distance between two neighbouring molecules, when it will cease to be
distinguishable, but, assuming the molecular theory of magnetism to be
true, the above statement will still hold good for the intermolecular
gap. The same pressure P will be exerted across any imaginary section
of a magnetized rod, the stress being sustained by the intermolecular
springs, whatever their physical nature may be, to which the
elasticity of the metal is due. The whole of the rod will therefore be
subject to a compressive longitudinal stress P, the associated
contraction R, expressed as a fraction of the original length, being
R = P/M = (B² - H²) / 8[pi]M,
where M is Young's modulus. This was found to be insufficient to
account for the whole of the retraction exhibited by iron in strong
fields, but it was pointed out by L. T. More[36] that R ought to be
regarded as a "correction" to be applied to the results of
experiments on magnetic change of length, the magnetic stress being no
less an extraneous effect than a stress applied mechanically. Those
who support this view generally speak of the stress as "Maxwell's
stress," and assume its value to be B^2/8[pi]. The stress in question
seems, however, to be quite unconnected with the "stress in the
medium" contemplated by Maxwell, and its value is not exactly
B^2/8[pi] except in the particular case of a permanent ring magnet,
when H = O. Further, Maxwell's stress is a tension along the lines of
force, and is equal to B^2/8[pi] only when B = H, and there is no
magnetization.[37] Some writers have indeed contended that the stress
in magnetized iron is not compressive, but tensile, even when, as in
the case of a ring-magnet, there are no free ends. The point at issue
has an important bearing upon the possible correlation of magnetic
phenomena, but, though it has given rise to much discussion, no
accepted conclusion has yet been reached.[38]
7. EFFECTS OF MECHANICAL STRESS UPON MAGNETIZATION
The effects of traction, compression and torsion in relation to
magnetism have formed the subject of much patient investigation,
especially at the hands of J. A. Ewing, C. G. Knott and the
indefatigable physicists of Tokyo University. The results of their
experiments embrace a multiplicity of details of which it is impossible
to give an adequate summary. Only a few of the most important can be
mentioned here; the reader who wishes for fuller information should
consult the original papers.[39]
It was first discovered by E. Villari in 1868 that the magnetic
susceptibility of an iron wire was increased by stretching when the
magnetization was below a certain value, but diminished when that value
was exceeded; this phenomenon has been termed by Lord Kelvin, who
discovered it independently, the "Villari reversal," the value of the
magnetization for which stretching by a given load produces no effect
being known as the "Villari critical point" for that load. The Villari
critical point for a given sample of iron is reached with a smaller
magnetizing force when the stretching load is great than when it is
small; the reversal also occurs with smaller loads and with weaker
fields when the iron is soft than when it is hard. The following table
shows the values of I and H corresponding to the Villari critical point
in some of Ewing's experiments:--
+------------------------------+-----------------------------+
| Soft Iron. | Hard Iron. |
+-----------------+------+-----+-----------------+------+----+
|Kilos per sq. mm.| I. | H. |Kilos per sq. mm.| I. | H. |
+-----------------+------+-----+-----------------+------+----+
| 2.15 | 1220 | 7.3 | 27.6 | 1180 | 34 |
| 4.3 | 1040 | 4.3 | 32.2 | 1150 | 32 |
| 8.6 | 840 | 3.4 | 37.3 | 1110 | 29 |
| 12.9 | 690 | 3.05| 42.5 | 1020 | 25 |
+-----------------+------+-----+-----------------+------+----+
The effects of pulling stress may be observed either when the wire is
stretched by a constant load while the magnetizing force is varied, or
when the magnetizing force is kept constant while the load is varied. In
the latter case the first application of stress is always attended by an
increase--often a very great one--of the magnetization, whether the
field is weak or strong, but after a load has been put on and taken off
several times the changes of magnetization become cyclic. From
experiments of both classes it appears that for a given field there is a
certain value of the load for which the magnetization is a maximum, the
maximum occurring at a smaller load the stronger the field. In very
strong fields the maximum may even disappear altogether, the effect of
the smallest stress being to diminish the magnetization; on the other
hand, with very weak fields the maximum may not have been reached with
the greatest load that the wire can support without permanent
deformation. When the load on a hardened wire is gradually increased,
the maximum value of I is found to correspond with a greater stress than
when the load is gradually diminished, this being an effect of
hysteresis. Analogous changes are observed in the residual magnetization
which remains after the wire has been subjected to fields of different
strength. The effects of longitudinal pressure are opposite to those of
traction; when the cyclic condition has been reached, pressure reduces
the magnetization of iron in weak fields and increases it in strong
fields (Ewing, _Magnetic Induction_, 1900, 223).
The influence of traction in diminishing the susceptibility of nickel
was first noticed by Kelvin (W. Thomson), and was subsequently
investigated by Ewing and Cowan. The latter found the effect to be
enormous, not only upon the induced magnetization, but in a still
greater degree upon the residual. Even under so "moderate" a load as 33
kilogrammes per square mm., the induced magnetization of a hard-drawn
nickel wire in a field of 60 fell from 386 to 72 units, while the
residual was reduced from about 280 to 10. Ewing has also examined the
effects produced by longitudinal compression upon the susceptibility and
retentiveness of nickel, and found, as was to be expected, that both
were greatly increased by pressure. The maximum susceptibility of one of
his bars rose from 5.6 to 29 under a stress of 19.8 kilos per square mm.
There were reasons for believing that no Villari reversal would be found
in nickel. Ewing and Cowan looked carefully for it, especially in weak
fields, but failed to discover anything of the kind.[40] Some
experiments by A. Heydweiller,[41] which appeared to indicate a reversal
in weak fields (corresponding to I = 5, or thereabouts), have been shown
by Honda and Shimizu to be vitiated by the fact that his specimen was
not initially in a magnetically neutral state; they found that when the
applied field had the same direction as that of the permanent
magnetization, Heydweiller's fallacious results were easily obtained;
but if the field were applied in the direction opposite to that of the
permanent magnetization, or if, as should rightly be the case, there
were no permanent magnetization at all, then there was no indication of
any Villari reversal. Thus a very important question, which has given
rise to some controversy, appears to be now definitely settled.
The effects of longitudinal pressure upon the magnetization of cast
cobalt have been examined by C. Chree,[42] and also by J. A. Ewing.[43]
Chree's experiments were undertaken at the suggestion of J. J. Thomson,
who, from the results of Bidwell's observations on the magnetic
deformation of cobalt, was led to expect that that metal would exhibit a
reversal opposite in character to the effect observed in iron. The
anticipated reversal was duly found by Chree, the critical point
corresponding, under the moderate stress employed, to a field of about
120 units. Ewing's independent experiments showed that the magnetization
curve for a cobalt rod under a load of 16.2 kilogrammes per square mm.
crossed the curve for the same rod when not loaded at H = 53. Both
observers noticed analogous effects in the residual magnetization. The
effect of tension was subsequently studied by Nagaoka and Honda, who in
1902 confirmed, _mutatis mutandis_, the results obtained by Chree and
Ewing for cast cobalt, while for annealed cobalt it turned out that
tension always caused diminution of magnetization, the diminution
increasing with increasing fields. They also investigated the magnetic
behaviour of various nickel-steels under tension, and found that there
was always increase of magnetization. Thus it has been proved that in
annealed cobalt and in nickel-steel there is no Villari reversal.
It has been pointed out by J. J. Thomson (_Applications of Dynamics to
Physics and Chemistry_, 47) that on dynamical principles there must be a
reciprocal relation between the changes of dimensions produced by
magnetization and the changes of magnetization attending mechanical
strain. Since, for example, stretching diminishes the magnetization of
nickel, it follows from theory that the length of a nickel rod should be
diminished by magnetization and conversely. So, too, the Villari
reversals in iron and cobalt might have been predicted--as indeed that
in cobalt actually was--from a knowledge of the changes of length which
those metals exhibit when magnetized.
The complete reciprocity of the effects of magnetization upon length and
of stretching upon magnetization is shown by the following parallel
statements:--
_Iron._
Magnetization produces increase Tension produces increase of
of length in weak fields, magnetization in weak fields,
decrease in strong fields. decrease in strong fields.
_Cast Cobalt._
Magnetization produces decrease Tension produces decrease of
of length in weak fields, magnetization in weak fields,
increase in strong fields. increase in strong fields.
_Nickel and Annealed Cobalt._
Magnetization produces decrease Tension produces decrease of
of length in all fields. magnetization in all fields.
_Nickel-Steel._
Magnetization produces increase Tension produces increase of
of length in all fields. magnetization in all fields.
Nagaoka and Honda (_Phil. Mag._, 1898, 46, 261) have investigated the
effects of hydrostatic pressure upon magnetization, using the same
pieces of iron and nickel as were employed in their experiments upon
magnetic change of volume. In the iron cylinder and ovoid, which
expanded when magnetized, compression caused a diminution of
magnetization; in the nickel rod, which contracted when magnetized,
pressure was attended by an increase of magnetization. The amount of
the change was in both cases exceedingly small, that in iron being
less than 0.1 C.G.S. unit with a pressure of 250 atmospheres and H =
54. It would hardly be safe to generalize from these observations; the
effects may possibly be dependent upon the physical condition of the
metals. In the same paper Nagaoka and Honda describe an important
experiment on the effect of transverse stress. An iron tube, having
its ends closed by brass caps, was placed inside a compressing vessel
into which water was forced until the pressure upon the outer surface
of the tube reached 250 atmospheres. The experiment was the reverse of
one made by Kelvin with a gun-barrel subjected to internal hydrostatic
pressure (_Phil. Trans._, 1878, 152, 64), and the results were also
the reverse. Under increasing magnetizing force the magnetization
first increased, reached a maximum, and then diminished until its
value ultimately became less than when the iron was in the unstrained
condition. Experiments on the effect of external hydrostatic pressure
upon the magnetization of iron rings have also been made by F.
Frisbie,[44] who found that for the magnetizing forces used by Nagaoka
and Honda pressure produced a small _increase_ of magnetization, a
result which appears to be in accord with theory.
