U N IV ER S I T Y O F I L L I N O I S
E N G I NE ER I NG EX P ER I M E NT S T A T I ON
B U LLE TI N
No
.
N OVE MB E R
62
T H E ELEC T RO N T H EORY
By
E LME R H WI LLIAMS
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,
OF
A S S OC IATE
,
1 9 12
MAG NET I SM
IN
PH Y S I C S
C O NT ENTS
I ESS ENTIAL F E AT U RES O F T H E ELE C TRO N T HEOR Y
O F M A G NE TI SM
.
P
I ntroduction
K inds of M agnetism
G ene r al P r ope r ties of Electrons
Electromagnetic Fo r ce D u e to an Elect r on in M otion
Diamagnetism
M agnetic Ene r gy
P aramagnetism
C u r ie s R u le
Lan ge v i n s T h eo r y
Electronic Or bit
M olecula r Field of Fe rr omagneti c Su bstances
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I I EXP E RIM E NTAL DETERMI NATIO N O F T H E M A G N E TIC
P ROP E RTI E S O F C RYSTALS
.
P y r rhotite
and M et h ods for Dete r mining t h e M agnetic
P roperties of P y rrh otite
C omponent of M agnetization P e r pendic u lar to t h e Field
C omponent of M agnetization P arallel to t h e Field
Th e M olec u la r M agnets of P yr rh otite
W eiss La w of M agnetization of P yr r hotite
M agneti zation in Di fferent Di r ections
H yste r esis P h enomena
Energy of R otating H yste r esis
M agneti c P r ope r ties of H ematite
M agneti c P r ope r ties of M agnetit e
Apparatus
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’
2 581 9 6
AGE
I II
U P O N T H E M A G N E T IC P RO P E RTI E S
O F B OD I E S
P
M et h od of I nvestigation u sed by C u r ie
R es u lts O btained by C u r ie
R e s u lts of d u B ois and H onda
A nalogy between t h e M anner I n w h ic h t he I ntensity of M a g
n e t i z a t i o n of a M agnetic B ody I nc r eas es unde r t h e I nfluence
of T empe r at u r e and t h e I ntensity of t h e field and t h e
M anne r in whic h t h e Density of a Flui d I nc r e as es u nde r
t h e I nfluence of T e m peratu r e and
.
EFF E CT
OF
T E M P E RAT U R E
AGE
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,
IV
.
EXP E RIM ENTAL EV I D E N C E
FA V OR O F
T H E OR Y O F M A G NETISM
IN
TH E
EL E CTRO N
M olec ular M agnetic Field of Py rrh otite
V a r iation of t h e I n t en s ity of M agnetiza t ion of M agnetite wit h
T empe r atu r e
Specific H eat and M olec ular Field of Ferromagne tic Sub
Th e
.
M agnets o f I ron Nickel and Magnetite
T h e H ysteres is Loop of I ron
Exceptions to the Electron T h e ory
V B IB LIO G RAPH Y
T h e Elementa ry
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50
ELEC T RO N TH EOR Y
I
.
ESSE NTIAL FEAT U R E S O F
TH E
O F M A G NET I SM
ELE C TRO N T HEOR Y
O F M A G N ETISM
I n trodu c ti on
Du r ing th e last decade t h e development of t h e
subj ect of magnetism has made rapid st r ides No t only h ave t h e older
t h eories and met h ods been extended by imp r oved facilities but new
t h eories h ave been advanced w h i c h are intended to co rr elate t h e great
mass of data and facts and t h us enable our p r esent knowledge to be
extended along new lines A mong t h e new t h eories which have been
advanced by various a u t h ors t h e elec tr on th eor y of magn eti sm is one of
t h e most important and inte r esting T h is t h eory seems to account fo r
magneti c p h enomena in a ver y direct way W e h ave only to assume
t h at t h e molecular currents of A mp e re w h ich fo r m t h e elementary
magnets are revolving electrons in o r de r to express Amp e re s theory o f
magnetism in terms of the electron t h eory H oweve r a closer study of
t h eir orbits due to V oigt and J J T h omson s h owed t h at t h ese currents
cannot account su fficiently for the p h enomena of diamagneti c and
paramagnetic bodies I t was onl y on the basis of the researches o f
C urie t h at Lan gevin was able to g ive a m ore satisfactor y t h eor y of
diamagnetism and paramagnetism
T h e theory worked out by Langevin for paramagneti c gases onl y
was later extended by Weiss to ferromagnetic substances Weiss
introduced a new notion into t h e theory of magnetism v i z t h at o f an
int r insic or molec u lar magnetic field by means of which he could account
in a very beautiful way for the magnetic p r operties of the crystal
py r rhotite and many of the magnetic properties of iron ni ckel and
cobalt H e has also contr i buted most es sentially to our experimental
knowledge of t h e ferromagnetic phenomena
O ne of the c o wo r kers of W eiss in the fundamental investigations on
pyr rh otite was J K unz , w h o also contributed to t h e theory of magnetism
by determinin g the elementary magnetic moment and t h e c h arge of the
electron from purely magnetic phenomena I n his lectures on the
electron t h eory given at t h e Unive r sity of I llinois K unz gave an a c
count o f t h e present t h eory of magnetism and of the experimental and
theoretical work of W eiss T h e aut h or of t h is bulletin has used these
lectu r es as a basis drawing in addition fr om the works of the various
au t h ors who have made fu r t h er expe r imental advances
W eiss recently advanced a new theory in whic h t h e magnetism of a
substance appea r s to b e made up of magnetons j ust as a negative el e c tri
cal c h arge i s an aggr egation of elect r ons T h is theo r y i f confirmed by
furt h er expe r imental evidence represents a new fundamental step in
the development o f our knowledge of t h e material universe Th e
experimental evidence however seems hardly strong enough to warrant
a detailed discussion of i t in this bulletin
Th e present theory o f magnetism as developed by Langevin and
Weiss is Open to certain obj ections and fails to exp lain a considerable
number of magnetic p h enomena I t gives for instance no connection
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ILLI NOIS
4
EN
G I NE E RI N G
E
X P E RIM E NT STATIO N
between t h e elasti c and magnetic pheno m ena of fer r omagnetic s u b
stances I t is possible t h at even the foundation of t h e present theory
will undergo c h anges b u t t h e experimental facts w h ich h ave been con
s i d er ed in developin g t h e p r esent form of the t h eory will still be of val ue
I t seems advisable th erefo r e in order to gi ve to t h is b ulletin a more
permanent value to lay considerable stress on t h e expe r imental methods
applied by W eiss and his followers and to give also the results obtained
since the time when t h e classi cal book on magnetism was wri tten by
Ewi ng
Th e first part of the present bul letin conta ins therefore the essential
features of t h e electron t h eory o f magnetism t h e second and the th i rd
parts give an account o f the properties of ferromagnetic c rystals w h ile the
fourth part gi ves f urther e xperimental evi dence in favor of t h e electron
t h eory of magnetism toget h er with an acco u nt of some of t h e
phenomena for w h ic h the t h eory in its presen t fo r m fails to give a satis
factory explanation
2 K i nds of M agn eti sm
B odi es are divided from t h e point of
v i ew of the i r magneti c properti es in to t hr ee distinct groups :
f erro
magnetic paramagnetic and diamagneti c
Under f e r romagnetic s u bstances are classed those substances o f
which the intensity of magnetization at saturation is of t h e same order
of magn i tude as t h at o f iron T hey are iron nickel cobalt magnetite
p yrrhotite and the H e u sler alloys ( which consist of copper manganese
and aluminum )
P ar amagnetic s u bstances are those wh i ch while they become mag
A mong para
n e t i z e d i n the direction of the field do so ve r y feebl y
magneti c bodies are found oxygen ni trogen dioxide palladium plati
num manganese and t h e salts of various metals
Diam agnetic bodi es which incl u de the g r eater number of all simple
and compo und bodi es h ave p r operties ve ry di ff erent from those of either
f erromag netic or paramagnet i c bodies W he n placed in a magnetic
field t h ey become Slig h tly magnetized in a direction opposite to the
di rection of t h e field
Some bodies such as i ron w h en heated Show a grad ual trans i tion
from the f erromagneti c to t h e paramagnetic state or vi ce versa but as
yet no body with the exception of tin has been f o u nd which by change
o f physical conditions will pass f r om t h e diama gnetic to t h e param ag
neti c state
Within the last decade a la r ge amo u nt o f work has been done on
t h e ferromagnetic substances magnetite h ematite and pyrrhotite
wh i ch are f ound In nature i n c rystals of such size and shape as wi ll per
mit o f a study of their magnetic prope r ties H owever it is not possible
to obtain comprehensive results wi th magnetic cryst al s mer e ly by adap t
in g to them the methods t h at have been applied wit h success to
isotropi c substances
I n the case o f isotropic s u bstances t h e intensity of magnetization
h as always the same direction as t h e field and as in all directions t h e
behavior is the same i t is sufficient to apply to the substan ce a ma gnetic
field Of any direction and to determine t h e i n t e n s ity of magnetization
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WI LL IAMS
E L E C TRO N THEOR Y O F MA G NETISM
5
correspondi ng to each of its values I t is true that i t is nec essary to take
into account the di fferent s econdary phenomena hysteresis retentivity
etc which influence considerably the characte r of the principal phe
.
.
no
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,
,
men a
.
For allotropic substances it i s necessar y to consider besides the
magni tude of t h e field and of t h e intensity of magnetization their di re c
tions which in general are di ff erent for t h ese two quantities I n place
of a function of one variable there will be a system o f three f unctions
of three variables if one represents the field and the magnetization by
their components A s t h e secondary p h enomena are as complicated
as i n i sotropi c substances it is easy to see t h at t h e complete investiga
t i on of the magnetic properties of a c r ystal constitutes a ve r y diffic u lt
problem
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r
E
e
t
o
s
l
c
n
f
—T h e
electron th e o r y of magnetism
supposes t h at the atom i s made up of positive and negative electric i ty
t h e latter always occurring as exceedingl y small particles called electrons
and that t h ese elect r ons whenever they occur a r e always of the same
size and always carry the same quantity of electricity I t i s this p ec ul
iar way in whic h t h e negative electricity occurs bot h in the atom and
when free f rom matter t h at gives to the theory its name An electron
”
is then an atom o f electr i city or the Smallest amount o f electr i c i t y
wh i ch can be isolated T hese elect r ons are given o u t by al l bodies at a
su fficientl y hig h temperature accompanyin g the p h enomena o f radia
tion These electri cal particles leave the metals and other substances
under the action of vi sible and inv i sible lig h t R oentgen ray s radium
ray s etc The y appear i n most of t h e radioactive processes and in
chemical reactions T hus when a metal is oxidized it emits electrons
Whatever be the source o f the elect r on its electrical char g e has always
been found to be from
to
absolute electro
X
X
static u ni ts Th e mass of the electron is about
times smaller than
the mass o f the atom o f hydrogen which is the li g htest chemical element
and which h as a mass of about
grams Th e mass o f the
X
electron is not ord inary che mi cal or ponderable matter but apparent or
electromagnetic mass and i s due to the electromagnetic field whi c h
surrounds the e l ectron in motion T h e radius o f the electron has been
found to be
cm To i llustrate the size o f an electron as
X
compared wi th an atom i magine a hydro gen atom increased in volume
to that o f a large cathedral t h e electron being inc r eased proportionally
T hen the volume of the electron would be that of a fly fly i ng about in
the vast space I n spite of t h is min u te Size of the electron or rather
because of this minute size t h e actions of t h e elementary c h arge are
surpr i sin gly great T hus t h e electrical field on t h e surface o f the elec
15
12
or 1 0 times stronger t h an any whi ch we are able to
tron is
x 10
produce by artificial means
3
.
r
e
t
es
o
i
p
Gen er a l
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An electri c current i n a metal consists of electrons in motion , wh i le a
current through electrolytic solut i ons and t h rough gases at o r di nary and
reduced pressures consists of posit i ve and negative ions A s t h e pres
sure i n a dischar g e tube becomes smalle r the electrical current is car
.
,
ILLI N OIS
6
EN
G I NE E RI NG
E
X P ERIME NT STATIO N
ried more and mo r e by free electrons or cathode rays whi ch by t h ei r
impact on a solid Obstacle gi ve rise to R oentgen rays
T h e electron t h eory aims to e xplain all the p h enomena of lig h t
electricity and magnetism and in many cases it IS the only t h eo r y t h at
is able to exp lain t h e great var i ety of p h ysical phenomena T h e
electron forms a part of eac h atom of the u Iij v erse and it plays an i m
portant role In t h e che mi cal theories of matter I t IS probable t h at the
forces of affinity in t h e chemical r eactions can be reduced to electrical
forces between t h e electron and th e positive charge of the atom T hus
c h emical p h enomena are drawn into the circle of t h e electron t h eory
Even mec h ani cs the oldest branc h of exact natural science is aff ected
by t h e discovery that the mass of the electron depends on its velocity
so that Newton s eq u ations of dynami cs t h e b asis of t h e p h ysical
*
science have to be Slightly c h anged
Finally in the radioactive
transformations in which one element i s transformed into anothe r
element the elect ron plays an essential r61e
An electron in motion is surrounded by a magnetic field
When
an electron moves in a closed orbit it is accompanied by a permanent
magneti c field identical with that o f an elementary magnet A mpe re
considered the elementary magnets of iron as due to electrical current s
flowi n g in closed molecular orbits wit h out resistance I f we replace
these currents of Amp e re s theo ry by electrons moving i n closed orbits
we have the fundamental idea of the electron theory of magneti sm
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Elec tr omagneti c For ce Due to a n Elec tr on i n
Moti on
’
Rowland s
experiments Show that a moving elect r on is surrounded by a magneti c
field C onsider a small element dl Fig 1 o f the conductor carryi n g
the current i
Let m be t h e magnetic pole and (b the angle between t h e
direction of the current and t h e radius r T h en the electromagneti c
force produced at m by t his element is
mi dt sin
4
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dK
_
2
T
Su ppose
m
1
(1)
Suppose
now t h at t h e c urrent i is that due to an electron moving wi th
a velocity v w h ere v is not greater than one t h ird that of the velocity
o f l i ght I f the electron moves th r oug h t h e distance dl in the time dt
we will have
,
,
.
dl = vdt
.
g i n eer i n g purpo se s a n d fo r t h e mo t i o n of t h e h e a v e nl y b o di es t hi s
ch a nge Is t o o small to b e c o ns id ere d I t is o nl y wh e n t h e v e lo ci tyy of t h e mas s
a ppr o a ch es I n m agn i t u d e t h e v e lo ci t y of l i gh t t h a t t h e e ff e c t 18 app re ci a b l e
Fo r
all en
.
.
WIL L IAMS
L CTRO N THEORY
E E
FI G
Substituting ( 2 )
.
OF
MA G NETISM
1
and ( 3 ) in ( 1 ) we get
)
ev sin <1
dK =
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
I f we consider a sphere o f radius r Fi g 2 with an e lectron at the
center moving w i t h a velocity v the magneti c fo r ce at t h e po i nt m W I l l
be from equation ( 4 )
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FI G
.
2
This
is t h e same for all points on the surface of t h e sp h e r e w h ere d)
is the same T h erefore t h ere is a circle around t h e sp h ere where t h e
magneti c f orce is constant T h e direction of t h e magnetic f orce is at
right angles to the motion of e or in a plane perpendicular to t h e x—
axis
A s defined before a diamagnet ic body is one
K Di ama gn eti sm
wh i ch when placed i n a magnetic field becomes slig h tly m agn et i z ed in
a direction opposite to t h at o f par amagnetic substances T hus a
cylindrical diamagnetic body will set itself perpendi c u lar to a magneti c
field
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ILLI NOIS E NG I NEERI NG
8
E
XP E RIM E NT STATI O N
in any atom an electron of mass m and charge e Fi g 3
mov in g wi th a velocity v in an orbit of ra d ius r t h e plane of which is
pe rpendicular to a magnetic field of intensity H I n the absence of the
magneti c field t h e centri fugal force on the electron Is Opposed b y elast i c
forces, wh i ch we will suppose to be di rected toward the center of the orbit
and to be proport ional to i t s radius T hen
C onsider
,
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,
.
mu
2
7
where f is t h e force of attraction toward the cente r when
r = 1 cm
.
FI G
.
