Chapter I: Part 1

Transcriber's notes:

(1) Numbers following letters (without space) like C2 were originally
printed in subscript. Letter subscripts are preceded by an
underscore, like C_n.

(2) Characters following a carat (^) were printed in superscript.

(3) Side-notes were relocated to function as titles of their respective
paragraphs.

(4) Macrons and breves above letters and dots below letters were not
inserted.

(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
letters.

(6) The following typographical errors have been corrected:

ARTICLE MAGNETOMETER: "... the determination of the magnetic
elements on board ship is a matter of very considerable
importance." 'determination' amended from 'determinaton'.

ARTICLE MAGNETO-OPTICS: "The relation of the magnetic rotation to
chemical constitution has been studied in great detail by Perkin,
Wachsmuth, Jahn and Schönrock." 'constitution' amended from
'consitution'.

ARTICLE MAGNUS, HEINRICH GUSTAV: "... ('Magnus's green salt' is
PtCl2, 2NH3), of sulphovinic ..." 'PtCl2' amended from 'Ptll2'.

ARTICLE MAHOMET: "With this change we may perhaps couple the
adoption of the name Allah for the Deity ..." 'Deity' amended from
'Diety'.

ARTICLE MAHOMMEDAN LAW: "It was rather the Moslem leaders who were
compelled to abandon their ideas and for the sake of the spread of
Islam to accept and incorporate much that was diametrically opposed
to the original legislation either of the Koran or of Mahomet's
recorded decisions." 'decisions' amended from 'decisons'.

ARTICLE MALAY ARCHIPELAGO: "In 1611 the headquarters of the Dutch
was changed from Bantam to Jakarta, which in 1619 was renamed
Batavia, and was thenceforward the Dutch capital." 'Jakarta'
amended from 'Jakatra'.

ARTICLE MALAYS: "When the first Europeans visited the Malay
Archipelago the Malays had already acquired the art of
manufacturing gunpowder and forging cannon." 'cannon' amended from
'canon'.

ARTICLE MALAY STATES: "The country is mountainous except close to
the coast. The principal rivers are the Patani and the Teloban,
long, winding and shallow, and navigable for small boats only."
'the' amended from 'tle'.

ARTICLE MALOCELLO, LANCILOTO: "This was a Genoese expedition, which
about 1270 seems to have sailed into the Atlantic, re-discovered
the 'Fortunate Islands' or Canaries" 'Atlantic' amended from
'Alantic'.

ENCYCLOPAEDIA BRITANNICA

A DICTIONARY OF ARTS, SCIENCES, LITERATURE
AND GENERAL INFORMATION

ELEVENTH EDITION

VOLUME XVII, SLICE IV

Magnetite to Malt

ARTICLES IN THIS SLICE:

MAGNETITE MAJOR, JOHN
MAGNETOGRAPH MAJOR
MAGNETOMETER MAJORCA
MAGNETO-OPTICS MAJORIAN
MAGNOLIA MAJORITY
MAGNUS, HEINRICH GUSTAV MAJUBA
MAGNY, CLAUDE DRIGON MAKALAKA
MAGO MAKARAKA
MAGPIE MAKART, HANS
MAGWE MAKING-UP PRICE
MAGYARS MAKÓ
MAHABALESHWAR MAKRAN
MAHAFFY, JOHN PENTLAND MAKSOORA
MAHALLAT MALABAR
MAHAN, ALFRED THAYER MALABARI, BEHRAMJI
MAHANADI MALABON
MAHANOY CITY MALACCA
MAHAR MALACHI
MAHARAJPUR MALACHITE
MAHAVAMSA MALACHOWSKI, STANISLAW
MAHAYANA MALACHY, ST
MAHDI MALACOSTRACA
MAHDIA MALAGA (province of Spain)
MAHÉ MALAGA (city of Spain)
MAHESHWAR MALAKAND PASS
MAHI MALALAS, JOHN
MAHI KANTHA MALAN, SOLOMON CAESAR
MAHMUD I. MÄLAR
MAHMUD II. MALARIA
MAHMUD NEDIM PASHA MALATIA
MAHMUD OF GHAZNI MALAYALAM
MAHOBA MALAY ARCHIPELAGO
MAHOGANY MALAIR
MAHOMET MALAY PENINSULA
MAHOMMED AHMED IBN ABDULLAH MALAYS
MAHOMMEDAN INSTITUTIONS MALAY STATES (British)
MAHOMMEDAN LAW MALAY STATES (Siamese)
MAHOMMEDAN RELIGION MALCHIN
MAHONY, FRANCIS SYLVESTER MALCOLM
MAHOUT MALCOLM, SIR JOHN
MAHRATTAS MALDA
MAHSEER MALDEN
MAI, ANGELO MALDIVE ISLANDS
MAIA MALDON
MAIDA MALEBRANCHE, NICOLAS
MAIDAN MALER KOTLA
MAIDEN MALESHERBES, CHRÉTIEN DE LAMOIGNON DE
MAIDENHAIR MALET, LUCAS
MAIDENHEAD MALHERBE, FRANÇOIS DE
MAID MARIAN MALIBRAN, MARIE FÉLICITÉ
MAIDSTONE MALIC ACID
MAIHAR MALIGNANT
MAIL MALIK IBN ANAS
MAILLY, LOUISE JULIE MALINES
MAIMANA MALLANWAN
MAIMAND MALLARMÉ, FRANÇOIS RENÉ AUGUSTE
MAIMBOURG, LOUIS MALLARMÉ, STÉPHANE
MAIMING MALLECO
MAIMON, SALOMON MALLEMUCK
MAIMONIDES MALLESON, GEORGE BRUCE
MAIN (river of Germany) MALLET, DAVID
MAIN (power or strength) MALLET, PAUL HENRI
MAINA and MAINOTES MALLET, ROBERT
MAINE, ANNE LOUISE DE BOURBON MALLET DU PAN, JACQUES
MAINE, SIR HENRY JAMES SUMNER MALLING, EAST and WEST
MAINE (French province) MALLOCK, WILLIAM HURRELL
MAINE (U.S. state) MALLOW (town of Ireland)
MAINE DE BIRAN, FRANÇOIS-GONTHIER MALLOW (botanical genus)
MAINE-ET-LOIRE MALMEDY
MAINPURI MALMESBURY, JAMES HARRIS
MAINTENANCE MALMESBURY, JAMES HOWARD HARRIS
MAINTENON, FRANÇOISE D'AUBIGNÉ MALMESBURY
MAINZ MALMÖ
MAIRET, JEAN DE MALMSEY
MAISTRE, JOSEPH DE MALOCELLO, LANCILOTO
MAISTRE, XAVIER DE MALOLOS
MAITLAND, EDWARD MALONE, EDMOND
MAITLAND, FREDERIC WILLIAM MALONE
MAITLAND, SIR RICHARD MALONIC ACID
MAITLAND, WILLIAM MALORY, SIR THOMAS
MAITLAND, EAST and WEST MALOT, HECTOR HENRI
MAITREYA MALOU, JULES ÉDOUARD XAVIER
MAIWAND MALOUET, PIERRE VICTOR
MAIZE MALPIGHI, MARCELLO
MAJESTY MALPLAQUET
MAJLÁTH, JÁNOS MALSTATT-BURBACH
MAJOLICA MALT