The relations of torsion to magnetization were first carefully studied
by G. Wiedemann, whose researches are described in his _Elektricität_,
iii. 671. The most interesting of his discoveries, now generally known
as the "Wiedemann effect," is the following: If we magnetize
longitudinally a straight wire which is fixed at one end and free at the
other, and then pass an electric current through the wire (or first pass
the current and then magnetize), the free end of the wire will twist in
a certain direction depending upon circumstances: if the wire is of
iron, and is magnetized (with a moderate force) so that its free end has
north polarity, while the current through it passes from the fixed to
the free end, then the free end as seen from the fixed end will twist in
the direction of the hands of a watch; if either the magnetization or
the current is reversed, the direction of the twist will be reversed. To
this mechanical phenomenon there is a magnetic reciprocal. If we twist
the free end of a ferromagnetic wire while a current is passing through
it, the wire becomes longitudinally magnetized, the direction of the
magnetization depending upon circumstances: if the wire is of iron and
is twisted so that its free end as seen from the fixed end turns in the
direction of the hands of a watch, while the current passes from the
fixed to the free end, then the direction of the resulting magnetization
will be such as to make the free end a north pole. The twist effect
exhibited by iron under moderate longitudinal magnetization has been
called by Knott a _positive_ Wiedemann effect; if the twist were
reversed, the other conditions remaining the same, the sign of the
Wiedemann effect would be _negative_. An explanation of the twist has
been given by Maxwell (_Electricity and Magnetism_, § 448). The wire is
subject to two superposed magnetizations, the one longitudinal, the
other circular, due to the current traversing the wire; the resultant
magnetization is consequently in the direction of a screw or spiral
round the wire, which will be right-handed or left-handed according as
the relation between the two magnetizations is right-handed or
left-handed; the magnetic expansion or contraction of the metal along
the spiral lines of magnetization produces the Wiedemann twist. Iron
(moderately magnetized) expands along the lines of magnetization, and
therefore for a right-handed spiral exhibits a right-handed twist. This
explanation was not accepted by Wiedemann,[45] who thought that the
effect was accounted for by molecular friction. Now nickel contracts
instead of lengthening when it is magnetized, and an experiment by Knott
showed, as he expected, that _caeteris paribus_ a nickel wire twists in
a sense opposite to that in which iron twists. The Wiedemann effect
being positive for iron is negative for nickel. Further, although iron
lengthens in fields of moderate strength, it contracts in strong ones;
and if the wire is stretched, contraction occurs with smaller
magnetizing forces than if it is unstretched. Bidwell[46] accordingly
found upon trial that the Wiedemann twist of an iron wire vanished when
the magnetizing force reached a certain high value, and was reversed
when that value was exceeded; he also found that the vanishing point was
reached with lower values of the magnetizing force when the wire was
stretched by a weight. These observations have been verified and
extended by Knott, whose researches have brought to light a large number
of additional facts, all of which are in perfect harmony with Maxwell's
explanation of the twist.
[Illustration: FIG. 26.]
Maxwell has also given an explanation of the converse effect, namely,
the production of longitudinal magnetization by twisting a wire when
circularly magnetized by a current passing through it. When the wire is
free from twist, the magnetization at any point P is in the tangential
direction PB (see fig. 26). Suppose the wire to be fixed at the top and
twisted at the bottom in the direction of the arrow-head T; then the
element of the wire at P will be stretched in the direction Pe and
compressed in the direction Pr. But tension and compression produce
opposite changes in the magnetic susceptibility; if the metal is iron
and its magnetization is below the Villari critical point, its
susceptibility will be greater along Pe than along Pr; the direction of
the magnetization therefore tends to approach Pe and to recede from Pr,
changing, in consequence of the twist, from PB to some such direction as
PB´, which has a vertical component downwards; hence the lower and upper
ends will respectively acquire north and south polarity, which will
disappear when the wire is untwisted. This effect has never been
actually reversed in iron, probably, as suggested by Ewing, because the
strongest practicable circular fields fail to raise the components of
the magnetization along Pe and Pr up to the Villari critical value.
Nagaoka and Honda have approached very closely to a reversal, and
consider that it would occur if a sufficiently strong current could be
applied without undue heating.
One other effect of torsion remains to be noticed. If a longitudinally
magnetized wire is twisted, circular magnetization is developed; this is
evidenced by the transient electromotive force induced in the iron,
generating a current which will deflect a galvanometer connected with
the two ends of the wire. The explanation given of the last described
phenomenon will with the necessary modification apply also to this; it
is a consequence of the aeolotropy produced by the twist. There are
then three remarkable effects of torsion:
A. A wire magnetized longitudinally and circularly becomes twisted.
B. Twisting a circularly magnetized wire produces longitudinal
magnetization.
C. Twisting a longitudinally magnetized wire produces circular
magnetization.
And it has been shown earlier that--
D. Magnetization produces change of length.
E. Longitudinal stress produces change of magnetization.
Each of these five effects may occur in two opposite senses. Thus in A
the twist may be right-handed or left-handed; in B the polarity of a
given end may become north or south; in C the circular magnetization may
be clockwise or counter-clockwise; in D the length may be increased or
diminished; in E the magnetization may become stronger or weaker. And,
other conditions remaining unchanged, the "sense" of any effect depends
upon the nature of the metal under test, and (sometimes) upon the
intensity of its magnetization. Let each of the effects A, B, C, D and E
be called positive when it is such as is exhibited by moderately
magnetized iron, and negative when its sense is opposite. Then the
results of a large number of investigations may be briefly summarized as
follows:
(W) = weakly magnetized. (S) = strongly magnetized.
_Metal._ _Effects._ _Sign._
Iron (W) A, B, C, D, E +
Unannealed Cobalt (S) A, D, E +
Nickel-Steel (W) A, D, E +
Nickel A, B, C, D, E -
Annealed Cobalt D, E -
Iron (S) A, C, D, E -
Unannealed Cobalt A, D, E -
Several gaps remain to be filled, but the results so far recorded can
leave no doubt that the five effects, varied as they may at first sight
appear, are intimately connected with one another. For each of the
metals tabulated in the first column all the effects hitherto observed
have the same sign; there is no single instance in which some are
positive and others negative. Until the mysteries of molecular
constitution have been more fully explored, perhaps D may be most
properly regarded as the fundamental phenomenon from which the others
follow. Nagaoka and Honda have succeeded in showing that the observed
relations between twist and magnetization are in qualitative agreement
with an extension of Kirchhoff's theory of magnetostriction.
The effects of magnetization upon the torsion of a previously twisted
wire, which were first noticed by Wiedemann, have been further studied
by F. J. Smith[47] and by G. Moreau.[48] Nagaoka[49] has described the
remarkable influence of combined torsion and tension upon the magnetic
susceptibility of nickel, and has made the extraordinary observation
that, under certain conditions of stress, the magnetization of a
nickel wire may have a direction opposite to that of the magnetizing
force.
8. EFFECTS OF TEMPERATURE UPON MAGNETISM
_High Temperature._--It has long been known that iron, when raised to a
certain "critical temperature" corresponding to dull red heat, loses its
susceptibility and becomes magnetically indifferent, or, more
accurately, is transformed from a ferromagnetic into a paramagnetic
body. Recent researches have shown that other important changes in its
properties occur at the same critical temperature. Abrupt alterations
take place in its density, specific heat, thermo-electric quality,
electrical conductivity, temperature-coefficient of electrical
resistance, and in some at least of its mechanical properties. Ordinary
magnetizable iron is in many respects an essentially different substance
from the non-magnetizable metal into which it is transformed when its
temperature is raised above a certain point (see _Brit. Assoc. Report_,
1890, 145). The first exact experiments demonstrating the changes which
occur in the permeability of iron, steel and nickel when heated up to
high temperatures were those of J. Hopkinson (_Phil. Trans._, 1889, 180,
443; _Proc. Roy. Soc._, 1888, 44, 317). The metal to be tested was
prepared in the form of a ring, upon which were wound primary and
secondary coils of copper wire insulated with asbestos. The primary coil
carried the magnetizing current; the secondary, which was wound inside
the other, could be connected either with a ballistic galvanometer for
determining the induction, or with a Wheatstone's bridge for measuring
the resistance, whence the temperature was calculated. The ring thus
prepared was placed in a cast-iron box and heated in a gas furnace. The
following are the chief results of Hopkinson's experiments: For small
magnetizing forces the magnetization of iron steadily increases with
rise of temperature till the critical temperature is approached, when
the rate of increase becomes very high, the permeability in some cases
attaining a value of about 11,000; the magnetization then with
remarkable suddenness almost entirely disappears, the permeability
falling to about 1.14. For strong magnetizing forces (which in these
experiments did not exceed H = 48.9) the permeability remains almost
constant at its initial value (about 400), until the temperature is
within nearly 100° of the critical point; then the permeability
diminishes more and more rapidly until the critical point is reached and
the magnetization vanishes. Steel behaves in a similar manner, but the
maximum permeability is not so high as in iron, and the fall, when the
critical point is approached, is less abrupt. The critical temperature
for various samples of iron and steel ranges from 690° C. to 870° C.; it
is the temperature at which Barrett's "recalescence" occurs. The
critical temperature for the specimen of nickel examined (which
contained nearly 5% of impurities) was 310° C. F. Lydall and A. W.
Pocklington found that the critical temperature of nearly pure iron was
874° C. (_Proc. Roy. Soc._, 1893, 52, 228).
An exhaustive research into the effects of heating on the magnetic
properties of iron has been carried out by D. K. Morris (_Proc. Phys.
Soc._, 1897, 15, 134; and _Phil. Mag._, 1897, 44, 213), the results
being embodied in a paper containing twelve pages of tables and upwards
of 120 curves. As in Hopkinson's experiments, ring magnets were
employed; these were wound with primary and secondary coils of insulated
platinum wire, which would bear a much higher temperature than copper
without oxidation or fusion. A third platinum coil, wound
non-inductively between the primary and the secondary, served to carry
the current by which the ring was heated; a current of 4.6 amperes, with
16 volts across the terminals, was found sufficient to maintain the ring
at a temperature of 1150° C. In the ring itself was embedded a
platinum-thermometer wire, from the resistance of which the temperature
was determined. The whole was wrapped in several coverings of asbestos
and placed in a glass vessel from which the air was partially exhausted,
additional precautions being taken to guard against oxidation of the
iron.
[Illustration: FIG. 27.]
Some preliminary experiments showed the striking difference in the
effects of annealing at a red heat (840° C.) and at a low white heat
(1150° C). After one of the rings had been annealed at 840°, its
maximum permeability at ordinary temperatures was 4000 for H = 1.84;
when it had been subsequently annealed at 1150°, the maximum
permeability rose to 4680 for H = 1.48, while the hysteresis loss for
B= ±4000 was under 500 ergs per c.cm. As regards the effects of
temperature, Morris's results are in general agreement with those of
Hopkinson, though no doubt they indicate details with greater
clearness and accuracy. Specimens of curves showing the relation of
induction to magnetic field at various temperatures, and of
permeability to temperature with fields of different intensities, are
given in figs. 27 and 28. The most striking feature presented by these
is the enormous value, 12,660, which, with H = 0.153, is attained by
the permeability at 765° C., followed by a drop so precipitous that
when the temperature is only 15° higher, the value of the permeability
has become quite insignificant. The critical temperatures for three
different specimens of iron were 795°, 780°, and 770° respectively.
Above these temperatures the little permeability that remained was
found to be independent of the magnetizing force, but it appeared to
vary a little with the temperature, one specimen showing a
permeability of 100 at 820°, 2.3 at 950°, and 17 at 1050°. These last
observations are, however, regarded as uncertain. The effects of
temperature upon hysteresis were also carefully studied, and many
hysteresis loops were plotted. The results of a typical experiment are
given in the annexed table, which shows how greatly the hysteresis
loss is diminished as the critical temperature is approached. The
coercive force at 764°.5 is stated to have been little more than 0.1
C.G.S. unit; above the critical temperature no evidence of hysteresis
could be obtained.
[Illustration: FIG. 28.]
Hysteresis Loss in Ergs per c.cm. Max. H. = ±6.83.
Temp. C.° Ergs. Temp. C.° Ergs.