3
No w apply the e xternal magnetic field , and the electron i s subj ect
to a f orce at right angl es to the field and to the di rect i on o f its motion
that is alon g the radius o f its orb i t Th e magni tude of this force is
found as ab ove b y appl yi n g the f undamental l a w of electromagneti sm
As be fore we have
mi dl sin (b
,
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,
.
m
i
l
?
r
li n ¢
Hcv Si n 4)
If the an gle ¢ =
the force whi ch the m agneti c field exerts on the
e l ectron mo vi n g throu g h the di stance dl is
dK
Hcv
’
A ppl yin g A mp e re
s rul e we see that i f t h e electron i s n eg at i ve l y
charg ed the force is di rected outward al ong the rad i us Since t h e e l ec
t ro magn et i c f orces actin g on the electron are perpendi cul ar to the di r ec
tion o f i ts motion the ma gnitude of its velocity v is unchan g ed b y the
action of these forces
Denoting t h e period of the n ew o rbit produced when the fie l d H i s
acti n g by T and its radius by r we have
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,
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’
’
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fr
’
— H ev
WILLIAMS
( 6)
-
L C TRO N TH E OR Y O F MA G NETISM
9
E E
( 5) gives
T h erefo r e
T he r efore
Substituting ( 8)
and ( 9 ) in ( 7)
471 m
-
2
m
2
7r
4
__
T
’2
T
2
w h ence
T his
may be written
He
2 7rm T
’
1
( 0)
No w the diamagnetic p h enomena a r e ve r y small t h erefo r e we can wit h
,
out appreciable error put
T
T
’
’
Substit u ting
t h ese values
2T
TT
T
in ( 10) we have ,
2
H
6T
’
—
—
T T
2
4 7rm
(1 1)
I n order to calculate t h e intensity of t h e induced magnetization let
us replace the revolving elect r on by an equivalent cu rr ent flowing in
a circuit coincident wit h its o r bit Th e st r en gth i of t h e eq u ivalent
cur r ent is given by
,
.
7:
1
6
T
No w the magneti c moment of a ci r c u it of a r ea A carryi ng a cu rr ent i is
given b y
M1
[1 7
4
ILLI N O IS E N G I N E E R I NG
10
In
t h e case of an
u
E
XP ERIM EN T STATIO N
ndistu r bed elect r on r evolving in an at o m
e
“
1
T
A=
1rr
and
wh ere r is t h e radius Of the orbit
T h erefo r e t h e moment of t h e equivalent
2
.
e
lementa ry magne t
e
=
T
Wh en the magne t ic field H is applied t h is becomes
M1
=
e
T
A M1
M1 M1
be the induced magneti c moment for one revolving electron
T herefore
,
r
—
we have N electrons revolving
moment per unit volum e is
If
A
M
=NA
In u
.
,
T
nit volume the induced magnetic
,
r
M 1 = Ne 1r
2
T
r
I
T
-
’
From ( 8)
From ( 9 )
f
T
Substitute
( 13)
2
f
v
T
’
_
1
2
47
and ( 1 4 ) in ( 1 2 ) a nd
‘
2
Ne 1( v
A M
T
(
,
4 19
T
_
F r om ( 1 1 )
“
)
.
’
—
T T
T he r efo r e
( 1 5) become s
Ne
vHT
? 2
Subst i tute
( 13)
2
in ( 1 6 ) and there is obtai ned
4m
is the induced magnetism per uni t volume d ue to
magnetic field H T h e r efo r e A M is propor t ional to H or
—
A M
kH
T h is
,
.
,
whe r e
[
is defined to be the diamagnetic s u sceptibility
.
an
external
ELE C TRO N TH E OR Y O F MA G NETI SM
W I LLI A Ms
11
the quantities on t h e right hand side of this equation are essential
l y positive h ence A M is negative and the body is diama gneti c whatever
t h e sign of the electronic charge e T h us all substances possess the
diamagneti c property a c c o rdin g t o the above t h eo r y Some substances
are also paramagn etic that is On e p h en omen on is superimposed on
t h e other
I n the above calculations i t has been assumed t h at all the electroni c
o rbits are so arranged t h at t h eir axes are in the direction of the magneti c
intensity of t h e inducing field an d t h eir planes perpendic ul ar to their
direction I t would be more accurate to assume t h at the axes are
dist r ibuted in all di r ections H owever t h e c h ange introduced by this
assumption would consist onl y in multiplying the right hand side of the
last equation by a proper f rac tion whose value is not very d ifferent f r om
unity
M ultiplying numerator and denominator of t h e above expression
for k by m t h e mass o f an electron then
Al l
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'
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,
,
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,
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,
,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
w h ere p is t h e density of the electrons or the mass of the electrons per
unit volume I t is seen that t h e effect produced contains as one f actor
,
.
,
the square o f the rat i o
i
,
and since this ratio is at least a thousand times
greater for t h e negative electrons t h an f or the posit i ve corpuscl es it
is t h e f ormer whic h are present in all substances t h at play the e ssential
rO
l e in the production of diamagnetism
6
I n t h e case o f water o f whi ch the diamagneti c constant is 8 X 1 0
the density p of the negative electrons whi ch constitute only a part of
the molecule i s less than unity and probabl y greater t h an
the
ratio o f the mass of a ne g ative electron to t h at of t h e atom of hydrogen
Th e ratio e/m is kno wn and i s
,
,
.
-
,
.
,
,
,
.
7
absolute elect r omagneti c units
Substituting the above values in eq u ation ( 1 7
) we get using
.
r
Substituting 1 2 000 for
p
c
,
m
>2
for
p,
.
we get
r
1
X
c
m
.
T herefore
2 X
r
E
determinations i ndicate that r act u ally lies wit h in t h ese
1i m
its
xperimental
A s the electronic orbits are considered to belong to the interior of
the atom , w h ich is not a ff ected by tempe r a ture , we should expect that
.
t h e diamagnetic susceptibility does not depend upon temperature
C urie s results i ndicate that in general this is the case although d u
B ois and H onda fou nd a l ar g e number of except i ons
Also the position
.
’
,
,
,
.
12
I L LI NOIS E NG I N E E RI NG
E
X P ERIME NT STATIO N
o f t h e lines o f the spectrum w h ich are due to the revolution of elect r ons
Ins I d e the atom I S almost entirely in dependent o f the temperature
Equation ( 1 6 ) above may be interpreted simply as follows
Th e
equation
,
,
.
.
H Ne r
4m
z 2
expresses the i ncrease in the magneti c moment per uni t volume whic h
contai ns N electrons For one e l ectron the increase in the magnetic
moment 1 8
,
.
T hi s
may be written
Ho A
2
_
4 7rm
4 7rm
if the electron describes a circ u lar orb i t whose area is 7r7 Th e chan ge
o f the magneti c moment o f the electronic orbit i s determined by the
flux o f m agneti c induct i on H A which i s produced by the external field
pass i n g th roug h t h e orbit
T h is is exactly the result that is obt ai ned by merely applying to
the electronic orbits the elementary laws o f induction for the elementary
circui ts Let us suppose that the resistance o f the orbit is zero and
the self inductance equal to A L I f i i s t h e cur rent the equation for
the induced e m f gi ves
d ( A Li )
2
‘
.
.
.
,
-
.
.
.
,
.
dt
whence
A
if H is zero in t h e beginning
A
.
M1
HA
Li
A
:
A1
4 1rm
Substitut ing the val u e of H A given by
A
3
At
2
A
M
I t is sufficient to take
Wh ence s in ce
the apparent self induction is proportional to th e mas s of t h e
electron and to the square of its radius and inversely p r oportional to
the square of the charge T his self induction wi ll identify itself wit h a
real self induction corresponding to t h e creat ion of a magnetic field by
the electroni c orbit only if the inertia o f t h e electron is w h olly of elect r o
ma gneti c origin
T hus
-
,
-
.
-
,
.
WI LL IAMS
L C TRO N THEOR Y O F MA G NETISM
13
E E
I f we assume that the sel f i nduction o f the current is due to the
electromagneti c inerti a of the electron
-
,
,
wh ere
Wh enc e
6
2
m4
2 ‘2
1r 7
T
T
2
2
3
4 1t e
3
w h ich corresponds to the value of
L
2
f ound above
.
Th e
diamagnetic mo di fication corresponds to a slig h t change in t h e
magnetic moment of the ori ginal circuit We have seen that this mag
netic moment has the value
.
Mt
= Ai =
A
T his
ma gnetic moment , owi ng to the variation of t h e magnetic field
undergoes a chan g e
,
He r
4m
2 2
Th e
relative variation o f the ma gnetic moment is
A
l
[g
M1
_
H Te
4 7177
7
,
which i n the cas e o f all d i amagnet i c bodies is very small
.
Now
2
—
7
7
o f the order o f 1 0 for negative electrons and still l ess f or pos i t i ve parti cles
T must necessar i l y have a value lar g er than that o f the per i od o f li g ht
15
wh i ch is o f the order o f 1 0
f or if the time o f vi brat i on were so small
the magnet woul d be a spontaneous source o f li g ht and permanent
magnetism would be i mpossible Let us assume that T is of the order
4 2
10
wh i ch corresponds to the l on g est wave l en gth that h as been i sol a
.
-
,
,
.
,
ed i n the spectrum of mercury vapor
T hen
.
i n order to make
A
;
l ‘1
M1
No w we are
approach uni ty H needs to be o f the order o f onl y 1 0
5
able to produce fields o f the order o f 1 0 whi ch , on the above assu mp
ti on wou l d cause a change in the magnet i c moment of the di amagneti c
substance o f one tenth o f that o f its origin al val ue
6
.
,
,
,
.
Magneti c
Energy
I n order to c al cul ate th e ener gy requi red
to produce the diamagnetic mo di fication , l et us assume an electronic
orbit wh i ch i s without mo tion dur i ng the establishment o f the magnet i c
field H Th e ma gneti c f orce is perpendi c u lar to the plane o f the orbit
and there f or e produces no work I f there i s a displacement dl al on g the
6
.
.
.
.
ILLI N OIS
14
o r bit ( Fig
.
4)
and
EN
G I N EERI NG EXPERIM E NT STATIO N
electri c fo r ce is E t h e work done
d W1 = c Edl cos a
e ( E dx
E, dy
E dz)
th e
is
,
z
r
Wl
=
f
e
c
( H dx
B ld g 4 E dz )
!
x
z
FI G
.
.
4
During the time T of one revolution of the electron w h ic h is of the
order of
seconds a time extremely S h ort in comparison w i th the
time necessary for the establishment of the field by t h e creation of
currents or the displacement of ma gnets E E E will not change
appreciably and the work W may be calc u lated by an application of
Stokes s T h eorem
,
,
,
x ,
,
’
.
W1
q
ff
( E dx + E dy + E d2
r
y
d Ez
ax
)
cos ms
e
> ]
cos
c OS n y +
where n is the normal to the su r face
I nt r oduce M axwell s eq u ations
nz
dA
.
.
’
,
aEz
1
c
(a
at
1
_
c
at
1 aH ,
c
at
6 Ex
(
“
1
1 22
(
_
62
_
6 E2
6r
a
(6
8E
23
6 11
)
>
)
the r at i o b et ween electrical ene r gy expressed in electrostatic and
electroma gnetic units is al r eady included in E E and E o f equation
t h erefo r e it S h ould be omitted from equation ( 2 1 ) before su b st i t u
tion Substituting ( 2 1 ) in
we have
’
0,
,
x,
.
aH ,
at
cos
nx +
6H,
at
,
E L E C TRO N TH E OR Y O F MA G NE TI SM
W ILLI A M s
c
os n x +
'
=
n
n
z
H
o
s
c os
y + zc
y
H
15
H
T h e refo r e
Si
nce
dH
18
E
Th e
t h e same for all po i nts of the area A
.
wo r k done by t h e i ncreasin g magnetic field
time
e
__
_
T dt
l
I
I
§
dt
_ _
T herefore
Th e wo rk do n e
‘
in t h e time dt is
M 1 dH
d Wl
w h ence
M l dH
( 22)
where M 1 is t h e magnetic moment of t h e elec tronic current in the di rec
tion dH T h is work done during t h e establishment of the magneti c
field H by the current or by t h e displa cement of a magnet is tran s
formed into ki netic or potential ene r gy of the elect r on which produces t h e
electroni c current I t represents the potential energy between the
revolvin g electron and the magneti c field H T his t r ans f ormation o f
energ y accompanies the production of the diamagnetic state
I f t he initial magneti c moment of t h e revol v i n g electron i s equa l to
M the external field being zero the magneti c moment under the action
of the field wi ll be
.
,
,
,
.
.
.
,
M +
O
A
M 1 = M0
_
From ( 22 )
j;
H
M
(
M H+
O
O
6
2 2
11
8m
2
I f the molec u le has N o r bits the resultant initial moment M will be
M MN
whence
,
O
HN
8m
z 2
e r
MH
2
I f t h e body is purely diamagneti c M is zero and we h ave simply
,
W
H
2 2
e r
8m
2
N
IL L I NOIS
16
EN
G I NEE RI N G EXPERIME NT STATIO N
T h is
is t h e ene r gy b r o u g h t into play in purely diamagnetic p h enomena
I t is al ways present even in t h e case w h ere t h e body is pa r ama gnetic
but is small in comparison wi t h t h e energy of the latter
W e have seen t h at in all cases t h e creation
7 P ara magneti sm
of an exterior magnetic field modifies the elec troni c orbits by polari zing
diamagnetical ly all t h e molecules T his phenomenon is manifested
only i n the case where the resultan t moment of t h e electronic orbits is
ze r o when the matter is diamagneti c in the ordinary sense of the word
I f t h e resul tant moment is not zero upon the diamagnetic phenomena
is s u perimposed anot h e r p h enomenon due to the orientation of the mol e c
ular magnets by t h e external field Th e substance is then paramagnetic
if the mutual action between molecul ar magnets is negligible as in the
case of g ases and of solutions and fer r omagnetic i n the case where the
mutual actions play the essential r61e A S soon as the paramagnetism
appears it is a s a r ul e enormous in comparison wit h t h e diamagnetism
and therefore completely conceal s it Th is explains t h e absence of
continuity bet ween pa r amagnetism and diamagnetism ; paramagnetism
may not exist ; but if it exists it h ides completely the diam agnetism
T herefore substances whose atoms have their electrons in revolution
in s u ch a way that the i r e ffects are additive are paramagnetic T h e
atoms o f such substances may be looked upon as elementary ma gnets
Th e ener gy o f such an elementary magnet may be represented by
W
MH cos a
where a i s the an gle that the magnet makes with t h e magnetic field H
If a magnet i c field acts on a paramagnetic substance in a gaseous
state and if the molecules have no thermal a gitation they wi ll rearrange
themselves in a direction parallel to t h e magnetic field B y vi rtue of
this rearrangement they will like a fall ing body lose their o ri gi nal
potential energy and acq u ire ki netic energy
Le t us cons i der a p a ramagnetic bod y i n the
8 Cu ri e s Ru le
g aseous state such as o xy gen whose molecules have a magnet i c moment
M Th e molecules of such a body will tu rn when under the influence
o f a uniform ma gneti c field H in such a way as to place the i r m a gne tic
ax es paral le l to the field Let us calculate the m agn eti c moment pe r
un i t vo l ume af ter the rearrangement has taken place
If the ma gnet i c moment makes an an gle a Wi th the di rection of the
uniform field H then t h e molecule posses ses a potential energy equal to
— MH cos a
Th e i ncrease of this potent i al energy is derived from the kinetic ener gy
of rotation of t h e molecules in t h e same way in wh i ch the potential
energy of gravi tation of the molecules of a gas is de r ived from t h e kinetic
energy of translation
when
it
is
ris
i
ng
Th e res u ltant inequal ities i n the
“
dist r ibution of kinetic energy between t h e orientations and the degrees
of freedom of t h e molecules , rotati on an d translation are not compatible
with thermal equilibrium A rearrangement takes place at t h e instant
of the collisions durin g whi ch t h e magneti c polarity appears and t h e
ene r gy
— H dM
of t h ermal agitation turns into potential ene r gy o f magnetization
.
,
.
.
.
,
.
,
.
,
.
,
,
.
,
,
.
.
,
,
.
,
.
.
,
.
,
,
.
’
.
.
,
,
.
,
,
.
.
,
.
,
.
.
