8 Al. No.6 7,4

per 4.

c.

44 iio11

86..448

No. 8, Y, per c. Al. 44

6.15

.10

8.33

20.22
22.39 22.47
25.01
24.17
2267..5007 i6.89
27.28

.01300 .013I7 .OI577 .OII32 0OI267
.OI222
.-3I665
.01459

These tests prove conclusively that beyond a certain mninimum value of M. M. F. F 18 to 20 amipere turns per cm., the metal-
lic maonetic relactivity p (inverse value of 1 6 7r x where x is the

1892.]

STEINMETZ ON HYSTERESIS.

643

magnetic susceptibility) rigidly follows a straight line, p xa + a F, showing that the metallic indnction, L - B - E,
approaches, for infinitely high M. MK. F's.. as limit of abso'ute mag-
netic saturation,

Hence, beyond a minimum value of M. M. F., all the magnetic properties of cast-iron can be expressed by three constants, the
Coefficient of magnetic hardness, a;
Coefficient of magnetic saturation, a; Coefficient of magnetic hysteresis, v. These three coefficienlts are given for the eight tested samples of cast-iron in Table XVIII., together with the absolute saturation
1 = 1 and the minimum value F, where p coincides with the
straight line.
TABLE XVIII.
MAGNETIC CONSTANTS OF CAST-IRON.

A bsolute

Coefficient of Coefficient of Coefficient of Saturation

F>Magnetic Magnetic Magnetic i

Hardness Saturation Hysteresis La, - -

aa

a~~~-~~6~0

No. i............ 20

2.40

No. 2............ 20

2.43

No. 3.......... 20

2 -76

No. 4.......... I8

2.05

No. 5............ i8

2-34

No. 6 ......... i8

2.07

No.7,Yi8 perct. Al. 20

2.37

No.8,'2 per ct. Al. 20

2.92

Average .......

2.4

.0940
.0943 .0954
.09725 .0950 .0972 .0976 .0948
.096

.OI300 .OI317 2OI577 .OII32
.OI267
.01220
.01365
*O1459
.OI3

Io. 66 io.6o
10.48
10.28
10.55 '10.29
20.25
IO.55
20.50

Furthermore, these tests prove that for cast-iron the dissipation of energy during a complete magnetic evele between the liinits
-Ij and 1A2 iS expressed by the equation
ii = a (A I2_ 1.6
The cycles 1, 2. 6 anid 7 of Table XI., made between opposite and equ-tal limits of m. M. F. onl cast-iron No. 1., are shown in Fig. 3.
Fig. 4 gives the cycles 2, 3, 4 and 5 of Table XI., referring also to cast-iron No. I.

644

STEINYMETZ OV HYSTERESIS.

[Sept. 27,

The results of all the 11 magnetic cycles of cast-iron No. 1 are,
shown in Fig. 5. The drawn line is the curve of hysteresis,
H= .013 (1I 1)6

The observed values are marked by crosses +, when taken be-

tween opposite and equal litmits, t - A12; by circles 0, when

taken between unequal linmits of Mi. MI. F. In the latter case the

average magnetization, L

+ 2

'',

is

written

in

Fig.

5.

The dot-

ted line represents the ma-gnetic characteristic.

Further cast-iron characteristics are slhown in Fig. 17.

00o
6000

700 500

FiG. 3.-Cast-Iron. Ilysteretic Cycles.
II. TOOL STEEL OF DIFFERENT DEGREES OF HARDNESS.
To determine the influence of hardening upon the magnetic constants, three pieces were cut from the same rod of tool steel, turned off cylindrical to 15 cm. length and 1 cm.2 cross-section, and then the one piece was annealed, the second piece was heated and hardened in oil, the third piece hardened in cold water and
thereby made glass-hard. To reach higher M. M. F. than possible
with test pieces of 4 cm.2 cross-section and the instrument at my disposition, the pole-faces of the inagnetometer were brought closer together, to 6.35 cm. distance, and only 1 cm.2 of test piece used, whereby M. M. F.'S. up to F 350 ampere turns, that is, field intensities up to Hf > 400, were available.

1892.]

STEINJMETZ QI HTYSTERESIS.

645,

The test pieces were laid in holes in the pole-faces of the magnetometer, of 1 cm.2 cross-section, and after a preimT1nary determination of their magnetic characteristic, a number of magnetic cycles were completed with each of them between different limiting values of F.
Then all the three samples were found permanently and strongly
magnetized. Hence, I deinagnetized them by means of a powerful alternating current in the following mnainner :-A wire spool
was slipped over each piece, and solid Norway iron blocks laid against its enids to concentrate the alternating magnetism thro ugh the whole length of the piece and to afford low transient reluctance frorn piece to air. Then, with a frequency of about 17T0

50000

10' 0/
40 3 0 20 10 + 0120 +310 40

en: :~~~o

FIG. 4.-Cast-Iron. Hysteretic Cycles.
complete periods per second, an alternating current was sent tlhrough the wire spool, representing about 5000 to 6000 amperetturns. The test piece got ratlher lhot after somne nminutes' application of the alternating current, but, nevertheless, in the glass-hard
piece the permianent maagnretisnm was not fully destroyed even yet
bv this alternatingomagnetic strain, but the cy-cles taken with it were afterwards found unsymmetrical.'
1. This sample of glass-hard steel was the only one which I was not able to demagnetize by a rapidly alternating x. _M. F. Otherwise an alternating M. M. F. of '000 to 4000 ampere-turns I found always able to destroy remanent and permanent magnetism within a few minutes so comoletely that not the least, trace could be discovered.

646

STEINMETZ ON HYSTERESIS.

[Sept. 27,

Nevertheless, the magnetic constants of all the three pieces were found considerably changed in the way a partial annealing
would do it. Then the magnetic characteristic of each piece was determined
by the method of reversals, that is, by reversing the magnetism repeatedly before each reading, since this seems to be the only method which gives constant anrd therefore reliable results, while the deterinination of the curve of rising magnetism becomes, especially for small AI. M. F.3S., unreliable because of not giving always the same value for the same M. M. F.; and then again a number of cycles completed witlh either of the pieces.

26,000

28,000-
24,000

40

M e.i1eiCyeof L___ _ -

30

Grey CasItron

11

22,00 --0

10,00

618003--

1£003 -

24000

&

--9.0

B- 10 20 00 00 00 600700 bu

0
0 70
15

The three pieces are marked with H glass-hard,
0-oil-hardened!
S annealed, and the values derived before the application of the alternating current marked with an h: llh, Oh, Sh.
Unfortunately, before the application of the alternating current the magnetic characteristics hadl been determini ed only preliminarily, so that the values given therefor can be considered only as
approximations, b0t sufficiently near to allow perceiving the in-
fluence fo the application of the alternatineg cnrrent.

1892.]

STEINMETZ ON HYSTERESIS.

647

Table XIX. gives the magnetic characteristics of the three samples in their two states.

TABLE XIX.
MAGNETIC CHARACTERISTICS OF TOOL-STEEL.

Hh

H

Oh

0

Sh

b

F p L P L po L ,0 L P L P L

20
30 40 50 23.0 6o 2I.0
70 I9-5 So i8-5
90 19.0
I00|

250

200

X

250 0 300 +

[400

[500

2.I7 2.86
3.58
4.25
4-74
5.00
6.22 6.54 6.78 7.o8 7.30

27 0 2.2
23.0 1-74 20.0 2.50
i8.0 3.33
17-3 4.04
17.2 4.65
17.5 5.15
0 5.47
12 5.765-745 -. 6.95 0 7.35
+ 7.64 g 8.02
830

5.8 5.I8 5.4 7.40
5.6 8.94 6.05 9.92
6.6 io.6o II T10
I1.54
|| 12.76
12.70 0 I3.25 + I3.6o b 23.80
C 14-.5 1 4.34

9.0 2.22
4.9 6.22
4-7 8.so
5.0 20.00
5.3 ir.34
I2.20
12.60
1I3.00
I3.25
4 24-255 + I4.78
5-.I3
° 15.40 0 I5.68 It i5.9o

3.8 7.90
4-0 10.00
4-45 I1.24
5.0 12.00
22.68
1 3-05 I3.37 I3.67
24-50 + 25.04
2I533 0 I5-55
I5.8 Ii 6.oo

3.o 6.67
3.2 9-37 3.6 II.I0
12.20
21 2.87 1 23.34
I3-75
21 4.08 + 14-37
15;I6 25.75 i6.05
i6,25
i6.521 I6.72]

Abs- lute saturation ... 8.28

9.53

I5.26

i6.70

26.70

I7,40

F = M. M. F. in ampere-turns per cm. metallic induction in thousands of lines of magnetic force per cm.2
p metallic reluctivity L ia thousandtbs.
The samnples are denoted by Rh, H, Oh, 0, Sk, S. The tables XX. to XXVII. give inagnetic cycles performned witlh the pieces, and Table XXVIII. the results of these cycles.

,648

STEINMETZ ON HYSTERESIS.

[Sept. 27,

TABLE XX.
HYSTERESIS OF TOOL-STEEL .Hh.

(I)

(2)

(3)

(4)

F L,d Lr Ld Lr Ld Lr Ld

Lr

+273
260 240 220 200
I80 I6o I40
120
80
-60 48 + 20 O
- 20
- 40
I- 6o - 83

i 5.93

5.92

5.9I

5.9I 5.83

5.90 5.78
5.89 5.70 5.88 5.60 5.87 5.45
5.82 5.28

5.73 5.10
5.6i 4.70 5.43 4.IO

5.20

2,90

4.80 .40

4.10 -1.90

± 3.30

+ 5-94
5-93 5.92 5.92 5.85 5.91 5.8o 5.90 5.72
, 5.89 5.64
5 88 5.52
5.84 5.40
5-79 5.21
5.70 4.98
5.57 4.47
5.28 3.53 4.90 '.75 4.36 - 70 3.6o -i.86
2.37 -2.63
.30 -3.12 --I.75 -3.5I
-3-76

+ 5-95

5-94

5-93

5-93

5.86

5.92

5.8o

55..9910

5-74 5.68

5.88 5.38 5.84 5.46

5.78

5.29

5.68 5209

5-5D

4-75

5.33

4.22

4-97

3-35

4.47

2.15

3.80

I.00

2.50

*45

.40

.07

0

L-F2 45]

+ 5-97

5.96

5-95

5-92

5-93

5-94

5-92

5-93

5.88

5.92

5-85

5.90

5.80

5.87

5-74

5.82

5.68

5-75

5.6o

5.6o

5.43

5.38

5.I8

5.00

4.82

+ [F2

4.66
+

30o

H

82.04

59-04

L=

5.93

4.85

26.52
2 972

2.42
*655

^r-

.07533

.07480

.07342

.07546

TABLE XXI.

HYSTERESIS OF TOOL-STEEL Hh.

(5)

F Ld

Lr

0
(6)
Ld Er

(7)

(7)

Ld

Lr

+I24
II10 100
90 80
70 6o 50 40 30
20
+Io
0 -40 -20
-30
-4I
H= L=

± 5.I2

5-09

4.90

5.o6

4.64

5.00

4-35

4.90
4-79

4.00 3-40

4.65

2.60

4.50

i.6o

4-30

.40

4.05

-I.00

3.80

-I.90

3-45 -2-55

+ 3.10

64.50
5.I2

+ 5-I3

5.I2

4-95

5.20

4-77

5.o6

4.56

5.00

4.30

4.90

4.05

4-75

3-75

4.60

3-33

4-43

2.90

4.22

2.33

4.00

1.73

3-75

2.20

3.40

*75

3.00

*45

2.30

.25

I.20

.10

2I1.46 2-5,65

5 5.I7

5.I3

5.04

5.22

4.92

5-07

4.80

5.0I

4.68

4.9I

4.56

4-76

4-44

4.6I

4 32

4-44

4,I6

4.23

4.03

+ 3.88
[F2 = + I5.

2.36 .645

.07493

.07533

07560

1892.]

STEILNMETZ ON HYSTERESIS.

649

TABLE XXII.
HYSTERESIS OF TOOL-STEEL H.

(I)

(2)

(3)

(4)

(5)

(6)

F Ld Lr Ld Lr Ld Lr I Ld Lr -Ld Lr Ld L,

+120
220 I00
9o
80
70 6o
50 40 30 20 + I0
0
20 20
30
40 50 6o
- 70 8o
90 -100 -I10
-120

+ 6.25
6. I5 6.oo 6.03 5.65 5.90 5. I5 5-72 4.50
5-53 3.50 5-32 2.50
5.o6 2.24
4-80 0
4.50 -2.2I5 4.I5 -2.95
3-72 -2.60
3-30 -3-05
2.62 -3-50
I.84 -3.85
*75 -4.I6
- .55 -4-43
-1.75 -4.68 -2.90 -4.90
3.84 -5.I0 -4.60 -5.29
-5.o8 -5-45 5.40 -5.60 5-64 -5.72 _5 .8o

+6.25 6.i6 6.oo

6.04 5-73

5-90 5.42
5-75 5.o8
5-58 4.70

5-42 4.30

5.22 3.8o

5-00
4-75
4.45

3.20
2.50
I.80

4.12 2.25

3-70 *77

3.20 .42

2.55

.20

2.55

.03

.20 .o8
-.I2

[F2 -47]

+6.25
6.23 6.I3
6.I8 6.oo
6.II 5.86

6.02 5.7I

5.89 5.57

5-73 5-42
5-56 5-27

5.30

5.12

+4-95
[F2 = + 28.1

[Fi = 28] -4-57
5.0I 4.68

5.22 4.84

5-37 5.00
5.50 5-I9
5.6o 5.36

5-70
5.8o 5.86

5.52
5.67 5.8o

-5.90

+6.25
6.23 6.13 6.i8 6.oo
6.1I 5.87 6.02 5-72 5.89 5.959
5.6I 5-45
+5.25 [F2 = + 47.]

[Fi =-47-]
-4-93 5-32 5.o8
5-52 5.23
5.63 5.38
5-73 5-53 5.82 5.67
5.87 5.82
-5.90

Hf = L

68.52
6.025

24.68 3.185

i.96

1.29

.665

.50

2.22 *485

.06I36

.06I24

.06i88

.06178

.06I97

.06Io3

F
+260
'240
220 200 i8o I60 I40 120 I00
8o 6o 40
+ 20 o
- 20
-30
H= L=

TABLE XXIII. HYSTERESIS OF TOOL-STEEL Oh.

. (I)
Ld Lr

(2)
Ld Lr

(3)
Ld Lr

± 23.25 I3.22 I3.29

I3.19 13,10

13.15 13.10

I3.00 12.88

13.05 12.77

I2.99
I2.85
i2.66

12.66
22.40
22.03

I2.42 II.95
II.00

II.50 I0.30 7.00

9.40 - I.70
+ 6.70

+ I3.25 13.22 I3.19
13.19 13.10

13.15 I3.10 I3.05

13.0I
12.90
22.80

I3.00
I2.87
12.68

12.70
12.46
I2.22

22.45 ii.62

12.00 II.20

20.50 8.6o

9.80

4.60

7.20 - .30

I .80 - I.90

+ 2 24

+ I3.25

I3.22

13.2I

13.19 13.I7

13.15 13.I0

13.12
13.06

13.05

I2.99

I3.00 12.88
I2.69

I2.92 12.76
22.50

I2.47

12.15

12.02

iI.65

II.22

II.04

+ io.6o
LF2 = + 30.1

i06.20 I3.25
] =o695

44-78 7-745
.02683

2.75
1.325
.02778

650

STEINMETZ ON HYSTERESIS.

[Sept. 27,

F
+80
70 6o 50 40 30
20
+10 O
-IO -2C)
-26
hr=
L=

TABLE XXIV.
HYSTERESIS OF TOOL-STEEL Oh.

(4)
Ldi Lr

± II.30

II.10 10.70 20.85 9.85

10.55 8.75

I0. I0

6.6o

9-50 *2.70 8.6o - I.20

7-50 - 4.30 ± 6.oo

82.20
II1.30
.02692

tS)
Ld Lr

+II.30

22.2I0

I2-75

io.85

IO.I0

I0.55

9-30

I0.I0

8.20

9-55

6.70

8.70

4-30

7.60

2.00

6.20

.6o

4-30 - .20 I.6o - .6o

-.70

28.96 6.oo

.026II

(6)
Ld Lr

+II.30

11.10

I0.82

10.90
io.68

10.50
20.22

10.26

9.95

9.48

(F2 = i-27]

I248 .91
.02727

F
II2 I00
90 8o 70 6o
50 40 30
20 I0
H=
L=

TABLE XXV.
HYSTERESIS OF TOOL-STEEL 0.

(I)
Ld Lr

±13.65

13.54 23.32
23.40 22.88

23.22 I2.32

23.20 22.72

I2.73 20.90

12.30 925,) II-75 7.00

II.00

2.50

IO.I0 - 2.90

9.00 - 5.55

i 7.50

III.64 I3.65

.02700-

(2)
Ld Lr

+13.65

23.54 23.40

I3.35 I3.05

I3.22

12.74

23.00

I2.42

12.70

12.08

12.30

II.70

II.75

II.28

I 1.09

Io.80

+I0.48

[F2 = + 24]

3.52
I *585
.02669

(3)
Ld Lr

+I3.64

I3.54

13.40

I3.40

13.I6

23.22

22.93

13.00

I2.71

12.70

12.46

12.30

12. I6

+I2.95

[F2 = + 43]

I232 .85
.027I3

1892.]

STEINMETZ ON HYSTERESIS.

651

TABLE XXVI. HYSTERESIS OF TOOL-STEEL Sh.

