Chapter LXIII: repeats the promise of freedom to the English church (5)

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.

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.

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.

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 |

_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]