764.5 120 | 457 2025
748 328 | 352 2565
730 426 | 249 3130
695 797 | 137.5 3500
634 1010 | 24 3660
554 1345 |
A paper by H. Nagaoka and S. Kusakabe[50] generally confirms Morris's
results for iron, and gives some additional observations for steel,
nickel and cobalt. The magnetometric method was employed, and the
metals, in the form of ovoids, were heated by a specially designed
burner, fed with gas and air under pressure, which directed 90 fine
jets of flame upon the asbestos covering the ovoid. The temperature
was determined by a platinum-rhodium and platinum thermo-junction in
contact with the metal. Experiments were made at several constant
temperatures with varying magnetic fields, and also at constant fields
with rising and falling temperatures. For ordinary steel the critical
temperature, at which magnetization practically disappeared, was found
to be about 830°, and the curious fact was revealed that, on cooling,
magnetization did not begin to reappear until the temperature had
fallen 40° below the critical value. This retardation was still more
pronounced in the case of tungsten-steel, which lost its magnetism at
910° and remained non-magnetic till it was cooled to 570°, a
difference of 240°. For nearly pure nickel the corresponding
temperature-difference was about 100°. This phenomenon is of the same
nature as that first discovered by J. Hopkinson for nickel-steel. The
paper contains tables and curves showing details of the magnetic
changes, sometimes very complex, at different temperatures and with
different fields. The behaviour of cobalt is particularly noticeable;
its permeability increased with rising temperature up to a maximum at
500°, when it was about twice as great as at ordinary temperatures,
while at 1600°, corresponding to white heat, there was still some
magnetization remaining.
Further contributions to the subject have been made by K. Honda and S.
Shimizu,[51] who experimented at temperatures ranging from -186° to
1200°. As regards the higher temperatures, the chief point of interest
is the observation that the curve of magnetization for annealed cobalt
shows a small depression at about 450°, the temperature at which they
had found the sign of the length-change to be reversed for all fields.
In the case of all the metals tested a small but measurable trace of
magnetization remained after the so-called critical temperature had
been exceeded; this decreased very slightly up to the highest
temperature reached (1200°) without undergoing any such variation as
had been suspected by Morris. When the curve after its steep descent
has almost reached the axis, it bends aside sharply and becomes a
nearly horizontal straight line; the authors suggest that the critical
temperature should be defined as that corresponding to the point of
maximum curvature. As thus defined the critical temperatures for iron,
nickel and cobalt were found to be 780°, 360° and 1090° respectively,
but these values are not quite independent of the magnetizing force.
Experiments on the effect of high temperatures have also been made by
M. P. Ledeboer,[52] H. Tomlinson,[53] P. Curie,[54] and W. Kunz,[55]
R. L. Wills,[56] J. R. Ashworth[57] and E. P. Harrison.[58]
_Low Temperature._--J. A. Fleming and J. Dewar (_Proc. Roy. Soc._, 1896,
60, 81) were the first to experiment on the permeability and hysteresis
of iron at low temperatures down to that of liquid air (-186° C.).
Induction curves of an annealed soft-iron ring were taken first at a
temperature of 15° C., and afterwards when the ring was immersed in
liquid air, the magnetizing force ranging from about 0.8 to 22. After
this operation had been repeated a few times the iron was found to have
acquired a stable condition, and the curves corresponding to the two
temperatures became perfectly definite. They showed that the
permeability of this sample of iron was considerably diminished at the
lower temperature. The maximum permeability (for H = 2) was 3400 at 15°
and only 2700 at -186°, a reduction of more than 20%; but the percentage
reduction became less as the magnetizing force departed from the value
corresponding to maximum permeability. Observations were also made of
the changes of permeability which took place as the temperature of the
sample slowly rose from -186° to 15°, the magnetizing force being kept
constant throughout an experiment. The values of the permeability
corresponding to the highest and lowest temperatures are given in the
following table. Most of the permeability-temperature curves were more
or less convex
+------------------+--------+------------+-------------+
| Sample of Iron. | H. | µ at 15°. | µ at -186°. |
+------------------+--------+------------+-------------+
| Annealed Swedish | 1.77 | 2835 | 2332 |
| Unannealed " | 1.78 | 917 | 1272 |
| " " | 9.79 | 1210 | 1293 |
| Hardened " | 2.66 | 56 | 132 |
| " " | 4.92 | 106.5 | 502 |
| " " | 11.16 | 447.5 | 823 |
| " " | 127.7 | 109 | 124 |
| Steel wire | 7.50 | 86 | 64.5 |
| " | 20.39 | 361 | 144 |
+------------------+--------+------------+-------------+
towards the axis of temperature, and in all the experiments, except
those with annealed iron and steel wire, the permeability was greatest
at the lowest temperature.[59] The hysteresis of the soft annealed iron
turned out to be sensibly the same for equal values of the induction at
-186° as at 15°, the loss in ergs per c.cm. per cycle being
approximately represented by 0.002 B(1.56) when the maximum limits of B
were ±9000. Experiments with the sample of unannealed iron failed to
give satisfactory results, owing to the fact that no constant magnetic
condition could be obtained.
Honda and Shimizu have made similar experiments at the temperature of
liquid air, employing a much wider range of magnetizing forces (up to
about 700 C.G.S.) and testing a greater variety of metals. They found
that the permeability of Swedish iron, tungsten-steel and nickel, when
the metals were cooled to -186°, was diminished in weak fields but
increased in strong ones, the field in which the effect of cooling
changed its sign being 115 for iron and steel and 580 for nickel. The
permeability of cobalt, both annealed and unannealed, was always
diminished at the low temperature. The hysteresis-loss in Swedish iron
was decreased for inductions below about 9000 and increased for higher
inductions; in tungsten-steel, nickel and cobalt the hysteresis-loss
was always increased by cooling. The range of ±B within which
Steinmetz's formula is applicable becomes notably increased at low
temperature. It may be remarked that, whereas Fleming and Dewar
employed the ballistic method, their specimens having the form of
rings, Honda and Shimizu worked magnetometrically with metals shaped
as ovoids.
_Permanent Magnets._--Fleming and Dewar (loc. cit. p. 57) also
investigated the changes which occurred in permanently magnetized
metals when cooled to the temperature of liquid air. The metals, which
were prepared in the form of small rods, were magnetized between the
poles of an electromagnet and tested with a magnetometer at temperatures
of -186° and 15°. The first immersion into liquid air generally produced
a permanent decrease of magnetic moment, and there was sometimes a
further decrease when the metal was warmed up again; but after a few
alternations of temperature the changes of moment became definite and
cyclic. When the permanent magnetic condition had been thus established,
it was found that in the case of all the metals, except the two alloys
containing large percentages of nickel, the magnetic moment was
temporarily increased by cooling to -186°. The following table shows the
principal results. It is suggested that a permanent magnet might
conveniently be "aged" (or brought into a constant condition) by dipping
it several times into liquid air.
+---------------------------------+--------------------------------+
| | Percentage Gain or Loss |
| Metal. | of Moment at -186° C. |
| +----------------+---------------+
| | First Effect. | Cyclic Effect.|
+---------------------------------+----------------+---------------+
| Carbon steel, hard | -6 | +12 |
| " " medium | Decrease | +22 |
| " " annealed | -33 | +33 |
| Chromium steels (four samples) | Increase | +12 |
| Aluminium steels (three samples)| -2 | +10 |
| Nickel steels, up to 7.65% | Small | +10 |
| " " " 19.64% | -50 | -25 |
| " " " 29% | -20 | -10 |
| Pure nickel | Decrease | +3 |
| Silicon steel, 2.67% | " | +4 |
| Iron, soft | None | +2.5 |
| " hard | Decrease | +10 |
| Tungsten steel, 15% | " | +6 |
| " " 7.5% | " | +10 |
| " " 1% | " | +12 |
+---------------------------------+----------------+---------------+
Other experiments relating to the effect of temperature upon permanent
magnets have been carried out by J. R. Ashworth,[60] who showed that
the temperature coefficient of permanent magnets might be reduced to
zero (for moderate ranges of temperature) by suitable adjustment of
temper and dimension ratio; also by R. Pictet,[61] A. Durward[62] and
J. Trowbridge.[63]
_Alloys of Nickel and Iron._--A most remarkable effect of temperature
was discovered by Hopkinson (_Proc. Roy. Soc._, 1890, 47, 23; 1891, 48,
1) in 1889. An alloy containing about 3 parts of iron and 1 of
nickel--both strongly magnetic metals--is under ordinary conditions
practically non-magnetizable (µ = 1.4 for any value of H). If, however,
this non-magnetic substance is cooled to a temperature a few degrees
below freezing-point, it becomes as strongly magnetic as average
cast-iron (µ = 62 for H = 40), and retains its magnetic properties
indefinitely at ordinary temperatures. But if the alloy is heated up to
580° C. it loses its susceptibility--rather suddenly when H is weak,
more gradually when H is strong--and remains non-magnetizable till it is
once more cooled down below the freezing-point. This material can
therefore exist in either of two perfectly stable conditions, in one of
which it is magnetizable, while in the other it is not. When
magnetizable it is a hard steel, having a specific electrical resistance
of 0.000052; when non-magnetizable it is an extremely soft, mild steel,
and its specific resistance is 0.000072. Alloys containing different
proportions of nickel were found to exhibit the phenomenon, but the two
critical temperatures were less widely separated. The following
approximate figures for small magnetizing forces are deduced from
Hopkinson's curves:--
Percentage of Susceptibility lost Susceptibility gained
Nickel. at temp. C. at temp. C.
0.97 890 --
4.7 820 660
4.7 780 600
24.5 680 -10
30.0 140 125
33.0 207 193
73.0 202 202
Honda and Shimizu (_loc. cit._) have determined the two critical
temperatures for eleven nickel-steel ovoids, containing from 24.04 to
70.32% of nickel, under a magnetizing force of 400, and illustrated by
an interesting series of curves, the gradual transformation of the
magnetic properties as the percentage of nickel was decreased. They
found that the hysteresis-loss, which at ordinary temperatures is very
small, was increased in liquid air, the increase for the alloys
containing less than 30% of nickel being enormous. Steinmetz's formula
applies only for very weak inductions when the alloys are at the
ordinary temperature, but at the temperature of liquid air it becomes
applicable through a wide range of inductions. According to C. E.
Guillaume[64] the temperature at which the magnetic susceptibility of
nickel-steel is recovered is lowered by the presence of chromium; a
certain alloy containing chromium was not rendered magnetic even by
immersion in liquid air. Experiments on the subject have also been
made by E. Dumont[65] and F. Osmond.[66]
9. ALLOYS AND COMPOUNDS OR IRON
In 1885 Hopkinson (_Phil. Trans._, 1885, 176, 455) employed his yoke
method to test the magnetic properties of thirty-five samples of iron
and steel, among which were steels containing substantial proportions of
manganese, silicon, chromium and tungsten. The results, together with
the chemical analysis of each sample, are given in a table contained in
this paper, some of them being also represented graphically. The most
striking phenomenon which they bring into prominence is the effect of
any considerable quantity of manganese in annihilating the magnetic
property of iron. A sample of Hadfield's manufacture, containing 12.36%
of manganese, differed hardly at all from a non-magnetic substance, its
permeability being only 1.27. According to Hopkinson's calculation, this
sample behaved as if 91% of the iron contained in it had completely lost
its magnetic property.[67] Another point to which attention is directed
is the exceptionally great effect which hardening has upon the magnetic
properties of chrome steel; one specimen had a coercive force of 9 when
annealed, and of no less than 38 when oil-hardened. The effect of the
addition of tungsten in increasing the coercive force is very clearly
shown; in two specimens containing respectively 3.44 and 2.35% of
tungsten the coercive force was 64.5 and 70.7. These high values render
hardened tungsten-steel particularly suitable for the manufacture of
permanent magnets. Hopkinson (_Proc. Roy. Soc._, 1890, 48, 1) also
noticed some peculiarities of an unexpected nature in the magnetic
properties of the nickel-steel alloys already referred to. The
permeability of the alloys containing from 1 to 4.7% of nickel, though
less than that of good soft iron for magnetizing forces up to about 20
or 30, was greater for higher forces, the induction reached in a field
of 240 being nearly 21,700. The induction for considerable forces was
found to be greater in a steel containing 73% of nickel than in one with
only 33%, though the permeability of pure nickel is much less than that
of iron.