ILLI N OIS
18
EN
G I N EE RI NG EXPERIM E N T STATI O N
C omparing ( 24 ) wit h
b i l ity ,
we see t h at k the paramagneti c su sc ep t i
must va r y inversely as t h e a S l ut e temperature t h at is
,
BfT
t h e constant A
k
,
called C u r ie s R u le and
is sometimes called
constant W h en this rule was first ven out by C urie it was
t h ought to be gene r al but Since then some s st a n c es have been f ound
in whic h temperature does not aff ect the diamagnetic susceptibility k
0 act u ally increases with inc r ease of temperature
and others i n whic h 7
9 La n gevi n s Th eor y
T h e followi ng comparison which is due to
*
Langevin
wi ll make clear t h e t h eory whic h precedes I ma gi ne a gas
cous mass contained in a given receptacle Fig 5 wit h out being subj ect
to t h e action of gravity T h e molecules will distribute themselves in
such a manner t h at the density of t h e gas will be t h e same at all points
which is similar to t h at which takes place in t h e case of a magnetic g as
such as oxygen in t h e absence of an exterior magnetic field w h en t h e
molecules h ave their axes distrib u ted unifo r mly in all di r ections Fig 7
T his is
’
C urie s
’
,
'
fib
.
,
,
,
.
’
.
.
,
‘
,
.
.
,
.
,
,
,
.
,
FI G
.
FI G
5
.
6
.
If the force o f gravitation is applied , Fig 6 the molecul es will
acqu i re an acceleration directed toward the base and i n the absence of
mutual collisions each molecule will have a greater velocity at the
botto m than at t h e top o f the vessel B u t th i s ineq ual i ty o f velocity is
incompatible wi th thermal equil i bri um and a re a rrangement w i ll take
place due to the mutual collisions af ter wh i ch the distribution which i s
established is g iven by the formula o f barometr i c pressure T h e center
o f gravity i s lowered and i n order to m ai ntain the g as at the initial
temperature it is necessary to remove f rom i t a quantity of heat equ iva
lent to the product o f the mass of the gas b y th is loweri n g o f the center
o f g ravity , or equ i valent to the loss o f potential ener gy O ne deduces
from a t h ermodynamic reasoning analogous to that gi ven above that
this loweri n g o f the center of gravi ty is i nversel y proport i onal to the
absolute temperature
A f ter the rearran g ement i n a mass of g as of uni form temperature
the distri but i on o f the mo l ecules takes place between t h e var i ous re gions
in a manner such that the molecules wi ll be more numerous Wh ere the
.
,
,
,
,
.
,
,
.
,
,
.
,
.
,
‘
P
.
Lange vin , Ann de
.
Ch em
.
et
de
Phys
,
Ser 8 ,
.
Vol
.
5, p
.
70
,
1 908
.
—
E L ECTRO N THEOR Y O F MA G NETISM
W I LLI A Ms
19
potential ener gy is t h e least t h at is to say at the lowest points in t h e
case of gravity B oltzmann h as calculated t h e di stribution by g en erali z
ing the law of barometric pressu r e Th e ratio o f the densities of the
gas in two points between whi c h t h e potential ene r gy varies by W is
,
,
.
.
6
where e is the base of Nape r ian logarit h ms T the absolute tempera
ture of the gas and R t h e constan t of t h e equation of a perfect gas a
constant suc h that according to t h e ki netic theory RT represents two
thirds o f the mean kineti c energy of translation
T h e change when the magneti c field H is applied to a paramagnetic
gas such as oxygen Fi gs 7and 8 is t h e same as in the case o f gravity
except that here we have a rotation of the axes of t h e elementary mag
H ere too t h ere is a loss of poten
nets which assume the direction o f H
tial energy and a gain o f heat t h e rise in temperature bein g due to the
t h ermal a gitation o f the molec u les which produce a certain amount of
h eat due to the i r rotat i on
,
,
,
,
.
,
.
,
.
,
.
FI G 7
FI G 8
T h e dist r ibution of the molecules between t h e va r ious o r ientations
will be determined by t h e stati c equilibrium which will establish itself
u nder t h e supe r imposed influence of the potential magneti c energy
M H cos a and the energy RT of t h ermal agitation the molecules being
f r om preference oriented in t h e direction of least potential energy t h at
is to say , wit h t h ei r magn e tic axes in t h e direction of t h e field I f one
conside r s t h e distribution o f th e magnetic axes between the various di
r ections the density per unit of solid an gle will vary from one direction
to the other proport ional to
.
.
,
,
,
,
-
.
,
6
all directions being equally probable i f M or H = 0 Th e number o f
molecules w h ose axes are directed with in t h e solid angle da Fi g 9 wi ll be
ME c o s
.
,
.
,
a
.
where the element da
field
: K6
RT
dw
is a zone of aperture da around t h e direction of the
dn j
'
dw = 2 7r Sin a da
.
a
.
varying from
0
to
7
r
.
ILLI N OIS
20
EN
G I NEE R I N G
T h e r efo r e
II H
.
dn
Th e
= Ke
c os
E
XP ERIM ENT S T AT I O N
a.
RT
sin a da
2 7r
total numbe r of m olec u les per unit vol ume N will be
N = 2 7r
S i n a da
wh e r e
cos
a
=x
— S in
N
a
da
2 7rK
sin h
a
T h erefo r e
sin h a
whence
total magnetic moment of t h e N molecules is evidently dir ected
pa r allel to the field and is equal t o the s u m of th e proj ectio ns of the
component moments on t h is direction Fo r the u nit of volume supposed
to contain N molecules this resultant moment represents t h e intensity
of magnetization I
Th e
.
,
.
[
M cos
Substitute
for
dn
a
dn
.
its value given by equation ( 26 ) and
M cos aK e
a
co
”
2T
sin
a
T h erefore
we
:
do
da
—
W I LLIA M s
L CTRO N TH EORY O F MA G NETISM
21
E E
FI G
we
dx
.
9
2
t h e r efo r e
4 7rM K
I
Su bs tit u te
th e val u e of K given by eq u ation ( 2 7) and
a
cosh
1
I = MN
<i
s nh
)
5
a
For a given n u mbe r of molecules N I is t h e r efo r e a f u nction solely of a
that is of H T in acco r dance wi t h t h e r esu lts given by t h ermo dy
n amI c s
,
,
.
.
Th e
:
81
231 3 é)
expression
1
,
vanis h es with
,
whic h is p r oportional
a,
to H and tends towa r d u nity wh en a increases indefinitely th e intens i ty
of magnetization app r oac h ing the maxim u m value Im = MH which cor
responds to satu r ation t h at is t h e condition w h en all the molecula r
magnets are oriented paral lel to the magneti c field
T h e c u rve of magnetization of a magneti c gas at constant tempe r
ature OD E Fig 1 0 r epresenting I /I m as a f u nction of a t h at is as a
f u nction of H wo u ld be represented by t h e expression
cosh a
1
sin h a
a
H
T
)
f(
I t is evident t h at t h e magnetic s u sceptibility will not be constant
and I will be propo r tional to H only for values small compared with
u nity
Developing equation ( 28) in series we have
,
,
,
,
.
,
.
,
,
,
,
.
.
I
c osh a
1
1
2
“
“
3
+
4
2
( 9)
454 2
sin h a a
3
go
T aking acco u nt only of the terms of t h e fi r st degree with respect to
we find
a
IL L I N OIS
22
EN
G I NE ERI NG
wh e re
E
X P E RIM E NT STATIO N
MN
2
SRT
t h at
is t h e paramagnetic susceptibility I s inve r sely p r opo r tional t o t h e
absolute tempe r ature w h ic h ag r ees wit h t h e r u le obtained expe rimental
l y by M C urie
I f all the molec ul es we r e o r iented parallel to t h e field t h at I s if t h e
body we r e magnetized to the point of s atu r ation th e intensity of
ma gnetization wo u ld be
I m = MN
C ombining t h is wi t h t h e expression above we get
2
2
2
I
MN
,
.
.
,
_
,
,
,
19
35
7
SRTN
) being t h e pressure of t h e gas at which 10 i s measured
7
6
C urie found for oxygen at the standard pressure 1 0 and at a tempe r
ature Of 0
.
°
per u nit of volume
.
Im = k >
< 3p
2
w h ence
I
T his woul d correspond for liqui d oxygen which is at least
more dense t h an the gas to a maxi mum magnetization
,
500
times
.
,
I
= 3 25
wh i ch is not very much smal ler t h an t h at o f i r on I n fact liquid oxygen
possesses suc h intense magnetic prope r tie s th at it forms a liq u id b r idge
between t h e poles of an electromagnet
From the above one i s able to obtain the order of magnitude of t h e
quantity a under ordinary experimental conditions
M H M NH I H
.
,
.
,
.
NRT
RT
_
NR T
B ut NR
is the constant of a perfect gas for t h e uni t of volume w h ic h is
s u pposed to contain N molec u les Under the no r mal conditions fo r
w h i ch I m has been calc u lated one wi ll have
.
,
NRT =
“
= 1 06c
p
g 8 u ni ts
.
.
T he r efore
x 10
a
.
H
.
.
For a field of
u ni ts a will be
and one would still be
near the origin of t h e curve of magnetization Fig 1 0 w h ere t h e curve
coincides with the straig h t line I n order to make a 1 t h e region where
the curve commences to leave t h e straigh t line it wo u ld be neces sary
to h ave fields greater than
whic h we are not able to produce
O ne sees then in the ferromagneti c substances t h e i mport ance of
the mutual actions between molec u les w h i c h alone makes possibl e mag
netic saturation For the same exterior fields magnetic satu r ation is
still far removed in t h e case of pa r amagnetic substan ces whe r e mutual
actions are not appreciable
.
,
,
,
.
,
.
,
,
.
,
.
WIL L IAMS
E
L E C TRO N THEORY
OF
MA G NE TISM
Fi g 1 0
.
F r om t h is point of view C u r ie s comparison of the transition b e
tween pa r amagnetism and fer r omagnetism to the t r ansition between
gaseo u s and liq u id states w h ere t h e mutual actions play an essential
r ole is pe r fectly j u stifiable I n t h e pure gaseous state as in para
magnetism each molecule reacts individ u ally by its o wn kineti c ener gy
against t h e exterio r fo r ces o f pressure and magneti c field
’
,
.
,
,
,
.
Elec troni c 0 r b i t
I f one assumes th at the magnetic moment
M of one oxygen molecule is due to only one electron of c h arge eq u al to
t h at of t h e atom of hydrogen obtained in electrolysis movi ng along a
ci r c u la r o r bit w h ose radius is equal to the radius of t h e molecule of air
cm one can calc u late t h e velocity of t h e electron along t h e
X
orbit W e have
10
.
.
,
,
.
,
.
Im =
M N = Ne
t h e p r oduct Ne is given by elect r olysis since
atom of h yd r ogen Unde r no r mal conditions
B ut
,
e
is t h e c h a r ge of t h e
.
Ne
electrostati c un i ts
elect r omagnetic units
.
T h erefore
whence
v
2 X 10
8
c
m per
.
sec
.
I LL I NOIS
24
EN
G I NEE RI NG EXPERIM ENT STATIO N
Suppose
t h e revolving negative c h arge e Fig 1 1 to be att r acted
toward the cente r of its o r bit by an equal positive c h a r ge T h en t h e
centrifu gal force equals th e centripetal force t h a t is
.
,
,
.
,
mv
2
2
e
6
mr
wh e r e
is
e
m e as u r e d in elect r ostatic u nits
X
X 10
X
e
‘
r
m
.
8
0
m
.
gra m
.
T h erefo r e
X 10
X 1 5 X 10
16
X 10
8
X 1 0 cm per sec ,
‘
28
8
-
.
v
or
whic h is in accordance wit h t h e value fo u nd by th e above met h od
I t is a rema r kable t h ing t h at th e magneti c moment of t h e molecule
of oxygen can be d u e to t h e re v olution of a single el e ct r on T h e same
is p r obably tr u e in t h e case of i r on of whic h t h e maxim u m magnetiza
tion is as we have seen of t h e same order of magnit u de as t h at of oxy
gen T h e other electrons in t h e a tom neut r aliz e e ac h ot h e r as in t h e
p u rely diamagnetic body
T h e pa r amagnetic electron also p r obably plays a part in c h emical
actions t h e number of elect r ons of a molecule acting being eq u al to the
valence T he r efore the pa r amagnetic properties of an elem e nt c h ange
with change of molecular combinations w h ile diamagnetism seems t o be
an internal and inva riable property of the atom
.
.
.
.
,
,
.
.
,
.
,
,
.
M olecu la r Fi eld of Ferr oma gneti c S u b sta nces
Weiss Hy po th e
sis :Each magnetic molecule i n a fe rr omagneti c substance is subj ect to
a uniform intrinsic magnetic field NI p r opo r tional to t h e intensity of
magnetization I and acting in t h e same di r ection T h is mole c u la r mag
neti c field is due to t h e action of th e neigh bo r ing molecules I t may be
called t h e internal magneti c field in compa rison wit h th e internal
pressu r e of V o n der W aal s equation T h is field added to t h e exte rnal
field accoun t s for t h e g r e at intensity of magnetization of ferromagnetic
bodies by means o f t h e laws of paramagnetic bodies in t h e same way
as t h e internal pressure added to t h e external p r ess u re acco u nts fo r
th e g r eat density of t h e liquids by invoking t h e comp r essibility of the
gas
T h is hy pot h e s is has proved to be i n agreement with expe r imental
facts in a la r ge number of c ases A mo n g t h ese cases may be named t h e
properties of pyrrhotite t h e h eat developed when a substance passes
from the pa r amagnetic to t h e fer r omagnetic state and t h e l a w of temper
at u re and intensity o f magnetization of magnetite Th e properties of
hysteresis of i ron can be given a theoretical inte r pretation and from
NI wh ere N is a constant I t h e intensity of magnetization and H t h e
11
.
.
.
.
’
.
,
,
,
,
,
.
'
.
,
.
,
,
I LL I NOIS E NG I NEERI N G EXPERI ME NT STATIO N
26
A pparatus a nd M eth ods for D etermi ni ng th e M agneti c P roperti es
—
P y rrh oti te
Weiss , in his e xperimental determination of the ma gnetic
13
.
f
properties o f pyr r hotite used two met h ods :
( 1 ) the ballistic method
in which a ballistic galvanometer was used to m easure t h e quantity of
electri city ind u ced in a coil surrounding t h e sample by vari ations in
the magnetic field ( 2 ) a method In whic h h e measured the couple pro
d u c e d on the crystal by the field
T h e l atter method is the more sensitive and
permits of t h e examination of much smal ler speci
mens
I n this method a disk of pyrrhotite P
Fig 1 2 f rom 1 cm to 2 cm in diam eter and
about
mm t h ick is p laced between the poles
o f a magnet of fi e ld stren gth H and the magnetic
properties of the crystal are studied with t h e disk
in various posi t ions T h e intensity of magnetiza
tion is not necessarily in t h e direction of H in
f act it i s in t h is direction onl y in one position of
the disk i e when the direction in w h i ch the di sk
is most eas ily magnetized co i ncides with the di
rection o f H
I n general the inte nsity of m ag
n et i z a ti o n makes an angle a with H
o
,
,
,
.
.
,
.
.
.
,
.
,
,
,
.
,
,
,
.
.
,
.
,
.
Componen t of M a gn eti za ti on P erpendi c ula r
—
Suppose the c rystal is turned so t h at
to th e Fi eld
the elementary magnet , wit h center at 0 , Fig 1 3 ,
with the direction o f t h e field , H
14
PM
12
.
.
makes an angle
Le t N be
net T hen
a
.
the moment o f the couple acting on the elementa ry mag
.
N
,
= 2l m H
u
sin
H Si n
a
a
whe r e 2 1 i s t h e len gth of the magnet m its pole strengt h and p the mag
netic moment o f t h e e l ementary magnet
I the i ntens i ty of magnetization i s equal to n p w h ere n is t h e num
ber o f elementary ma gnets per unit volume T h erefo r e
N=a
Si n 0
,
.
,
,
,
,
.
.
I H
Sin a
.
where N i s the moment o f the couple acting on the crystal
Now I s i n a equals the component o f the i ntensity of magnetization
perpendi c ul ar to H T herefore
N = HI ( p ) 0 0
where C i s the constant of the apparatus and a is the deflection of the
mirror I f the magne t i s mounted in a horizontal plane so t h at it can be
turned about a vertical axi s the pe r pendic u lar component of t h e in t en
s i ty of ma g netization can be studied f or various rela t ive positions of the
magnet and crystal
.
,
.
’
.
,
.
We iss Jo ur de P hy s
‘
,
.
,
ser
.
4,
Vol
.
4 , p 469 , 1 90 5
.
.
WILLIAMS
E
LE C TRO N THEOR Y O F MA G NE TISM
27
Weiss results s h ow that this i s a pe ri odic function whic h repeats
’
!
itself every
T h e c u rve shown in Fig 1 4 rep r esents the ideal curve
obtained in t h is manner I n practice the curve is not smooth but h as
i r regula r ities
.
.