F Ld Lr

240

±i 6.6o

220

I6.58 I6.52

]12CJ0

I6.52 I6 40

I80

I6.45 26.27

I

I6o

I6.38 I6.Io

140

I6.28 I5.90

r26

I6.17 I5.60

IOC,

I5.95 I5.20

25.66 14.70

40

I5.20 I3.30

24.20

9. 6o

20

I2.00 2. 20

0

27.20

-20

-26

i

Io8.00

=

i6 6

.029I

(2)
Ld Lr

+16.60
I6.58 I6.53 I6.52 I6.42 I6.45 I6.30 I6.38 I6.13

16.28 15.95

I6.I7 I5.68

I5.95
I,.66

13.30
I4.90

1j.20

13.60

I4.25

10.80

22.40

4.50

8 20 -3.20

1.50 -7.50 -8.oo

66.oo
12.30

.01887

3.I6 2.80
.OI955

TABLE XXVII.
HYSTERESIS OF TOOL-STEEL S.

(I)

(2)

(3)

((44))

F Ld Lr Ld Lr Ld Lr Ld Lr

II12

±14-55

I4.55

24.45 I4.3I '4.45 I4.32

9S0o

24.25 I4.09
24,25 '3.74

'432 I4. IO 24.25 23.76

70 14.09 13.28 14.12) 23.3I

6o 23.87 I2.74 13.87 12.77

50

I3.57 I2.94

I3.57 II.99

40 I3.o8 20.070 I3.o8 IO. 89

30 22.32 8.6o I2-35 9,55

20 II.20 5.o6 12.30 7.20

IO 9.55- 8o 9.90 3.60

0

±6.40

7.70 - .90

-IO

4.60 -3.80

-20

-2.70 -6.20

-30

-7.20

H=

66.74

L=

14-55

4I2.22
IO.875

.OI457

.01434

+I4-55

I4.48

24.42

14.40

24.28

14.29

24.I2

14. I2 13.88

23.83

23.58

13.46

23.20

13.C2 I2.78

22.42

22.30

[F, 4.24]

2.43 I*325
.OI444

+14.55
24.52I 4.49 24.43 24.38 24.34 24.25
14.120 14.07
I3.97 13.85 23.63 I3.55
[2+I=3.+28 43]
.48 .635
OI434

652

STEINMETZ ON HYSTERESIS.

[Sept. 27,

TABLE XXVIII.

HYSTERESIS OF TOOL-STEEL-RESIULTS.

No.

F, F2 F1-F2 L,
2

L2 L2-L2 H '2 105 AYj = %

2

obs.

Rh, Glass-hard............... Av. _1- .07476 '.075

(I) a -+275 275

(2) jS +275 - 83

(3) Is +275

45

(4) Js +275 + 30

(5) a +124 -124

(6) I +I24 - 41

(7) I +124 + 25

275
179
i6o
I22.5
I24
82.5
54.5

+ 5-93 + 5-94
+ 5-95 _ 5-97 ~- 5.I2
- - 5.I3 + 5.I7

5-93
3.76
=0
+ 4.66
- 5.I2
-0
+ 3.88

5-93
4.85
2-975 .655
5.I2
2.565
.645

82.o4 59.04 26.52
2-42
64.50
21.46 2-36

.07533 .07480 .07342 .07546
.07493
.07533 .07560

-57 -4 +134 - 70
- I7
57
+ I6

- .8
- .I +I.8
9+
- .2
- .8
+ .2+

If, Glass-hard, af(terapplicationoft Av. - .06130 1.061

(I) a +I20

20

(2) Is +I20

47

(3) Is +120 + 28

(4) I - 28 -120
(5) Is +120 + 47

f (6)

- 47 -120

I20
83, 46
46
36.5
36.5

+ 6.25
6.25
+ 6.25
- 4.57
+ 6.25
- 93

5.8o
I.2
+ 4-95
- 5.90
+ 5.25
5.90

6.025
3.185 .65 .665
.50 .485

68.52
24.98
i.96
2.03
I.29
1.21

o06I36
.06I24
.o6i88
.06I78
o06I97
.06i03

-6
+6
- 58 48
- 67
+ 27

.
+ .I
- .9+
- .8+
-1.1+
+ *4+

Oh, Oil-hardened ..... ........ Av. .02670 -.027

(I) a I+260 - 20

(2) Is +260 - 30

(3) fi +260 - 30

(4) a + 8o

80

(((656)))

fIsiI-+-8o
Is + 8o

26|
+ 27

260
'42
I25 80
523
26.5

13.25 -I3.25
+I3.25 +2I.30
-14I-iII..330 +II,30

-13.25
- 2.24
+IO.60 -II.3C0
*770
+ 9.48

23.25 IO6.20

7.745 44-78

1.325

2.75

II.30

82.20

6.. oo ~ |228.296

.9I

1.48

.02695 + 25

.02683

I23

.02778 -io8 o.2692 - 22
. .206i6iI|++ 59
.02727 - 57

+ .9
.5
-4.-0+
- .8
+2.2 - 22..00++

0, Oil-lhardened, alternatcurrent.f Av. ^ .02700 ~ .027

(I) a +II2 -II2
(2) Is +II2 + 24
(3) I +212 + 43

112
44 34.5

+I3.65 -i3.65 |13.65

113.65 +IO-48 I.585

+13.6| +11-95

.85

III.64
3.52 I.32

.02700
.02669
.02723

0
+ 32 13

+1.2+
--5+

Sh, Aniiealed ......... .

. Av. 3 .01899 1--.019

(I) (2)

Ias

++224400

-24206

(3) fi +240 + 26

240
1I0373

++I66..6600

-i6.6o
8.oo

I

6.60
12-30

io8.oo o1I9II I2 .6
66.oo .0I887 |j+ I2 + .6

+I5.6o +22.00 i.80o . 6 I055 56 3.+

S. Annealeledd aafltteerranaptpeliccautriroennto.fj AivV..' -- .014455 .0145

(i) a +I12 2II2

(2) I II2 30

(3)
(4)

+II2
4+122

1+

24-
24

I12
72
44
34.5

±24-55 |1I4-55
+I144.5255

-I4.55
- 7.20
++I3.I2.1980

|I4IO-.52875.3|2462561.-I2J4723441O..*IIO00I1444443534474

2-II5 8-8

IIII-55

+ ,8
+I

II5 |+ :8+

1892.]

STEINMETZ ON HYSTERESIS.

653

F1 and F2 = maximum values of M. M. F. in ampere-turns per cm.

.1-L and 12 maximum values of metallic induction in kilolines

per cm.2

F-

-
2

and I

-22are the amplitudes of the varia-

tion of M. L. F. and induction.

.11_ observed value of the dissipation of energy, in kilo-ergs per

cycle and cm.'

coefficient of hysteresis calculated therefrom, and

0-120 080 I06u42u11
14000
FIG. 6.-Welded Steel. Hysteretic Cycles.
A iy, the difference between the individual values and the average value of ^, where again the cycles of small amplitude and therefore of lesser exactness are excluded in calculating the average of r. (The values not used for calcuilating av. A are marked by crosses
+, as in the former tests.)
Again, we find the hystere-tic loss dependent onily upon the amplitude of the magnetic variation, but not upon their absolute values, a.nd derive as constants of the six samples,
p + aF,
(2
the values given in Table XXTX.

654

STEI1VMETZ ON HYSTERESIS.

[Sept, 27,

TABLE XXIX.
MAGNETIC CONSTANTS OF TOOL-STEEL.

Absolute

Coefficient of Coefficient of Coefficient of Saturation

F

Magnetic
Hardness

SMaatgunraettiiocn

Magnetic
Hysteresis

=

Hlt ............

90

H .go.9.......... 0

Oh .........

70

0 .. .......

6,o

Sz 0...............of

S.

40

8.o

.I21

.0748

7.8

. I05

.06I3

1.9

.o66

.0267

1.54

.o6o

.0270

.0.30 3 o5 .0I90

1.22

.0575

.0145

8.28 9.53
I5.I6
I6.70
I6.70
I7.40

Fig. 6 gives a cycle of either of the three samnples after the ap)-
plication of the alternating currenit HI, 0, S between the opposite
and equal M.M. F'S. F- ± 112 [Table XXII., (1); Table XXV., (1); Table XXVII., (1)].

FIG. 7.-Glass-hard Steel. Hysteretic Cycles.
Fig. 7 gives thle six magnetic cycles of H represented in Table XXII.
III. CAST-STEEL.
In the same manner as in Test II., two pieces of annealed caststeel were treated.
Two pieces of annealed cast-steel were obtained from the same manufacturer, of the same casting, turned off to standard size, 20 cm. long and 4 cm.2 cross-section, and by comparing them on the

1892 ]

STEINMIETZ WV HYSTERESIS.

655

magnetomneter, found to be exactly alike. Then one was left an nealed, the other heated and hardened in cold water. Althouigh cast-steel, it was after this found neehanically verv much harder. In Table XXX. are given the mnagnetic characteristics of both samples, annealed and hardened.
TABLE XXX.
MAGNETIC CHARACTERISTICS OF CAST-STEEL.

Annealed.

Hardened.

F

,n

L

P

_L

Io

2.8o

3 57

I5

2.23

6.70

20

2.I6

9.30

25

2.29

10.90

30

I2,00

40

_Z6

13. I5

6o

11

14.60

8o

0D

25.40

I00

CIO

15.90

I50

I6.73

[200

I7.I0

300 400

n 4S
,:I

I7-55 17.84

500

27,95

5.20
4.60
4.20
0
1i
N 14
+
b 1
41j

3.85 5-43 6.67 8.24
10. 20
II.40 22.35
I3-90
14.82 I5.88 I6.5o
i6.88]

Absolute satu-

ration.......

I8.*0

I8.5o

As seen, for low Mr. M. F'S. the two samples are magnetically very different, but approach each other for higher m. M. F's. and reach the same valuie of saturation.
TABLE XXXI.
HYSTERESIS OF HARDENED CAST-STEEL.

(1)

(2)

(3)

(4:

F Ld LEr Ld Lr ldid li1r, jlIL-Td Lr

(5) Ld Lr

+82 70
50 40 30
20
40 -I0
-20
-30 -40 -53

i: II1.58

II.35 IO.94

Moo0 I0.20

10.57

9.12

Io.o6 7.05

9.51 3.40 8.90 - I.8o

8.20 -5-70 ± 7.33

+II1.D8 11.32 I0.87
II.02 I0. I 2
I0.63 9 I8
10.13 7.72
9.62 2.05
9-03 - .10
8.32 -4-35 7.40 -5293 5.70 -6.8o 2.50 -7-52 -3.65 -8.o6 -6.90 -8-53
9.07

+I2I.28 II.28 I0.98
I0.92 I0 34
10.20 9 6o
20.00 8.70
9-47 7.65
8.92 5.8o 8.28 .8o
76..3600--..7300
1.25 - .82 -.8i
[F2 =-26-5]

+I]I-58
22.29 11.14 I0.96 I0.62
20.53 9.89
io.o8 9.37
9.69 9.00
9.32 8-72 8.93 8.49
-t-2.42
[F2 = 0]

H=

87.63

72.905

32.5I

3.645

L=

II1.58

I0.325

6.195

I.058

Ti ==

.02760

.02758

.02784

-02779

II.58

22.35 II.2I

I1.04 10.75
io.6o 20.23 10.33 io.o6

IO.I3

I0.05

10.05

[F2 = + 27-5]

1.14
*765
.02770

656

6STEINIMETZ ON HYSTERESIS.

[8ept. 27,

TABLE XXXII.
HYSTERESIS OF HARDENED CAST-STEEL.

(6)

(7)

(8)

(9)

(I0)

F Ld Lr Ld Lr Ld Lr Ld Er Id Ir

(II)
d Lr

+45.6
40 35
30 25
20
I5 I°
+5
0
5
-IO
-'5
-20
-25
-3I 6

±8.70
8.50 7-77 8.28 6.35
8,o3 4.5I 7.77 2.42 7.46 -.33 7 07 2.53
6.63 -3.88
6.12 -4.82
±5254

+8-75 8.57 8.07 8.38 7.31 8. i6 6.35
7.92 5.03
7.63 2.70
7.29 -52
6.85 -2. I2 6.38 -2.90
5.83 -3.44
5.26 -390 4-54 -4.28 3.I9 4.6I
-1.00 -4.90
3-90 -5.10
-5.3I

+8.96

+8.96

8.76 8.30 8.76 8.30

8.51 7-70 8.51 7-70

8.25 7.00 8.25 7. IO

7.97 6. I I 7-96 6.27

7.63 4.86 7.66 5.28

7.31 2-72 7-33 4. I8 6.87 .66 6.93 3. 9

6-43 .22 6.5o 2.3I

5.90 0 6.o5 r.65

5.28 -.17 5-44 1.25

4-5I -33 3.30 -.48 .30 -.62

4.73 10oo
3.63 .92
+92

.'70 [F2 =-I8.j] [F, 22]

+8.96 8.76 8-34 8.53 8.o2
8.27 7-78 8.02 7.59 7.73 7-48
7.57 7-42
+7.42

+8.96 8-76 8-4I
8.53 8.22
8.33 8.20
+8.20
[F2 - + 27]

56.II

38.72

22.42

i6. IO

I .TO

.38

8-70

7.03

4.83

4.02

*77

.38

.02792

.02836

.02859

.02754

.02649

.02832

TABLE XXXIII.
HYSTERESIS OF CAST-STEEL RESULTS.

No.

F, F2 F-F2, LI
2

lI

L5-.L, 2

LI
--~obs.

5'

=

Hardened . ... .... Av. r -.02792 -.028

(I)

+882

82

a

(2)

82

53

1} (3)

+82 -26.5

(4)

82

=0

(2) 11}9

(6)
(7) (8)

1} 1a }

8 +27-5 -45-4 -45-4
45-4 -3I.6
-45-8 -22

Ai (9)

+45.8 -I8.5

Ai (so)

+458 _3D

Ai (I 1)

+45.8 +27

82 67.5 54-2 4I
27.2
45-4
38.
339 32.1 I6.I
9.4

+1I.58 +II.58 +II.58
1i.58
+1I58 8.70
8.75
8.96
8.96
+ 8.96
+ 8.96

.II58 9-07
.8i
+ 8.42
+I0.05
-8.70 - 5-31 - .70 _ .42
.2
+ 8.20

I1.58 I0.325 6.I95
I.58
.765
8.70
7.03 4.83 4.02
*77
.38

187.63 72,905 32.51
3.645 1.14 56. ii
38.72 22.42 I6.io
I.I0 .38

.02760 .02758 .02784 .02779 .02770 02792 .02836 .02859 .02754 .02649 .02832

+ 32 34
+8
+ 13 + 22
0
- 44 - 67
38
-+-I43
40

+I. I +1.2
+ .3
+ *+
+ .7+
0
-i.6 -2.4 +I.4 +5*1+
-I.4+

Annealed.

Av. -.008481 -.0085

(I) a ±100 -100
(2) |a | 44 - 44

100 |I5.85 -I5.85 15.85 35.00 .008502| 2.1

.4

44 ±I3.62 -1I3,62I31 6 44-40 |008460o +2.1 + '4

Tables XXXI. and XXXIT. give a number of cycles made with
the hardened piece h, and Table XXXIII. the results of these

1892.]

STENIMETZ ON HYSTERESIS.

657

cycles and of two cycles made with the annealed piece, the denotation being the same as before.
Herefroini we derive the results for this east-steel,
po aa L+i a _F,

F>

Soft cast-steel s,

30

Hardened cast-steel A, 40

Magnetic Hardness.
CZ
.88 2.7

Coefficient of

Magnetic

Magnetic

Saturation.

Hysteresis.

aa

.054 .00848

.054 .02792

FiG. 8.-Hard Cast-Steel. Hysteretic Cvcles.
The magnetic characteristics of these two samples of cast-steel,
together with many other characteristics, are represented in Figs. 17 and 21. Fig. 8 gives the five cycles of hardened cast-steel from Table XXXI.

658

STEINMETZ OI HYSTERESIS.

[Sept. 27,

Numerouis data on the magnetic constants of different kinds of cast-steel are given in (Chapter III. and collected in tables XLVII. and LI, represented in Figs. 16, 17 and 21.
IV. DIFFERENT KINDS OF IRON AND STEEL.
A number of tests were made with different kinds of iron and soft steel, to deterinine the magnetic constants a, a, ^.
Here the differential imethod was used for the determination of the coefficient of magnietic hysteresis ^, that is the test )iece was balanced step by step against a sample of known magnetic hy-
steresis, usnally Norway iron or the sheet iron of Chlapter I. and
so the difference in the dissipation of energy by hysteresis in both samnples read. Since in the former tests I believe to have proved the coincidence of the observed values with the general formula,
ij - - L2)1l6

here usually only one cycle, between opposite and equal values of M M. F. F was determined, and calculated therefromn.
Tests were made on Norway iron, by comiiparing it with the sheet-iron tested by alternating currents in Chapter I., which
gave v .0035.
Wrouglit-iron, a solid bar of 4 cm.2 cross-section (standard size).
AIlitis metal, cylindrical piece of standard size.
A sample of very soft annealed cast-steel, inarked No. 6. A sample of soft annealed cast-steel, from another muanufacturerl, marked No. 5. Very tlhin sheet-iron, known as " ferrotype." This " ferrotype " was found magnetically rather hard, and of a high value of the coefficient of hysteresis. Therefore it was annealed by an electric current and tested again, whereby it was found improved.
Tin plate, 2 samples, thin and of medium thickness. Galvanized wire, apparently of soft steel. The magnletic characteristics of these materials are given in
Table XXXIV., and to a great part showvn as curves in Fig. 17.

TABLLE XXXIV. Different Kinds of Iron and Steel.

Very Soft Soft Annealed

Norway Iron, Wrought- Iron A nnealed

Standard.

in Bars, Cast-SteelNo.6.