The magnetic qualities of various alloys of iron have been submitted to
a very complete examination by W. F. Barrett, W. Brown and R. A.
Hadfield (_Trans. Roy. Dub. Soc._, 1900, 7, 67; _Journ. Inst. Elec.
Eng._, 1902, 31, 674).[68] More than fifty different specimens were
tested, most of which contained a known proportion of manganese, nickel,
tungsten, aluminium, chromium, copper or silicon: in some samples two of
the substances named were present. Of the very numerous results
published, a few of the most characteristic are collected in the
following table. The first column contains the symbols of the various
elements which were added to the iron, and the second the percentage
proportion in which each element was present; the sample containing
0.03% of carbon was a specimen of the best commercial iron, the values
obtained for it being given for comparison. All the metals were
annealed.
A few among several interesting points should be specially noticed.
The addition of 15.2% of manganese produced an enormous effect upon
the magnetism of iron, while the presence of only 2.25% was
comparatively unimportant. When nickel was added to the iron in
increasing quantities the coercive force increased until the
proportion of nickel reached 20%; then it diminished, and when the
proportion of nickel was 32% the coercive force had fallen to the
exceedingly low value of 0.5. In the case of iron containing 7.5% of
tungsten (W), the residual induction had a remarkably high value; the
coercive force, however, was not very great. The addition of silicon
in small quantities considerably diminished permeability and increased
coercive force; but when the proportion amounted to 2.5% the maximum
permeability (µ = 5100 for H = 2) was greater than that of the nearly
pure iron used for comparison, while the coercive force was only
0.9.[69] A small percentage of aluminium produced still higher
permeability (µ = 6000 for H = 2), the induction in fields up to 60
being greater than in any other known substance, and the
hysteresis-loss for moderate limits of B far less than in the purest
commercial iron. Certain non-magnetizable alloys of nickel,
chromium-nickel and chromium-manganese were rendered magnetizable by
annealing.
+--------+---------+-----------+---------+----------+--------+
|Element.|Per cent.| B | B | µ |Coercive|
| | |for H = 45.|residual.|for H = 8.| Force. |
+--------+---------+-----------+---------+----------+--------+
| C | 0.03 | 16800 | 9770 | 1625 | 1.66 |
| Cu | 2.5 | 14300 | 10410 | .. | 5.4 |
| Mn | 2.25 | 14720 | 10460 | 1080 | 6.0 |
| Mn | 15.2 | 0 | .. | .. | .. |
| Ni | 3.82 | 16190 | 9320 | 1375 | 2.76 |
| Ni | 19.64 | 7770 | 4770 | 90 | 20.0 |
| Ni | 31.4 | 4460 | 1720 | 357 | 0.5 |
| W | 7.5 | 15230 | 13280 | 500 | 9.02 |
| Al | 2.25 | 16900 | 10500 | 1700 | 1.0 |
| Cr | 3.25 | .. | .. | .. | 12.25 |
| Si | 2.5 | 16420 | 4080 | 1680 | 0.9 |
| Si | 5.5 | 15980 | 3430 | 1630 | 0.85 |
+--------+---------+-----------+---------+----------+--------+
Later papers[70] give the results of a more minute examination of
those specimens which were remarkable for very low and very high
permeabilities, and were therefore likely to be of commercial
importance. The following table gives the exact composition of some
alloys which were found to be non-magnetizable, or nearly so, in a
field of 320.
+---------------------------------------------------------------+
| An. = Annealed. Un. = Unannealed. |
+------+----------------------------------------+---------------+
|State.| Percentage Composition. |I, for H = 320.|
+------+----------------------------------------+---------------+
| Un. | Fe, 85.77; C, 1.23; Mn, 13. | 0 |
| An. | Fe, 84.64; C, 0.15; Mn, 15.2 | 0 |
| An. | Fe, 80.16; C, 0.8; Mn, 5.04; Ni, 14.55.| 3 |
| Un. | Ditto | 0 |
| Un. | Fe, 75.36; C, 0.6; Mn, 5.04; Ni, 19. | 3 |
| An. | Fe, 86.61; C, 1.08; Mn, 10.2; W, 2.11. | 5 |
+------+----------------------------------------+---------------+
A very small difference in the constitution often produces a
remarkable effect upon the magnetic quality, and it unfortunately
happens that those alloys which are hardest magnetically are generally
also hardest mechanically and extremely difficult to work; they might
however be used rolled or as castings. The specimens distinguished by
unusually high permeability were constituted as follows:--
Silicon-iron.--Fe, 97.3; C, 0.2; Si, 2.5.
Aluminium-iron.--Fe, 97.33; C, 0.18; Al, 2.25.
The silicon-iron had, in fields up to about 10, a greater permeability
than a sample of the best Swedish charcoal-iron, and its
hysteresis-loss for max. B = 9000, at a frequency of 100 per second,
was only 0.254 watt per pound, as compared with 0.382 for the Swedish
iron. The aluminium-iron attained its greatest permeability in a field
of 0.5, about that of the earth's force, when its value was 9000, this
being more than twice the maximum permeability of the Swedish iron.
Its hysteresis-loss for B = 9000 was 0.236 per pound. It was, however,
found that the behaviour of this alloy was in part due to a layer of
pure iron ("ferrite") averaging 0.1 mm. in thickness, which occurred
on the outside of the specimen, and the exceptional magnetic quality
which has been claimed for aluminium-iron cannot yet be regarded as
established.
A number of iron alloys have been examined by Mme. Curie (_Bull. Soc.
d'Encouragement_, 1898, pp. 36-76), chiefly with the object of
determining their suitability for the construction of permanent magnets.
Her tests appear to show that molybdenum is even more effective than
tungsten in augmenting the coercive force, the highest values observed
being 70 to 74 for tungsten-steel, and 80 to 85 for steel containing 3.5
to 4% of molybdenum. For additional information regarding the
composition and qualities of permanent magnet steels reference may be
made to the publications cited below.[71] Useful instructions have been
furnished by Carl Barus (_Terrestrial Magnetism_, 1897, 2, 11) for the
preparation of magnets calculated to withstand the effects of time,
percussion and ordinary temperature variations. The metal, having first
been uniformly tempered glass-hard, should be annealed in steam at 100°
C. for twenty or thirty hours; it should then be magnetized to
saturation, and finally "aged" by a second immersion in steam for about
five hours.
_Magnetic Alloys of Non-Magnetic Metals._--The interesting discovery was
made by F. Heusler[72] in 1903 that certain alloys of the non-magnetic
metal manganese with other non-magnetic substances were strongly
magnetizable, their susceptibility being in some cases equal to that of
cast iron. The metals used in different combinations included tin,
aluminium, arsenic, antimony, bismuth and boron; each of these, when
united in certain proportions with manganese, together with a larger
quantity of copper (which appears to serve merely as a menstruum),
constituted a magnetizable alloy. So far, the best results have been
attained with aluminium, and the permeability was greatest when the
percentages of manganese and aluminium were approximately proportional
to the atomic weights of the two metals. Thus in an alloy containing
26.5% of manganese and 14.6% of aluminium, the rest being copper, the
induction for H = 20 was 4500, and for H = 150, 5550. When the
proportion of aluminium to manganese was made a little greater or
smaller, the permeability was diminished. Next to aluminium, tin was
found to be the most effective of the metals enumerated above. In all
such magnetizable alloys the presence of manganese appears to be
essential, and there can be little doubt that the magnetic quality of
the mixtures is derived solely from this component. Manganese, though
belonging (with chromium) to the iron group of metals, is commonly
classed as a paramagnetic, its susceptibility being very small in
comparison with that of the recognized ferromagnetics; but it is
remarkable that its atomic susceptibility in solutions of its salts is
even greater than that of iron. Now iron, nickel and cobalt all lose
their magnetic quality when heated above certain critical temperatures
which vary greatly for the three metals, and it was suspected by
Faraday[73] as early as 1845 that manganese might really be a
ferromagnetic metal having a critical temperature much below the
ordinary temperature of the air. He therefore cooled a piece of the
metal to -105° C., the lowest temperature then attainable, but failed to
produce any change in its magnetic quality. The critical temperature (if
there is one) was not reached in Faraday's experiment; possibly even the
temperature of -250° C., which by the use of liquid hydrogen has now
become accessible, might still be too high.[74] But it has been shown
that the critical temperatures of iron and nickel may be changed by the
addition of certain other substances. Generally they are lowered,
sometimes, however, they are raised[75]; and C. E. Guillaume[76]
explains the ferromagnetism of Heusler's alloy by supposing that the
naturally low critical temperature of the manganese contained in it is
greatly raised by the admixture of another appropriate metal, such as
aluminium or tin; thus the alloy as a whole becomes magnetizable at the
ordinary temperature. If this view is correct, it may also be possible
to prepare magnetic alloys of chromium, the only other paramagnetic
metals of the iron group.
J. A. Fleming and R. A. Hadfield[77] have made very careful
experiments on an alloy containing 22.42% of manganese, 11.65% of
aluminium and 60.49% of copper. The magnetization curve was found to
be of the same general form as that of a paramagnetic metal, and gave
indications that with a sufficient force magnetic saturation would
probably be attained. There was considerable hysteresis, the
energy-loss per cycle being fairly represented by W =
0.0005495B^(2.238). The hysteretic exponent is therefore much higher
than in the case of iron, nickel and cobalt, for which its value is
approximately 1.6.
10. MISCELLANEOUS EFFECTS OF MAGNETIZATION
_Electrical Conductivity._--The specific resistance of many electric
conductors is known to be temporarily changed by the action of a
magnetic field, but except in the case of bismuth the effect is very
small.
A. Gray and E. Taylor Jones (_Proc. Roy. Soc._, 1900, 67, 208) found
that the resistance of a soft iron wire was increased by about 1/700
in a field of 320 C.G.S. units. The effect appeared to be closely
connected with the intensity of magnetization, being approximately
proportional to I. G. Barlow (_Proc. Roy. Soc._, 1903, 71, 30),
experimenting with wires of iron, steel and nickel, showed that in
weak fields the change of resistance was proportional to a function
aI^2 + bI^4 + cI^6, where a, b and c are constants for each specimen.
W. E. Williams (_Phil. Mag._, 1902, 4, 430) found that for nickel the
curves showing changes of resistance in relation to magnetizing force
were strikingly similar in form to those showing changes of length. H.