.
d
e
l
P
i
I
f
t
h
e
disk
h
F
M
a
t
za
o
n
ara
ll
e
o
t
e
t
t
n
e
i
i
l
g
f
[
is now placed between the poles of the magnet in a vertical position
’
2
l
n
f
see
dotted
line
o
f
Fig
so
t
h
at
the
the disk makes an angle
1
a
o
e
(
p
)
of 3 or 4 with the direction of the field H and so t h at it can turn about
a horizontal axis it will be in a positio n to stud y t h e component of t h e
intensity of magnetization w h ich is parallel to t h e field
15
.
Compon en t
o
.
.
°
°
,
,
.
FI G 1 5
R eso l ve t h e intensity of magnetization into a h o r izontal and a
Let I be t h e h orizontal component
ve r tical component ( see Fig
I f the disk is placed so that I h makes an angle of 3 or 4 with t h e di r ec
tion of H , Fig 1 6 , there wi ll be a restoring fo r ce tending to turn t h e di sk
back into a plane par allel to t h e field H Th is can be measured in a
manner similar to t h at S h own in Fig 1 2 The restorin g force is
.
.
.
°
.
.
.
H I ) ; Si n 7
.
I
07
°
I L LI N OIS
28
EN
G I NEE RI NG
E
XP E RIM EN T STATIO N
’
w h ere 7 is t h e deflection of t h e mirro r T h e r efore if 7 is kept constan t
t h e restoring force is p r oportion al to I h No w I h c os 7 t h e component of
I h parallel to t h e field is ve ry nea r ly eq u al to I h since 7 is onl y 3 or
H ence if we t u rn t h e disk t hr ough
we obtain t h e components of
the intensity of magnetization Ip pa r allel to t h e field
.
,
.
,
°
,
,
,
,
.
Th e
component of t h e intensity of magnetization pa r all e l to t h e
field may also be st u died by t h e m e t h od of ind u ction by u se of a sole
n o i d al coil S wit h a seconda r y S inside
I f t h e py rrh otite disk d is
th r u st into t h e seconda ry wit h i ts plane parallel to t h e axis of t h e cylinder
as sh own in Fig 1 7 t h e r e is a c h ange of t h e flux t h ro u gh t h e secondary
and h ence a deflection of the ballistic galvanomete r T h e galvanometer
will not be affected by the component of magne tization perpendicular
to H but only by that parallel to H T he r efo r e by rotating t h e disk
one can study t h e relation between I p and t h e angle Of r otation of t h e
disk W eiss by di r ect experiment obtained r es ults w h ich a r e s h own in
Fig 1 8 in w h ic h th e abscissas a r e t h e azim u ths of a cons tant magnetic
field T h e o r dinates of t h e upper curve a r e t h e components of the
magneti zation pa r allel to the field w h ereas t h ose of th e lowe r c u r ve are
t h e components pe rp e ndic u lar to t h e field T h e p h enomenon repeats
itself eve ry
I n order to interp r et these c u rves W eiss makes u se of the fo l lo wing
illustrati on Suppose a ma gnetic field is made to tu rn in t h e plane of
an elliptic plate of soft i r on A t t h e axes t h e magnetization coincide s
with the direction of the field T h e longer axis will have a maxim u m
t h e s h o r ter axi s a minimum of magneti za t ion Fo r all ot h e r di r ections
Of the field t h e magn etization will be mo r e nea r ly that of t h e l o nge r axis
than of t h e field W it h t h e continuo u s ro tation of t h e magnetic field
the magn etization will t u rn more slowly th an t h e field in t h e neigh bor
hood o f t h e long axis and mo r e rapidly in t h e neig h borh ood of th e s h ort
axis I f t h e ellipse is ve ry elongated t h e component of magnetization
perpendicular to the field will pass almost ins tantly f r om a ve ry large
negative value to a ve r y la r ge positive value as r epresented in Fig 1 4
while the direction of t h e fi e ld c h anges from one side to t h e ot h er of t h e
s h ort axis T h e lower c urve of Fig 1 8 may e v idently be obtain e d by
t h e addition of t hr ee cu r v es si mila r to t h a t of Fig 1 4 di splaced wi th
respect to each othe r by 6 0 and
’
,
.
.
,
.
,
.
.
.
,
,
,
,
,
.
,
.
,
.
.
,
.
.
,
,
.
.
,
.
,
,
.
.
.
,
,
°
F r om t h e above analogy W e iss ass umes t h at t h e co m plex st r u ct u r e
of t h e c rystal of py rr ho t ite res ults f r om t h e j u xtaposition of elementary
crystals of which t h e mag ne t ic planes a r e pa r allel and w h ic h possess eac h
a direction of maximum and m ini m u m magnetizati o n at righ t angles to
eac h other and t h at t h ese c rys t als a r e associated in t h e magneti c plane
by the an gl es o f
o r w h at a m o u nts to t h e same t h ing
,
,
’
,
t h e ab r u pt va riations of t h e component of magnet
to t h e field give th e relative impo rtance of the
t h ree components of magneti z ation d u e to s u pe r posi tion of t h e crystals
T h e angles of t h e uppe r c u rve of Fig 1 8 co rr e spond to t h e minima of
t h e magnetization pa r all e l to the fi e ld of eac h of t h e components
T h e amplit u des of
i z at i o n pe r pendic u la r
.
.
.
WILLIAMS
—
E
L ECTRO N T H E ORY O F MA G N E T ISM
FI G
FI G
FI G
.
29
16
.
17
.
18
M ol ec u la r Ma gn ets of P yr rh oti te
I n o r der to m ake a clea r
representation of t h e prope r ties of a crystal of pyrrhotite i m agine t h a t
it be composed of r ows of small needle m agnets equidistant f r om eac h
ot h e r pointing in t h e di r ection of easy magneti zation 0 3:
th e
( Fig
axis 0 g being t h e direction of difficult magnetization Let t h e axis of
rotation be perpendicular to t h e m agneti c p lane Su ppose t h at t h ese
magnets a r e small in compa r ison wit h t h e distances w h ic h sepa r ate t h em
and st r ong eno u g h to exercise on eac h ot h e r a directing action I m ag
ine mo r eover t h at becau se of a co m pensation or of a g r eater distance
t h e rows do not affect one anot h e r Left to t h e m selves t h e magnets
of a row will adopt a position of eq u ilib r ium in w h ic h t h e nort h pol e of
eac h magnet will face t h e so u t h pole of t h e following magnet O n t h is
ass u mption t h e substance wo u ld be satu r ated in t h e di r ection of easy
m agneti z ation 0 a:
wit h little or no exte rnal field Let a field H making
an angle a wit h t h e direction of t h e r ows act on t h e above system T h e
m a gnets wi ll be deviated by an angle cp A s soon as t h e magnets a r e
deviated from t h e di r ection 0 33 t h e r e will be a fo r ce tending to r estore
16
.
Th e
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,
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,
,
.
I L LI N OIS E NG I NE ERI N G
30
FI G
E
.
X P E RIME NT STATIO N
19
t h em to t h eir original position I f t h ere we r e only t wo magnets t h i s
force would take th e direction indicated by t h e dotted line ( 1 ) Fig 20
but the combined e ff ect of all t h e magnets will give t h e force a di rection
which i s mo r e nearl y t h at of 0 x Let us assume t h at this force
makes an angle wi th t h e direction 0 33 T h e resultant action of the rows
then exercises on each small magnet a magnetizing field A p cos ¢ in the
—
di r ection 0 13 and in t h e di r ection 0 g a demagneti zin g field Eu Sin
where A and B are constants and whe r e p ml is the magnetic moment of
an elementa r y ma gnet Let H and H , be the sum o f the components
of the forces acting in th e £1:
and y directions respectively
.
,
.
,
.
.
,
,
,
.
.
H = H c os
H , = H s in
x
a
+A
a
FI G
-
.
B
p c os
p si n
¢
¢
20
For t h e condition of equilibri u m
H sin ¢ = H y c os
T herefore from ( 3 0) and ( 3 1 )
i
H
a
>
n
b
cos
sin
A
c
s
S
o
a
H
q
d
(
)
p
(
,
H si n
(
a
B
A
+
)
(
p si n
By
¢
c os
cos d)
qb
.
2
3
( )
—
W I LLI A Ms
E
L E C TRO N TH E OR Y O F MA G NETISM
31
W r iting
B u
NI m
(A
where N is a constant and I m i th e intensity of magnetization per unit
volume
H sin ( a
( p)
NI sin qt cos d)
4
3
( )
T h us wit h t h e above assumptions we arrive at an expression w h ic h as
wi ll be shown later is the expression for t h e law of magnetization of
py rr hotite dete r mined expe r imentally
1 7 Wei ss La w of M a gn eti za ti on of P y rrh oti te
( a ) Effect of
Alternating F i eld
I t has been s h own t h at t h e elementary magnets
of pyr r h otite lie in the plane of t h e base of t h e c r ystal T h e direction
i s called t h e direction of easy magnetization ; t h e pe r pendicular d i re c
a:
tion y that of the di fficult magnetization I f H is in t h e direction of
easy magnetization satu r ation takes place from th e beginning I f in
t h is case t h e field is reversed in di r ection t h e h ysteresis cu r ve will run
t hr ough a cycle w h ic h is r ectangula r in s h ape ( see Fig
W h en the
field h as acq u ired a ce r tain value =i=H t h e elementa r y magnets become
u nstable and suddenly all of t h em swing a r ound into t h e ot h er position
of eq u ilib r i u m Expe r iment gives very nea r ly a rectangle
,
",
,
.
’
.
.
.
.
.
,
'
'
,
.
,
,
.
c,
.
.
FI G
.
21
I f a constant field is applied and
( b ) Effect of R otating Field
rotated in the magneti c plane inte r esting p h enomena present t h emselves
T h e elementa r y magnets h ave a tendency to r emain in t h eir original
position so t h at w h en t h e field is rotated t h e di r ection of t h e intensity
of magnetization turns slowe r t h an t h e field I f a field of
uni ts
acts in t h e di r ection 0 11:
Fig 22 and t h en r otates toward the di r ection
t h e direction of t h e intensity of magnetization turns round muc h
mo r e slowly and w h en H is in t h e di r ection 0 g I t h e intensity of mag
n et i z a t i o n will be in t h e di r ection OI
T h en when t h e field rotates a
little far th er the magnets swing around very quickl y so t h at in t h e
neigh bor h ood of 0 g t h e rate of change of t h e direction of the intensity
of magnetization is muc h g r eater t h an t h at of the field
Whatever
t h e intensity of t h e field t h e vector representing the intensity of mag
.
.
.
.
,
,
,
.
,
,
,
,
.
,
ILLI NOIS
32
EN
G I NEE RI N G
E
X P E RIM E N T S TATIO N
falls wit h in a ci r cle C whose radi u s is equal to I m t h e maxim u m
intensity of magnetizat i on wh ic h is t h e value obtained w h en t h e
di r ection of t h e field coincides with t h e di r ection of easy magnetization
T h is circle is called t h e ci r cle of sat u r ation
units the intensity of
W hen t h e field is relatively weak say
magnetization vector follows th e circle of satu r ation for only a S h ort
distance afte r whic h it describes a c h o r d pa r allel t o 0 15 W h en t h e
field h as a st r engt h of
u nits o r more we have sat u ration in eve r y
di r ection of t h e field and t h e intensity of magnetizat ion vec t o r follows
mo r e closely the ci r cle of sat u ration C
T h u s in order to t u rn and maintain t h e magnets in t h e direction of
difficult magnetization Oy it is necessa r y to apply in th is di r ection a
field of at least
u nits
While fo r saturation in t h e direction 0 x little o r no field is r eq u i r ed
t h e field nec e ssary to produce sat u ration in the direction 0 g m u st have
a rat h er high v a lue Furth e rmo r e t h e intensity of magneti zation re
mains cons t antly i n th e plane Ox y t h e component of magnetization in
t h e di r ection Oz pe r pendic u la r to t h is plane being ve ry sma l l in com
parison wit h t h e magne t izatio n in the c h a r acteristic plane T h u s w h ile
u nits
th at in th e
t h e demagnetizing field in th e di r ection 0 g is
direction Oz is
u nits o r abo u t 2 0 ti m es g r eate r
Let a and d) be the angles whic h H and I make with
( Fig
resolve H into co m ponent s Ha di r ected al o n g Oy and H 1 pa r all el t o t h e
int ensity of magne t i z ation T h e r e is a constan t r atio
n et i z a t i o n
,
,
.
.
,
,
.
,
,
.
,
,
.
,
.
,
.
,
.
.
Ha
I
si n
d)
between th e compon e nt s Hd of th e field and t h e c o mponents of mag
n e t i z a t i o n in t h e di r ection 0 g
T his fact was e s tabli s h ed expe r imen t al
l y by W eiss a s t raig h t line relation betw e en IL, and I s i n «p being o h
t ain e d
T h e v al u e of t h e con s tant N fo r t h e s a m ple t h a t h e u sed was
found to b e
00
7
3
d
—
I S i n d)
47
Everyt h ing tak e s place as if t h e r e were acting in t h e di r ection 0 g a
demagnetizing force d u e to t h e s tr u cture of t h e c rystal p r opo r tional to
t h e component of t h e intensity of magne t ization in th e di r ection of
difficult magnetization 0 g and as if the remaining component of H we r e
paral lel to t h e di r ection of easy m agnetization 0 1 7
F r om Fig 23 we see t h at
EH
H sin ( a
AH
H
.
,
.
,
,
”
_
,
,
,
.
.
a
Su bs t it u ting ( 36 )
_
z
)
c os (1
in ( 3 5) gives
,
H S in ( a
cos
H
sin ( a
d) )
d)
Si n
cos cp
.
I L LI N OIS E NG I NEE RI NG EX P ERIM E NT STATIO N
34
For t h e same field t h ere is a second position of equilibri u m
Fig
O ne migh t imagine
24 sym metri cal to t h e first wit h respect to Oy
—
that a coercive force H di r ected along Ox cau ses t h e va r io u s rows of
the elementary magnets to turn f r om t h e fi r st into t h e second position
of equilibrium T his coercive fo r ce in th e c ase of pyrr h otite is about
1 5 units whereas the demagneti zing field or t h e field necessa r y to make
the elementary mag nets stand at ri gh t angles to t h e direction of easy
magnetization is about
units T h e relation between t h e t wo
quantities h as not yet been explained but it h as been suggested t h at it
h as to do with the distu rbed r egion of t h e extremity of th e rows
.
,
.
c
.
,
,
,
,
.
,
.
FI G 24
.
M agneti za ti on i n Difi erent Di rec ti ons
Let u s now consider
t h e l aws o f magnetization in directions ot h er t h an th at of Oz and Og
AS stated above when a magnetizing field is applied in t h e di r ection of
easy magnetization saturation takes place from the be gi n nin g I f we
plot intensity o f magnetization I against field st r en gth H we will obtain
the str ai g h t line A B ( Fig
parallel to the axis OH ; t h at is t h e in t en
si t y o f ma gnetizat i on remains the same whatever the value of t h e
magnetizing field Saturation occurs even without an y external field
No w if we apply a magnetizing force in t h e di r ection Oy we Obtain
from the g eneral law of magnetization of pyrrhotite
H co s qb = NI sin ¢ cos d>
18
'
.
.
.
,
.
,
,
.
,
.
.
,
,
H = NI sin d>
wh ence
ii :
N
constan t
i
T h i s holds for fields be l ow that necessary to produce saturation and is
represented by t h e line 0 0 Fig 25 For fields equal to or greater than
that necessary to produce saturation the curve is the same as for easy
magnetization T h erefore the whole curve for the intensity of magneti
z at i o n when the field is applied in the d i rection Og is given by OCB Fig 25
We have now to inqui re what h appens when t h e direction of t h e
ma gnetizing field is intermediate between th e di rection Oz:
and Oy W e
get di ff erent expressions for the law o f magnetization depending on th e
way in whic h I is r esolved For a field of constant direction we ma y
.
.
.
.
.
.
.
WIL L IAMS
-
E
LE C TRO N THEORY O F MA G NE TISM
FI G
35
25
.
take the c o mponent of t h e intensity of magnetization in the direction
of the field I n this case ( from Fig 2 6)
—
=
I h I cos ( a cp)
I n general
H sin ( a
Si n d) cos ct
For satu r ation t h is equation becomes
—
H sin ( a qb ) = NI sin qt cos
and ( 3 8) becomes
—
=
I h I m cos ( at qt )
El i minating qS between (39 ) and ( 4 0) we find
N
’
2
—
— sin 2 a
— NI , cos 2 a
I m 1 h
.