Cast-Steel No. 5.

Mitis Metal.

F fp L

, L , L f)

Ferrotype, Commercial.
P, L

Ferrotype, Annealed.
PL

Tinll 'late, l'hin.
oL

l'in Plate, Medium Thickness.
f) L

Soft (-a'vanized Steel Wire.
1) AT

5-5

II.83 *54 10.20

7.5

3.o08 .64 io.96

IT.50

.77
*79

7.15 1. TO
8.88 1.0I

5.00 7.44

I .05

7.I5

.75 00.00

.98

7.65 1.79

4.20

8.'5
110

13.56 .70 12.If 14.10 *77 13.06

115 I I4.56 .85 I3.57

12.5 C, 14.80 -

13 98

I5
20

A

5.30

i6.oo

14-55

11

I5.30

25

ol

i6.42

135.8o

30

w I6.72

0 I6.io

40

I 7. 10

+ i6.6o

8S0o

T7.54 I7.74

0 17.03

2VOo100
200

178.3II7.85
i8. i5

1t 17.72

12.66

I

13-45

O 04.-03

A- T4.84

b

I5.40

0n 15.75

I

I6.28

-

I6.78

> 17.08

I7.25

17.60

12-33

11

13.I2

0

I3.80

14,68

.3

O

I15.68

6x I6.28

io.85

,q

17.10

17.55

17.73

.8

10.54

.88 II.43 1.04

9.63

.97 10.32

,92 I2.50 02.75 I.IO II,38 1.03 12.15

13.44 I.20 I2.50

13.40

I4.40

__

1I3.75

14.93

15.07

+o1 '5.55

Cn 0

I6. i8

I6.85

b 07.20

Ul

17.45

I7.90

4.80
I'545 1I6.40

+ 17-48

o

i8.oo

b 18.40

1,19.30

UI.I2

I5 .85 I6.40

17.23

18.03

b :I8.55

9D I8.80

0
U,

T9.45

.78 I2.85

Z 14.28

51 I4.80 1I5.60

'I

T 6.o8

N
+

16.40 I6.85

ol I7.30

0 17-55 T7.68

.98 1O. 20 1.71

5.85

I2.38 T.70 7.37
I3.44 1.75 8 6o

IO

14.45

15.15

10.05
TO 80

5s 68

11 I I. 50)

w

I6.30o

I7. T2

I7.50

07.75

12.10

12.94

+~
b

03.44 13.80

11. I8.30

I4.50

~1.
C13
'1'1

.1-t

Absolute Satu-

ration .....1.T.8.40

I8.03

I7.95

I8.45

18.37

20.10

20.10

I8.30

15.15

Coefficient of hysteresisl =.002275

.003260

..
.00318T

.004573

.004281

.00548

.00458

.002863

.004255

.00349

660

STEINMETZ ON BYSTERESIS.

[Sept. 27,.

The results of the tests, without exception proved the law of metallic magnetic reluctively,

p -a + aF.
The results are,
(1.) Norwttay -Ion. This is the softest metal magnetically and has the lowest coefficient of hysteresis I ever observed, little larger than the "soft iron wire" of Ewing. It is the piece used as Standard in the Differential Magnetometer. The whole instrument is built of this material. The dissipation of energy by hysteresis, and the other magnetic constants were found,

+F 1 l

a

a2

75 17.7() 14.25 .002275 .166 .05435 18.40

for F_ 5

(2.) Ordinary Good lVroaght-Iron in Bars.

The hysteresis and the other mnagnetic constants are,

+ F ± L HA

a

a

17.20 19.50 .003260 .20 .0o5547 18.03

for FE~r 1 2

(3.) MJiUs Jletal.

The hysteresis and the other magnetic constants are,

± F ± I i^

a a 18.

75 17.11 25.40 .004281 .30 .05444 18.3.7

for F z 12

As seen, nagnetically this mitis metal behaves almost exactly

like wrought-iron and sheet-iron. Its coefficient of magnetic

hardness is ac .30, wlhile for different kinds of sheet-iron and

wrought-iron I found values varyingo between .166 (Norway iron)

and .35 (thick sheet-iron), and in unannealed ferrotype even .45.

The coefficient of magnetic saturation a .05444 is about the

average found for different samnples of wroutght-iron, which vary

b)etween .058 (the sample of sheet-iron, given in Chapter 1.) and

.04975 (ferrotype), while Norway iron has a .05435, that is,

almyiost the samrse as mitis metal.

The coefficient of hysteresis a .00428 is somewhat larger,

blut still within the limits of sheet-iron, which reaches .0045 in a

sanmple described on p. 26 in my former paper and was found still

higher in ferrotype. HIence, the conclusion to be derived here-

from is

1892.]

STEIUMETZ ON HYSTERESIS.

661

"For all _practical purposes rints metal %5 to be considered
magnetically as identical with ordinary good wrought-iron."

(4.) Very Soft Annealed Cast-Steel, No. 6. The hysteresis and the other magnetic constants are,

±F ±

IHI

a

a

I,

75 17.00 18.67 .003181 .232 .05567 17.95

for F _ 6

As seen, this annealed cast-steel is far superior to ordinary

good, wlrought-iron, and almost approaclhes Norway iron.

The mnagnetic lhardness ac .232 is about inidway between

that of Norway iron, and the lowest value found in ordinary

good sheet-iron.

The coefficient of magnetic saturation is about the samie as that

of wrouglht-iron and sheet-iron.

The coefficient of magnetic hysteresis is lower than for average

wroug,ht-iron.

(5.) Soft Annealed Steel, No. 5.

The hysteresis, and the magnletic constants are,

± F ±i

II

az a Ir0

75 17.00 26.84 .004a73 .260 .05511 18.15

for F_ 10 Even this annealed cast-steel is in its magnetic hardness a - .260 still superior to average wrought-iron, in magnetic satu-
rationi equal, and with its coefficient of hysteresis, still in the range of wrought-iron. Both the materials, Nos. a and 6, are used for the magnetic field in the Eickemeyer-Field street car mIlotors.
(6.) F6erotype.
Twenty-three strips of 20 cm. length, 1.27 cmn. width and .01 5 cm. thickness (calculated fromn weiglht, by specific gravity 7.7), that is of .019 cm.2 cross-section, were used, giving a joint crosssection of .438 cm.2 This material is rem-arkable in so far as it reaches a very high value of magnetic saturation, over 20,000 lines of magnetic force per cm.2 But with regard to magnetic
hardness and hysteresis it was found poor; perhaps it was rolled rather cold, and thereby hardened. Hlence, after testing it once,
I annealed it. Each strip was fastened with its ends between
two clam-ps, and a (continuous) current of about 50 60 amperes
sent through, which heated it to bright red. The current was applied repeatedly. About 10 per cent were burnt off, leaving a,
joint cross-sectionl of .396) cmn.2

662

STEINMETZ ON iYSTERESIS.

[Sept. 27,

The h-ysteresis and the magnetic constants are,

± F ± L I1

a

a1r:>

not annealed: 65 1X.6 34.04 .00548 .4o .04975 20.10

annealed: 65 18.2 30.00 .00458 .337 J

F_ 15 , 20.

As already stated, this material is remarkable for its high mag-

netic saturation.

(7.) T4b-Plyate.

Two samples of ordinary, cominercial tin-plate were tested, of

the thickness .0268 cm. and .0378 cm. (calculated from weight

and including the tin.) The length of the test pieces was 20 cim.,

the width 2.55 cm.

Of the thicker sample 22 pieces were used, of a joint crosssection of 2.12 cm.2, of the tlhinner sample 30 pieces were used,
of 2.u5 cm.2 joint cross-section. Considerable difference was

fouind between the two samples, while the tlhieker samnple equalled ordinary and even rather poor sheet-iron, the thinner sample was

superior to any sheet-iron, and came very near to Norway iron.
The hysteresis and the magnetic constants are,

Thicker sample .0378 cm. thick.

±F ± IIX

aa

_L F_

26 15.31 21.0 .004229

62 17.15 25.5 .004282

av. .00423O .321 .05315 18.81 14
Thinner sample .0268 cm. tlhick. 26 16.13 15.4 .002853 62 17.33 17.4 .002873

av. .002863 .192 .05464 18.30 12
In these values no reductioln has been ihade for the tin-covering of the sheet-iron, but these figures refer to the whole crosssection of the tin-plate, including the tin. Therefore, especially in the thinner sample, in the iron proper 1;, will be a little higher than given.

(8.) Galveaized lhonb (Steel ?) WTire.
One hundred and forty-thiree pieces of wire, of 20 cm, length and .0193 cm.2 cross-section (calculated from weight, specific gravity 7.7), that is of .157 crn. diameter, were used, giving a joint cross-section of 2.76 cm.2

1892.1

STEINMETZ ON HYSTERESIS.6

663

The hysteresis and the magnetic constants are,

±F 1 1 H ^

a

a

coD.

80 13.35 13.78 .003455

32 11.50 10.85 .003454

1 8 9.70 8.50 .003550

avr. §- .00349 .67 .066 15.15

.0035 for F _ 20

As seen, the constants a anid a. have values found in soft caststeel, but C is remnarkably low, in the range of average wroulghtiron.

V. AMALGAM OF IRON.

In the amalgaims of iron we have a very iinteresting class of
alloy,s in-so-far as they bridge over the wide gap existing between
the paramagnetic materials, as iron, niekel, cobalt, etc., and tlhe non-
mnagiietic imaterials, as air, etc. It is not easy to get amalgam of iron, since iron does not dissolve in mercury, and is Inot eveni
wetted tlhereby. But when separated in molecular form, iron
dissolves readily. So by electrolyzing a solition of ferro-sulphate
8 04 Fe with mercury as cathode by a dense electric current, the
iron, deposited in [nolecular form, dissolved in quicksilver; and by pressing the quicksilver through a piece of linen, a solid, crystallinie amalgam was separated from a liquid one. This liquid amalgam still conltained a certain amount of iron in solu-
tion, as its attraction by the magnetic-pole showed; but was not sufficiently magnetizable to imake tests with it.
WXTithl great cutrrenit density and small snpply of nmercury, some-
times a crystallized amalgam of dark steel color was separated, in needle-formed crystallization. This amualgam evidently contained
still moore iron, but was not tested. The crystalline ainalgamn, which was still pliable enougl-h to be
pressed into a solid body, contained 11 per cent. of iron, and small traces of foreigni mnatter, as a chemical analysis slhowed. Since it evidently still contained traces of the liquid amalgam, it may about correspond to the foriiula,
Fe H12 All these amalgams were liable to slow decomposition, and
separated in a few weeks a part of tIme iron as fine black powder. Hence they had to be tested soon after preparation. It was placed in a fibre tube and compressed by two wronght-iron pieces which fronm either side serewed into the tube, thereby

3664

STEINIETZ ON HYSTERESIS.

[Sept. 27,

affording a path for the magnetism. These Norway iron cylinders were balanced by an equal pair of cylinders at the other side of the iinstrument, anid the amalgam tested then.
The dimiiensions of the tested piece of amalgam were, Length, 4 cm. Cross-section, 4.45 cm.2, cylinder.
Although showing strong attraction against a magnet-pole, the .amalgam had only about twice the permeability of air.
Table XXXV. gives the magnetic characteristic of the amal-
gam containing 11 per cent. of iron, with the usual denotation, L metallic induction, p metallic reluctivity.

TABLE XXXV.
MAGNaTIC CHARACTERISTIC OF AMALGAM OF IRON, '.

F

L

20

22

40

49

6o

76

80

103

I00

130

120

157

:140

:184

I60

21I

2180

238

200

265

220

290

240

31ro

22880o

3342582i

300

36o

320

374

340

387

362

399

[Absolute Satura-

tion .......

900]

,

c bs.

calc.

909

86

790

775

0

769

764
761

759

<

775556

IV

759

II

774

0o

792

4

833

856 879

902

For higher values of M. M. F., F_ 240, the metallic reluctivity can ctpproxinately be expressed by the equation,
, 500 + 1.12i F
though the bend in the curve is so smnall, that the constants a and ai are rather uncertain.
Table XXXVI. gives a cycle of hysteresis,

1892.1

ASTEIYMETZ ON HYSTERESIS.

665

TABLE XXXVI.
%. HYSTERESIS OF AMALGAM OF IRON, 11

F

Ld

Lr

320

+ .375

250

.326

.308

200

.285

.252

150

.238

.I85

I00

.I82

.II2

50

.II8

.°33

0

*045

H

3.04

L=

-~~~~~~~~~~375

lir

.2314

The results are,

+-F L

I Coercitive

Ainalgamsofiron, 320 .375 3.04 .2314 500 1.12 .900 F= 28.

,Common air, 320 .400 0 0 S00 0 (

All the three coefficients, ~, a, q, are unusually high in this rnaterial, the " absolute saturation" amounting to only,

Lao 900.

Fig. 9 gives the magnetic characteristic and one cycle of hys-

teresis of this arnalgam of iron:. The dotted straight line denotes

the magnetic characteristic of air, If which lhas to be added to

get the whole induction, B - 1I + .L
Sinice 11 per cent. of weight corresponds to about 17.5 volume

per cent., the magnetic constants referred to the volume of iron

contained in the amalgam are,

a]

a

a

L

.0815

87.5

.196

5.10

§ is still higher than the highest values found for glass-hard steel.

(cf Chapter V.) In the same nmanner as aimalgam of iron, amalgam of nickel
was prepared by electrolysis, and gave the three analgams:

1. A liquid amialgam, colisisting of quicksilver with traces of

nickel, but showinig no perceptible influence upon the magnet-

needle.

2. A silver-colored, pliable amalgam, containing apparently

about 10 per cent. of nickel. This amalgam seems to be entirely

noni-magnetic, since I could get no deflection of the compass-

666

STEINMETZ ON HYSTERESIS.

[Sert. 27,

needle by it. It dissociates very rapidly, even when dry. By heating in boiling paraffin, or at ordinary temperature within a day, it was always found dissociated into quicksilver (or the first

FIG. 9.-Amalgam of Iron.
amalgam) and the third amalgam. 3. A gray-colored amalgam, hard, or when freshly prepared by
heating- the second amalgam, still pliable, deflects the compass-

1892.]

STEINMETZ ON HYSTERESIS.

667

needle strongly, and becomnes permanently (and relatively strongly) magnetized in the magnetic field. Though an allotropic modification of this amalgam seenms to exist, which is unimagnetic. No exact tests have yet been made with these amnalgams.
VI. POROUS IRON. By heating this amalgam of iron to dull red heat, the mercury evaporated, and a very porous mass of iron, containing some, percentage of oxides, remained. The material contracted con-
siderably hereby, from 14.75 cm.3 to 8.055 cm.', but was, never-
theless, full of smnaller and larger pores, containing very nearly 30 volume perceiitage of iron.
T'ABLE XXXVII.
MAGNETIC CIHARACTERISTICS OF POROUS IRON, 30 VOLUME PER CENT.

()

(2)

0 4°.83

40

6o

.97

.22
11 .83.8.o

80

1.08

o.6

100

I i6

.68

120

1.23

1

*75

+

150

I-30

1.82

200

1.37

.92

| 2305000°. 1

1*.45 53

I .04 I.T6

Absolute satto-

ration

I .66

*.I41

TABLE XXXVIII.
HYSTERESIS O1F POROUS IRON, 30 -VOLUME PER CENT.

|F
140 130 120 110
200
9o0
80 70 6o 50 40 30 20 I20 0
H L

Ls

Ljr

1.28

1.26

1.26

1.23

1.23

1.20

1.19q

1. 17

1.15

I.3

1.11

I.09

r. o6

1.04 .98

T.00
.93

.92

.84

.86

.73

.78

.59

.69

.35

29

-.o6

±4 3

3.98
1.28

.0422

668

STEINMETZ ON HYSTERESIS.

The test piece had the following dimensions, Length, 4.45 cm. Cross-section, 1.81 cm.2, almost square. Volume, 8.055 cm.3.

[Sept. 27.

FIG. 10.-Porous Iron.
Its magnetic characteristic is given in Table XXXVII., in columni 1, a cycle of hysteresis in Table XXXVIII.

1892.]

STEINNMETZ ON HYSTERESIS.

669

The results are,

± F ±L -H

a

a L0

140 1.28 3.98 .0425 25.4 .604 1.66

F_ 90.

Another piece of such porous iron, of the dimensions.
Length, 6.03 cm.; cross-section, .53 cm.2; voluime, 3.2 cm.3;

containing 31 volume per cent. of solid matter, buit much im-

purer, gave the characteristic in Table XXXVII., Coluimn 2,

expressed by the equation,

p a76 + .71 F
for F_i 90.

IHere again are noteworthy the high values of magnetic hard-

ness and hysteresis, and the low value of magnetic saturation,

I , , which lies at 1660 viz. 1410.

Fig. 10 gives the magnetic characteristics of both samples

with the air-characteristic as dotted lines for comnparison, and one

cycle of hysteresis. It is noteworthy, that the hysteretic cycle

is entirely unlike that of the iron-aimalgam, where the porous

iron was derived from, and resembles much more a cast-iron

cycle, but of one-eighth the height of ordinates. The first sample was heated to dull red heat. for evaporating the mercury, the

second one heated over the alcohol lamp, had not become as hot.

This may account for its far greater magnetic hardness.

Referred to the volume of the iron contained in the test pieces,

30 and 3t per cent. respectively, their magnetic constants are,

^q

a

a

100

(1) .0206

7.6

.181

O 52

(2)

23.6

.22

4.55

The value i .0206 corresponds to that of medium hard steel, and so the test pieces behaved, getting strongly and permanently inagnetized.