Tomlinson (_Phil. Trans._, 1883, Part I., 153) discovered in 1881 that
the resistance of a bismuth rod was slightly increased when the rod
was subjected to longitudinal magnetic force, and a year or two later
A. Righi (_Atti R. A. Lincei_, 1883-1884, 19, 545) showed that a more
considerable alteration was produced when the magnetic force was
applied transversely to the bismuth conductor; he also noticed that
the effect was largely dependent upon temperature (see also P. Lenard,
_Wied. Ann._, 1890, 39, 619). Among the most important experiments on
the influence of magnetic force at different temperatures are those of
J. B. Henderson and of Dewar and Fleming. Henderson (_Phil. Mag._,
1894, 38, 488) used a little spiral of the pure electrolytic bismuth
wire prepared by Hartmann and Braun; this was placed between the
pole-pieces of an electromagnet and subjected to fields of various
strengths up to nearly 39,000 units. At constant temperature the
resistance increased with the field; the changes in the resistance of
the spiral when the temperature was 18° C. are indicated in the
annexed table, from which it will be seen that in the strongest
H. R. | H. R.
0 1.000 | 27450 2.540
6310 1.253 | 32730 2.846
12500 1.630 | 38900 3.334
20450 2.160 |
transverse field reached the resistance was increased more than
threefold. Other experiments showed the relation of resistance to
temperature (from 0° to about 90°) in different constant fields. It
appears that as the temperature rises the resistance decreases to a
minimum and then increases, the minimum point occurring at a higher
temperature the stronger the field. For H = 11,500 the temperature of
minimum resistance was about 50°; for much lower or higher values of H
the actual minimum did not occur within the range of temperature dealt
with. Dewar and Fleming (_Proc. Roy. Soc._, 1897, 60, 425) worked with
a similar specimen of bismuth, and their results for a constant
temperature of 19° agree well with those of Henderson. They also
experimented with constant temperatures of -79°, -185° and -203°, and
found that at these low temperatures the effect of magnetization was
enormously increased. The following table gives some of their results,
the specific resistance of the bismuth being expressed in C.G.S.
units.
+-----------+-----------------------+------------------------+
| | Temp. 19°C. | Temp. -185°C. |
| Field +-----------+-----------+-----------+------------+
| Strength. | Spec. Res.| Comp. Res.| Spec. Res.| Comp. Res. |
+-----------+-----------+-----------+-----------+------------+
| 0 | 116200 | 1.000 | 41000 | 1.00 |
| 1375 | 118200 | 1.017 | 103300 | 2.52 |
| 2750 | 123000 | 1.059 | 191500 | 4.67 |
| 8800 | 149200 | 1.284 | 738000 | 18.0 |
| 14150 | 186200 | 1.602 | 1730000 | 42.2 |
| 21800 | 257000 | 2.212 | 6190000 | 151 |
+-----------+-----------+-----------+-----------+------------+
At the temperature of liquid air (-185°) the application of a field of
21,800 multiplied the resistance of the bismuth no less than 150
times. Fig. 29 shows the variations of resistance in relation to
temperature for fields of different constant values. It will be seen
that for H = 2450 and H = 5500 the minimum resistance occurs at
temperatures of about -80° and -7° respectively.
_Hall Effect._--If an electric current is passed along a strip of thin
metal, and the two points at opposite ends of an equipotential line are
connected with a galvanometer, its needle will of course not be
deflected. But the application of a magnetic field at right angles to
the plane of the metal causes the equipotential lines to rotate through
a small angle, and the points at which the galvanometer is connected
being no longer at the same potential, a current is indicated by the
galvanometer.[78] The tranverse electromotive force is equal to KCH/D,
where C is the current, H the strength of the field, D the thickness of
the metal, and K a constant which has been termed the _rotatory power_
or _rotational coefficient_. (See Hopkinson, _Phil. Mag._, 1880, 10,
430). The following values of K for different metals are given by E. H.
Hall, the positive sign indicating that the electromotive force is in
the same direction as the mechanical force acting upon the conductor. A.
von Ettinghausen and W. Nernst (_Wien. Ber._, 1886, 94, 560) have found
that the rotational coefficient of tellurium is more than fifty times
greater than that of bismuth, its sign being positive. Several
experimenters have endeavoured to find a Hall effect in liquids, but
such results as have been hitherto obtained are by no means free from
doubt. E. A. Marx (_Ann. d. Phys._, 1900, 2, 798) observed a
well-defined Hall effect in incandescent gases. A large effect,
proportional to the field, has been found by H. A. Wilson (_Cam. Phil.
Soc. Proc._, 1902, 11, pp. 249, 391) in oxygen, hydrogen and air at low
pressures, and by C. D. Child (_Phys. Rev._, 1904, 18, 370) in the
electric arc.
Metal. K × 10^15 | Metal. K × 10^15
|
Antimony +114000 | Copper -520
Steel +12060 | Gold -660
Iron +7850 | Nickel -14740
Cobalt +2460 | Bismuth[79] -8580000
Zinc +820 |
[Illustration: _Fig._ 29.]
_Electro-Thermal Relations._--The Hall electromotive force is only one
of several so-called "galvano-magnetic effects" which are observed when
a magnetic field acts normally upon a thin plate of metal traversed by
an electric current. It is remarkable that if a flow of heat be
substituted for a current of electricity a closely allied group of
"thermo-magnetic effects" is presented. The two classes of phenomena
have been collated by M. G. Lloyd (_Am. Journ. Sci._, 1901, 12, 57), as
follows:--
_Galvano-Magnetic Effects._ _Thermo-Magnetic Effects._
1. A transverse difference of i. A transverse difference of
electric potential (Hall effect). electric potential (Nernst effect).
2. A transverse difference of ii. A transverse difference of
temperature(Ettinghausen effect). temperature (Leduc effect).
3. Longitudinal change of iii. Longitudinal change of
electric conductivity. thermal conductivity.
4. Longitudinal difference of iv. Longitudinal difference of
temperature. electric potential.[80]
+---------------------+
| C |
| |
| A B |
| D |
+---------------------+
If in the annexed diagram ABCD represents the metallic plate through
which the current of electricity or heat flows in the direction AB,
then effects (1), (2), (i.) and (ii.) are exhibited at C and D, effects
(4) and (iv.) at A and B, and effects (3) and (iii.) along AB. The
transverse effects are reversed in direction when either the magnetic
field or the primary current (electric or thermal) is reversed, but the
longitudinal effects are independent of the direction of the field. It
has been shown by G. Moreau (_C. R._, 1900, 130, pp. 122, 412, 562) that
if K is the coefficient of the Hall effect (1) and K´ the analogous
coefficient of the Nernst effect (i.) (which is constant for small
values of H), then K´ = K[sigma]/[rho], [sigma] being the coefficient of
the Thomson effect for the metal and [rho] its specific resistance. He
considers that Hall's is the fundamental phenomenon, and that the Nernst
effect is essentially identical with it, the primary electromotive force
in the case of the latter being that of the Thomson effect in the
unequally heated metal, while in the Hall experiment it is derived from
an external source.
Attempts have been made to explain these various effects by the electron
theory.[81]
_Thermo-electric Quality._--The earliest observations of the effect of
magnetization upon thermo-electric power were those of W. Thomson (Lord
Kelvin), who in 1856 announced that magnetization rendered iron and
steel positive to the unmagnetized metals.[82] It has been found by
Chassagny,[83] L. Houllevigue[84] and others that when the magnetizing
force is increased, this effect passes a maximum, while J. A. Ewing[85]
has shown that it is diminished and may even be reversed by tensile
stress. Nickel was believed by Thomson to behave oppositely to iron,
becoming negative when magnetized; but though his conclusion was
accepted for nearly fifty years, it has recently been shown to be an
erroneous one, based, no doubt, upon the result of an experiment with an
impure specimen. Nickel when magnetized is always positive to the
unmagnetized metal. So also is cobalt, as was found by H. Tomlinson.[86]
The curves given by Houllevigue for the relation of thermo-electric
force to magnetic field are of the same general form as those showing
the relation of change of length to field. E. Rhoads[87] obtained a
cyclic curve for iron which indicated thermo-electric hysteresis of the
kind exhibited by Nagaoka's curves for magnetic strain. He also
experimented with nickel and again found a resemblance to the strain
curve. The subject was further investigated by S. Bidwell,[88] who,
adopting special precautions against sources of error by which former
work was probably affected, measured the changes of thermo-electric
force for iron, steel, nickel and cobalt produced by magnetic fields up
to 1500 units. In the case of iron and nickel it was found that, when
correction was made for mechanical stress due to magnetization, magnetic
change of thermo-electric force was, within the limits of experimental
error, proportional to magnetic change of length. Further, it was shown
that the thermo-electric curves were modified both by tensile stress and
by annealing in the same manner as were the change-of-length curves, the
modification being sometimes of a complex nature. Thus a close connexion
between the two sets of phenomena seems to be established. In the case
of cobalt no such relation could be traced; it appeared that the
thermo-electric power of the unmagnetized with respect to the magnetized
cobalt was proportional to the square of the magnetic induction or of
the magnetization. Of nickel six different specimens were tested, all
of which became, like iron, thermo-electrically positive to the
unmagnetized metals.
As to what effect, if any, is produced upon the thermo-electric
quality of bismuth by a magnetic field there is still some doubt. E.
van Aubel[89] believes that in pure bismuth the thermo-electric force
is increased by the field; impurities may neutralize this effect, and
in sufficient quantities reverse it.
_Elasticity._--The results of experiments as to the effect of
magnetization were for long discordant and inconclusive, sufficient care
not having been taken to avoid sources of error, while the effects of
hysteresis were altogether disregarded. The subject, which is of
importance in connexion with theories of magnetostriction, has been
investigated by K. Honda and T. Terada in a research remarkable for its
completeness and the ingenuity of the experimental methods employed.[90]
The results are too numerous to discuss in detail; some of those to
which special attention is directed are the following: In Swedish iron
and tungsten-steel the change of elastic constants (Young's modulus and
rigidity) is generally positive, but its amount is less than 0.5%;
changes of Young's modulus and of rigidity are almost identical. In
nickel the maximum change of the elastic constants is remarkably large,
amounting to about 15% for Young's modulus and 7% for rigidity; with
increasing fields the elastic constants first decrease and then
increase. In nickel-steels containing about 50 and 70% of nickel the
maximum increase of the constants is as much as 7 or 8%. In a 29%
nickel-steel, magnetization increases the constants by a small amount.
Changes of elasticity are in all cases dependent, not only upon the
field, but also upon the tension applied; and, owing to hysteresis, the
results are not in general the same when the magnetization follows as
when it precedes the application of stress; the latter is held to be the
right order.
_Chemical and Voltaic Effects._--If two iron plates, one of which is
magnetized, are immersed in an electrolyte, a current will generally be
indicated by a galvanometer connected with the plates.