.
",
,
_
1
2
h
FI G
.
26
I f I h app r oac h es I m , th e fi r st term o f t h e rig h t side of t h e equation
app r oac h es 0 0 ; in other words if H becomes 0 0 I h approac h es I m T here
fo r e t h e curve between the i ntensity of magnetization I h and t h e
magnetizing fo r ce H approac h es t h e line of saturation A B Fig 2 5
asymptotically and t h e law of magnetization for directions intermediate
,
.
,
,
.
,
ILLI N OI S
36
EN
G I NEE RI NG
E
XP E RIM E N T STATI O N
between Or:
and Oy is given by the cu r ve ODE Fig 2 5 I t is possible
to explain all t h e o r dina r y curves of magnetization by a superposition
of p r ope r ties analogo u s to th ose of py rrh otite in t h e di r ection of easy
difficult and inte r mediate magnetization
As h as al ready b e en s h own t h e r elation
—
H sin ( a cp)
NI s 1n d) c os d>
ded u c ed f r om t h e t riangle OH E ( Fig
is t h e analytic exp r ession of t h e
T h is expression multiplied by I gives t h e
law of magnetization
couple o r mech anical m oment exerted by t h e field on th e substance
2
—
=
M H I sin ( a dJ ) NI sin (1) cos d)
.
.
,
.
,
,
.
.
,
,
.
21 1
2
N1
2
s i n cp
2
sin
2
Th i s
cos ¢
2 ct
co u ple is a maxim u m w h e n
Im
I
I f we m e as u r e M as a function of a t h e angle of orientation of the
field wit h respect t o t h e s u bstance we s h all find a couple wh ic h becom es
constant as soon as t h e field is strong enoug h to bring about saturation
of t h e intensity of magnetizat ion a fter th is vector I h as described an
arc of 4 5 or mo r e along t h e circle of saturation T his has been very
*
clearly demonst r ated by Weiss in w h ic h h e obtains the following curves
( Fig 2 7
) experimentally I n t h ese c u rves t h e angles of rotation of
t h e field with respect to th e s u bstance are used as abscissas and the
couples expressed in mm divisions of the scale are u sed as ordinates
I t will be noticed t h at the maxima for curves I II I V and V are a ppro x i
mately the same notwithstanding t h e fact th at t h e magnetizing fields
in t h e t h ree cases are widely diff erent I n order to reduce t h ese co u ples
to thei r absol u te val u es p e r u nit of volume it is necessa r y to mul tiply
by 9 50
,
,
°
.
.
.
,
,
.
.
,
,
,
.
.
N ”
maximum couple is
2
F r om eq u ation
!
t h e value of
th e
2
T aking I m = 4 7
,
.
one obtains f r om t h e mean o f t h e th r ee values of this
couple a demagneti zing field
H d N1 ” 7
3 00
wh ich ag r ees with experimental determination
i
H
1 9 H ysteresi s P h eno men a
e
a
ternating
yste
r
es
s
h ave
Al
W
( )
seen that wh en a field H H = 1 5 gauss is applied parallel to t h e d ire c
tion of easy magnetization of pyrr h otite the elementary magnets turn
completely over yet it tak e s
gauss to make them stand at righ t
angles to t h is di r ection
Weiss h as Sh own that if one considers t h e di r ection of easy magneti
z at i o n in a substance t h at is infinite and wi thout fractures t h e intens ity
of magnetization would remain cons tant as t h e magnetizing field in
creases and if the magnetizing force were to describe a cycle the
theoretical hysteresis loop wo u ld be a r ectangle as indicated by the
,
z
,
.
-
.
.
.
c
,
.
,
,
,
,
We i ss Jo u r
,
.
de
Phy s
,
ser
.
4,
V ol
.
4 , p 46 9 . 1 905
.
.
WILLIAMS
—
L CTRO N T H E ORY
E E
FI G
C ur v e
C urv e
C ur v e
C ur ve
C u r ve
I
II
III
IV
V
.
.
.
.
.
.
27
H = 1 99 2
H = 4000
H= 7
3 10
H = 1 02 7
5
H = 1 1 1 40
FI G
.
OF
28
g a u ss
g a u ss
g au ss
g a u ss
g a u ss
MA G N ETISM
37
I L LI N OIS
38
EN
G I NEE RI NG EX P ERIM E NT STATIO N
dotted line in Fig 28 Th e more unifo rm the magnetic mate r ial is the
less t h e expe r imental curve de vi ates from t h e t h eo r etical c u rve W eiss
fo u nd that t h e distance between t h e ascendi ng and descending branc h es
of the e xpe r imental c ur ve measured pa r allel to t h e axis of abscissas is
approximately constant and equal to
gauss
T h us in order to move
t h e vector of magnetization alon g t h e diamete r of eas y magnetization
it i s necessar y to overcome a constant coe r cive field
H :
gauss
Th e energy dissipated pe r cycle in t h e form of heat in a unit of
volume is
E = 4 HJ m = 4 X 1 5 4 X 4 7
2 90 0 ergs
Excludi ng t h e di r ection of easy mag
( b ) R otating H yste r esi s
n e t i z a t i o n the knowledge of magnetization in t h e magneti c plane has
been obtained by causing a field of constant magnitude to t u rn in this
plane From these expe r iments one can obtain information on t h e form
of hysteresis t h at has been called rotating hyste r esis as disting u ished
from alternating hysteresis which h as been conside r ed above I f we
rotate the field from the di r ection of eas y magnetization OX ( Fig 29 )
through the angle X OY the vector of t h e in t ensity of m a gnetization
describes the arc A B of the c i rcle o f saturation Then t h e field passing
the d i rection of difficult magnetization OY t h e vector of the intensity
of magnetization describes quickly t h e c h ord B ED after w h ich it de
X)
scribes the arc D E as the field desc r ibes th e an gle Y O
.
.
,
.
,
,
.
.
e
u
.
.
,
.
.
.
,
.
,
,
,
-
.
FI G
.
29
H ysteresis occu r s only i n t h e di recti on o f difficult ma gnetization OY
when the molecul es swi ng f rom one position of equi libri um into the
other
I n other words hysteresis accompani es t h e change of intensity
o f magneti zation as the vector moves al ong B ED W hen the magne
t i z in g field H reac h es t h e value 73 00 gauss the intensit y of magnetiza
tion I follows t h e ci r cle o f saturation and the rotating hysteresis dis
appears I t f ollows f rom t h is t h at the hysteresis area along the circle
of saturation is equal to ze r o I n t h e curves of Fig 3 0 taken from
expe r imental results obtained by W eiss wi t h a sample of pyrrhotite
in a field of about 6 00 gauss 0 rep r esents t h e re gion in t h e direction
of easy mag netization and 9 0 that in t h e direction of di fficult ma gneti
z at i o n
I t is seen t h at the two cu r ves coincide exactly fo r some distance
.
.
,
.
.
,
°
.
.
,
W ILLI A M s
EL E CTRO N THEORY O F MA G N ETISM
39
in t h e neig h bo rh ood of easy magnetization I n t h e neig h bor h ood of t h e
direction OY ma r ked b y a t h e two curves are di stinctly di fferent
Th e smaller t h e field with w h i ch one works the greater the dive r gence
but whatever be the field t h e curve corresponding to rotation i n one
direction can be superimposed on the retu rn c u r ve by a h o r izontal
displacement
.
,
.
,
,
.
FI G
.
30
— So
long as t h e intensity of
f Rota ti n g H y steresi s
magnetization I follows t h e curve of sat u ration there is no hysteresis
loss Th e loss takes place along S B S Fig 3 1
T h e force necessa r y
to turn the elementary magnet over at S is less t h an at A
C all t h is
’
fo r ce H
Experiment has shown t h at
H
Hc
C onst
20
.
En ergy
o
’
.
.
.
.
0
.
,
c
[m
Im
t h erefore
To
I ,,
.
—
C( I m I y)
obtain t h e value of C let
H
c
CI m
FI G
.
31
H
0
.
I L LI NOIS E NG I NE ERI NG EXPERIME N T STATIO N
40
T h e r efore
t h e coercive force
(I m
and t h ere is no h ys t e r esis loss
Iy)
.
No w t h e ene r gy dis s ipated in
n alte r nating h yste r esis t h a t is a
h ysteresis along A D ( Fig
was fo u nd above to be equal to 4 I mH
’
Th e r otating h yste r esis loss along S S is 4 H B S
a
,
.
o
.
'
,
(
2
I
.
Z
f)
— —u
w h enc e
T h erefo r e t h e
e
ne rgy dis s ipated in one rotating h ysteresis cycle is
4H
1, = o
this r e d uces to t h e valu e for alternating h yste r esis Since t h e d e mag
n e t i z i n g fo r ce if t h e substance is infinite and continuo u s is
.
,
,
Hd
z
NI ”
—E
f
u
A
_
Substi t u ting t h i s
in e q u a tion ( 4 2 )
E = 4 H Im
,
(
we
«e
h av e
H
ene r gy E dissipated in alternating h yste r esi s r e m ains con s t an t
wh e r eas t h at of rotating h yste r esis decreases wit h inc r ease of I
T h is
is s h own graphically in Fig 3 2 by t h e full line curve A B T h e points
in t h e neig h bo rh ood of t h is c u r v e a r e t h e r esults of
( marked
T h ey are
measurements made by W eiss wit h a h ysteresis mete r
—
subj ect to the co r rection
sam ple as was used
n I ,, since in a finite
in the experiment
Th e
,
a ,
.
.
-
.
ILLI NOIS E N G I N EE RI NG
42
E
XPERIM E NT STATI O N
B esides t h e ferromagnetic
M agneti c P roperti es of M agneti te
c rystals pyrr h otite an d hematite t h e r e is a t h ird m a gnetite whose
magnetic properties are similar in many ways to t h ose of t h e other t wo
I t is classified as belon ging to t h e regular system of c ry stals but its
magneti c properties indi cate t h at it does not belon g to this system
‘
*
Th e magneti c properties of magnetite h ave been stu di ed b y C urie
Wei ss 1 Qui ttn er i and ot h ers who found that they were more pro
n o u n c e d than those of hematite b u t less prono u nced t h an those of
pyrrhotite From about 53 5 C the temperature of magnetite trans
formation to 1 3 75 C the temperature of f usion of magnetite C uri e
fo u nd that the i ntensity of magnetization is independent of the field
and that it decreases ve r y re gularly with the increase of temperature
For a part of thi s temperature range C uri e formulated the followi ng
law : Th e coe ffi cient o f magnetization of magnetite varies inversely
”
as the absolute temperature between 850 C and 1 3 6 0 C
22
.
.
,
,
.
,
.
,
'
,
,
°
.
.
°
.
“
.
°
°
.
FI G
.
.
33
W eiss and Q ui ttner found that the magneti c propert i es i ndi cate that
the crystal s o f magnetite do not belon g to t h e regular syste m T his was
s h own b y taki n g a plate o f magnetite cut parall el to the surface of the
cube and placing it i n the magnetic field in a hori zont al position and
then rotating t h e magnetic field round about i t P lottin g their resul ts
wi th the angles of rotation of the m agneti c field as absci ssas and as
ordinates the deflection of the suspension whi ch is proport i on al to the
intensity of magnetization in a direction perpendi cular to the magneti c
field they obtained t h e curves o f Fi g 3 3 Each of t h ese curves is the
mean o f the t wo curves obtained by rotating t h e field f rom 0 to 3 60
and then back to
A portion of the t wo curves f r om whi ch curve
III is obtained is represented by the dott ed l i nes T h e area between
the two curves is the hysteresis area of rotation
.
.
,
.
,
.
°
.
.
P Cu ri e Ann de C hem ser 7 Vol 5 p 3 9 1 1 895
t P We iss Arc h iv es d es S ci en ces Vol XXX I 1 9 1 1
I V Q u i tt n er Ar chives d es S ci en c e Vol XXV I 1 908
.
.
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,
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,
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,
,
,
,
,
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,
,
.
.
.
,
.
°
WI LL IAMS
EL E C TRO N TH E OR Y O F MA G NETISM
43
I f the symmetry were t hat o f the cub i c system the curve s h o u ld
show a pe r iod of
t h us f ormin g between 0 and 360 four simila r
waves I nstead of this the fig u r e shows only two identical waves
between 0 and 3 60 for H = 573 gauss Th e symmet r y is t h e r efo r e
not t h at of t h e cubi c system Now t h e geomet r ical p r ope r ties of t h e
crystal leucite are such t h at it is usually classed as an isome r ic c rystal
yet when it is investigated Optically it is found to be isot r opic H o w
ever as t h e temperature is raised the Optical properties also become
t h ose o f t h e regular system I t would be inte r esting to see whet h e r
the prope r ties of symmetry of magnetite from t h e magnetic point of
view change wi th change of tempe r atu r e I f according to its magnetic
properties magnetite does not belong to t h e regular system t h e question
arises to w h ic h system does i t belong f r om a magnetic point of view ?
°
°
.
.
°
°
.
.
.
,
.
,
,
.
,
.
,
,
,
curves of Fig 3 3 Sho wthat the two p r incipal axes sit u ated in
the plane of t h e cubi c plate are not equivalent I t remains to be
dete r mined w h ether t h e t h ird axis pe r pendic u la r to t h e plane of t h e
plate is eq u ivalent to eit h er of t h e ot h er two or whether it be h aves
di ff erently from the magnetic point of view I n t h e first case we would
have the symmetry of the quadri c system in t h e secon d t h at of the
o t h o r o mb i c
system T h us i f t h e system is c u bic the r e s h ould be
between 0 and 1 80 t h ree identical waves ; if it is quad r ati c t h e r e
s h ould be two similar waves and a third whic h is di fferent ; and finally
for the symmetry of the o t h oromb i c system t h e t hr ee waves s h ould be
di fferent wit h t h e possibility t h at one o r even two of these waves may
disappear completely
Qu ittner in his researc h es fo u nd the th r ee
waves to be di fferent and t h at their relative magni tudes depend on the
magnitude of t h e magnetic field We must conclude the r efo r e t h at
magnetite so far as its ma gnetic properties are concerned possesses
t h e symmet ry of the ot h oromb i c sy stem
Th e
.
.
,
,
.
,
,
,
,
.
°
°
,
,
,
.
,
.
,
,
.
I n order to see the i rregularities in the magneti c behavi or of a
c r ystal of magnetite and t h e dependence of the ma gnetic p r opert ies on
the value of t h e magnetizing field we need only to observe t h e c u rves
Fig 3 4 obtained by Quittner wi th a plate cut f r om a crystal in s u ch a
way that its plane makes equal angles wi th the three axes I t will be
noticed that for a field H =
gauss all three waves are practically
equal ; for a field H = 3 68 1 gauss there a r e onl y two waves which are
greatly reduced and displaced the t h ird being barely visible I f the
field is still inc r eased one again finds fo r H = 757gauss t h ree well de
fined waves which however , are displaced by half a wave len gt h
,
,
.
,
.
.
.
,
-
,
,
.
,
Th e
theoretical interpretation o f t h ese ve r y complicated phenomena
is hardly possible in th e p r esent state of our knowledge but t h e investi
gators o f magnetite have p r oposed t h at t h e c r ystal is made up o f equal
parts o f t h ree elementa r y magnets w h ose magneti c planes are per
i
l
n
e
d
c
u
ar to each other suc h as wo u ld be t h e case if it were possible
p
to superimpose three plates of pyrrhotite cut parallel to the plane of
easy magnetization in such a manner t h at t h eir planes wou l d be
mutually perpendicu l ar to e ach oth e r
,
,
.
ILLI N OIS
44
EN
G I N E E RI NG
E
XP E RIM E N T STATI O N
U PO N T H E MA G NE TI C P ROP E RTI E S
O F B OD I ES
2 3 M eth od of I n vesti ga ti on Used b y Cu ri e
Extensive investiga
tions of t h e eff ect of temperat u re u pon t h e magneti c p r operties of various
*
substances have been made by H opkinson C ur ie t and othe r s C urie s
method was to place the body to be tested in a non uniform magnetic
field and measu r e t h e r es u ltant force of t h e magnetic actions by utilizing
t h e to r sion of a wire Let A B CD ( Fig 35) represent the h ori zontal
arms of an electromagnet and let t h e axes of t h ese t wo a r ms form an
angle wit h each other T h e body to be inv estigated is placed at the
point 0 on t h e line Ox w h ich is t h e intersec tion of the ho r izontal plane
passing t h rough t h e axis of t h e arms of the electromagnet and t h e
vertical plane of symmet r y W hen the electrom agnet is excited a
force f of att r action or repulsion acts along Or
C all H u t h e intensity
of t h e magnetic field at O T his field is directed by re as on of sym
metry along Oy perpendic u lar to 0 13 Let I be t h e specific intensity of
magnetization t h at is the intensity of magneti zation per unit mass
and m the mass of t h e body t h en
I II
.