VII. MAGNETITE.

With a piece of magnetite (Magnetic Iron Ore) of 6 cm.2 cross-section (square) and 6.5 cm. length, a very puire sample, derived from the Tillv Foster Mines, Brewsters, Putnami County,
State of New York, a large number of tests were made. The magnetic characteristic is given in Table XXXIX.

670

STEINMETZ ON HYSTERESIS.

[Sept. 27,

TABLE XXXIX. MAGNETlC CHARACTERISTIC OF MAGNUTITE (MAGNETIC IRON ORE).

F

L

I0

I5

.7I

2I1.0

20

1.09

18.4

25

I.47

I7.0

30

I6.7

35

2.07

16.9

40

2.28

'7.5

45

2.43

30

2.56

6o

2.77

80

3.08

I00

±-

120 140

3.48

,1

'So

3 -72 3-81

3.89

1-4

3~oo

4.'I

300

4.33 1

Absolute Saturation......

4.69

TABLE XL. HYSTERESIS OF MAGNETITE (MAGNETIC IRON ORE),

(2)
F Ld Lr Ld Lr

(3) Ld Jr

(4)
hLd Lr

Ld Lr

I,d

I,r

0

+ .6o

+80

±.89

t94

5

.92 -.20

I.I6 -.36

1.24 -46

1.28 -5

10 1.17 +-30 1.43 +-14 I.50 +.o6 1.54 -.03

[-I6]

'3

I'39 o80

I.68 .67

I,73

.58

1-76 t'44

+I.82

20

I.55 1.20

1.87 1,10

I.90 1.02

I.96

.90

I.97 I.85

25

i.68 I.52

2.04 1.46

2.10 1.39

2.14 1.30

2.I5 I.99

I "ol1

30
35
40

-- IT.77
[ 29]

2.19 2.32 2.43

I.75
2.00
2.20

2.27 2.40 2.53

1.70 '.95 2.I6

i.31.64
2 43 1.89
2.55 2.I0

2.30
2.43
2.53

2.13
2 24
2.36

+2. 3,2

2.44

.34

2.56 2-4,

45

2.-53 237

2.64 '.34

2.66 2.29

2.63

2 48

2.6' 2.5!4

2 61I 2.52

2.72 2 47

2.75 2-43

2.74 2.58

2.74 2.64

50

2.68 2.66

2.81 2.59

2.84 2.55

2.82 2.69

2.82 2 72

± 2.69

2.88 2 70

2.91 2.66

2.90 2.78

2.90 2.82

65

[+ D7]

2.94 2.80

2.98 2-77

2.96 2.87

2.96 2.89

70

3.00 2.90

3-04 2.87

3.0I 2.95

3.0I 2.90

S75o

3.o6 3.00 3.II 3.08

3.10 2.97
3-I5 3.o5

3.o6 3.02 3-II 3.o0

3.o6 3.03 3.I1 3 I0

83

3.15 3.14

3.20 3 12

3.15 3-14

3.15 3 153

90

3.1I8

'.3-24 3;-8

+3 .18

95

[+88]

3-29 3-23

[+88]

[+8o]

100

3-33 3.28

3-37 3.32

113

.-41 3-37 3-44 3-4I

3-48 3-45

125

3-5I 3-49

130

3.55 3-53

'33

3-58 3-57

140

| + 3. 6I

H

3.69

L

'.77

7.23
2.69

9-45
3 5I8

11.;2

.8I

3.6I

.68

.38 .43

4Zo =

.02345

.02352

. 0235 3

. 02 342

Ar. r - .02348.

.02379

.02324

1892.1

STEINMETZ ON HYSTERESIS.

671

Beyond the M. M. F. F 40 the magnetic reluctivity strictly
follows the linear law,
p = 8.9 + .2132 F,
giving a characteristic similar to that of cast-iron, only that
absolute saturation is already reached at the metallic induction,
10 -4.69.
To determine whether the law of the 1.6th power holds for the hysteretic loss of energy in magnetite also, a number of magnietic cycles were taken, which are given in Table XL., first between opposite and equal limits, ± F- 29, 57, 88, 140 then between high values of induction of the same sign, between F1 + 88 and F2- 30 and 16 respectively.
The results of these cycles are given in Table XLI.

TABLE XLI. HYSTERESIS OF MAGNETITE (MAGNETIC IRON ORE) RESULTS.

No. F, F, 'l2'- L1 L .l2 Aob2.. .

1L0 AL %H

(6) jis + 88 + 30 29

(5) A + 88 + I6 36

(I) a + 29 - 29

29

(2) a + 57 -57 57

(3) a + 88 - 88 88

(4) a +140 -I40 140

+3.-8
+3.I8

+2.32
1.82

.43
.68

+I.77 -2.77 1.77

+-2.69 -2.69 2.69

_-3,I8 -3.I8 3.I8

--3.6I -3.6I 3 6I

.38 .8i 3.69 7.23
9.45
II.52

.02324
.02379 .02345
.02352
.02353
.02342

+24
-31
+3 .-2 4
.2 5 +6

+±10
-I.3
+ .1
+ *3

Av. Yj

.02348

They prove conclusively, that the same law of hysteresis holds for magnetite.

H-_ § (It ...1 2J
and give as magnetic constants of nagnetite,

a

a

Loo F_

.02348

8.9

.2132

4.69

40

Fig. 11 gives the cycles of Table XL., 1, 2, 3 and 4, made

between oppositely equal limits.

The two tests made on another sample and published in the paper of January 19tlh, 1892 give, ; - .020, that is nearly the

same

-l'X:01,l_)-Ld3_49S.a+2068il-9+10a672

ST'EINAETZ ON HYSTERESIS.

[Sept. 27.

VIII. EWING'S TESTS.
Before leavin-g the consideration of,,the phenomenon of hysteresis in ireon and its alloys and cornpounds, I may be allowed to dwell upon some determinations of the loss of energy by hysteresis, made by Ewing, and given in his book on "Mlagnetic Induction in Iron and other Metals."

_1_130-120-01 T I6I0

2-

I

-

t TS

X

F X~X~~X~~-z

1~~~~~~~~~~~~~~~~06

FIG. 11.-Magnetite. Ilysteretic Cycles.

TABLE XLII.
MAGNETIC CYCLES OF SOFT IRON WIRE. (Ewing, p. io6.)

| Fr

|H L | oEbisC.

H H-H =%
calc. calc. obs.

I 20
1.56
2.05
2-41
3.01
3-97 5.30 5.63 21.2 o60.2

1.974

4I

3.83

i.i6

595

2.19

7.I8

2.94

8.79

3.99

10.59

5.56

II.47

6.i6

11.95

6.59

I3.69

8.69

25-48

10.04

Av.

.002

'375
I.082
2.I90
2.956
4.o8
5.51I
6.26
6.69 8.3-I I 0.II

+-035
+.o08
.oi6
-.090
+.050 -.I0 +.I-130800 -0. 70
± 090

1-8 5 +5.0
- *5
2.3
---.9 -I.7
+-14.-54
- .7
± 2.5

1892.]

STEIYKETZ ON HYSTERESIS.

673

TABLE XLIII.
MAGNETIC CYCLES OF ANNEALED PIANOFORTE STEEL WIRE. (Ewing, p. I09.)

F F.,2 F1-F2 L, L2 L1-L2 H H H-H -%

2

2 obs. calc. calc. obs.

_- 8 _ -I2
2-I5.2
_-I8.4
+65

8 I-0.4
-I5.2 -19.2
.--246T

8
11.2 25.2 I8.8
2645 (?)

_

I-I.5I
3.64

5v.66

7.53

_ 9.4850

- 94
- 2.32
- 4-90 - 7.43
--3.9.8505

1.225
2.98
5.28 7.48
I39..85o0

2.20 2 52 +.32 +2I

5-50 6-32 + .82 +13

25.90 15.80 - .10 - .6

27.30 27.50 + .20 + .8

47II..9800

4703..5200

-+1..7700

4.2
+ 2.2

Av. a-= .01742.

H.

14,00
I
10200h

/F
__~~~~~~~~ 50

18,888~~~~~~~~~~~~~~~~~~~~~~~~

88000

-

I-

0

40008

20____- 1

I ~~~~~1^I

B- 2000 4000 G000 8000 10,000 12,000 11,000 16,000 18,000 FIG. 12.-Soft Iron. Curve of Hysteresis. [Ewing,]
In Table XLII. and Fig. 12 are given the results of the graded cycles of hysteresis of very soft iron wire (pages 106-7 Ewing).
In Table XIII. and Fig. 5 are given the results of the graded cycles of hysteresis of medium good cast-iron, (No. 1).
In Table XLIIl. and F'ig. 13 are given the results of the graded cycles of annealed pianoforte steel wire (page 109 Ewing). These latter are taken from the plotted curve published by Ewing; hence only a considerable lesser exactness can be expected since the numerical data are not published by Ewing, as far as I know,
and printed curves are never very exact, and not iniproved by measuring.

674

STEINMETZ ON HYSTERESIS.

[Sept. 27,

The data in Table XLIL. are of interest in so far as they are the lowest values of hysteretic loss ever observed on iron. so far as I know. From these figures I found the law of the 1.6th power,
two years ago, when trying to find a misprint which got into the
table of the hysteretic loss, given in Kapp's " Alternate-Current Maehinery " and calculated from these tests.
The denotations are the same as before,
F, and F2 the highest and the lowest values of E. M. F., in
ampere turns per cmn. B1 and B2 - the highest and the lowest value of magnetic in-
duction, in kilolines per cm.2.
:PH _ FEEEI'

60;000 _ A0nnealeMdagPniaeniocfoJrCtyeclSstecel Wire, /

60

5(Ewing,pJ109)

ss,OOo/

5

40,000 -

40

30,000

-t

,

-0

20,000

20

o._- -_

lOjOO-_, -I- . --

E
E

FIG. 13.-Pianoforte Steel Wire. Curve of Hysteresis. [Ewing.]

F F 2 id B

B2 - their amplitudes, or half

their variations. ff = the energy consumed by hysteresis, during, one complete
cycle, in kiloergs per cm.3. = coefficient of hysteresis, caleulated therefrom. Two further cycles, with annea[ed and with glass-hard piano-
forte steel wire (Ewing page 84) give the results,

1892.1

STEINMETZ ON HYSTERESIS.

675

TABLE XLIV.
MAGNETIC CHARACTERISTIC OF SOFT NICKELWIRE.

F

L

JO

F

L

p0

7-5

2.03

3.7

8

2.36

3-4

9

2 73

3-3

40

5.23

50

5.26

6o

5.36

-

20

3-03

3-3

80

5.48

8

12

3.58

3-35

2OO

5.56

14

3.95

3.55

120

5.6i

°

i6

4.2I

3.8

140

5.65

+

I8

4.43

-

i6o

5.68

20

4-55

25

4.76

1180

5.70

H

200

5-72

30

4.92

35

5.04

[300

5.77

4.

500

5.8I]

Absolute Saturation .

..................

5.88

TABLE XLV.
HYSTERESIS OF NICKEL.

F
235
120 IIO IOO
90
80 75 70 65 6o 55
50 45 40
35
30
25 20
25
20
5
0
H=
L=
=

Soft Nickelwire.
Ld L,

± 5.64 5.6i
5.59
5.56 5.53 5.49 5.48

5.43 5.40

5.37 5-30

5.32 5.2I 5.26 5 20

5.20

4-99

5.24 4.88

5.o6 4-75

4.96 4.56

4.80

4.30

4.60 3.88

4.30 3.I2

3.90

2[.90

3.33 -.40
±2.50

I22.26
5.64
OI220

Ewing.

Soft-

Hard

NSickelwire.

Ld Lr

lid Lr

[Fi = ± 83]

±4.95

±4-15

4.94 4.-2

4.92

4.89

4.90 4.85

4.88

4.80

4. I3

4j2O

4.2I

4.o6

4.09

4.00

4.07

3.94

4.84

4.75

4.80

4.70

4.76 4.63

4.04

3.87

4.00

3.78

3.95

3.68

4 72

4-55

4.65 4.47

4.58 4-37

4.49

4.25

4.40

4.08

3.90

3.53

3.84 3.34

3.78 2 97

3.72

2-47

3.64

I.65

4.28
4. I4

3.80
3.00

3.56
3-47

0 - 70

3.95 -2.00
± 3.56

3.32 -2.63 + 3,II

I2.74
4.95
.0562

23.67 4. I5
.038 49

676

STEINMETZ ON HYSTERESIS.

[Sept. 27,

IX. NICKEL.
Somne tests were made on commercial soft nickel wire. The cross-section of the wire was = .0156 cin.2. The diameter,- .141 cm. For the determination of the niagnetic characteristic 45 wires, of 20 cm. length, were used, giving a joint cross-section of .7
cm.2.
For the determination of the hysteresis 83 wires, of 1.23 cm.2 joinit cross-section were used.
The wire was found magnetically softer than that of Ewing.
The magnetic characteristic is given in Table XLIV., one cycle
of hysteresis in Table XLV., first column. The denotations are the usual.

11l0-10 +i X 8o_l- 0 1-= °-3 -20-} -10 l-l 4000 i 0 50 60 1 1 t l

FIG. 14.-Nickel. iHysteretic Cycles.

As magnetic constants were found,

Coefficient of magnetic hardness,
a 1.00

Of magnetic saturation.
a .17

Of magnetic hysteresis.
= .0122

for F_ 18.

Hence,

p =t.00 +.1 F

F> 18

Absolute saturation.
L1, = 5.8&

H .0122 2
The existence of the law of 1.6th power for the hysteresis of nickel has been proved by Kennelly, by two sets of tests communicated in the " Electrical Engirneer," April 6th, 1892.
Ewing (page 87) gives two cycles, for soft and for hardened nickel wire. From these curves are taken the values given in Table XLV., second and third column.

1 89,-. ]

STEINMETZ ON HYSTERESIS.

677

The two cycles are not quite symmetrical, as given by Ewing. The figures given in Table XLV. are the mean values of the positive and of the negative part of the curve. The results are,

±F H1I

a

L0

Soft nickel wire

83 4.95 12.74 .0156

Ew

Har3ened Very soft" "

83 4.15 23.67 .0385
135 5.64 12'26 .0122 1.00 .17 5.88

These tests give for soft nickel about the same coefficient of hysteresis as for cast-iron, but a greater magnetic softness, while

-4 10
800V
60001

2000

-100

00

20

0

20 4- 1

60

6000
80001

FIG. 15.-Cast Cobalt. Hysteretic Cycle. [Ewing.]

the value of absolute magnetic saturation, I ., is a little
nore than half that of cast-iron.
The miagnetic characteristic is shown in Fig. 17, the three cycles of h-iysteresis in Fig. 14.

X. Cobhalf.

Table XLVI. and Fig. 15 give an hysteretic cycle of cast-

cobalt, froin Ewing, page 89, which gives the resuilts,

±F -iL±

I

112 10.00 30.00 .0120

l'hat means, cast-cobalt behaves inagnetically very mnuch like

cast-iron, gives the sarne coefficient of hysteresis, and about the

same value of magnetic saturation. Thoulgh it would be interesting

to repeat these tests with different kinds of cobalt, of different

degrees of softness.

678

STEINMETZ ON HYSTERESIS.

rSept, 27o,

TABLE XLVI.

HYSTERESIS OF CAST-COB ALT (EWING).

F

Ld

Lr

II2
200
90
8o 70 6o 50 40 30
20
10 5
HL=

10.00

9 75

9.6 9-4

09..I45

9.1

8.7

8.8

8.3

8 .3

7-75

7-8

6.95

7.2

5.8

6.4

4-0

5.2

.j

4-5

-2.0

3.

30.00
IO.00

.01194 .012

CHAPTER III.-RESULTS.
Comnbining now the results of the foregoing tests, we arrive at the conclusions:
1. lihe dissipation of energy into teat by molecular hysteresis, daring a complete cycle of magnetization, performed betwtleen
the lim,i1ting values of magneti?c induction 1, and 12, ris ex-
pressed by theformula.
( - A1.62)
where 1, and L2 very likely have to represent the metallic mag-
netic induction,
while, when eddy-or -Foucault-currents are indcuced by the
cyclic variation of magnetization, the dissipation of energy is
given by,
H 2( (1 2)1 + (B,-B2)2
where the first term is the loss by molecular hysteresis, the second term, the loss by eddy-currents, N denotes the frequency.
2. Beyand a certain minimum value of Mi. IA. F. Fm, the metallic magnetic reluctivity, p 'and consequently the inverse

1892.]

STELYMETZ ON l-YSTERESIS.

679

value,

of susceptibdlity,

x,

which

is,

1
=

l6Ow'r
T e) follows

the

linear law,

,o - a + a F

Belowt this minimum valae of M. M. F. F, flrst the catrve of

alternating, then tha.t of Prising magnetism drops belowl, while the

curve of decir-easing maynetism rises above the curve cder-ved
from the ine r law,o a + a F.

3 LBeyond a certain minimaum valate F ., that is for medium
afit(l high 'At. M. F'S. all the main feat ares of the mnaga etic pro-

J}( ia stjf in;atet-iuls ca(n be exy)ressed by three constants, a, a, i,

a, the coefficient of MaLugneticfilarelness,

afs

' '' '' atutritOfns,

^r, ;

" "' JfystcrQesis.

instead ,of aaaet(n the three consan. ts may be ase(d,

Ir a the Value (ft atbsolutte maynetic saMturaotion.