As to whether the magnetized plate becomes positive or negative to the
other, different experimenters are not in agreement. It has, however,
been shown by Dragomir Hurmuzescu (_Rap. du Congrès Int. de Phys._,
Paris, 1900, p. 561) that the true effect of magnetization is liable
to be disguised by secondary or parasitic phenomena, arising chiefly
from polarization of the electrodes and from local variations in the
concentration and magnetic condition of the electrolyte; these may be
avoided by working with weak solutions, exposing only a small surface
in a non-polar region of the metal, and substituting a capillary
electrometer for the galvanometer generally used. When such
precautions are adopted it is found that the "electromotive force of
magnetization" is, for a given specimen, perfectly definite both in
direction and in magnitude; it is independent of the nature of the
corrosive solution, and is a function of the field-strength alone, the
curves showing the relation of electromotive force to field-intensity
bearing a rough resemblance to the familiar I-H curves. The value of
the E.M.F. when H = 2000 is of the order of 1/100 volt for iron,
1/1000 volt for nickel and 1/10,000 for bismuth. When the two
electrodes are ferromagnetic, the direction of the current through the
liquid is from the unmagnetized to the magnetized electrode, the
latter being least attacked; with diamagnetic electrodes the reverse
is the case. Hurmuzescu shows that these results are in accord with
theory. Applying the principle of the conservation of internal energy,
he demonstrates that for iron in a field of 1000 units and upwards the
E.M.F. of magnetization is
l I²
E = ------- × -------- approximately,
[delta] 2[kappa]
l being the electrochemical equivalent and [delta] the density of the
metal. Owing to the difficulty of determining the magnetization I and
the susceptibility [kappa] with accuracy, it has not yet been possible
to submit this formula to a quantitative test, but it is said to
afford an indication of the results given by actual experiment. It has
been discovered by E. L. Nichols and W. S. Franklin (_Am. Journ.
Sci._, 1887, 34, 419; 1888, 35, 290) that the transition from the
"passive" to the active state of iron immersed in strong nitric acid
is facilitated by magnetization, the temperature of transition being
lowered. This is attributed to the action of local currents set up
between unequally magnetized portions of the iron. Similar results
have been obtained by T. Andrews (_Proc. Roy. Soc._, 1890, 48, 116).
11. FEEBLY SUSCEPTIBLE SUBSTANCES
_Water._--The following are recent determinations of the magnetic
susceptibility of water:--
Observer. [kappa] × 10^6. Publication.
G. Quincke -0.797 at 18° C. _Wied. Ann._, 1885, 24, 387.
H. du Bois -0.837 (1 - 0.0025t - 15°) _Wied. Ann._, 1888, 35, 137.
P. Curie -0.790 at 4° C. _C. R._, 1893, 116, 136.
J. Townsend -0.77 _Phil. Trans._, 1896, 187, 544.
J. A. Fleming -0.74 _Proc. Roy. Soc._, 1898, 63,
and J. Dewar 311.
G. Jäger and -0.689(1 - 0.0016t) _Wied. Ann._, 1899, 67,
S. Meyer 707.
J. Koenigsberger -0.781 at 22° C. _Ann. d. Phys._, 1901, 6, 506.
H. D. Stearns -0.733 at 22° C. _Phys. Rev._, 1903, 16, 1.
A. P. Wills -0.720 at 18° C. _Phys. Rev._, 1905, 20, 188.
Wills found that the susceptibility was constant in fields ranging from
4200 to 15,000.
_Oxygen and Air._--The best modern determinations of the value of
[kappa] for gaseous oxygen agree very fairly well with that given by
Faraday in 1853 (_Exp. Res._ III, 502). Assuming that for water [kappa]
= -0.8 × 10^(-6), his value of [kappa] for oxygen at 15° C. reduces to
0.15 × 10^(-6). Important experiments on the susceptibility of oxygen at
different pressures and temperatures were carried out by P. Curie
(_C.R._ 1892, 115, 805; 1893, 116, 136). _Journ. de Phys._, 1895, 4,
204. He found that the susceptibility for unit of mass, K, was
independent of both pressure and magnetizing force, but varied inversely
as the absolute temperature, [theta], so that 10^6K = 33700/[theta].
Since the mass of 1 cub. cm. of oxygen at 0° C. and 760 mm. pressure is
0.00141 grm., the mass at any absolute temperature [theta] is by
Charles's law 0.00141 × 273[theta] = 0.3849/[theta] grm.; hence the
susceptibility per unit of volume at 760 mm. will be
[kappa] = 10^(-6) × 0.3849 × 33700/[theta]²
= 10^(-6) × 12970/[theta]².
At 15° C. [theta] = 273 + 15 = 288, and therefore [kappa] = 0.156 ×
10^(-6), nearly the same as the value found by Faraday. At 0° C.,
[kappa] = 0.174 × 10^(-6). For air Curie calculated that the
susceptibility per unit mass was 10^6K = 7830/[theta]; or, taking the
mass of 1 c.c. of air at 0° C. and 760 mm. as 0.001291 grm., [kappa] =
10^(-6) × 2760/[theta]² for air at standard atmospheric pressure. It is
pointed out that this formula may be used as a temperature correction in
magnetic determinations carried out in air.
Fleming and Dewar determined the susceptibility of liquid oxygen (_Proc.
Roy. Soc._, 1896, 60, 283; 1898, 63, 311) by two different methods. In
the first experiments it was calculated from observations of the mutual
induction of two conducting circuits in air and in the liquid; the
results for oxygen at -182° C. were
µ = 1.00287, [kappa] = 228 × 10^(-6).
In the second series, to which greater importance is attached,
measurements were made of the force exerted in a divergent field upon
small balls of copper, silver and other substances, first when the balls
were in air and afterwards when they were immersed in liquid oxygen. If
V is the volume of a ball, H the strength of the field at its centre,
and [kappa]´ its apparent susceptibility, the force in the direction x
is f = [kappa]´VH × dH/dx; and if [kappa]´_a and [kappa]´^0 are the
apparent susceptibilities of the same ball in air and in liquid oxygen,
[kappa]´_a - [kappa]´0 is equal to the difference between the
susceptibilities of the two media. The susceptibility of air being
known--practically it was negligible in these experiments--that of
liquid oxygen can at once be found. The mean of 36 experiments with 7
balls gave
µ = 1.00407, [kappa] = 324 × 10^(-6).
A small but decided tendency to a decrease of susceptibility in very
strong fields was observed. It appears, therefore, that liquid oxygen is
by far the most strongly paramagnetic liquid known, its susceptibility
being more than four times greater than that of a saturated solution of
ferric chloride. On the other hand, its susceptibility is about fifty
times less than that of Hadfield's 12% manganese steel, which is
commonly spoken of as non-magnetizable.
_Bismuth._--Bismuth is of special interest, as being the most strongly
diamagnetic substance known, the mean value of the best determinations
of its susceptibility being about -14 × 10^(-6) (see G. Meslin, _C. R._,
1905, 140, 449). The magnetic properties of the metal at different
temperatures and in fields up to 1350 units have been studied by P.
Curie (_loc. cit._), who found that its "specific susceptibility" (K)
was independent of the strength of the field, but decreased with rise of
temperature up to the melting-point, 273°C. His results appear to show
the relation
-[Kappa] × 10^6 = 1.381 - 0.00155t°.
Assuming the density of Bi to be 9.8, and neglecting corrections for
heat dilatation, his value for the susceptibility at 20°C. is equivalent
to [kappa] = -13.23 × 10^(-6). As the temperature was raised up to 273°,
[kappa] gradually fell to -9.38 × 10^[-6], rising suddenly when fusion
occurred to -0.37 × 10^(-6), at which value it remained constant when
the fluid metal was further heated. Fleming and Dewar give for the
susceptibility the values -13.7 × 10^(-6) at 15°C. and -15.9 × 10^(-6)
at -182°, the latter being approximately equivalent to [Kappa] × 10^6 =
-1.62. Putting t° = -182 in the equation given above for Curie's
results, we get [Kappa] × 10^6 = -1.66, a value sufficiently near that
obtained by Fleming and Dewar to suggest the probability that the
diamagnetic susceptibility varies inversely as the temperature between
-182° and the melting-point.
_Other Diamagnetics._--The following table gives Curie's determinations
(_Journ. de Phys._, 1895, 4, 204) of the specific susceptibility [Kappa]
of other diamagnetic substances at different temperatures. It should be
noted that [Kappa] = [kappa]/density.
Substance Temp. °C. -[Kappa] × 10^6.
Water 15-189 0.790
Rock salt 16-455 0.580
Potassium chloride 18-465 0.550
" sulphate 17-460 0.430
" nitrate (fusion 350°) 18-420 0.330
Quartz 18-430 0.441
Sulphur, solid or fused 18-225 0.510
Selenium, solid or fused 20-200 0.320
" fused 240-415 0.307
Tellurium 20-305 0.311
Bromine 20 0.410
Iodine, solid or fused 18-164 0.385
Phosphorus, solid or fused 19-71 0.920
" amorphous 20-275 0.730
Antimony, electrolytic 20 0.680
" 540 0.470
Bismuth, solid 20 1.350
" " 273 0.957
" fused 273-405 0.038
For all diamagnetic substances, except antimony and bismuth, the value
of [Kappa] was found to be independent of the temperature.
_Paramagnetic Substances._--Experiments by J. S. Townsend (_Phil.
Trans._, 1896, 187, 533) show that the susceptibility of solutions of
salts of iron is independent of the magnetizing force, and depends only
on the quantity of iron contained in unit volume of the liquid. If W is
the weight of iron present per c.c. at about 10°C., then for ferric
salts
10^6[kappa] = 266W - 0.77
and for ferrous salts
10^6[kappa] = 206W - 0.77,
the quantity -0.77 arising from the diamagnetism of the water of
solution. Annexed are values of 10^6[kappa] for the different salts
examined, w being the weight of the salt per c.c. of the solution.
Salt. 10^6[kappa] + 0.77 | Salt. 10^6[kappa] + 0.77
|
Fe2Cl6 91.6w | FeCl2 90.8w
Fe2(SO4)3 74.5w | FeSO4 74.9w
Fe2(NO3)6 61.5w
Susceptibility was found to diminish greatly with rise of temperature.
According to G. Jäger and S. Meyer (_Wien. Akad. Sitz._, 1897, 106, II.
a, p. 623, and 1898, 107, II. a, p. 5) the atomic susceptibilities k of
the metals nickel, chromium, iron, cobalt and manganese in solutions of
their salts are as follows:--
Metal. k × 10^6 | Metal. k × 10^6.
|
Ni 4.95 = 2.5 × 2 | Co 10.0 = 2.5 × 4
Cr 6.25 = 2.5 × 2.5 | Fe(2) 12.5 = 2.5 × 5
Fe(1) 7.5 = 2.5 × 3 | Mn 15.0 = 2.5 × 6
Fe(1) is iron contained in FeCl2 and Fe(2) iron contained in Fe2(NO3)6.
Curie has shown, for many paramagnetic bodies, that the specific
susceptibility K is inversely proportional to the absolute temperature
[theta]. Du Bois believes this to be an important general law,
applicable to the case of every paramagnetic substance, and suggests
that the product K[theta] should be known as "Curie's constant" for the
substance.
_Elementary Bodies and Atomic Susceptibility._--Among a large number of
substances the susceptibilities of which have been determined by J.