EFF E C T
OF
T EMP E RAT U R E
.
.
’
,
,
.
-
.
.
,
.
,
.
,
.
.
,
.
,
,
,
,
dH.
_
I f diamagneti c o r pa r amagneti c bodies a r e being studied the
demagnetizing fo r ce a r ising f r om the magnetization of the body is
insignificant and if K is u sed to designate t h e coefficient of specific
magnetization t h e r e is obtain e d
,
,
K H,
I
d
H
— H
f mK H y CE
No w K for most diamagnetic and pa rama gnetic bodies is practical
d ”
l y constant and therefore f is proportional to H
For greatest sen
si ti v e n e ss the body sho u ld be placed at the point on Or at which t h is
product is maximum C urie s met h od was to su rround t h e sample
under investigation by a vertical elect ri c furnace so t h at it coul d be
heated to any desired temperat u re T h e sample itself was mounted
on the end of a lever l m which was suspended by a torsion wire tm
T his leve r was connected to anot h er leve r mn so t h at any movement
of the sample would be g r eatly magnified at t h e other end of t h e system
Th e whole movable system was s u spended in such a manner t h at any
movement of t h e body which was ve ry small in the substances i n ves
t i g at e d by C urie would be along Ox
W ith h is appa r atus C urie claimed
to be able to m eas u re mo v ements of t h e obj ect to
mm A S the
body was heated to va rious tempe r at u r es whic h could be determined
b y means of a t h ermocouple the fo r ces of attraction or repulsion could
be determined f r om t h e movement of the levers and the constant of the
apparatus
=
z
.
’
.
.
.
,
.
,
.
,
,
.
,
,
.
H o ki n so n Phi l Tra ns
P u ri e A n n d e C h e m
.
,
t
.
,
.
p 44 3 , 1 889
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,
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,
ser
.
7 V ol
,
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5 , p 2 89 , 1 895
.
.
WILLIAMS
E
L E C TRO N THEORY
FI G
FI G
.
34
.
35
OF
MA G NE TI SM
45
I L LI N OIS E NG I NE ERI N G EXPERIME N T STATIO N
46
— A fter a
Resu l ts O b tai n ed b y Cu ri e
very extended study
—
cove ring a wi de range of substances
diamagnetic parama gneti c
a n d ferromagnetic
C urie came to t h e following conclusions :
Th e coefficient of specific magnetization of diamag netic bodi es
is independent of the intensity of t h e field and as a general rule
independent of t h e temperature Antimony and bismut h are ex c ep
tions to this rul e T h e coefficient of magnetization of t h ese bodies
diminishes wi t h increase of temperature For bismut h t h e law of
variation is a linear one T h e physical and chemical c h anges of state
often have onl y a slig h t e ff ect on t h e diamagneti c p r ope rties Thi s is
true in the case of t h e fusion of white p h osp h o r us at
and in t h e
various trans formations which are undergone w h en sul p h ur is heated
H owever this is not always the case ; the coefficient of magnetization
of white phosp h orus e xperiences a conside r able di mi nution when t h is
body is tran sformed into red phosp h orus antimony deposited by
electrolysis i n the all ot rOpi c state i s muc h less di amagneti c than the
ordinary variety and t h e coefficient of magnetization of bismut h b e
comes by fusion twenty fi v e times mo r e weak
P aramagnetic bodi es have also a coefficient of m agneti zation i n
dependent o f the i ntensity of the field but these bodies be h ave quite
di ff erently f r om the point of view o f the changes p r oduced by the change
of temperatu r e T h e coe ffi cient of specific magneti zation va r ies Simply
in inverse rati o to t h e absolute temperat u re
T h e diff erence in t h e e ffect of tempe r at u re on t h e coeffi cient of
magnetization of magnetic and diamagnetic bodies is very ma rked whic h
is in favo r of t h e t h eories which attribute magnetism and di amagnetism
to causes of a diff e r ent nature
Th e p r operties of ferromagneti c and pa r amagnetic bodies are on
t h e contrary intimately r elated W h en a fe r romagneti c body is h eated
it is t r ansformed gradually and takes the properties of a paramagnetic
bod y T h e cu r ve of Fig 3 6 represents grap h ically t h e relation between
temperature and intens ity of magnetizat ion I f o r a sample of i r on
subj ect to a magnetizin g field of
units I n the re gion B which
co mmences at 760 C and extends to 9 20 C t h e c o efli c ien t of specific
magnetization obeys exactly an hyperbolic l aw up to
after w h ic h it
dec r eases more rapidly ; B etween 820 and
at which point t h e
7 state be gins it is p r obable that a gradu al transformation takes place
I n the 7 state t h e iron possess es a susceptibility inversely proportional
to t h e absol u te temperature w h ic h is c h aracteristic of pa r amagnetic
At 1 2 80 where t h e last change of state takes place t h e
bodies
coefficient o f specific magnetization increases rapidly in the ratio of
2 to 3 after which it seems to take a variation in reverse r atio to t h e
absolute tempe r atu r e
24
.
.
,
,
,
,
.
.
.
.
.
.
,
,
,
-
.
,
,
,
.
.
,
.
,
,
.
.
.
.
°
,
°
,
°
,
.
,
°
.
,
.
— H
Resu lts of da B oi s a nd H on da
d u B ois and
extended the investigations of C urie to a large n u mbe r
25
H
.
d u B o is a n d K H o n d a , K o n i nk
596 6 02 , 1 909 1 9 10
.
.
0
.
A k ad
.
.
We ten s c h
.
,
Amste rd am ,
Pro c
.
1 2 , pp
.
W I LLI A M s
47
L CTRO N TH E OR Y O F MA G NETISM
E E
( 43 in all ) and decided t h at C u r ie s conclusions do not admit of s u c h
extensive gene r alizations as have been given to them T h ey found that
of the twenty o r more diamagnetic elements examined t h ere are only
six w h ich do not vary wi thin t h e whole tempe r at u r e range and t h at
during a c h ange of p h ysical state a discontinuity in t h e intensity o f
magnetization f r eq u ently occurs T h is change may consist of a large
or small b r eak in t h e curve s h owing t h e relation between intensity of
magnetization and temperature or of a rat h er su dden c h ange in t h e
s h ape of t h e cu r ve
’
.
,
,
.
.
756
°
82 0
°
9 20
°
F I G 36
.
O f the t h ermomagnetic examinations of polymo rp h ous t r ansfo rma
tions made by du B ois and H onda the most remarkable prope r ties
are S h own by tin T h ey found t h at if diamagnetic grey tin is slowly
h eated at 3 2 the intensity o f magnetization w h ich is negative sudden
l y c h anges ( like the density ) and at 3 5 passes t h roug h zero
Furt h er
h eating continuously inc r eases t h e magnetization u ntil t h e value fo r
pa r amagneti c tetragonal tin is reached at about
afte r w h ic h it
remains practically constant
,
.
°
,
,
,
°
.
.
A n a logy B etween th e M an ner i n Wh i c h th e I n ten si ty of M a gn eti
za ti on of a M a gn eti c B ody I n crea s es u n der th e I nfl uen ce of Temper a tu r e
a n d th e I n ten si ty of th e Fi el d, a n d th e M a n n er i n Whi c h th e D en si ty of a
Flu i d I n crea ses u n der th e I nflu en ce of Tempera tu re a n d P ressu re
T he r e
are many analogies between t h e fu nction f ( I , H , T)
O as applied to a
magnetic body and the function f (D , p , T) = O as applied to a fluid
T h e intensity of magnetization I co rr esponds to t h e density D , t h e
intensity of t h e field H co r responds to t h e p r essure p , and the absol u te
temperature T plays t h e same r ole in t h e two cases For a p aram ag
26
.
.
.
.
netic body or a fe rr omagnetic body at a temperature above t h at
of t h e transformation point the relation is found
,
I = A
ILLI N OIS E NG I NEE RI N G
48
E
XP E RIM E N T STATIO N
wh ere A is a constant
Similarly fo r a fl u id s u fficiently r emoved fr om
its temperatu r e of liquefaction one h as t h e r elation
.
I
=
P
R
T
__
l
wh ere
is a constant
-
Th e
law of t h e cons tancy of t h e intensity of
jé
magnetization when t h e field va ries and th e Inve r se l a w of t h e absolute
temperat u re for t h e coe fficient of magnetization cor r espond r espective
ly to the laws of B oyle and of C harles
T h e manner in which t h e intensity of magnetization as a function
of t h e temperature varies in t h e neig h borhood of t h e temperature of
t r ans formation the field remaining constant corresponds to t h e manne r
in which t h e density of t h e fluid as a function of t h e tempe r at u re va ries
in the neighborhood of the c r itical temperature t h e p r essu r e r emaining
constant T h e analogy between I = ¢ ( T ) and D = ¢ ( T) correspond
ing to pressures above the critical p r essu r es is shown grap h icall y in
Figs 3 7and 38 Although as C u r ie has S h own the analogy seems to
be almost perfect when t h e field stren gt h in the one case and pressure
in the other is kept constant yet it has n o t been s h own to hold in the
case whe r e temperature is kept constant in bot h phenomena
.
,
.
,
,
,
.
.
.
,
.
H = Co n stan t
P = Co n stan t
FI G
.
37
FI G
38
.
I n the case of m ag netization if t h e temperature is kept constant
and t h e field strengt h altern ated a hyste r e sis loop is obtained wh en
intensity of magnetization I is plo tted against field str e ngth H Th at
this is true in t h e case of a fluid when the temperat ur e is kept constant
and the relation between density and p r essure plotted h as not b een
s h o wn I t i s true that in the case of soli ds t h e p h enomena of lag occurs
with variation of density and pressure at constant temperature and it
may be true to a small degree in the cas e of liquids but it is ha r d to
conceive of it as being true in the case of g ases
.
.
,
,
.
EXPERIME NTA L EV I D EN C E
FA V OR O F T H E ELE C TRO N T H EOR Y
O F M A G NE TI SM
Let us ass ume
2 7 Th e M olecu la r M agneti c Fi eld of P y rr h oti te
t h at we have two fields H and H m acting in a crystalline s u bstance
and that the crystalli ne structure possesses three rectangular planes of
symmetry coincident wi th the planes o f the system o f co ordi nates and
t h at each component of the molecular field i s proportional to the corre
spon d in g component of the intensity o f magnetization wit h a coefficient
IV
.
IN
.
.
,
,
,
I L LI N OIS E NG I NEERI NG
50
T h en
N1 1
H mm
I
cos
c os d>
E
XPERIM ENT STATIO N
H sin a
N21 si n cp
qt
w h ence
2
2
N91
I H cos a s in cp
N11 c os d:si n cp
I H sin a c os ¢
T r ansposing and simpl ifying
2
—
—
—
=
i
I H sin ( ct ct )
I
N
s
n
cos
N
c
2)
p
¢ 0
( 1
s i n cp c o s <p
,
H sin
(
—
( N1 N2 ) I sin cp cos ¢
—
a
c
p)
H sin ( a
and
sin ¢ c o s d>
T h is equation expresses the l aw of mag netization of pyr r hotite
W
see
equation
page
determined
ex
erimentally
by
eiss
9
as
(
)
p
T h e r efore t h e above h ypot h esis acco u nts for t h e experimental proper
ties o f pyrrhotite in the my plane T h ese prope rties are di ff erent from
those in the sea plane only in the magni tude of the con stant
T h e equation
2
—
H I Si n ( a
( NI N2 ) I Sin ¢ cos ¢
states t h at the couple H I s in ( a
exerted by th e e xternal field on the
2
—
intensity of mag netization is equal to the couple ( N1 N2) I sin <t cos cp
which is due to the structure o f the cry stal and wh i ch woul d remai n if
t h e external field were suppressed T h e latter couple tends to brin g the
elementary magnets back into the d i rection o f eas y magnetization T h e
position of equi l ibrium corres pond ing to the ori entation o f t h e magnets
in t h e di r ection 0 2:
i s stable onl y when N1 > N2 > N3
28 Va ri a ti on of the I ntensi ty of M agneti za ti on of M agneti te wi th
Temper a tu re
I t h as been Shown p ag e 2 1 that
I
cos h a 1
Im
Sinh a a
w h ere
,
.
.
.
,
.
.
.
.
.
,
,
4
( 3)
I n t h e case o f ferromagneti c substances we have in addi tion to t h e
exte rnal field an anterior o r molecular field H m whic h is due to t h e action
of the molec u les upon each other and which h as been called by W e i ss
”
the intrinsi c molecular field
J ust as liqui ds can exi st when the
exte rnal p r ess u re is zero so f erroma gnetic bodi es can take a finite
intensity of magnetization in the absence of exte ri or fields I f t h e
interior field acted alone the intensi ty of magneti zation would be
p r opo rt ional to it and we would have
“
,
,
.
.
,
.
H m = NI
and equation ( 43 ) would become
I
a RT
MN
wh e r e N is t h e factor of p r oportionality
.
W I LLI A M s
L C TRO N T H E ORY O F MA G NE TISM
51
E E
equation is represented in Fig 4 1 by t h e straig h t line OA
while equat i on ( 4 1 ) is represented by the curved line OB A T h e In
tensit y o f magnetization being satisfied by equ ations ( 4 1 ) and
th e
po i nts of intersection of t h e curve and t h e straigh t line give t h e values
of I
O ne solution of t h ese equations is
T h is
.
.
.
I
a
0
0
H
0
f r om w h i c h it follows t h at
FI G
.
41
I t can be s h own however t h at only t h e point A r ep r esents a state of
stable equilibrium o f magnetization Fo r suppose t h at we were able
to decrease the intensity of magnetization I directly
Fo r t h e same
value of I and T t h e value of a given by the st r aig h t line ( namely a l ) is
larg er than (1 2 given by t h e c u r ve ( See Fig
a l is t h e value due to
the molecular field w h ich is much stronger t h an the external field w h ose
action is represented by the curve and by (1 2 Now a decrease in t h e
intensity of magnetization means t h at f ewer elementa r y magnets
h ave t h eir magneti c axes pointing in the same direction R eferring
to F i g 20 it will be seen that if t h e molecular field or the field due to
t h e action of one elementar y magnet on another is stronger t h an the
extern al field H equilibrium will be establis h ed only w h en the magnets
have oriented t h emselves into a position such t h at t h e components
o f the moments o f the two fields a r e the same that is when t h e intensity
of magnetization has risen to t h e point A
O n the other hand the
point 0 represents a value at whic h t h e intensity of magnetization is
zero t h at is where as many elementary magnets point in t h e direction
o f easy magnetization as in the oppos i te di rection A sligh t mechani cal
or magnetic disturbance wi ll cause hal f o f the elementary magnets to
swing around into the direction o f easy ma gnetization where they remain
in stable equilibr i um T hus the point 0 corresponds to unstable magne
t i z ati on and the point A to stable ma gnetization
As the parama gnet i c susceptibilit y is V ery small enormous magneti c
fields would be required to increase this spontaneous ma gnetization
,
,
.
.
,
.
.
.
.
,
,
,
,
,
.
,
,
.
.
.
I LL I NOIS E NG I NEERI NG EXPERIME NT STATI O N
52
wh ic h is due to t h e extern al field Ass u ming t h e mec h ani cal analogy
of W e i ss in which the increase in the density of a liq u id requires e xternal
pre ss u res that are i ncomparably greater than those by means of whi ch
t h e density of gas is changed we arrive at the concl u sion that for t h e
’
absolute temperature T the ordinate A A re presents the saturation
A ccording to this a fe rr o
value of the intensity of magnetization
magnetic substance is saturated wi thout t h e least external field T houg h
this inference drawn from the theory seems in contradi ction to t h e
larger number of experimental facts observed yet it agrees perfectly
wi th the phenomena of magnetization observed in cry stals and es
T h is c rystal h as t h e very val
pe c i all y in those of normal pyrrhotite
u ah l e propert y of a magneti c plane in w h ich all t h e elementary magne t s
are situated I n this m agnetic plane is a di rection i n which saturation
takes place wi th very little or no e xternal field while a field of about
units is requi red to bring about satur ati on in a pe rpendi cular
di recti on Th e assumption o f a molecular field accounts ve ry sat isfa c
t ori l y f or the laws that g overn the m agnetization of the normal pyrrho
ti te as a f unction o f the extern al field T h e intensity of magnetization
as a function o f the temperature is a very complicated phenomenon
varyi n g f rom one substance to another and also varyi ng in the same
substance wi th the magnetic field ; there fore it appears do u btful whether
the most simple hypothesi s o f the u ni form molecular magnetic field w il l
be able to account for all the observed p h enomena I n the case of
magnetite howeve r Weiss has sho wn that the theoret i cal cu rve coin
cides wi th the e xperimental curve between the temperatures
79 C
O n the ass umption that a piece o f ordinary iron is
and
587 C
composed of small cry stals havi n g t h e p r operty of a magneti c p l ane
Weiss has al so shown that the hysteresis loops of anne al ed iron can be
given a theoretical interp r etation
I n order to determine the absolute v alues of the in tern al ma gnetic
field we have to exam in e t h e magneti c properties o f the f erromagneti c
substances in the neighbo rh ood o f the point where the spontan eous
magnet i zat i on disappears T h us iron loses its spontaneous m ag netiz a
t i on at the temperature of 756 C B etween th i s po int and 920 C
iron has still a considerable susceptibility the magn etism however
appeari n g onl y under the combined action of the e xte rnal and i nt erna l
fields I n this regi on we have
.