F thMat A. AM. F., whkert halfsaturtio /9 would b
/ cachedf if thte [linear la of relu 'tivity hole/s alreacdyfn --.
II>j - 4 Lrf l'i thelmaeita(tiltn vatue of hysteretic diss{pation o)f enbergy, tf e ab8solute satuiataiona.
Tlheni we hiave tlhe equationis:
R ELUCTIVJITY

o

+F

IIYSTERESIS,

^2

(-2)2I

In the latter case the exponeint 1.1 only covers an-i absolute

nlnni)er, while the coefficient of hy steresis IfZ is of th-e diinen-

sion " work or " eniergy,"- (ci. g sec-2)

4. These form alas hold,/hor all kinds oqf wv?rotught and east-

iron1 and steel, for nickel, cand maynetite, cand most likely

foJb amalgaia of iron, hence apparently for all magnetizable

materials.

For air simply a and ^ 0. a - &00.

In Table XLVII. are given in the first six coluimns the three

mnagnetic constants of all imiaterials tested,

a a,r, viz. Lr, F, 1I.

,............ .............. ............. ...... MATERIAL.

Wrought-Iron, Norway Iron ..................... .......

i'

Ordinary Wrought-Iron ..... ... .....

Sheet-Iron thickness. 8 .042 em.

.0268

...... ...."...

V038 ( .

.......

.07I

.... .....

.07..

......1......