Koenigsberger (_Wied. Ann._, 1898, 66, 698) are the following
elements:--
Element. [kappa] × 10^6. | Element. [kappa] × 10^6.
|
Copper -0.82 | Tellurium - 2.10
Silver -1.51 | Graphite + 2
Gold -3.07 | Aluminium + 1.80
Zinc -0.96 | Platinum +22
Tin +0.46 | Palladium +50 to 60
Lead -1.10 | Tungsten +14
Thallium -4.61 | Magnesium + 4
Sulphur -0.86 | Sodium + 2.2
Selenium (red) -0.50 | Potassium + 3.6
In a table accompanying Koenigsberger's paper the elements are arranged
upon the periodic system and the atomic susceptibility (product of
specific susceptibility into atomic weight) is given for each. It
appears that the elements at about the middle of each row are the most
strongly paramagnetic; towards the ends of a row the susceptibility
decreases, and ultimately becomes negative. Thus a relation between
susceptibility and atomic weight is clearly indicated. Tables similarly
arranged, but much more complete, have been published by S. Meyer
(_Wied. Ann._, 1899, 68, 325 and 1899, 69, 236), whose researches have
filled up many previously existing gaps. The values assigned to the
atomic susceptibilities of most of the known elements are appended.
According to the notation adopted by Meyer the atomic susceptibility k =
[kappa] × atomic-weight/(density × 1000).
Meyer thinks that the susceptibilities of the metals praseodymium,
neodymium, ytterbium, samarium, gadolinium, and erbium, when obtained
in a pure form, will be found to equal or even exceed those of the
well-known ferromagnetic metals. Many of their compounds are very
strongly magnetic; erbium, for example, in Er2O3 being four times as
strong as iron in the familiar magnetite or lodestone, Fe2O3. The
susceptibilities of some hundreds of inorganic compounds have also
been determined by the same investigator (loc. cit.). Among other
researches relating to atomic and molecular magnetism are those of O.
Liebknecht and A. P. Wills (_Ann. d. Phys._, 1900, 1, 178), H. du Bois
and O. Liebknecht (ibid. p. 189), and Meyer (ibid. p. 668). An
excellent summary regarding the magnetic properties of matter, with
many tables and references, has been compiled by du Bois (_Report to
the Congrès Int. de Phys._, Paris, 1900, ii. 460).
+--------------------+--------------------+-------------------+
| _Element_ 10^6k | _Element_ 10^6k | _Element_ 10^6k |
+--------------------+--------------------+-------------------+
| Be +0.72 | Cu -0.006 | Cs -0.03* |
| B +0.05 | Zn -0.010 | Ba -0.02* |
| C -0.05 | Ga - | La +13.0 |
| N ? | Ge - | Ce +34.0 |
| O + | As ? | Pr +\ |
| F -0.01* | Se -0.025 | Nd +| Strong|
|....................| Br -0.033 | Sa +| |
| Na -0.005* |....................| Gd +/ |
| Mg +0.014 | Rb -0.02* |...................|
| Al + | Sr -0.02* | Er +41.8(?) |
| Si +0.002 | Y +3.2(?) |...................|
| P -0.007 | Zr -0.014 | Yb + (?) |
| S -0.011 | Nb +0.49(?) | Ta +1.02(?) |
| Cl -0.02* | Mo +0.024 | W +0.1 |
|....................| Ru + | Os +0.074 |
| K -0.001* | Rh + | Ir + |
| Ca -0.003* | Pd +0.55 | Pt +0.227 |
| Sc ? | Ag -0.016 | Au -0.031 |
| Ti +0.09 | Cd -0.015 | Hg -0.030 |
| V +0.17 | In +0.01* | Tl -0.93 |
| Cr +\ | Sn +0.004* | Pb -0.025 |
| Mn +| | Sb -0.069 | Bi -0.023 |
| Fe +|Strong | Te -0.039 |...................|
| Co +| | I -0.040 | Th +16.0(?) |
| Ni +/ |....................| U +0.21 |
+--------------------+--------------------+-------------------+
* Calculated.
12. MOLECULAR THEORY OF MAGNETISM
According to W. E. Weber's theory, the molecules of a ferromagnetic
metal are small permanent magnets, the axes of which under ordinary
conditions are turned indifferently in every direction, so that no
magnetic polarity is exhibited by the metal as a whole; a magnetic force
acting upon the metal tends to turn the axes of the little magnets in
one direction, and thus the entire piece acquires the properties of a
magnet. If, however, the molecules could turn with perfect freedom, it
is clear that the smallest magnetizing force would be sufficient to
develop the highest possible degree of magnetization, which is of course
not the case. Weber therefore supposed each molecule to be acted on by a
force tending to preserve it in its original direction, the position
actually assumed by the axis being in the direction of the resultant of
this hypothetical force and the applied magnetizing force. Maxwell
(_Electricity and Magnetism_, § 444), recognizing that the theory in
this form gave no account of residual magnetization, made the further
assumption that if the deflection of the axis of the molecule exceeded a
certain angle, the axis would not return to its original position when
the deflecting force was removed, but would retain a permanent set.
Although the amended theory as worked out by Maxwell is in rough
agreement with certain leading phenomena of magnetization, it fails to
account for many others, and is in some cases at variance with observed
facts.
J. A. Ewing (_Proc. Roy. Soc._, 1890, 48, 342) has demonstrated that it
is quite unnecessary to assume either the directive force of Weber, the
permanent set of Maxwell, or any kind of frictional resistance, the
forces by which the molecular magnets are constrained being simply those
due to their own mutual attractions and repulsions. The effect of these
is beautifully illustrated by a model consisting of a number of little
compass needles pivoted on sharp points and grouped near to one another
upon a board, which is placed inside a large magnetizing coil. When no
current is passing through the coil and the magnetic field is of zero
strength, the needles arrange themselves in positions of stable
equilibrium under their mutual forces, pointing in many different
directions, so that there is no resultant magnetic moment. This
represents the condition of the molecules in unmagnetized iron. If now a
gradually increasing magnetizing force is applied, the needles at first
undergo a stable deflection, giving to the group a small resultant
moment which increases uniformly with the force; and if the current is
interrupted while the force is still weak, the needles merely return to
their initial positions. This illustrates the first stage in the process
of magnetization, when the moment is proportional to the field and there
is no hysteresis or residual magnetism (see _ante_). A somewhat stronger
field will deflect many of the needles beyond the limits of stability,
causing them to turn round and form new stable combinations, in which
the direction assumed by most of them approximates to that of the field.
The rearrangement is completed within a comparatively small range of
magnetizing force, a rapid increase of the resultant moment being thus
brought about. When the field is removed, many of the newly formed
combinations are but slightly disturbed, and the group may consequently
retain a considerable resultant moment. This corresponds to the second
stage of magnetization, in which the susceptibility is large and
permanent magnetization is set up. A still stronger magnetizing force
has little effect except in causing the direction of the needles to
approach still more nearly to that of the field; if the force were
infinite, every member of the group would have exactly the same
direction and the greatest possible resultant moment would be reached;
this illustrates "magnetic saturation"--the condition approached in the
third stage of magnetization. When the strong magnetizing field is
gradually diminished to zero and then reversed, the needles pass from
one stable position of rest to another through a condition of
instability; and if the field is once more reversed, so that the cycle
is completed, the needles again pass through a condition of instability
before a position of stable equilibrium is regained. Now the unstable
movements of the needles are of a mechanically irreversible character;
the energy expended in dissociating the members of a combination and
placing them in unstable positions assumes the kinetic form when the
needles turn over, and is ultimately frittered down into heat. Hence in
performing a cycle there is a waste of energy corresponding to what has
been termed hysteresis-loss.
Supposing Ewing's hypothesis to be correct, it is clear that if the
magnetization of a piece of iron were reversed by a strong rotating
field instead of by a field alternating through zero, the loss of energy
by hysteresis should be little or nothing, for the molecules would
rotate with the field and no unstable movements would be possible.[91]
Some experiments by F. G. Baily (_Phil. Trans._, 1896, 187, 715) show
that this is actually the case. With small magnetizing forces the
hysteresis was indeed somewhat larger than that obtained in an
alternating field, probably on account of the molecular changes being
forced to take place in one direction only; but at an induction of about
16,000 units in soft iron and 15,000 in hard steel the hysteresis
reached a maximum and afterwards rapidly diminished. In one case the
hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B =
15,900, and only 1200 ergs for B = 20,200, the highest induction
obtained in the experiment; possibly it would have vanished before B had
reached 21,000.[92] These experiments prove that actual friction must be
almost entirely absent, and, as Baily remarks, the agreement of the
results with the previously suggested deduction affords a strong
verification of Ewing's form of the molecular theory. Ewing has himself
also shown how satisfactorily this theory accords with many other
obscure and complicated phenomena, such as those presented by coercive
force, differences of magnetic quality, and the effects of vibration,
temperature and stress; while as regards simplicity and freedom from
arbitrary assumptions it leaves little to be desired.
The fact being established that magnetism is essentially a molecular
phenomenon, the next step is to inquire what is the constitution of a
magnetic molecule, and why it is that some molecules are ferromagnetic,
others paramagnetic, and others again diamagnetic. The best known of the
explanations that have been proposed depend upon the magnetic action of
an electric current. It can be shown that if a current i circulates in a
small plane circuit of area S, the magnetic action of the circuit for
distant points is equivalent to that of a short magnet whose axis is
perpendicular to the plane of the circuit and whose moment is iS, the
direction of the magnetization being related to that of the circulating
current as the thrust of a right-handed screw to its rotation.
Ferromagnetism was explained by Ampère on the hypothesis that the
magnetization of the molecule is due to an electric current constantly
circulating within it. The theory now most in favour is merely a
development of Ampère's hypothesis, and applies not only to
ferromagnetics, but to paramagnetics as well. To account for
diamagnetism, Weber supposed that there exist within the molecules of
diamagnetic substances certain channels around which an electric current
can circulate without any resistance. The creation of an external
magnetic field H will, in accordance with Lenz's law, induce in the
molecule an electric current so directed that the magnetization of the
equivalent magnet is opposed to the direction of the field. The strength
of the induced current is -HScos[theta]/L, where [theta] is the
inclination of the axis of the circuit to the direction of the field,
and L the coefficient of self-induction; the resolved part of the
magnetic moment in the direction of the field is equal to
-HS²cos²[theta]/L, and if there are n molecules in a unit of volume,
their axes being distributed indifferently in all directions, the
magnetization of the substance will be -(1/3)nHS²/L, and its
susceptibility -(1/3)S²/L (Maxwell, _Electricity and Magnetism_, § 838).
The susceptibility is therefore constant and independent of the field,
while its negative sign indicates that the substance is diamagnetic.
There being no resistance, the induced current will continue to
circulate round the molecule until the field is withdrawn, when it will
be stopped by the action of an electromotive force tending to induce an
exactly equal current in the opposite direction. The principle of
Weber's theory, with the modification necessitated by lately acquired
knowledge, is the basis of the best modern explanation of diamagnetic
phenomena.
There are strong reasons for believing that magnetism is a phenomenon
involving rotation, and as early as 1876 Rowland, carrying out an
experiment which had been proposed by Maxwell, showed that a revolving
electric charge produced the same magnetic effects as a current. Since
that date it has more than once been suggested that the molecular
currents producing magnetism might be due to the revolution of one or
more of the charged atoms or "ions" constituting the molecule. None of
the detailed hypotheses which were based on this idea stood the test of
criticism, but towards the end of the 19th century the researches of J.
J. Thomson and others once more brought the conception of moving
electric charges into prominence. Thomson has demonstrated the existence
under many different conditions of particles more minute than anything
previously known to science. The mass of each is about 1/1700th part of
that of a hydrogen atom, and with each is indissolubly associated a
charge of negative electricity equal to about 3.1 × 10^(-10) C.G.S.
electrostatic unit. These particles, which were termed by their
discoverer _corpuscles_, are more commonly spoken of as _electrons_,[93]
the particle thus being identified with the charge which it carries. An
electrically neutral atom is believed to be constituted in part, or
perhaps entirely, of a definite number of electrons in rapid motion
within a "sphere of uniform positive electrification" not yet explained.