,
,
.
.
,
,
,
,
.
.
,
.
.
,
,
.
,
,
°
.
°
.
,
.
.
°
°
.
.
,
,
,
.
T=
aR
where M i s the r esulting magneti c moment of each molecul e and H
the e xternal field Equation
pag e 2 1 giv es
I
c s h a 1 —l
4
2
,
.
o
a
a
lon g as we consider only the begi nning of the curve OB o f Fi g
=
o
c
rr
9
756
e sponds to the temperature
whose tan g ent at the ori gin
As
,
.
41
WIL L IAMS
53
E L E C TR O N THEORY O F MA G NETI SM
27
3 = 1 029 ,
we may consider only t h e first term on the right h and side
o f the l ast equation T hen
4
( 7)
-
.
Up to the temperature 6 we hav e spontaneous f erromagnetism where
the ext ernal field H is ne gligible in comparison wi t h NI the internal
magnetic field so that in equation
we may wr i te
M NI m a
e
,
3 R0
whence
D i v i din g ( 46 ) by ( 4 8)
or from ( 47)
th i s equat i on reduces to
(
—
T O
) I
T h i s equation represents an equ i lateral h yperbola and allows
determine t h e coefficient N W e i ss found fo r
i ron
N
ni cke l
N
Hm
magneti te
N
7
us
to
.
If the mol ecul ar magnets act upon one another wi th magnetic
forces o f this enormous amount the potential energy due to the mol ec
ular ma gneti c fie l d must have very lar g e values
,
.
H ea t an d M ol ec u lar Fi el d of Ferromagn eti c Su b sta n ces
Th e mutual energy of a numbe r of magnets of invariable mag neti c
moment M i s
—
2
W
% M H cos a
H be i n g the field in wh i ch i s placed one o f the elementary magnets and
which i s due to all the ot h er magnets and a bein g the angle between
H and M
W hen this summation is extended to all the elementa ry
magnets contai ned in 1 cc H becomes t h e molecular field
and the
i ntensity of ma gnetization I is t h e geometri c sum of the magneti c
moments M Th e energy of ma gnetization per unit of volume is then
29
.
Specifi
c
.
.
.
.
W=
ILLI NOIS
54
Th e
EN
G I NE E RI NG
E
XPERIM E NT STATIO N
molecular field is related to t h e intensity of magnetization I by
H m = NI
whe r e N is a con stant coefficient
T h erefore
2
1
2 NI
W
.
Since
this ene r gy is negative it is necessa r y to add energy in order to
demag netize T h us t h e intensity of magnetization decreases continu
o u sl y as t h e temperature i ncreases f r om absolute zero to t h e tempera
ture 6 of t h e disappearance of spontaneous ferromagnetism T h e
total quantity of heat absorbed by the magnetic p h enomena per uni t
of mass of t h e body between t h e temperature w h ere t h e intensity of
magnetization is I and the temperature 9 Is
.
.
,
NI
:
gm
2
2
JD
where J is t h e mec h anical equivalent of t h e calorie and D is t h e densi t y
T h e Specific heat d u e to change in t h e i ntensity of magnetization is
t h en
.
wh i ch must be added to the o r dina ry specific h eat A ccording to
C urie s experimental results I the intensity of magnetization fo r
iron at ordinary temperatures is equal to 1 7
00 and
.
’
,
,
T herefore
Th e
N
3 850
.
NI
energy of d i a ma gn et i z ati on per unit mass is
2=
7
N1
70 6 X 1 0 er g s
.
.
°
At 2 0 C
.
calories
Th e
data
.
follo wing r esults for i r on we r e obtained from C u r ie s expe rimen t al
’
.
I /D C G S
.
.
.
ca l
I n th e
.
I nterva l
16 8
127
.
0
.
( by extrapolation )
From this we see that at ordinary temperatur es t h e specific heat is
al tered due to the ma gnetic phenomena b y only a small amount while
in the neighborhood o f 6 t h e temperature at which spontaneous mag
or about two fi fths
n eti z ati on di sappears the effect amounts to
of the total val ue
,
,
,
,
.
,
WILLIAMS
E
L E C TRO N THEOR Y O F MA G NETISM
55
results of W eiss and B eck S h ow a very interesting relation
between t h e va r iations of the ordi nary specifi c h eat and
Th e
"i ”
At
as functions of t h e tempe r atu r e T h ei r results are represented g r aph
i c al l y in Fig 4 2 curve A representing t h e relation between o r dinary
specific h eat and temperature and cu r ve B t h at between 3 t h e specific
heat due to magnetization and temperature T h e same close agree
ment has been found in t h e ferromagnetic s u bstances ni ckel and
magnetite
.
.
,
,
.
,
.
FI G
.
42
M a gnets of I ron Ni c kel a nd M a gn eti te
Th e
elect r on t h eo r y of fer r omagnetism gives us a means of determining
t h e moment M of t h e molecula r magnets of t h ose substances w h ose
internal magneti c field h as been dete r mined V a r ious met h ods may b e
applied for t h is p u rpose b u t t h e one used by J K un z i is probably t h e
most Simple I n h is met h od K u nz makes use of t h e equation
M N]
30
.
Th e El emen ta r y
,
,
.
.
L
.
,
.
RT
w h ere N is a constant For t h e absolute temperatu r e 6 t h e tempera
tu r e at w h ic h the spontaneo u s ferromagnetism disappear s we h ave the
r elation
.
,
,
a
/3
Wei ss and B e ck Jo ur d e Phy s ser 4 Vol 7 p 2 49
t J K u n z Phy s Re v Vol XXX N o 3 M a r ch 1 9 1 0
.
,
.
,
.
.
,
,
.
,
.
,
.
.
,
.
,
,
,
.
1 9 08
.
ILLI NOI S E N G I NE ERI N G EXP E RIM ENT STATIO N
56
Su bstituting ( 5 1 ) in
we find
where 6 is the pa r tic u la r temperature considered
equation o f gases
p
.
R is gi ven
= RN1 T
where
T here fore
4 5
R
X 10
the saturation value of t h e intensity of magn etization at the a b so
I
lute zero o f temperature h as to be determi n ed from the above th eory
b y means of t h e val ue I the inte nsity of ma gnetization for the case of
saturation at t h e temperatur e t
I n the case o f i ron we have from C urie s results , I
17
00 for
ordinary temperatures and a field stren gth o f 1 3 00 units and I
1 950
*
and 6
T akin g N
3850 the value fo u nd by W eiss an d B eck
27
1 029 we fi n d b y subst itution in equation ( 50)
756
3
M
X
absolute electromagnetic uni ts
Le t N1 be the number of molecul ar mag nets i n u nit volume at the
absolute ze r o Th en we h ave
N1 M = I m = 1 950
.
,
,
°
.
’
,
,
.
,
,
,
,
.
.
22
=
N1 4 3 86 X 1 0
.
.
I f th is n u mber N; o f elementary ma gnets is at the same time t h e
num ber o f molecules of iron and if the mass of one molecul e o f iron is
equal to p we have
,
,
where
N1 1]
0
.
is the density of iron at the absolute zero
=
5/N1
X
grams
p
Le t us assume that the molecul e o f i ron consists of two atoms
then it will be
times heavier than the ato m of hydrogen and the
mass o f the atom of hydrogen uH will be equal to
6
.
,
,
—22
L7
92 X 1 0
—24
x 10
gram s
’
Du B ois and T aylor J on es r found the i ntens ity of m agnetizati on
of iron cont inues to increase up to field stren gths o f 1 500 units At
this val ue they found the value of I for ordi nary temperatures to be
1 850
00 the value obtained by
Substituting t his val u e instead of 1 7
C ur i e we have
=
1 66 X
grams
pH
.
.
,
,
.
We iss
24 9 , 1 908
B e ck , J o ur d e Phy s , V ol 7
, pp
an d T a y lo r J o n es , El ek tr o t Z ei ts c h r , V ol 1 7
544 , 1 896
, p
an d
TD u B o is
.
.
.
.
.
.
.
.
.
ILLI N OIS
58
EN
G I N E E RI NG
E
XP E RIM E NT STATIO N
atomic weight of nickel is
h enc e ass u m ing t h at eac h m olecula r
mag net contains two atoms we find
Th e
,
,
-
22
4 8 x 10
H
—24
,
.
a val u e t h a t is j u s t t hr ee times larger t h an that given by R u t h e rfo r d
AS the deg r ee of accu r acy is t h e same in t h e case of i r on nickel and
magnetite t h e expe r imental evidence indicates t h at t h e molecular mag
net o f nickel is made u p of Six atoms or t h at t h e numbe r of deg r ees of
freedom is o nly one t h ird as g r eat as in t h e case of i r on I n a recent
*
i nvest igation St i fle r h as dete r mined t h e above q u antities for cobalt
H e obtained t h e following val u es :
.
,
,
,
,
.
,
.
N
I
6
M
6 21
.
N1 1}
X 10
4 °
0
.
X
p
10
-
22
t h e atomic weig h t o f cobalt is 59 we obtain on
t h at eac h molecul ar magnet contains t wo atoms
22
X 10 —
u
Since
,
th e
,
assumption
,
-
H
-
_
3 22 X 1 0
.
1 18
a val u e t h at is j ust t wo times larger than R u th e r fo r d s val u e If we
ap ply t h e ab o ve r easoning we must concl u de that t h e elementary
magnet of cobalt is m ade up of fo u r atoms
T h e q u antities conside r ed above a r e given in t h e followi ng table :
n is t h e n u mber of atoms corresponding to one elementa r y ma gnet
’
.
“
.
.
S u b sta n ce
°
—
] = 20
°
9 C
.
NI =
N
75 6
Fe
Fe3 04
Ni
Co
430
500
4 90
57
0
M X 10
H
53 6 33 2 00 1 4 306
20
H
X 10
4
n
_
2
0 00
0 00
6
4
AS
the ratio of t h e density of nickel and iron
is nearly equal
to t h e ratio of t h e atomi c weig h ts
of t h e t wo metals t h e numbe r
of molec u les per unit volume m u st be t h e same for both metals assum
ing t h at eac h molec u le contains two atoms Since t h e moment of the
molecular magnets of nickel is only about 1 8 per cent smaller than t h at
of iron we s h ould expect that t h e intensity of magnetization of nickel
would va r y by abo u t t h is amo u nt f r om t h at of iron w h ile in reality the
magnetization of iron is
times greater th an t h at of nickel T h is
consideration indicates again t h at eit h er t h e molecula r magnet of nickel
contains Si x atoms o r th at only every third molecule is an elementary
magnet
,
,
,
,
.
,
,
.
,
.
W W
.
.
S t i fle r ,
Phy s
.
Re v
.
,
Vol XXX I II N o
.
,
.
4 , p 26 8 , 1 9 1 1
.
.
WILLIAMS
—
E
L E C TRO N T H E ORY O F MA G N ETISM
59
fundamental di fference in the molecular magnets of iron and
nickel must be taken into account w h en explaining some of the very
interesting di ffe r ences in the magneti c be h avior of the two metals
T h us t h e first layer of electrol ytically deposited nickel i s stronge r
magnetically t h an the subsequent laye r s while for Iron the opposi te i s
t r ue t h at is t h in layers o f i r on a r e much less magneti c than t h icker
layers I n addition a longit u dinal compression decreases the magneti
z a t i o n of iron and increases t h at of nickel
I n a recent article the
aut h or has shown that t h e e ffect of t r ansverse j oints in nickel bars is
t inc r ease t h e magneti c induction rathe r t h an decrease it as in t h e case
0
I r on
T h is
.
,
,
,
,
.
,
.
?
.
FI G
Th e H y s teresi s Loop
.
43
r
o
n
L
e
I
us
assume
t
h
at
t
h
e
element
t
f
a r y crystal of iron has properties analogous to those o f t h e crystal
of pyrr h otite and t h at t h e direction of easy magnetization is distributed
uniformly th r ough out t h e vol u me
W orking wit h weak fields let us
fi r st consider only t h e i rreve r sible phenomena W hen the substance
is in t h e neutral state t h e magnetization vecto r s o f the di fferent element
ary c rystals will te r minate on t h e su rface of a sp h e r e with unifo r m
density I f t h e field H acting in the di r ection Ox Fig 43 exceeds t h e
coercive field H ” all t h e elementa r y magnets w h ic h were originally
directed in t h e negative direction will swing round so t h at all t h e
intensity of magnetization vecto r s will be cont a ined in a cone ha v ing
OH for its axis and Of semiangle qb whic h is given by
H /H
0 0 8 65
Each of t h e elementa r y magnets t h at swings a r o und will contribute
its moment 111 1 to the resulting intensity of magnetization in t h e di re c
tion x Now the number o f vecto r s ending on the sp h ere is equal to
N the number of elementary c r ystals with a plane of magnetization
31
.
o
.
.
.
,
.
,
.
,
.
c
.
.
,
,
E H Wi ll i a ms Phy s
.
.
,
.
Rev
.
,
Vol XXX I II N o
.
,
.
1 , p 59 , 1 9 1 1
.
.
ILLI N OIS
60
EN
G I NEE RI N G
E
XP E RIM E NT STATIO N
and the n u mber ending on t h e zone s u btended by the angle <1) befo r e
t h e field is applied will be
Th e
momen t due
,
to
thes e magnets in the dire ction Ox is
,
)
sin d
c o s d>
q
.
Th e
moment d u e to all the magnets that swing round into the direction
Ox is
si n cp c os d> d c
.
si nce the number origi nally in the positive di rection is equal to t h e
number that have been turned around t h e resulting moment in t h e
direction Ox wi ll be
,
M=2
cos et
H
c
/H
there f ore
J
”
?
[1
where M is the resultant magnetic moment per unit vo l ume , that is
the i ntens i ty of ma gnetization I
.
,
—
WIL L IAMS
E LE C TRO N THEOR Y O F MA G N ETI SM
Th e
61
g r aphic representati on of t h e equation
( 54 )
is gi ven by Fig
.
44
.
asymptote i s given by
by H
0
and if H
satura tion
.
T his resembles
Im
=
7
an h yperbola whose hori zontal
and whose vertical as ymptote is given
If H is equal t o H the intensity o f magnetizat i on I
0
I
B ut p h ysicall y t h is must b e t h e value of
the r e fore we shall write
.
00
v
,
[
5
( 5)
I
I f we were to draw the curve correspondi n g to th i s equation we shoul d
find a curve o f exactl y the same character as the prev i ous one except
that for a gi ven value o f H the ordinate I would be twi ce as l arg e as
before
,
.
FI G 4 5
.
H
If one causes the fiel d to oscillate between the value
H and
the graph i cal representati on o f the curve o f equation ( 55) wi ll be gi ven
—
by Fi g 45 When the fie l d H i s appl i ed the figurative points wi ll be
collected on th e negat i ve Side o f the Sphere of Fi g 43 With the
sampl e in th i s condition let us be gin the description of a cycle vary ing
—
the fiel d from
H to i ncreasin g positive values
T h e i ntensity of
ma gnet i zat i on wi ll change ver y little so l on g as the field i s less than
H
At th i s po i nt i t be gi ns to chan g e very rapidly and wi ll descr i be
a curv e s i m i lar to the curves considered above
T h is curve wi th the
port i on o f t h e straight line alread y described wi ll constitute hal f o f a
H Th e
c y cle correspo n di n g to a variation o f the fiel d f rom
H to
cy cle i s completed , f rom s ymmetry , b y return in g to the ori gin
,
.