........

~~~2 ~~.001145 "FerrotCLype, CAonmnmeearlceida.l...
.027 '~Tin-Plate ....

Very Soft Iron-Wire (Ewing) ............ Cast-Iron No. -- ............. .............

4..2......... ............. ...............

;'

4

6.

7 ( s per cent. Aluminium) ..

..

8 ('Y2

Cast-Steel, Hardened.

................ ..;;

" Annealed.

..~

(Aeae...... ..............................
...... ~ ~ ~ ~ ~~~.... ........... .. ... ..... .. I....... ...... . ......

..

.... .. ........... ...........................
...... .... .......... ............ ..........

TAB3LE XLVII. Magnetic Constants.
Centimetre Measure.

aq

F0 H01,

.166 .05435 .002275 I8.40

.20 .05547 .003260 I8.03

.275 058 .00350 I7.24

.275 .0507

19.7

.250 .056i

17.8

.30 .0522

I9.2

.35 .0542

.450 04975 .00 48 .337 .04975 .004 6

2228C0..51IO0

.I92 .o5464 o02863 i8-309

.321 .053I5 .004255 i8.8i

.20 .o635 .002 I5.75 2.40 .0940 .OI300 To.66 2.43 .0943 .OI317 Ioc.6o

2.76 .0954 ,01577 10.48

2.05 .09725 .OI132 TO.28

2.34 .0950 .01267 20.52

2.07 .0972 .0OI220 20.29

2.37 .0976 .OI365 10.25 2.92 .0948 *OI459 TO155

2.7 .054 .02792 I8.5

.88 .054 .00848 I8.5

2.00 .09 3 .012

.82 .052I

I9.2

*74 .0509

I9.6

.76 .0534

28.7

1.26 .093I

IO.7

.736 .o568 .009 17,6 .68 .0587

3.05 15.17 3.6I 21.09 4-74 21.01
5.42
5.I7
5-75 6.46 9.05 42.07 6-77 35. I6 3.51 I8.92 6.04 29.37
3.25
25 5 36. I8 25.8 36.26 29.0 42.70 21. I 29.72 24.7 34.56 2I.3 32 .o8 24.3 35. 77
3o.8 39 *94
50.0 I87*7 I6-30 57 .00 2I.9 35. II 15.74 14.54 I4.23 13.64 I2.96 55.-85 II.s8

Inch Measure.

a or1I

71 0

.o65 .0084 .OOI89 II9

.079 .oo86 .0027I II'6

.109 .0090 .C0290 III

.109 .0079

227

.I14 .0087

II5

.II8 .oo82

I22

.238 .0084

I1Q

.I77 .0077 .00455 130 .133 .0077 00380 230 .076 .oo85 .00237 II8

.1I27 .0082 .2)0353 122
.079 .oog6 .OOI66 204
.95 .0145 ,OI08 69 .96 .0146 .0209 69

1.09 .0148 .0131 68 .8I .015I .0(94 66

.93 .OI47 .0105 68

.82 .0150 .0214 67

.94 .015I

66

I.I5 .0147

68

I.07 .0084 .0232 II9

*347 .0084 .0070 I29

*79 .014I .OIO 71

,323 .008i

224

.292 .0079

227

.299 .0082

122

.495 .0144

69

.290 .0088 .0075 214

.268 .009I

IIO

7.8
9.2
1I33.,18
13.I 14.6 16.4 23.0 I7.2 8.9 25.4
8.o
65
66
74
54
63
54 62
78 I27 4I.4 55-7
40.0 37.0 36.2 34-7 33.0
29.5

Centimetre Inch Measure. Measure.

'f) rXlO6 'rlX106

245

24.4

I2 .0

345

20.6

27.1

345

22.1

28.4

690
574
310 480 I74 592
594
700
486 566 526 584 655
3070
935
573

34.6 28.9
I8. I
26.8
I2.6 82.0 83.0 99-5 71.4
79-9
77.0 86.1 92.1 176.o
53-5
75-7

28.7 24.0
25.0
22.3 IO.5 68.
69
82
59
66
64
7I
76
I46 44 63

9I2

56.8

47

0
rnI

...................... .I....... ...............

.545 .0575 .44 .0553

I7.4 9-48 18.I 7.96

.2I5 .0089 .I73 .0086

II2 23.'0 ti6 20.2

CD

'.3

M ATERI AL.

TABLE XLVII.-Continued. Magnetic Constants.

Centimetre Measure.

Inch Measure.

aa

Fo

al,16T, Lt Fol

CeMnetaismuerter.e

Inch Measure.

rx1(6 rlx106

Cast-Steel (Average of 5 Samples) .... .................

.*33544

.0535 .0543

.005

I8.7
28.4

6.54 34.19
6.34

.138 .oo83 .0041 12I -I6.6 56o

.I36 .oo84

II9 i6.i

3I.6

26

N... ............ ..........................
.. .....................................
No. 6.
Mitis Metal. ......................................
MitiMsetal .................................. ..... ....
Oh .............................

.430 .300 .300 .308 .260
.232
.300
.67 8.o 7.8
I.Q 2.54 2.33

.0700
.052I
.0543
.0565
.0552I .004573
.05577 .003i82
.05444 .00428T .o66 .00349
.0748 I05 .0613 .o66 .0267 .o6o .0270
.o6o .0I90

24-3
29.2
I8.4 27-7
i8.I5 I7.95 I8.37
25.15
8.28
9-53 I.5i6
i6.70
I6.70

6. 24
5.76
5.52 5-45 4.72 29.82 4.16 20.38 5-5I 28.46 10.15 17.03 66. i 138.9 74 3 142.6
'54-. 28.8 I30.5
25.7
22.2 I08.4

.170 .oio8

93

.IT8 .0070

I27

.uI8 .oo84

II9

.I21 .0087

1I15

.Ioi ,oo85 .00380 ii8
.092 .oo86 .oo264 ii6

.1I8 .oo84 .00355 II9

.264 .0102 .00290 98

3.15
3.o8

.OI87
.OI62

..oo652o08

54
62

.75 .OI02 .0222 98

.OI58 .6 I .0093 .0224 io8

.53 .0093

io8

I5.6 I4.6
14.0
13.8 22.0 480 io.6 334
I4.0 466
25.7 280 i68 2280 i88 2340 73 2240
65 2530 57 I780

28.9
20.1
27.0
22.0 472
387 i68
I70 120

24.0 I6.7 22.4 I8.3
392
322
140
14I
IOO

0 i7o

88.3 I1.22 .0575 .0245 17.40 2I.2

.48 .0089 .OI2I I12 54 I440

9I.5

76

Annealed Pianoforte Steel Wire (Ewing)

....

........

Porous Iron.

... ... ........................ 25.4

57006

Amalgam of Iron

Magnetite..

.....................

89

Soft NickelWire .........................

I .00

.604
.72
.2I32 .17

.0174 .0425
.2324
.02348
.01220

.OI44'

i.66 42

6.03 20 .094 .0353 io.6 I07

99

2.41 I07

30 .I10

9.2 270

.90 447
4.69 42.7

12.33 I97 I7.56 3.5

.173 .9I2 .0330 .0195

5.8 II40 203
30 io.6 287

5 88 5.88 13-10 .394 .0263 .00I25 38 I4.9 215

268
2460
148 77

223
1220
123 64

Nickel-Wire, Soft (Ewing).............................

~ ~~~~~IMagnetomter Hardened (Ewing)..........

..

Cobalt, Cast

................... Tet...............

Coiled Iron-Wire, Crossways..Wir

... ...............

86.3

Lainated Iron, Crossways......................... ...
Electro-Dynamometer Tests....

32.6 62.5

Iron Filings, 30 per cent.

77.5

c c
.209
*375

.O156 .0385 .0I2I94 .0403
00721 .0465
.0656

4.80 300 2.67 207

.OI30

.0320 .0099

34

.0334

22.4

.0060

38-4 24.6 .0324 .0410 32.0 763

20.0 30-5 .os8 I0543 I27.2 525

627 327

254
45.5
312
413

211
37.8
259
342

682

STEINMETZ ON HYSTERESIS.

[Sept, 27,

k
cc,
.__
r-

In Fig. 16 are given the values of a as abscissae with the corresponding values of a as ordinates.

1892.]

STEINMETZ ON HYSTERESIS.

688

_j CD

m

t

aO

ac

'xi- co a -Of

Cac

- _ -l . .

(3astIlon 10.25-10.66 _ --

ca t SteelI.7 -19.6 .5

C_

_

L_

_

* +<

Iron Fillnm s h--

-l 8.3~2.6-5.0 e 17.

-5

Wr ught &SheetIrn 1.1

..

H

a

S

Wro-ught and sheet-iron, cast-iro-n and magnetite are marked by crosses X (since these two can not possibly be mistakein.)
Cast-steel is marked by circles c), and welded steel by three-
cornered dots, ', Mitis metal and Nichiel are marked by six-cornered stars.

684

STEINMETZ ON HYSTERESIS.

[Sept. 27,

In Fig. 17 are shown the magnetic characteristics of the most

interesting of these materials.

5. Referring now to inch measure, and denoting all the quan-

tities referrinlg to inches, by indices, we have

M. M. F., ampere-turns per inch,

F' 2.54 F

Magnetic induction, linles per square inch, B' 2.542 B

= 6.451 B

Magnetic Hysteresis, ergs per cubic ineh, HI_ 2.54' Hf

16.386 ZY

Consequently, the magnetic constants are for inch measure,

Coefficient of Magnetic Hardness, a' 2 54 a .394 a

"' " " Saturation, (I

I =1 .155 a

"( "4

";

Hysteresis, v'

2.543

X

1
2.5432

Consequently, Reluctivity,

= 254.2 .- 83 lX _6.451 _L
Fol 2.54 Fo
= 16.386 I,x

I+ aI F' Fo= + F

2.54 Fo +F'
=.394a+ .155oaF'= 6.451 L00
Hysteresis,
H'l = ~1 (Il - - I (AlI2). tt1 §1 tt2 tz) =E I2 L
= .83 q (L11 -21 6 - 16.386 HI (L' _ )1-6

For the materials tested, these valu-es of the magnetic comstants in inch measure are given in column (7) to (12) of Table XLVII., as,
a 5I 1 cIon F1,I v1l
6. From the Coefficient of Magnetic Hysteresis, the loss of
power by molecular hysteresis in the iron under the influence of

1892.]

STEINMETZ ON HYSTERESIS.

685

an alternating current of 1N complete periods per second, that is the heating effect of this current, can easily be calculated. It is,
In centimetre measure,
IV= NiI H-1 7)NX107(1 j'I watts.

In inch measure,
1 _ 10-1_IH N1lO-7 ( 1 12)

.83 A7 10 ( 71 21) watts.

Or, if we express the magnetization in kilolines, or thousands of lines of magnetic force, we get,
Centimetre measure,
- N1-7X 10001.6 (172)16 = _( r7L2) watts.

where

r 10-2.2 .00631 q

Inch measure,

,r ~_1Nj1(-7 X 100( 1.6 (t112) Nyr1(I4-L2)l& watts.

where

.00524^q

Thtese coefficients r and 1-' are given in column (13) and (14) of
Table XLVlI. Hence, miiaking use of this Table XLVII., to find the Mlag-
netic Induction, or Mfagnetization, and the IIysteresis, given the M. Mt. F. F, in ampere-turns per centimetre length of magnetic circuit [F - .8 Hif HY is the "field intensity "], we get from coluiins 1 and 2, a arid a and have the reluctivity,

Pa + a F Hence the metallic induction, in kilolines per cm.2.

0
and the whole induction, B _ L + If= L + .8 F
Usually the H can be neglected, and I - B.
Taking now r from the 13th column of Table XLVII., we get the dissipation of energy under the influence of an alternating current of H complete periods per second, in watts per cubic ce-ntimneter.

686

STEINMETZ ON HYSTERESIS.

[Sept. 27,

W-r_N L'8
where 13 is to be taken in kilolines. To get B and bVin inch measure, the Ai. M. F. F1 being given
in ampere turns per inch lenrth of the magnetic circuit [conse-

quently the field intensity H

= .245 F'] we proceed

in the same way, but talke the values a', a', r' from columns 7,
8 and 14 of Table XLVII., and derive,
F1

Wl -> JX_1.6
7. As Ai. Al. F. here ampere-tuirns per unit length of the magnetic circuit are always used. To reduce to absolute measure, we have,

Field intensity, i -j- F = F'

Susceptibility,

10
x = 16 7w2 p

Permeability, fA

47r x + 1

10
4 ,T p+ 1

Intensity of Magnetization, or

Magnetic Moment, I = x HI

F

Magnetic Induction,

B -I + H 4 1Ir+ H (4 wr x + 1) H =1 H
-Fp+ 4-rFii

8. If now on the hand of the data collected in Table XLVII. and the culrves represented in Fig. 17, we look over the numerical values of the magnetic constants of different materials, we see, that in

Wroyught-Iron and Sheet-Iron.

The Coefficient of

Magnetic Hardness, a, varies from .166 to .450

Magnetic Saturation, a, "

.04975 " .058

Magnetic Hysteresis, rj,

"

.002275 " .00548

Consequently the value

of absolute saturation, L,, " 17.24 " 20.10

1892.]

2S'EINIETZ OV HYSTERESIS.

687

The variations are considerable enough to make it advisable

everywhere, where a somewhat greater accuracy of calculation is

required, especially to determine the individual constants of the

material enmployed, which can be done easily, since only three

observatioins are required hereto, two of L, or p, and one of Hf.

As a fair average of good wrought or sheet-ironi we can con-

sider an iron of the constants,

(1-.30

a .055

=.0030

I< = 18.0

In Tables XLVIII., XLIX., L. and Figs. 18, 19, 20 the mag-

netic curves of this average wrought-iron are given.

14000 -_
12,----

10oCoS- - -of

4,0(01

-

-

1 1- 6 1

20 F= 40 60 80 100 120 140 160 180 200 C

FIG. 18.-Average Materials, Magnetic Characteristics.

Ca8t-fron.

Although cast-iron, as the raw-material, should be expected to

vary considerably, nevertheless the difference between the eight

samples tested-though derived from different sources-are

remarkably small, the

Coefficient of

Magnetic Hardness, a, varying from 2.05 to 2.92

Magnetic Saturation, a, "

.0940 " .0976

Magnetic Hysteresis. , "

.0113 " .0158

Consequently the value

of absolute saturation -L, "

10.25 " 10.66

688

STEINMETZ ON HYSTERESIS.

[Sept, 27,

Hence of east-iron it is much oftener permissible to take an

average set of magnetic constants,

a=2.40

q*_.95

a .013

100 1.5

In Tables XLVIII., XLIX., L. and Figs. 18, 19, 20, the mag-

netic curves of this cast-iron are given.

Welded Steel.
That is, that kind of steel which can be hardened, evidently
varies in its constants enormously with its degree of hardnless.

FIG. 19.-Average Materials. Curves of Hlysteresis.
For instance the tests referring to one and the same material of different degrees of hardness, give the variations in
Mlagnetic Hardness, a, from 1.22 to 8.0
Maginetic Saturation, a, " .0575 " .1 1 Magnetic Hysteresis, (, " .0145 " .0748
Absolute Saturation, L." S.28 "17.40
In comparison with cast material the relatively high coefficient of hysteresis is remarkable, as even for the softest annealed condition it is higher than the average of cast-iron.

1892.]

STEINMETZ ON HYSTERESIS6.

689

Tables XLVIII., XLIX., L. and Figs 18, 19, 20, give two sets of curves, in dotted lines, of soft material,

a =1.33

a .060

1= .020

-Lc* 16.67

and glass-hard material,

a 8.0

a = .10

= .070

o= lo.00

Coming now to

FiG. 20.-Average Materials. Curves of Hysteresis.
Cast-Steel.
We see that no averaging is possible at all, but cast-steel comprises and includes the whole range of materials, giving a continuous and unbroken range fromn the softest kind of sheetiron down to and beyond cast-iron and to medium hard welded steel, as a glance on Tables XLVII., LI. shows and especially on Fig. 16 (where the cast-steel is marked by circles), and Fig. 21, where some cast-steel characteristics are shown as drawn linestogether with the Norway-iron curve (N), the average wrought iron curve ( W), the soft welded steel curve (8) and the cast-iron curve (C) as dotted lines.

690

STEINMfETZ ON HYSTERESIS.

[Sept. 27,

Magnetic Hardness, a, from .232 to 2.7 Magnetic Satuiration, a, " .009 " .0931 Magnetic Hysteresis, i, ' .00318 " .0279
Absolute Saturation, -Loo " 10.7 " 19.6
Consequently, for good annealed cast-steell of high permeability-as it can be got now very easily-the average wronight-

BradUejf Poates Engr,1N.r
FIG. 21.-Cast-Steel. Magnetic Characteristics.
iron curves can be used, since they represent also a fair average of soft annealed cast-steel and of mitis metal.
Poorly annealed cast-steel of high permeability will give a curve similar to that of soft welded- steel, and cast-steel of
low permeability is as good as identical with cast-iron, as will be best seen on Fig. 21.
In Table XLVIII. are given magnetic constants of average materials, in Tables XLIX. and L. the magnetic characteristics and curves of hysteresis calculated therefrom. In Figs. 18, 19, 20,

1892.]

STEINMETZ ON HYSTERESIS.

691

these curves are shown, the two welded-steel curves dotted, the cast-iron and wrought-iron cuirves drawn.

TABLE XLVIII.
MAGNETIC CONSTANTS OF AVEI?AGE MATERIALS.

MATERIAL.

Coefficient of
Magnetic Magnetic Magnetic Absolute Hardness Saturation Hystercsis Saturation

Average Wrought and Sheet-Iron,

Soft A nnealed Cast-Steel and

Mi/is Metal .....

.3

.055

Average Cast-fron, Cast-Steel of

Low Permeability .2.4

°095

Average Soft Steel, Hard Cast-

Steel of High Permeability ...... 133

.o6

Average Glass-Hard Steel........ 8

.1

.003

18.2

7

,OI3

10.5

I8

.02

I6.7

40

.07

IO.0

90

TABLE XLIX.
MAGNETIC PROPERTIES OF AVERAGE MATERIALS.

Average Wrought Average and Sheet-Iron. Cast-Iron.

LF

HF

H

Average
Soft Steel

Average Glass-Hard Steel.

F

HI F

H

2

.2

2

.6

3

3

I.I

43

1.7

5

4

2.5

64

3.3

5

4.3

8

5

5.3

9

6

6.4

IO

7

7.5

1II

8

8.8

12 I I

IO. I

I3 '4

"I.5

14 i8

12.9

'5 26

14-4

I6 39

i 6 ,o

'7 67

I7.6

8 600

I9.3

10

ig.6

[L0o = I8.2]

7

.8

10

2.5

13

4.8

I6

7.5

23

Io.8

33

14.4

50

i8.5

8I

22.9

I48

27.6

500

32.6

10

35.5

Lo = IO.5]

6

I.3

9

3.8

II

7-3

13

iI 6

I5

i6.6

17

22.2

20

28.4

23

35.2

28

42-4

35

50 2

44

58-5

58

67.3

79

76-4

II7

86.i

200

96. I

500

io6.6

CO

113.7

[L10 = I16-7]

-26
42
54
66 83 I20 I88
320 720
10
[L0

4.4 13.4
25.6
40.6
58.o
77.8
99-4
X23-I
I148.5 I75.8
=1io.o]

692

STElNffETZ ON IYSTERESIS.

[Sept. 27,.

TABLE L.
MAGNETIC PROPERTIES OF AVERAGE MIATERIALS.

Average Wrought Average and Sheet-Iron. Cast-Iron.

Average

Average

Soft Steel. Glass-HardSteel

FL

HL

R IL H IL E

.4

I

.4

2

1.7

3

3.8

4

5.6

5

7.5

6

99

7 8

10.I
io.8

9 11.4

10

I i.8

12

12.5

I5

I3.4

20

24.3

235

I4.9

30 I5.4

35 I5.7

40

i6.o

45

i6.2

s0 26.4

6o I6.7

70

I6.9

80

I7.0

90 17.1

IOO

17.3

I20

17.4

140

17.5

I6o 17.6

ISO I7.6

200

17.7

.1

.4
i.6

3.0
4.8 .7
6.4

7.6
8.5

9.3

9.0

1.9

IO.8

12.1 3.7 13.5 4.6
5.2
15.1 5-7 6.I
i6.o 6.5 6.8

17.0 7.0

7-4
7-7 8.o 8.2 i8.o 8.4 8.7 8.9

g.I

9.2

I9.0 9,3

.2

.6

I

.8

1.7

I

.I

I.7

2

2.5

5

.3

I

3.-5

7 5.0

17

5

2

10

7.0

29

.7

4

12 8.3 38 .9

5

I4 9-3

I5

IO.1

44 1.2 50 '.5

7 9

I17

IO.7

55

1.9

13

I8 I1.2

59

2.3

17

I9

II.5

63

2.7

22

20

I2.I

69 3-5

33

22 12.6

23

I3.0

73
77

44..93

46 55

24

I3-4

80 5.2

63

25 I3.6

83 5.5

69

26 I4.I

87 6.o

78

27 24-4

go 6.4

85

28 14.6

93 6.7

9I

29 14.8

95 6.9

97

29

15.0

96

7.I

102

Absolute Saturation i8.2

19.6 I0.5

36 I6.7

I14 I0.0

176

TABLE LI.
MAGNETIC CHARACTERISTICS OF CAST-STEEL.

(I)

(2)

(3)

(4)

(5)

(6)

(7)

F p P F, P F o P F p p F p p F o p F P JO obs. calc.I obs. calc. obs. calc. obs. calc. obs. calc. obs. calc. obs. calc.

'I 3.00 3.00 17-5 1 7I 1-73 12 1.32 I-35 I2 I.42 2.40 8 1.72

27 4.47 4.47 25 2.15 2.13 I8 I.66 I.6( I4.5 I.56 1.54 20 1.70

76 9.00 8-94 32.5 2.52 2.52 25 2 02 2.0I 25 2.o8 2.09 15 1.76

2-46 92 IO34 10.40 63 4.10 4.IO 34

2-47 4I 2.95 2.95 20 I.95

73 4.6I 4 62 6I 2.86 2.85 79 4.98 4.98 25 2.I7

21 I.89 I.9I 10 I.5I

28.5 2.36 2.35 I8 I.62 I.58

37.5 2.88 2.88 34 2-46 2.48

)2 5-83 45 3.32 3.32 76 4.92 4.92

50 3.63 3.62

5.83

85 69 5.28 5.26 4.26 4.25 97 5 95 5 94 Average of 62 4.32 4-33

5 Samples.

a = 2.00

0f =

.09I3

=

,012

LOO = Ix.0

a - =F=2I.9
CT0

.82
.052I
I9.2
15.74

*74
.0509
I9.6 14.54

.76
.0534
18.7
14.13

*736
.o568 .009
I7.6
22.96

.68

*545

.0587

.0575

I7.0

17.4

II.58

9.48

1892.]

STEINMETZ 0N HYSTERESIS.

693.

TABLE LI.-Continued.

MAGNETIC CHARACTERISTICS OF CAST-STEEL.

(8)

(9)

:F p p F p

(Io)

(II)

(I2)

(I3)

F p p F p F pF p p

(I4)
F p p ('5)

obs. calc. obs calc. obs.calc. obs.calc. obs.calc. obs.calc. obs. calc.

I.04 I.05 I2 .99 .99 8 I.04 I5 I.o8 i.o8 .84 .84 IO I6 I.33 1.33 I3.5 I.o8 I.o8 I3 1.31 I.32 22 I.45 1.45 I9 I.34 1.33 I2

.85 .87 44 5.34 5.35
.97 .98 6i 6.95 6.94

t0

21 i.6o i.60 21 I.48 I.48 34 2.83 2 8I 34 2.I6 2.17 32 2.04 2.04 I5 1.14 I-I5 78 8.52 8.52 a

28 I.99 I.99 24.5 I.67 I.67 76 5.73 5.75 54 3-I2 3.II 76 4.43 4.43 I9 I.42 1.38 95 IO.10 10.10

40 2.64 2.65 30 I.98 1.97 92 6.90 6.87 70 3.95 3.95 95 5.45 5.46 23 i.62 I.62

Un

51 3.22 3.26 35 2.24 2.25
76 4.67 4.64 41 2.00 2.57

95 5.25 5-25

36 2.36 2.34
46 2.88 2.0I

95 5.7I 5.69 56 3.39 3.39

6I 3.79 3.76

65 3.87 3.87

73.5 4.45 4.46

73 4.31 4.3I

94 5.63 5.62

a-

*44

0- .0-*553

-/ =
LcO = I8.I
a F= 7.96
0. 0

*344

*43

.0543 .070

.300

.300

.0521

.0543

I8.4

14-3

19.2

18.4

-

6.34

6.14

5.76

5.5 2

.308 .0565
17-7 5.45

I.26 .35
.0931 .0535
.005
I0.7 I8.7
I3.64 6.54

With regard to cast-iron, I must remark, however, that some tests of Ewing and others show magnetizations as high as
16,000, while I was never able to reach much beyond
.19=10,000.
It must be assumed, therefore, that either the linear law of
magnetic reluctivity, p = a + a F ceases to hold for higher
mag,netizations than I was able to reach-which is not likely, however,-or we must assunme that there exist kinds of cast-iron far superior to all the samples I ever came across, and if so, then very great improvements are possible in the maiiufacture of castiron for magnetic purposes.

694

STEINMETZ ON HYSTERESIS.

[Sept. 27,

CHAPTER IV.-HETEROGENEOUS MATERIALS.

I. COILED WIRE. Since armatures of dynamno electric machines have quite
extensively been wound of iron wire, I thought it interesting to determine the magnetic reluctance of wire against a magnetic flux passing crosswire through it.
Therefore I wound on a brass wire of * in. diameter 6
layers of the galvanized wire, tested in Chapter II., rv., 8, the adjacent turns closely touching each other (with only the thin film of zinc between, which the wire is covered with). The consequent layers were wound always in the same direction into the interstices between the turns of the layer underneath, starting each layer separately. The outside diameter was 8 in., so
that the spiral just fitted into the holes in the pole faces of the
magnetometer, which have a cross-section of 4 cm2. The projection of the 6 layers of wire uponl a plane vertical to the axis was very nearly 3.9 cm2. The magnetism passed in the direction
of the axis of the spirals, thereby crossing from turn to turn. The mnaginetic induction 1 and the magnetic reluctivity p were calculated with regard to the whole space taken up by the spirals, 4 cm.2, no allowance being made for the hole in the middle, since it only amounted to 2 per cent. of the cross-section.
The magnetic reluctivity of this heterogeneous body was found remarkably high, about one-ninth that of common air; no decided trace of saturation was perceptible, which indeed is not astonishing, since the highest value of induction reached in the tests was only 1,900 lines per cm2.
The magnetic characteristic is given in Table LII. The metallic magfnetic reluctivity was found p 86.3. The different readings indeed varied considerable, an average of 4 per cent., but these variations were entirely irregular and to be expected, since the magnetic reluctivity was very small, and the smallest fractional standard to balance with is 1 cm.2 sheetiron, of which quarters can be estimated, so that, when taking the average of two readings, a sensitivity of about 10 to 15 lines of magnetic force per cm.2 can be reached by the instrument. Two magnetic cycles of this coiled wire are given in Table LIII.
Their results and the constants of the magnetic characteristics are,

1892.1

STE1-NMETZ ON HYSTERESIS.

695

±F

II

a

a7

35

.37

.505

.0393

14u

1.61

5.60

.0414

av. 7] -

.0403

86.3

- .04

__ _ 1600 / _ __ _100
-_1000 __
1000 _

-1-A10-'P- - -(Q1t

+ )t6 04 +101 +1Atl

4400 / z II

I

I|
t

I/I 1f-IQenAgthvG.aalyvsaft&izcecosS4taeyeils Witrhleo(usoifht-)spira-ls

{ /// I - 0-

MagnetometelTets.

I IfIfIfI 1217 II I-1l2e0|0