One or more of the electrons may be detached from the system by a finite
force, the number so detachable depending on the valency of the atom; if
the atom loses an electron, it becomes positively electrified; if it
receives additional electrons, it is negatively electrified. The process
of electric conduction in metals consists in the movement of detached
electrons, and many other phenomena, both electrical and thermal, can be
more or less completely explained by their agency. It has been supposed
that certain electrons revolve like satellites in orbits around the
atoms with which they are associated, a view which receives strong
support from the phenomena of the Zeeman effect, and on this assumption
a theory has been worked out by P. Langevin,[94] which accounts for many
of the observed facts of magnetism. As a consequence of the structure of
the molecule, which is an aggregation of atoms, the planes of the orbits
around the latter may be oriented in various positions, and the
direction of revolution may be right-handed or left-handed with respect
to the direction of any applied magnetic field. For those orbits whose
projection upon a plane perpendicular to the field is right-handed, the
period of revolution will be accelerated by the field (since the
electron current is negative), and the magnetic moment consequently
increased; for those which are left-handed, the period will be retarded
and the moment diminished. The effect of the field upon the speed of the
revolving electrons, and therefore upon the moments of the equivalent
magnets, is necessarily a very small one. If S is the area of the orbit
described in time [tau] by an electron of charge e, the moment of the
equivalent magnet is M = eS[tau]; and the change in the value of M due
to an external field H is shown to be [Delta]M = -He^2 S/4[pi]m, m being
the mass of the electron. Whence
[Delta]M H[tau]e
-------- = -------.
M 4[pi]m
According to the best determinations the value of e/m does not exceed
1.8 × 10^7, and [tau] is of the order of 10^(-15) second, the period of
luminous vibrations; hence [Delta]M/M must always be less than 10^(-9)H,
and therefore the strongest fields yet reached experimentally, which
fall considerably short of 10^5, could not change the magnetic moment M
by as much as a ten-thousandth part. If the structure of the molecule is
so perfectly symmetrical that, in the absence of any external field, the
resultant magnetic moment of the circulating electrons is zero, then the
application of a field, by accelerating the right-handed (negative)
revolutions, and retarding those which are left-handed, will induce in
the substance a resultant magnetization opposite in direction to the
field itself; a body composed of such symmetrical molecules is therefore
diamagnetic. If however the structure of the molecule is such that the
electrons revolving around its atoms do not exactly cancel one another's
effects, the molecule constitutes a little magnet, which under the
influence of an external field will tend to set itself with its axis
parallel to the field. Ordinarily a substance composed of asymmetrical
molecules is paramagnetic, but if the elementary magnets are so
conditioned by their strength and concentration that mutual action
between them is possible, then the substance is ferromagnetic. In all
cases however it is the diamagnetic condition that is initially set
up--even iron is diamagnetic--though the diamagnetism may be completely
masked by the superposed paramagnetic or ferromagnetic condition.
Diamagnetism, in short, is an atomic phenomenon; paramagnetism and
ferromagnetism are molecular phenomena. Hence may be deduced an
explanation of the fact that, while the susceptibility of all known
diamagnetics (except bismuth and antimony) is independent of the
temperature, that of paramagnetics varies inversely as the absolute
temperature, in accordance with the law of Curie.
13. HISTORICAL AND CHRONOLOGICAL NOTES
The most conspicuous property of the lodestone, its attraction for iron,
appears to have been familiar to the Greeks at least as early as 800
B.C., and is mentioned by Homer, Plato, Aristotle, Theophrastus and
others. A passage in _De rerum natura_ (vi. 910-915) by the Roman poet,
Lucretius (96-55 B.C.), in which it is stated that the stone can support
a chain of little rings, each adhering to the one above it, indicates
that in his time the phenomenon of magnetization by induction had also
been observed. The property of orientation, in virtue of which a freely
suspended magnet points approximately to the geographical north and
south, is not referred to by any European writer before the 12th
century, though it is said to have been known to the Chinese at a much
earlier period. The application of this property to the construction of
the mariner's compass is obvious, and it is in connexion with navigation
that the first references to it occur (see COMPASS). The needles of the
primitive compasses, being made of iron, would require frequent
re-magnetization, and a "stone" for the purpose of "touching the needle"
was therefore generally included in the navigator's outfit. With the
constant practice of this operation it is hardly possible that the
repulsion acting between like poles should have entirely escaped
recognition; but though it appears to have been noticed that the
lodestone sometimes repelled iron instead of attracting it, no clear
statement of the fundamental law that unlike poles attract while like
poles repel was recorded before the publication in 1581 of the _New
Attractive_ by Robert Norman, a pioneer in accurate magnetic work. The
same book contains an account of Norman's discovery and correct
measurement of the dip (1576). The downward tendency of the north pole
of a magnet pivoted in the usual way had been observed by G. Hartmann of
Nüremberg in 1544, but his observation was not published till much
later.
The foundations of the modern science of magnetism were laid by William
Gilbert (q.v.). His _De magnete magneticisque corporibus et de magno
magnete tellure physiologia nova_ (1600), contains many references to
the expositions of earlier writers from Plato down to those of the
author's own age. These show that the very few facts known with
certainty were freely supplemented by a number of ill-founded
conjectures, and sometimes even by "figments and falsehoods, which in
the earliest times, no less than nowadays, used to be put forth by raw
smatterers and copyists to be swallowed of men."[95] Thus it was taught
that "if a lodestone be anointed with garlic, or if a diamond be near,
it does not attract iron," and that "if pickled in the salt of a sucking
fish, there is power to pick up gold which has fallen into the deepest
wells." There were said to be "various kinds of magnets, some of which
attract gold, others silver, brass, lead; even some which attract flesh,
water, fishes;" and stories were told about "mountains in the north of
such great powers of attraction that ships are built with wooden pegs,
lest the iron nails should be drawn from the timber." Certain occult
powers were also attributed to the stone. It was "of use to thieves by
its fume and sheen, being a stone born, as it were, to aid theft," and
even opening bars and locks; it was effective as a love potion, and
possessed "the power to reconcile husbands to their wives, and to recall
brides to their husbands." And much more of the same kind, which, as
Gilbert says, had come down "even to [his] own day through the writings
of a host of men, who, to fill out their volumes to a proper bulk, write
and copy out pages upon pages on this, that and the other subject, of
which they know almost nothing for certain of their own experience."
Gilbert himself absolutely disregarded authority, and accepted nothing
at second-hand. His title to be honoured as the "Father of Magnetic
Philosophy" is based even more largely upon the scientific method which
he was the first to inculcate and practise than upon the importance of
his actual discoveries. Careful experiment and observation, not the
inner consciousness, are, he insists, the only foundations of true
science. Nothing has been set down in his book "which hath not been
explored and many times performed and repeated" by himself. "It is very
easy for men of acute intellect, apart from experiment and practice, to
slip and err." The greatest of Gilbert's discoveries was that the globe
of the earth was magnetic and a magnet; the evidence by which he
supported this view was derived chiefly from ingenious experiments made
with a spherical lodestone or _terrella_, as he termed it, and from his
original observation that an iron bar could be magnetized by the earth's
force. He also carried out some new experiments on the effects of heat,
and of screening by magnetic substances, and investigated the influence
of shape upon the magnetization of iron. But the bulk of his work
consisted in imparting scientific definiteness to what was already
vaguely known, and in demolishing the errors of his predecessors.
No material advance upon the knowledge recorded in Gilbert's book was
made until the establishment by Coulomb in 1785 of the law of magnetic
action. The difficulties attending the experimental investigation of the
forces acting between magnetic poles have already been referred to, and
indeed a rigorously exact determination of the mutual action could only
be made under conditions which are in practice unattainable.
Coulomb,[96] however, by using long and thin steel rods, symmetrically
magnetized, and so arranged that disturbing influences became negligibly
small, was enabled to deduce from his experiments with reasonable
certainty the law that the force of attraction or repulsion between two
poles varies inversely as the square of the distance between them.
Several previous attempts had been made to discover the law of force,
with various results, some of which correctly indicated the inverse
square; in particular the German astronomer, J. Tobias Mayer (_Gött.
Anzeiger_, 1760), and the Alsatian mathematician, J. Heinrich Lambert
(_Hist. de l'Acad. Roy. Berlin_, 1766, p. 22), may fairly be credited
with having anticipated the law which was afterwards more satisfactorily
established by Coulomb. The accuracy of this law was in 1832 confirmed
by Gauss,[97] who employed an indirect but more perfect method than that
of Coulomb, and also, as Maxwell remarks, by all observers in magnetic
observatories, who are every day making measurements of magnetic
quantities, and who obtain results which would be inconsistent with each
other if the law of force had been erroneously assumed.
Coulomb's researches provided data for the development of a mathematical
theory of magnetism, which was indeed initiated by himself, but was
first treated in a complete form by Poisson in a series of memoirs
published in 1821 and later.[98] Poisson assumed the existence of two
dissimilar magnetic fluids, any element of which acted upon any other
distant element in accordance with Coulomb's law of the inverse square,
like repelling and unlike attracting one another. A magnetizable
substance was supposed to consist of an indefinite number of spherical
particles, each containing equivalent quantities of the two fluids,
which could move freely within a particle, but could never pass from one
particle to another. When the fluids inside a particle were mixed
together, the particle was neutral; when they were more or less
completely separated, the particle became magnetized to an intensity
depending upon the magnetic force applied; the whole body therefore
consisted of a number of little spheres having north and south poles,
each of which exerted an elementary action at a distance. On this
hypothesis Poisson investigated the forces due to bodies magnetized in
any manner, and also originated the mathematical theory of magnetic
induction. The general confirmation by experiment of Poisson's
theoretical results created a tendency to regard his hypothetical
magnetic fluids as having a real existence; but it was pointed out by W.
Thomson (afterwards Lord Kelvin) in 1849 that while no physical evidence
could be adduced in support of the hypothesis, certain discoveries,
especially in electromagnetism, rendered it extremely improbable
(_Reprint_, p. 344). Regarding it as important that all reasoning with
reference to magnetism should be conducted without any uncertain
assumptions, he worked out a mathematical theory upon the sole
foundation of a few well-known facts and principles. The results were
substantially the same as those given by Poisson's theory, so far as the
latter went, the principal additions including a fuller investigation of
magnetic distribution, and the theory of magnetic induction in
aeolotropic or crystalline substances. The mathematical theory which was
constructed by Poisson, and extended and freed from doubtful hypotheses
by Kelvin, has been elaborated by other investigators, notably F. E.
Neumann, G. R. Kirchhoff, and Maxwell. The valuable work of Gauss on
magnetic theory and measurements, especially in relation to terrestrial
magnetism, was published in his _Intensitas vis magneticae terrestris_,
1833, and in memoirs communicated to the _Resultate aus den
Beobachtungen des magnetischen Vereins_, 1838 and 1839, which, with
others, are contained in vol. 5 of the collected _Werke_. Weber's
molecular theory, which has already been referred to, appeared in
1852.[99]