.
,
.
.
,
.
.
.
.
IL L I N OIS E NG I NE ERI N G EXPERIME NT STATIO N
62
Equation ( 55) assumes t h at the coeffi cients Nz and N3 of Fig 3 9
are zero
No w, in t h e case of i r on , t h is is only app r oximately t r ue
.
.
.
Making t h ese co r rections t h e t h eo r etical conside r ations give cycles
whic h a r e s h own in Fig 4 6 T h e scale h as been c h osen so as to rep ro
duce as nearly as possible t h e expe rimental c urves of Fig 4 7 w h ic h
*
are taken f r om t h e results of Ewing
T h e simila r ity of t h e ascending
and descendi n g cu r ves more particularly t h e oute r ones is very marked
T h e p r incipal di ff erences to be noted between t h e experimental and
theoretical c u rves are first t h at t h e upper limits of t h e cycles fo r
medi u m fields fall more nearly on t h e outer cycle in t h e experimental
th an in the theoretical curves and second t h at for fields b u t slightly
g r eater t h an H the theoretical c u rves are rectangu lar in Shape w h ile
the experimental curves are not
,
.
.
.
,
.
,
,
,
.
,
,
,
,
.
32
Excepti ons to the Ek c tron Th eor y
.
W h ile t h e elect r on theory
.
is capable of e xplaining many of t h e p h enomena of magnetism yet
in its present form and present stage of development it is u nable to ao
count for a la rg e number of cases
C urie s rules which are the basis of the p r esent t h eo r y hold rigidly
for very fe w substances T h us according to these r u les the diamagnetic
susceptibility is i ndependent of t h e tempe r atu r e H owever t h ere a r e
substances whose diama gneti c s u sceptibility increases with inc r ease of
temperature while in othe r substances t h e Opposite is the case Anoth er
of C urie s rules states that for paramagneti c s u bstances t h e su sceptibility
is inversel y proportional to the absolute temperature W hile t h is holds f o r
a very large number of substances there are cases w h ere t h e r ule fails
to represent the f acts as dete r mined by expe r iment
R ecently H
’
K amerling O nnes and A P e rri e r rhave shown t h at for several substances
the law does not hold for ve r y l o w tempe r atu r es Some substances at
temperatures below those at whi ch C u rie s c / T l a w is obeyed follow
,
.
’
,
,
.
,
,
.
,
.
’
,
,
.
,
.
.
.
.
’
0
more nearly a
VT l a w
None of the salts i nvestigated by t h e above
.
aut h o r s Show signs of saturation phenomenon P y r rhotite whose
magneti c properties conform to the electron theo ry ve r y closely u p to
6 t h e tempe r atu r e of t r ansformation is very abnormal above this
temperature
From h is experimental res u lts upon a limited number of subs t ances
C urie comes to t h e conclusion t h at t h e paramagnetic susceptibility i s
independent of the state of agg r egation of c h emical combination of
elements Now oxygen and boron a r e pa r amagnetic oxygen st r ongly
so yet t h e oxide of boron is diamagneti c Likewise Al s M 0 0 M 0
Th O U r O and ot h er oxides are diamagnetic
Th e law o f app r oach of the intensity of magnetization to the constant
value o f saturation holds only for cobalt and not for i r on an d nickel
,
.
,
,
.
,
,
.
,
,
.
,
0
,
.
,
.
E wi n g M agnet ic I n d u c t i o n
TH K a mer li n g O nn es a n d
Pr o c 14 p 1 1 5 1 9 1 1
,
.
.
,
.
,
.
,
3 rd Ed , p 1 0 6, Fi g 50
A P err i e r , K o n i n k A k ad
.
.
.
.
.
.
.
.
Wete ns c h
.
,
A ms t erd a m
WILLIAMS
FI G
.
46
E
L E CTRO N T H E ORY
OF
MA G N ETISM
63
ILLI N OIS E NG I NE ERI N G EXP E RIME NT STATI O N
64
Th e
large number o f exceptio n s to the elect r on t h eory i n its pres ent
form requi res either that it be abandoned or that the theory be modi
fi ed to fit more exactly e xper i mental results
Th e f act that it agrees
in such a lar g e number o f cases with experi ment and that by its appli ca
tion the f undamental quantities o f nature can be Ob t ai ned in suc h c l ose
agreement with observation gives hope that ul t i ma tely the presen t
t h eory wi ll be modified so t h at it will hold univers al ly
.
,
,
’
,
.
V
B I B L IO G RAPH Y
.
.
Th e
followi ng bibliography is i ntended to gi ve only t h ose works
and res ul ts which have contributed most toward the advancement
of t h e electron theory o f m agnetism to its present state of development
.
EX P ERI MENTAL
M a gn et iza t i o n P la ne of P yrrh o t i te J our
.
1
.
d e Phy s Ser 3
P W E I SS T h e
Vol 8 p 542 1 899
P C U RIE M a gn et ic Propert i es of B odi es a t V ario us Temperat ur es Ann
d e Ch em Ser 7 V ol 5 p 28 9 1 89 5
P WEI SS Th e M agn et ic Pr o pe rt i es of Pyrrh o t i t e J o ur d e Phys Set 4
Vol 4
J o ur d e Phys , Ser 4 Vol 4 p 829 1 905
469 1 90 5
WEI SS
m m T h e Therma l V arIa t Io n of t h e M a gnet iz at i o n of Pyrrh o ti te
J o ur d e Phy s Ser 4 V ol 4 p 847 1 90 5
J Kt l
1 1 8 M ag ne t ic Pro pert i es of H
ema t i t e Ar chiv es d es S ci en ces V ol 23
.
.
,
.
2
.
,
.
.
.
,
.
.
4
.
,
.
.
.
7
.
,
.
,
igg 1 907
W
P N
I I $p 5 1 908
E
.
IS S
LA
5
O
wmse
.
EB
,
.
.
,
,
.
,
,
,
B ECK
J o ur
Hy st eresis of
.
,
.
,
H ea t
cifi c
s
.
R o t a t in g Fi el d J o ur
th e
,
.
d e P hy s
,
Ser 4 ,
.
.
h
of Ferr o magn et ic Sub
M olec ular
and
Fi el d
7, p 24 9 , 1 908
Se r 4 , V ol
V Q U I IT N ER
agn e t i c Pro pe rt i es of M a gn e t i t e , Ar chi v es d es Sc Ien ces ,
Ser 4 , V ol 2 6 , p 358 1 908
D U BOIS
H ONDA Th e Th ermo ma gn e t ic P ro pe r t ies of El eme nts , K o mn k
A k ad We t e ns c h Am st e rd am , Pr o c 1 2 ,
59 6 , 1 9 1 0
WE ISS
FO EX
Th e M agnet iz a t i o n of errom a net ic B odi es Ar et es d es
Ar chiv es es S ci en ces , Se r 4 , V ol 3 1 ,
Sc i ces , Ser 4 , V ol 3 1 , p 5 , 1 9 1 1
l g1 1
p
,
W W S TI FLER Th e M agne t iz a t i on of Co b a l t as a F un c ti o n of t h e Tem
a t ur e a n d t h e D e t erm ma t i on of i ts I n t ri n s ic M a gn e t ic Fi e l d , Phy s Re v ,
0 1 33 , N o 4 , p 2 68 19 1 1
P WEI SS On a Ne w Pr o pe rt y of t h e M a gn e t ic M ol e c ul e , C om ptes Rend us ,
V ol 1 52 p 79 , p 1 87 p 3 6 7, an d p 688 , 19 1 1
WEI SS
B LO C K
On t he M
e t i z a t i o n of N ick e l , C o b a l t a n d t h e A llo y s of
N ick el an d C ob al t , Co mptes nd us , V ol 1 53 , p 9 4 1 , 1 9 1 1
de
Th e
.
’
.
.
,
.
,
.
,
.
.
.
.
.
.
9
.
.
,
.
.
.
c
.
,
.
.
,
stan es ,
8
.
.
p
6
,
.
,
.
5
,
.
.
,
.
,
.
3
.
,
.
s
.
.
,
.
.
.
.
.
.
.
.
.
.
g
.
.
gg
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
,
.
.
.
.
TH E ORETI CAL
E le c tron Hy po thesis an d Th eo ry of M agn e t ism
.
A n n d e Phy s
W VO I GT
V ol 9 p 1 1 5 1 902
Th e M i
2 J J TH OMSO N
e t ic Pr o pe rt i es of S y s te ms of Co rp us c l es D escri b i n g
1 903
Cir c ul ar Orbi ts Phi l IiIg
3
S
er 6 V ol 6 p 6 7
g
A nn d e Ch em e t
M
e t i z a t Io n an d t h e E l e c t ro n T h eo ry
3 P LAN G EV I N
d e Phy s Ser 8
ol 5 p 7
0 1 90 5
E E Fo m mn Th e E le c tr on T h eo Ch V I I I ( 1 906
N R CAM P B ELL M od ern E le c tri ca l qh eory Ch I V ( 1 907
P W EI SS T h e Hyp o t h es is of t h e M ole c ul ar Fi e ld an d th e F erro magn et i c
Pr o pert y J our d e Phys Ser 4 V ol 6 p 66 1 1 90 7
7 J K U N z T h e A b sol ute V al ue s of t h e M o men ts of t h e El emen tary M agn ets
of Iro n N ick el an d M agn et i te Phy s Re v V ol 30 N o 3 p 35 9 1 9 1 0
8 P WEISS
On t h e Ra t i onal i t y of t h e Ra t i os of t h e M ol ec ul ar M agn et I c M o
ments and t h e M agn et o n Ar chives d es S ci en ces Ser 4 V ol 3 1 p 40 1 1 9 1 1
1
.
.
.
.
.
.
,
.
,
.
.
,
.
,
.
/
.
,
.
.
.
.
.
,
.
.
.
.
.
,
.
,
0
.
.
,
,
.
.
,
.
,
.
.
,
,
.
.
.
.
,
.
,
.
.
,
.
,
,
.
.
.
.
,
.
,
.
.
y
.
.
,
.
.
,
.
,
.
,
.
,
,
.
,
.
,
.
,
.
P U BLICATIO N S
66
ullet i n
B
fi
ve
cent
s
No
81
F uel T ests
.
EN
TH E
OF
G I N EERI NG
E
t H ou se h e t i n g B o il rs
wi h
a
-
e
X P ERI M ENT STATIO N
J
by
.
M
.
S n o d g ss
ra
.
1 909
..
Fifty
.
.
ulleti n N 8 2 T h O cc l u d d G s s i C o l b y S W P rr d P rry B rk r 1 909
Fi fte n cents
B ul let i n N
88
T s t s of T u n gs ten L mps b y T H A m ri n d A Gue l l 1 90 9 Tw nt y c nts
84
B ullet i n N
T est s of T w Ty p s of T i le R f F ur n c es u nd r W t e r t u b B oil r b y J
1 9 09
Fifte n c nts
M S n o d g r ss
A S t ud y of B s
d B r i n g Pl t s fa C o l u mns
B ullet i n N
86
d B ms b y N C li fl d
Tw nt y cen ts
1 90 9
Ri c k r
Th
B ull t i n N
86
T h e r m l C o nduct i v i t y of Fi C l y t Hi g h T mpe r tu r s b y J K
C l ment d W L Eg y 1 9 0 9 Twenty ce t
B ullet i N
8 7 Un i t C o l
d t h e C o mp o s i t i o n of C o l A h b y S W P rr
d W F
Wh e l r 1 90 9 Th i rty fi ve c ents
T h W t h ri n g of C o l b y S W P rr
B u l let i n No 8 8
d W F W h e le r
1 90 9
Tw nt y
cents
fi
B ullet i n N
89
T sts of W s h d G r d s of I ll i n o i s C o l b y C S M G
1 909
S eventy
y
cents
fi
A S t u d y i He t T r nsm i ss i o n b y J K C lem nt
B ullet n N 40
d C M G rl nd
1910
cents
T
T sts f T i mb e r B e ms b y A r t h ur N T l b o t 1 9 1 0 Twe ty cents
B ullet i n N 4 1
T h Efl t of K y w y s o n t h S t ren gt h of S h f t s b y H rb rt F M oore
B ullet i n N
42
cents
T
19 10
F r ig h t T r i n R es ist n c e b y Ed w r d C S c h m idt 1 9 1 0 S ev nty fi c nt
B ull ti n N
48
A
I nv st i g t i o n of B u ilt p C olumns u nd r Lo d b y A r th ur N T lb o t
B ull t i n N
44
Th i t y fi
ce ts
191 1
d H rbe r t F M oor
T h S t r ngt h of O x y c e t y l n
W lds i S t l b y H r b rt L W h i tt m or
B ullet i n N
46
c nt
1 9 1 1 Th i r t y fi
T h S p o n t n ou s C o m b ust i o n of C o l b y S W P rr
d F W K
m
B ull ti n N 46
c ts
1 9 1 1 F ty fi
B ullet i n N 47 M g n t i c P rop r t i es of H u sl r All oy s b y E d w rd B S t p h nso n 1 9 1 1
cents
Tw nty fi
R si st n c t Fl o w t h ro u gh Lo c o m o t i v W t r Co l u mn b y A rt h ur N T l b o t
B ull t i n N 48
191 1
F ty c t
d M l i n L En g r
T es ts of Nick l S t el R i v t d J o i nts b y A r t h u r N T lb o t d He rb rt F
B ullet i n N
49
Th i rt y cent
M oor
191 1
T s ts of S u c ti o n G P ro du c e r b y C M G rl nd d A P K r t 1 9 1 2
B ull t i n N 6 0
Fifty c nt
B ull ti n N 6 1 S t r t Lig h t in g b y J M B ry nt d H G H ke 1 9 1 2 Th i rty fi v cent
I n s t i g t i o n of t h S t ren g t h of R o ll d Z i n c b y H r b r t F M oo r
62
A
B ulleti n N
Fift n ents
19 1 2
I nd u c t n c f C o ils b y M org n B roo ks d H M T u r n r 1 9 1 2 Fo ty cents
B ul l t i n N 6 3
M ec h n i c l S t ss s i T r nsm iss i o n L i nes b y A G u e ll 1 9 1 2 Twent y cents
B ul let i n N 6 4
S t r t i n g C u rr n ts of T r ns forme rs w i t h S p ci l R f r n c t T r nsform rs
66
B ull t i n N
1 9 12
Tw nt y cents
w t h S i li c o n S t e l Cor s b y T ry g e D Y
T ests of Co lumns :A I nv st i ti o n of t h V l u of C n c ret
R e i nfor ce
66
B l let i n N
m n t for S t ru c tu r l S t el C o lumns b y A r t h u r N T l t d A rt h u r R Lord 1 9 1 2 Tw nt y fi
cents
A R ev i e w of Pu b l i c t i o n N
127
B llet i n N 6 7 S upe r h e t d S t m i L o c o m o t i v Se r i c
of t h C r ne g i I n t i t u t i o n of W sh i n g to n b y W F M G o ss 1 9 1 2 Forty cent
68
A N w A n l y si s of t h C y l i nde r P rform nc of R c i p ro c t i g E n gi n s b y J
B ull t i n N
P ul C l y t o n 1 9 1 2 S i ty c nt
d T o nn g R t i n g
of Co ld We t h e r u po n T r i n R si st n c
Th
Efi
t
B ull t i n N 6 9
T went y c nts
1912
d F W M rq u i s
b y Ed w r d C S c h m d t
B ul l t i n N 6 0 T h e C o ki ng of C o l t L w T mp r tu res wi t h P r l imi n ry St ud y of th
T w nt y fi
19 12
c nts
d H L Ol i n
B y P ro d u c t s b y S W P rr
C h r c t ri st i cs d Li m i t t i o ns f t h S ri s T r ns form r b y A R A nd rso n
B ul let i n N
61
T w nt y fi ve ce t s
19 12
d H R W oo d ro w
1 9 12
Th i t y
T h Elec t ro n T h e ory of M g net is m b y Elm r H W i ll i ms
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r
T H I S B OOK I S D U E ON TH E LA S T D A T E
S TA MIP B D B EL OW
AN
C EN T S
W I LL B E A S S ES S ED F O R F A I L U R E T O R ETU R N
T H I S B O O K O N T H E D A T E D U E T H E P EN A LTY
W I L L I N C R EA S E T O 5 0 C EN TS O N T H E F O U RT H
DAY
A N D TO
O N T H E S EV EN T H
DA Y
O V ER D U E
I N I T I AL
FI N E
OF
25
.
.
SEP 1 5
1932
2
1
9
3
6
1
e
se
59
MAR 3 0
5
1936