II

17. 1117.lITI 11 1n1 1W1
13,000- ---

10,00
900 8000
6000-___
4000

I90 T Tl I 8k)

20 0

_
80 i0

I
50 60

781

80

90

1(I10

120

100

14-0

100

160

170

I
180

1030

I
200

240

220

230

FIG. 22.-Coiled wire and cross laminated iron.

-696

STEINMETZ ON HYSTERESIS.

[8ept. 27,

Fig. 22 gives the magnetic characteristic of this coiled wire,
and of the wire magnetized lengthwise, and the two cycles of
hysteresis.

TABLE LII.
MAGNETIC CHARACTERISTIC OF COILED WIRE.

F

L

0(

8.5
26
3I
52 66 IOO
II6 140 I5D

I04
I44
297 364
575 730 1228
1395 I555
I 670

Av. 1)

82.0
8o.o 87 5 85.o 90.5
90.4
8I.5
83.0 90.0 92.8
86.3

+4-3
+6.3
-I .2
+I .3
42
-4.'
+4.8
-3-7 6.5
+4.0

+5
-I +I
5 _4 +5 +4
__4
-8
±4.4

TABLE LIII.
HYSTERESIS OF COILED WIRE.

(I)

(2)

F

Ld

1r

F

Ld

Lr

240 130
920 IIo IOO
go 80 70
6o
50
40 30 20 IO 0
H=
L=

I.52 2.43 1.35 2.25
I.I7
i.o8
.99
.88
.77
.66
.-5 .43
.30

35

.50

30

2.38

25

1.27

20

2.15

I5

2.04

IO

.91

5

.77

0

.64

.50

.36

.22
.08
-.o6

5.6o -c.6i
.0414

I,II

.370

*335

.315

.295

.255

.2D5

.I9$

..217750

.130
.o6o

.II5

-.OIO

i .o65

.305
-37
.0393

Av. ^ .04035 , .04.
Since the reluctivity was found constant, it was interesting to ;determine, how far the re]uctance of the spirals can be replaced -hby an air gap. Therefore the coiled iron wire was laid into the

1892.]

STE1NMETZ ON HYSTERESIS.

697

holes in the pole-faces at the one side of the magnetometer, and in the holes in the pole-faces at the other side of the instrument two Norway iron cylinders, of 4 cm.2 cross-section and 8 cm.
length, were laid, with plane faces against each other, and their
distance adjusted until equilibrium was restored. The distance
from pole face to pole face was 10.9 cm., and it was found, that
for ml. M. F. of F> 80 the spirals canl be perfectly balanced by an air gap of 1.852 cm. length, between circular faces of 4 ciA.2
For M. M. F'S. lower than F 80 more lines of magnetic force
passed through the air-gap than through the spirals; but the difference was small.
It was found, that the difference between the number of lines
of force passing through the spirals, per cm.2, and the lines of force passing tlhrough the air gap (divided by 4, to reduce to 1
cm.2)
at F - 20 40 60 80 100 ampere turns per cm. was a 1 40 30 20 10 0 lines of forcepercm.2 while ;= 230 460 680 910 1140 was the number of lines of force per cm.2, calcu]ated by the formula,
F
86.3 X 10-3
These values, and especially the differences a L, are indeed too small to decide whether for low magnetization the reluctivity of the air-gap has increased or that of the coiled wire decreased, or both taken place.
In so far as for higher values of I the Norway iron at the sharp edges of the circular end faces, whicll form the gap, nay approach saturation, an apparent increase of reluctivity of the air gap is possible, wlhile a closer contact between the spirals of the coiled wire, caused by the magnetic pull at higher values of -F, may accounit for the decrease of their apparent reluctivity.
Comparing the reluctivity of this coiled wire with that of the wire wlhen magnetized lengthwise, in Table XXXIV. we see, that for the low magrnetizzitions reached in the spirals their niagnetic reluctance p3r 1 cm. length can be replaced by that of the same iron, including an air gap of the same cross section and of .106 cm., '- cm. length. That is, the reluctivity of coiled wire is equal to that of solid iron including about one-ninth of its length air reluctance. Indeed, these numerical values are
conclusive only for the conditions of this particular test, aiid will

B98

STEINMETZ ON HYSTERESIS.

[Fept. 27,

differ, when different sizes of wire are used, when the wire is wound on under strain, to make a closer contact, or when insulated wire is used, and thereby adjacent turns are separated further, and will differ with the magnetization reached.
But what these tests prove is, that the magnetic reluctivity of coiled wire against a magnetic flux passing crosswise through the wire, is enormnously higher than that of solid iron, is under circumstances equivalent to one-ninth of its length in air resistance.
As before stated, the reluctivity of the coiled wire is equivalent to that of solid iron including 10.6 per cent. of its length in air
reluctance. The distance between the pole faces of the magnetometer being 10.9 cm., the spirals were equivalent to solid iron plus an air reluctance of 10.9 X .106 = 1.1.5 cm. length and 4 cm.2 cross section. But they were directly balanced by an air gap of 1.852 cm. length between circulat faces of 4 cm2. hIence, to calculate the reluctance of air gaps bv the reluctance of air of the length of the air gap and the cross section of its faces,
length
= crosswise
as is even done in the new edition of Silvanus Thompson's "Dynamo Electric AMachinery," introduces a very serious error when the length of the gap is considerable compared with its cross section, caused by the spreading out of the lines of magnetic force. For instance, in the case mentionied here, the cr8oss section of the faces being circular and 4 cm.2, the length of the gap 1.852 cm., the usual manner of calculation, without taking into consideration the spreading out of the lines, will bring out the reluctance 61 per cent. too large. The reluctance of this air gap of I = 1.85 cm. between circular pole faces of 4 cnm.2 2.26 cm. diameter, is equal to the reluctance of an air cylinder of I = 1.85 cm. and 6.44 cm.' cross section, that is 2.86 cm. diameter, or the diameter
I
has to be increased approximately by - one-third the length of
the gap. Hence, The reluctance of an airgap of the length I between cylindrical
pole faces of the diameter d is approximately equal to the reluctance of an air cylinder of the samyie length I but of the diameter
I
d + -u-, hence it is,

40 =
(d + 31K24L

1892.]

STEINMETZ ON HYSTERESIS.

699

or, if the saine is true for rectangular air gaps, as will be in rough
approximation, if a and b are the sides of the rectangle, the
reluctance is: I
++

3

as long indeed only as the length I of the gap is not greater than its diameter.
I lhave dwelled upon this point somewhat longer, not that I consider the results as conelusive, but because I consider it as a good topic for furtlher investigationi.
One more point is remarkable witlh these wire spirals:
The cofficient of lbvsteresis is for cross magnetization:

.04

more than ten tiines larger than for length magnetization:

.0035.

This is astonishing. the more, as under cross magnetization the conditions resemble those of an open magnetic circuit.
In imy formiier paper I have already pointed out that in an open imagnetic circuit the coefflcient of hysteresis must be apparently larger than in a closed circuit, since in the closed circuit the magnetization is more homogenous than in ani open circuit where the density decreases near the air gaps.
Since the average of the 1.6th powers of different quantities is larger than the 1.6th power of the average of the different
quantities, the coefficient of hysteresis, if the magnetization is not homogenous, must come out larger by the ratio of

magnetic my average of 1 6th power of different
1.6tlh power of the average

densities. In

former paper I proved this on the instance of a magnietic circulit with two air gaps.
Ihere in the case of the coiled wire the magnetization must
be enormously heterogenous. While the greatest part of the iron is inagnetized very low, at those linear places where the turns touch each other, high saturation may be already reached. Besides, obviously a large amount of magnetism does not cross from turn to turn, but passes along the wire in spirals from pole to pole, so that really the iron is magnetized much higher than the readings give, which represent only the axial component of the mnagnetism. For, at the M. M. F. F 100, between

700

STEINMETZ OI HYSTERESIS.

[Sept. 27,

adjacent wire turns, is a difference of iyagnetic potenitial: F X cd, where d is the diameter of the wire; that is: 15.7 ampereturns.
Now the average length of a turn is 4 cm., and therefore act spirally upon the wire F -4 ampere-turns per cm., giving an induction L-- 2000, of which only an imperceptibly small por-
tion counts in axial direction. That is, in other words, the axis of maximum magnetization in the iron does not coincide with the direction of Ml. M\. F. in which the readings are taken but a circular miagnetization is superposed upon the length magnetization.
Furthermnore, it is not impossible that in such a heterogenous body as drawn wire the magnetic constants are different axially and radially. But a still better explanation of the high coefficient of hysteresis of these spirals will be pointed out in the next
chapter. II. LAMINATED IRON.
The test pieces of thick tin plate of 8 = .0378 cm. thickness
described in Chapter II., IV.f, Table XXXIV. were cut into
pieces of 1 in. X 3 in., built into a pile, clamped together and soldered, forming a solid block of iron witli intervening layers of tin, that is: laminated crosswise; or in the direction perpendicular to the direction of the M. M. F., of 16 cm. in length and 2.53 em. X 1.90 cin. 4.8 cmi.2 cross section.
The block contained 26 sheets per cm., and consequently 26 gaps filled with tin per cm. length. Each gap was equivalent to an airgap of about -, cm., as will be seen hereafter.
TABLE LIV.
MAGNETIC CHARACTERISTIC OF LAMINATED IRON, ACROSS THI1E
LA-MINATION.

F

L

,,,

A0

=%

7

.22

31.5

+ *I

+3

II

.33

32.3

- .7

-2.2

I6

50

32.0

- .4

--I.2

29

.97

30.0

+i.6

+5e3

39

1,.24

31.5

1

±3

50

I 263

30.7

t9

+2.8

53

i,62

32.7

-.I

3-5

65

2.09

31.2

+4

+I.2

66

2.04

32.3

-.7

-2.2

82

2.56

32.0

- .4

-I.2

102

3.29

3I.0

+ .6

+± .9

120

3.82

3I.2

+4

+1.2

I65

5.I2

32.2

.6

-.9

Av.

3.6

± .6

±2

1892.]

STEIWMEIZ ON fYbTEREESS.

701

TABLE LV.

HYSTERESIS AND MAGNETIC CONSTANTS OF LAMINATED IRON, ACROSS THE LAMINATION.

F L II

UC

6

70 2.20 1.63 .00732 40 I.26 .65 .007I22 Laminated with 26 plates per cm.,
each gap about o cm......... Average . 00722 3I.6 'o

Material proper ..

0...0426 .321 .05315

Mlagnetometer tests gave for the reluctivity the values given in Table LIV. The magnetic characteristic is shown as dotted line in Fig. 22. As seen, up to the highest magnetization reached,
of I - 5.12, the reluctivity is constant, ,o = 31.6, and the differ-
ences between the observed values and the average value are
entirely irregular, and not larger than the errors of observation account for, wlhieh in such a case are necessarily larger than with
homogenons nmaterials of high permeability. The results of two magnetic cycles of this cross-lamiinated iron are given in Table LV, slhowing a coefficient of hyisteresis ^q - .00722, while the material proper had the coefficient of hysteresis i .00426, that
is soinewhat more than half the formner value. Since the magnetic reluctivity of the material proper is known,
from the observed reluctivity of the lami-nated block and the niimber of sheets per cm. _ 26, we can compute the approximate widtli of air space equivalent to each layer of tin or gap between adjacent plates and find it equal to about Xv0 eni. Probably the gap is less in reality. In the average, the reluctivity of lanminated sheet-iron with the laminae very close together as in this case, is about 30 times higher than that of the sheet-iron in the direction of lai-ination. But even across the lamination, laminiated sheet-iron is still superior to coiled wire. The coefficient of hysteresis across the lamination is still about 70 per cent. higher than along the lamination, .0722 against .0426, though not by far as much higher as in the case of the coiled
wire.
This higher value of hysteresis may be partly due to a higher coefficient of hysteresis perpendicular to rather than in the plane

702

STEINMETZ ON HYSTERESIS.

[Sept. 27,

of the sheet-iron. But mainly I believe it is caused by the unequal magnetic density at the different points of the cross-section.
The separate laminie are evidently not absolute planes, and consoequently the interst-ices between them not of a constant width, but the plates at somne places alm-nost in molecular contact,
at other points farther apart. That ineans that cacll gap between adjacent latninme is nlot of constant width, b-ut of a widtlh -varyTing fronm alniost nothing to say .01 em. Butit, sinee the reluctalnce of
each gal) is about 30 titnes that of eaeh lamnina, the greatest part
of the -A. ii. i'. is co-riustmed in the gap, and the macrnetic lines of force will crowd togetlher at those points where the adjacent lamninoe conie nearest together. In th)e iron consequently the nagnetismn will n:ot flow perpendicularly across, but will largely spread sideways fronm the point niearest to the preceding ]amina to the point nearest to the next lamitna, anid in consequence of this irregular crois-s agnetization the mnagnetic density in the iron must be larger than tl-he mnagnetic denisitv in the direction of the
M. A. F., and consequently ^zy comes out larger. Numerical figuir-
ing slhows that this fact fully accounts for the higher value of q without any furtlher assunmption. This, effect must become less when the gaps betwveeni the lamuinoe are larger, for instance, sheets of paper are placed therein. Though I mLust leave this question also for future research.

1IT. IRON IFILINGS.
Remarkable results were obtained by testing the magnetic behavior of iron filings. The iron filings were produced by clamping a large number of sheets of the iron tested in Chapter 1. together, and cutting notches therein by means of a rotary
cutter of -& in. - .Th cm. width, thereby producing fine needle-
like irorn chips. Tests were mnade by the electro-dynaniometer method and by the magnetorneter method. In the dynamiiometer method the same magnetizing spools were used as in Chapter I., and by means of these spools and two U-shaped end-pieces a box-like receptacle formed. This was filled with the iron filings, and by vigorously beating it against the table the filings were made to settle down.
In the magnetometer method a brass tube of 4 cm.2 cross-section and 8 cm. length was filled with these iron filings, which were enclosed between two cylindrical Norway iron pieces, and there-

1892.]

STEIN-METZ ON HYSTERESIS.

70.3

after tested. The magnetic constants were found very much higher than in the electro-dynamometer tests.
Since in the electro-dynamometer tests the iron filings by beating to make them settle closer together had evidently assumed a kind of horizontal stratification, that is, stratification in the direction of the magnetic flux, while in the magnetometer tests the tube containing the filings had been filled froin the end, and consequently the filings had assumed a stratification perpendicular
to the direction of the magnetic flux, a higher magnetic hardness
was to be expected. Therefore a larger tube of 17.8 cm.2 cross sectioni was secured,
a slot cut in the tube lengthwise, the tuLbe fastened between the cylindrical pole blocks, and then filled with iron filings from the top through the slot, and by vigorously beating the filings were made to settle down in a stratification in the direction of the magnetic fluix, the same as in the electro-dynamometer tests. In all these tests approximately 30 per cent. of the volume filled by the filings consisted of iron.
One more test was made by wetting the iron filings with turpentine and stamping them tight inito the brass tube of 4 cm.2 cross section.

1. Electro-dynainometer Te8ts.

Length of miagnetic circuit, 30 cul.

Cross-section "1

" 13.7 cm.2

Tests were made with the frequenicies of 180 and 114 com-

plete periods per second, and a few readings with still lower

frequency.

The results are given in Table LVI., in the usual denotation.

704

STEINMETZ ON HYSTERESIS.

[Sept. 27,

TABLE LVI.
ELECTRO-DYNAMOMETER TESTS OF IRON FILINGS.

FrF~B~~~L~~oHsifI { 0°tr/1 ~[ B Calc.|AH

( calc.| =%

(1) 180 Complete Periods per Second, N 180.

24

323

27.7 420

36.6 523

4I.3 597
5I 738

750

826

70 98o 85 1130

98 2270

222 2I410

293 385
477
545
674
690 740
892
2024
II47
270

400 700 1000 2220
2900
1750
2200
2750 3480
4280
5020

82.0 io.8 [.0387] 470 - 70 [+15]

72.0 22.2 .0445 720 + 20 +3

77.0 II.4 .0447 2010 + IO +I

76.o ii.6 .044I 1260 +40 +3
-,. I22.5 .0489 1780 -220 -7

1

0439 I820 + 70 +4

0

.00473 2220 - 8o

4

11.2 .0450 2790 + 42 +2

1007.0454 3500 + 20 +2

20.4 .0463 4230 - 50 -I

20.2 .0468 4990 --230 3

[.0455] 470 + 70 [+'5]

.05II 730

30 +4

.05i8 I030 ± 30 +3

.05II 1270

50 +4

.0566 1790 2-I0 -6

.0502 i86o +IIO +6

*0557 2IO0 -IOO 5

.0523 2800 + 5 + 2
.053I 3490 + IO tO

.0557 4290 - 90 -2

.0554 4930 -290 4

Absolute Saturation,...

Lw =4590.

Av q=o2

5
0457

_0533 Z' 6
±6o

±299

.03

80
±8o

+33-33

(2) 114 Complete Periods per Second, N = 114

49.4 580 531 I070

47

724 665 2420

68 2000 9I5 2460

76 2IOO 2005 2980

96 I3IO 2290 3930

74.0 II.8
_Z I2 3
5l |I.8 II.6
+ I0.9

.0405 I050 - 20 2 .0378 2490 + 70 +5
.0390 2500 + 40 +2 .0405 292IO - 70 -2 .0404 3850 - 8o -2

.0467
.0432
.0450 .0468
.0472

I050 - 20 -2 I500 + So +5 25IO + 50 +2
2910 -- 70 -2
3820 2--IO -3

AbAsboSlourtuetsSa.taot-L r =5000. Av.;5= .0396

+ 56 +2.6 .0458

± 66 ±2.8

(3) 79 and 91 Complete Periods per Second, T7-

79 86 I260 2252 3380 74.5 11.7 1 .0370 3410 + 30 +I 1II09 15IO 1372 4580 79.3 12.1 .0375 4550 - 30 --I

.0418 3450 + 70 +2 .0436 4480 -IOO 2

p 56+.21 F. Av-

.0|373

± 30 +I |0427

± 85 ±2

F M. M. F.1 in ampere-turns per cm. B = whole mag:netic induction, in lines of magnetic force per cm.2

4 7r

L =

metallic inagnetic induction, = B

II, where H

is the field-initensity.

H= observed value of hysteretic loss, in ergs per cycle and cm.'
obs

p metallic iuagnetic reluctivity, in thousandths I

, magnetic permeability, - - 4 -

1892. ]

STEINMIETZ ON HYSTERESIS.

705

TB and TiL respectively = the coefficient of hysteresis, referring
to B anld I respectively, that is calculated by means of the formuae:

H Ti (B_ B2)1.6 andll

I 1.6

HE = calculated loss by hysteresis, and A - difference between
calc

H and H.

obs

calc

As seen, the magnetic reluctivity varies in the range of tests

fron p = T2 to o =- .

For Mi. M. F.'S. of _F 45 the observations agree with the law,

p = a + aF.

But the coefficients a and a are decidedly dependent upon the
frequency, increasing with increasing frequency, while the value
of absoluite magnetic saturation L,, decreases with increasing
frequency.
The coefficient of hvsteresis ^, is - with the only exception of
the one, lowest, reading - constant within the errors of observation, and proves tlhereby the law of 1.6th power.
But it canl not be decided whether H varies with the 1.6th power of B, or of I, since either agrees with the law of 1.6th power, B and I being near enough proportional to bring the differences within the limit of the errors of observation.
Therefore for either value, B and I, the coefficient of hystere-
sis is calculated and given, TiB and iL. The coefficient of hysteresis depends decidedlv upon the frequency, increasing with increasing
frequency. The coefficients of hysteresis are very large, giving
hard-steel values.

2. 2Wagnetometer Testt.
Table LVII. gives the mnagnetic characteristic derived from magnetomneter tests.
The first two columns give the values found along the stratification, that is in the same condition as the electro-dynamometer tests, with a cross-section of 17.8 cm.2; the first column found by the usual method of reversals, that is by reversing the current repeatedly before each reading; the second column gives the maxinmum values of magnetization taken from the slow magnetonmeter cycles in Table LVIII.

706

STEINMETZ ON HYSTERESIS.

[Sept. 27,

TABLE LVII.

MAGNETOMETER TESTS OF IRON FILINGS, MAGNETIC CHARACTERISTICS.

The third column gives the values found across the stratification, with 4 cm.2 cross-section. The fourth column gives the tests of iron filings wetted with turpentine and compressed.
Remarkable in all these tests is the considerably higher value of reluctivity, coefficient of hardness and especially coefficient of saturation, and consequently the much lower value of absolute magnetic saturation than that derived from electro-dynamometer tests.
The straight line law,
p=a + aF
holds for
F > 25.
The absolute magnetic saturation is very nearly the same across and alonog the stratification, a little more than half as high as found by the electro-dynamometer method. The magnetic hardness is considerably larger across than along the stratification, 106.3 against 77.5. The compressed iron filings reach a higher value of saturation, but contain more than 30 per cent. of iron.
Table LVIII. gives a number of cycles of these iron filings,

1892.]

STEINMETZ ON HYSTERESIS.

707

and their results, the coefficient of hysteresis I being given for B as well as for L.

TABLE LVIII.

MAGNETOMETER TESTS OF IRON FILINGS, HYSTERETIC CYCLES.

(I.)
I7.8 cm.2 Cross-Section.

(III.)

(I I.)

Compressed.

4 cm.2 Cross-Section. 4 cm 2 Cross-

Section.

F

(I)
Ld Lr

(2)
Ld L,

Ld(3)Lr- Ld(4)L,

(I)
Ld Lr

Ld

(2)
Lr

(I)
Ld Lr

i8o

± 1250

170

1220 1220

i60 II90 iI68

I50 II62 I123

140 1127 1073

130

I1090 1020

920 1050 960

IIo I0 Io goo

I00 964 837

9I7 770 ± 787 868 700 750 7I6

± 66o 620 6oo

[+75] ± 650

70
6o

[± 8I2 620 704 640

757 540 650 554

551

580 530
540 460

628

607

590

538

50 695 460 596 472 ±530

490 39)

± 390

548

460

40
30

630 370 540 388 462 400
560 280 480 296 408 305

[±±33422]

450 320 360 330 493
400 230 320 260 427

375 280

20 476 145 406 I70 340 180 280 I90 340 I30 280 I6o 350

165

10

370 55 310 -20 260 10 200 30 250

0 2I0 40 255

0

± 240

:± Ig90

± I50

±1I00

± I40

±ioo

± I50

H=
IL =

6034 1250

2820 787

1480 530

738
324

2300

96o

66o

390

2.022
650

(.L = .0669

.0656

.0648

.o651

.0709 io686

.0639

Av. T =-o6 6

.0698

.0639

B= XB -

I475 .0514

goo
.0541

6oo .0531

Av. 7iB = .0533

382 .0545

770 .0554

450 .0546

.550

744
.0514
.0514

These coefficients ; are larger than the values found by electro-
dynamomneter tests. Table LIX. gives a collection of the different values of the
magnetic constants of these iron filings, a, , -LX, vL, and ajB, as
found for the material proper (Chapter I.), for the filings by electro-dynamometer tests along stratification. for the frequencies of 180,1 l4, and about 85 complete periods per second; by mag-
netoineter tests along and across stratification, and compressed.

708

STEINMETZ ON HYSTERESIS.

[Sept. 27,.

Fig. 23 gives the different inagnetic 'characteristics, with theair line as dotted line. Fig. 24 gives the different curves of hys-

FIG. 23.-Iron Filings. Magnetic Characteristics.
teresis, the observed values being marked by crosses, and Fig. 25 gives the four magnetometer cycles of hysteresis, from Tablle LVIII., 1.
TABLE LIX.
MAGNETIC CONSTANTS OF IRON FILINGS, 30 VOLUME PER CEN!'.

Number of Coefficient of Magnetic

Complete Cycles

ISolruation

Second per

Hardness Saturation

Saturation

ForCoefficient of
For Magnetic
Hysteresis

_N

a

LOO F> L B

The Sheet-Ironl proper .. 67- r7o Filings,i3.7 cm.2cross-sfc. i8o

.275
64

.o58 .2I8

I"4

6i

.200

-85

56

.21

I7.8cm.2Magnetom'r. Very Slow. 77.5

.375

" 4cm.2 ,across stratifi'n .. " 4 cm. 2, compressed.. ..4

I o6.3

.384

97

.244

I7.24 4.59
5.00
4.76 2.67 2.60
4.10

8
-45 -45
-30 - 20
-25

.0035 °0035
.0533 .0457
.0458 .0396
.0427 .0373
.o656 .0533 .o698 .0550 .o639 .05I4

Herefrom it seems, that az, a and ^ are largest for very slow

1892.]

STEINMETZ ON HYSTERESIS.

709

magnetic cycles, as in the magnetometer tests, decrea8e for increeasing frequency, reach a minimum for a moderate frequency,

tsuu

I/I/

4f~000f

312I-I/
32212-

1001-

0
L= 200 400

-

-

--

--t

600 800 1000 1200 1420 1600

FIG. 24.-Iron Filings. Curves of Hysteresis.

and increase again for increasing frequency, though being at the frequency 180, still fat lower than for slow cycles.

6~~~~~00

100_0-1-1_0-1 10-21040 __ ,0

_

_ _ _ -600 F

___ 1000
1200
FIG. 25.-Iron Filings. Hysteretic Cycles.
For the electro-dynamometer tests, (L can be expressed by the forinula,
CL = .0330 + .000113 A

710

STEINMETZ ON HYSTERESIS.

[Sept. 27,

The conclusions derived herefrom are,
"Even for such heterogeneous materials as iron iling the
linear law of reluctivity,
p a +a[F
and the law of hysteresis,

hold true, But the coefficients a, a, a depend upon the speed of magnetic
variations, reaching a minimum for moderately slow frequencies."
That the reluctivity is very high was to be expected from the introduction of air resistance in the interstices between the iron
filings. But the high coefficients of hysteresis ai need still an
explanation, for it cari not be seen how molecular friction could be larger in iron filings than in solid iron, since even the smallest iron chip is still infinitely large compared with the sizes of molecules.
The iron filings containiing 30 per cent. _ .3 volumes of iron, in Table LX. the magnetic constants are reduced to the iron
proper by multiplying a and a, and dividing I, -L, and If by
.3,. consequenitly multiplying -L hy 3 6 .486.

TABLE IJX.
MAGNETIC CONSTANTS OF THE IRON CONTAINED IN IRON FILINGSI
30 VOLIUME PER CENT.

Number of

Coefficient of Magnetic

Complete

Absolute

Cycles

Saturation

per Second Hardness Saturation Hysteresis

N

a

La

The Sheet-Iron proper ..... 67-170

.275 *S58

.0035

17.24

Filings, 13.7 cm. 2 cross-sectioti. i8o

1Q.2

.0654

.0259

25.30

114

18.3

.0600

.0222

I6.67

T 7.8cm.2, magnetom'rtests Very .8S.5low. 1

i6.8
23.2

.0630

.0207

.1f25

.0318

185..8970

"4 cm. 2, across stratificatiorn.

31.9

.I152

.0339

8.67

As seen from this table, the highest values of absolute saturation L0, - 16.67, come pretty near the value of the iron

1892.]

STEINMETZ ON HYSTERESIS.

711

proper, 17.24; but the values derived from magnetometer tests
remain far below that. But even the lowest valuies of the coefficient of hysteresis ;; are
still hard-steel values. The values of C are 4 to 6 times as high as the highest values
ever found for sheet-iron (commnercial ferrotype) 7 to 11 times
as hiigh as average wrought-iron, and 10 to 17 tiimes as high as the lowrest wrought-iron values.
It is to bte expected Wliat the meehanical treatmtient in cutting the iron filinigs hias ii-icreased their magnetic hardness and hlysteresis somniewhlat. But it is entirely out of question that mechanical treatmtient can have inereased q 7 to 11-fold, the more as the value of absolute saturation _L 16.67 is in contradiction
thereto.
Thie only conelusion left is, therefore, thcat the looped curve of hysteresis does not represent the energy con;armed in, the iron, by inotleeucir f-iction.

CHAPTER. V.-CONCLUSIONS AND FALLACIES.
The tests comrnmunicated in the former chapters seem to prove that imiolecular friction in magnetizable muaterials under variations of magnetization is much more constant a phenomenon than has been usually supposed. The connection between loss by molecular friction Iland amplitude of induction it seems to be absolutely rigid, while the connection between inrduction I and iu. Mr. F. Fis decidedly flexible, especially with lower At. Al. F.7S, because L does not only depend upon the present, but also upon the formner conditions of F and 1I and even upon the time by a kind of viscous hysteresis or better called sluggislhness as observed by Ewing, and also noticed by ien under certain circumstances on the magnetometer, so that for a given IL the corresponding F can have a large range of different values, while II is univalent.
In concordance herewith is that for the correspondence between I and F no simple law could be found which holds over the whole range, while the law of interdependence of IL and II evidently does so.
Consequenitly I believe that the best chance to arrive at a fuller understanding of the phenomenon of magnetism we shall have wlhen starting in the research from the correspondence ff-I.
Ilowever, this law of 1.6th power I believe is not a differential

712

STEINMETZ ON HYSTERESIS.

[Sept. 27,

law, like for instance the quadratic law of gravitation, but in an nturegcal law like the law of prlobability with which it seems to be connected in soine way.
In the former chapters we have for the determination of the 4nolecular friction made use largely of the cyclic curve of hysteresis, that is the correspondence between the magnetic induction and the M. Mi. F. when the latters performs a complete cycle.
If the magnetization is given as magnetic intensity or moment,

I- 4Iwz x RI
and the M. M. F. as field intensity II, the area of this loop directly represents the energy expended by the variation of the Mi. M. F., in ergs per c1m.3 and cycle.
If the muagnetization is given as magnetic induction, L or B,
the M. M. F. as field intensity, If, the area has to be divided by 4 7w, to give the energy. But if the N1. M1. F. is given in current-
turns per cm., the area is equal again to the consumption of
energy, in ergs, or, if the M. Al. F. iS given in ampere turns per cM., F, since 1 ampere -10-1 absolute units, the area is 10 times the energy in ergs. This is another reason why I preferred
the use of ampere turns per cm., F, as A. M. F., to make this area
directly equal to the hysteretic energy, with a power- of ten as
factor, as usual in our system of practical units.
Giving IL in volt lines, Fin ampere turns, the area is directly equal to IIin volt seconds or joules.
As said before, this looped curve of hysteresis nmeasures the energy expended by the Mi. Al. F. during a comnplete cycle.
It has been assumed then, that the area of this loop represents the energy consumed by molecular friction in the iron. This is afallacy. The area of this looped curve is not the energy dissipated by molecular friction in the iron. Warburg and Ewing hiave shown-the former by supposing the cycle of M. Al. F. performed by changes in the position of steel magnets, and determining the energy expended in performing these changes in positioTn; Ewing by supposing the magnetic cycle produced by a cyclic variation of the exciting current in a magnetizing helix and calculating the energy constuned by the F. Al. F.'S. induced in the magnetizing helix by the cyclic variation of magnetic induction, that the energy expended by the M. M. F. during a complete cycle is equal to the area of this looped curve.

1892. 1i

STEI.NMETZ ON HYSTERESMS.

713

Hence, it has been concluded that the area of this loop represenits the energy expended by mnolecular friction in the iron.
Here is the mistake in the concluision. For
"T he area of the looped curve of hysteresis represents the energy dissipated by molecular magnetic friction then, and only then, when daring the magneti( cycle neither energy is exerted upon
the mnagnetic circuit by another source of energy, nor work done
by or in the magnetic eircu?t."
Instances of the first case have been observed-and misinter-
preted-nuinerously.
For instance, on pages 114-115, and on pages 319-320 in
Ewing's book is shown, that under the influence of vigorous
vibration, or of an alternating current passing lengthwise, that is in the direction of the magnetic flux, through the magnetized wire, the looped curve of hysteresis more or less collapses, hysteresis disappears. But not so molecular frietion. The energy dissipated by mrolecular friction is simply derived not from the cyelic varying M. M. F., but from theforce vibrating the tire, viz: from the alternating current. For wlhen violently vibrating a magnetized body molecular nmotions are produced by the mechanical
force which consume a part of its mechanical energy. But the
best proof is, that under circumstanees, by the action of suLch a mechanical force, the magnetic loop made by the correspondence of L to F can be overturned, so that the rising curve of magnetization is higher than the decreasing, that is the cycle repre-
sents, not expenditure, but production of energy. Since obviously molecular friction can not produce energy, here the action of inechanical force is plain.
In rotating the keeper before the poles of an electroinagnet,
magnetism. and inagnetizing current are mnade fluctuating, and
in. plotting the muagnetism as a function of the M. M. F., we derive
such an overturned loop. To such overturned loops, based on actual tests made on an
altermiating dynamo of the " hummning bird " type, are shown in
Fig. 26. Ilere simple mechanical energy has delivered not onily the
energy dissipated by molecular friction in the iron, but also the energy exerted by the varying magnetion upon the M. M. F., and while the M. Al. F. does not expend, but receives energy, the mechaniical force of rotation expends energy. Consequently, if the magnet is not an electro-magnet, but a steel-magnet, it will be

714

STEINMIETZ ON HYSTERESIS.

[Sept. 27,

strengthened, as is well known. Another instance is, if we
alternately tear the keeper off a permanent magnet and puLt it on
again. After a number of cycles the yermanent magnet will
come into a stationary condition, ineither lose nor gain in inagnetic potential. Nevertheless, by molecutlar friction in these parts of the steel magnet, and in the keeper, where the m-agnet-
isi-il varies in strengtlh anid direction, energy is dissipated. This
is derived consequenitly, froim tlhe source of miieclhanical energy.
The case mnay be similar in dynamao-armnatures. The opposite p1lenomenoii, that the hysteretic loop represents muore energy thian
expended bvy molecular friction, is still miore frequent.

FIG. 26.-Overturned Hysteiesis Loops of fHlumming Bird."
For instance, if eddy, or Foucatilt-currents are induced ii the iron, the hysteretic loop is considerably widened. and represents now nlot only the energy expended by molecular friction, but also the energy spent by the eddies.
But since the eddy currents are electric cuirrents also, anid
represent a certain M. M. F., in this case the difficulty is over come by stating that not the impressed M&. Ml. F., but the M. M. F.
resulting from the impressed M. M. F. and the M. M. F. of eddy currents has to be considered in determining the energy spent by molecu-

1892.]

STEINMETZ ON HYSTERESIS.

715

lar friction. This is still more plain in the case of the transformer,

where it evidently would be incorrect to represent the iniduction

IL only as a function of the impressed M. M. F. of primary cur-

rent, instead of the resultant M. M. F. of primary and secondary

current.

But in the magnetic circuit built up of iron filings, as treated

in Chapter IV., III., we have a case where without the existence of

secondary currents the hysteresis loop represents more energy

than spent by molecular friction.

In this case evidently mechanical motions take place in the

iron filings, which consuine energy, derived from the M. M. F.

The mechanism of action may be about the following:-When

the AM. M. F. increases, more and more iron filings fall in alignment,

by setting up chains of filings as soon as the M. M. F. iS large

enough to cause the motions required hereto. When the M. M. F.

decreases, these chains of filings will be maintained down to a

much lower M. M. F. than was required to produce them. The

consequence hereof is tlhat-independent of molecular hysteresis

-for the M. Mt. F. on the decreasing branch the apparent magnetic

reluctivity will be considerably smaller, hence the induction

larger, than for the same M. M. F. on the increasing branch-that

means, the hysteric loop will be widened, and widened by that

amount of energy expended by the mechanical motions of the

iron filings.

The same is seen in the case of the loose wire spirals, in

Chapter IV., I., where the increasing M. M. F. brings the spirals

in closer contact, while in the case of the crosswise laminated

iron, Chapter IV., II, no such expenditure of energy is possible,

and, indeed, experiment gives a nunch closer agreement between

the hysteretic loss of the cross laininated iron and that of the-

material proper, the difference being small enough to be explained

by the unequalities of magnetic distribution.

To test the correctness of this reasoning, I dipped the tube

containing the iron filinlgs in melted paraffin. After having

cooled down, I made another set of tests, of the hysteretic cycles

of these iron filings (magnetometer tests, along stratification) and

got the values:

±F:

±1

IIa

87

892

2606

.04959

50

616

1122

.03860

31

424

520

.03252

716

STEINMETZ ON HYSTERESIS.

[Sept. 27,

while the tests of these iron filings without paraffin had given:
= .0656.
The tests show a coiisiderable decrease of the value of (, wlhen the filings were hindered in their mnotion by fillinig the interstices with paraffin, especially for lower M. M. FSs, and thereby prove the
assumption. These tests were made on a hot suminier day, and the still coin-
paratively large values of C seem to indicate, that motions of the filings still took place, especially under larger magnetic strains,
that is, that with a M. M. F. F 8T the paraffin partly gave way before the push of the iron filinigs, at the same time these tests prove conclusively, that the value ^ decreases, if motions of the
iron filings are impeded, as was to be expected. The simplest case of this phenomenon is that of an electro-
magnet with keeper excited by a slowly alternating current, at a
certain M. M. F. the keeper will be attached, and then held down to a far lower x. M. F. since a much largei xM. M. F. is required to attract the keeper over a distance, than is required to keep it in contact. Consequently the loop performed by such an electromagnet will not represent the mnolecular friction only, but this molecular friction plus the mechanical work done by the magnet.
In tlle alternating current synichronous mo-tor with wireless shuttle armnature the whole mechanical energy is derived by an enlargement of the cyclic curve of inagnetization of tile field
magnet.
Very likely in the amalgam of iron we hiave such a case also.
An interesting fact is then, that the law of the 1.6th power holds for iron filings also, and consequently the expenditure of mechanical energy in the motions of the iron filings nmust follow the same law, and nevertheless these iron filings do not resemble at all the conditions claimed for the mnolecules of paramagnetic substanees. For these iron filings are neither permanent magnets, nor are their distances infinitely large compared with their dimensions, as must be assumed for molecules.
This explains also, why the coefficient ^ is largest for very slow cycles, decreases, and after reaching a minimum for a moderate frequency, increases again. This explains also the corresponding variation of absolute saturation.
That, nevertheless, the law of the 1.6th power holds, proves, that this law does not depend upon a particular constitution of
-the material but is of more general meaning.

1892.]

2]STEINMETZ ON HYSTERESIS.

717

Another consequence is, if, as we have seen, by mechanical
vibrations the hysteretic loop is made to collapse, this does not
mean, that by shaping the magnetic circuit so that the alternating magnetism produces vibration, the loss of energy by molecular friction would be avoided or overcome, as has been thought
by misinterpretation of the tests referred to above, but in the contrary such an arrangeinent would have just the opposite effect, to add to the unavoidable loss by nmolecular friction the loss by mechanical vibration. It is not yet proved, indeed, that
under the influence of mechanical vibration, or of an alternating longitudinal current the molecular friction is still the same, although this is made very likely by all that we know about the nconstancy of this molecular friction. Further tests will give more light upon this matter.
It is highly probable, that the initial inward bend of the magnetic characteristic, and the deviation of the metallic reluctivity from the linear law, caused thereby, is merely due to the expenditure of energ-y by the M.. M. F. for molecular friction, and that conisequently, if the energy of mnolecular friction is derived from another source, for instance mechanical vibration, the magnetic reluctivity follows the linear law from the beginning, as observed by Ewing, annd the inward bend of the mag,netic clharacteristic
dissapears. This explains the enormous increase of permeability for low
AM. Ml. F.'S., caused by vibration. In tlhe absence of an external
source of energy the rise of magnetic induction following the linear law of reluctivity is for low M. M. F.'S. made impossible by the fact, that in this case more energy must be expenided by
molecular friction, than would be derived from the iMi. M. F. by the E. M. F. induced in tle exciting circuit.

THEORY OF MOLECULAR MAGNETS.
Relatively the best explanation of the phenomena of nmagnettic induction and of magnetic hysteresis is afforded by the assumption, that the molecules of the paramagnetic materials are permanent magnets, which, as long as no outside directing force H acts, have no definite direction and consequently no resulting magnetic moment, but, following their mutual attraction,
are grouped in pairs and chains. By the application of an outside force H, the molecules are

718

STEINMETZ ON HYSTERESIS.

[Sept. 27,.

turned into alignment with F1, against the opposing forces of mutual attraction, and hereby deflected by a certain angle. Now
for certain positions of molecules exists an angle of deflection,
which makes ff a maximum, so that for a further increase of the angle of deflection a smaller value of hlis required, and consequently the II necessary to reach this critical angle of deflection
overthrows the molecuile-an irreversible process, which represents the loss of energy by what is ca.lled molecular friction.
This theory can not, indeed, be considered an explanation of
the phenomenon of mmagnetism, since it refers it back to permnaii-
ent molecular magnetis8n again; it is mnerely an explanation of' the particular shape of the magnetic characteristic and of the loss by molecular friction.

FIG. 27.-Theory of 3Molecular Magnets.
This theory of molecular magnets, and the unstable equilibrium reached by them for a certain H, has been worked out especially by Ewing. But in determining the fundamental equation of this theory, the equation of equilibrium of a pair of molecules
acted upon by an outside force kI, Ewing makes an assumption
which is in contradiction to all our present knowledge of molecular physics.
All the facts of the kinetic theory of gases, of thermodynamics, etc., carry to the conclusion, that the diimen8ioons of molecules are inf#i>tely small compared with their distances.
But Ewing supposes the distance of the centres of molecular magnets is not much greater than their length, to be able to make