MAGNETITE, a mineral forming the natural magnet (see MAGNETISM), and important also as an iron-ore. It is an iron-black, opaque mineral, with metallic lustre; hardness about 6, sp. gr. 4.9 to 5.2. When scratched, it yields a black streak. It is an oxide of iron having the formula Fe3O4, corresponding with 72.4% of metal, whence its great value as an ore. It may be regarded as a ferroso-ferric oxide, FeO·Fe2O3, or as iron ferrate, Fe´´Fe2´´´O4. Titanium is often present, and occasionally the mineral contains magnesium, nickel, &c. It is always strongly magnetic. Magnetite crystallizes in the cubic system, usually in octahedra, less commonly in rhombic dodecahedra, and not infrequently in twins of the "spinel type" (fig. 1). The rhombic faces of the dodecahedron are often striated parallel to the longer diagonal. There is no distinct cleavage, but imperfect parting may be obtained along octahedral planes.

Magnetite is a mineral of wide distribution, occurring as grains in many massive and volcanic rocks, like granite, diorite and dolerite. It appears to have crystallized from the magma at a very early period of consolidation. Its presence contributes to the dark colour of many basalts and other basic rocks, and may cause them to disturb the compass. Large ore-bodies of granular and compact magnetite occur as beds and lenticular masses in Archean gneiss and crystalline schists, in various parts of Norway, Sweden, Finland and the Urals; as also in the states of New York, New Jersey, Pennsylvania and Michigan, as well as in Canada. In some cases it appears to have segregated from a basic eruptive magma, and in other cases to have resulted from metamorphic action. Certain deposits appear to have been formed, directly or indirectly, by wet processes. Iron rust sometimes contains magnetite. An interesting deposit of oolitic magnetic ore occurs in the Dogger (Inferior Oolite) of Rosedale Abbey, in Yorkshire; and a somewhat similar pisolitic ore, of Jurassic age, is known on the continent as chamoisite, having been named from Chamoison (or Chamoson) in the Valais, Switzerland. Grains of magnetite occur in serpentine, as an alteration-product of the olivine. In emery, magnetite in a granular form is largely associated with the corundum; and in certain kinds of mica magnetite occurs as thin dendritic enclosures. Haematite is sometimes magnetic, and A. Liversidge has shown that magnetite is probably present. By deoxidation, haematite may be converted into magnetite, as proved by certain pseudomorphs; but on the other hand magnetite is sometimes altered to haematite. On weathering, magnetite commonly passes into limonite, the ferrous oxide having probably been removed by carbonated waters. Closely related to magnetite is the rare volcanic mineral from Vesuvius, called magnoferrite, or magnesioferrite, with the formula MgFe2O4; and with this may be mentioned a mineral from Jakobsberg, in Vermland, Sweden, called jakobsite, containing MnFe2O4. (F. W. R.*)

MAGNETOGRAPH, an instrument for continuously recording the values of the magnetic elements, the three universally chosen being the declination, the horizontal component and the vertical component (see TERRESTRIAL MAGNETISM). In each case the magnetograph only records the variation of the element, the absolute values being determined by making observations in the neighbourhood with the unifilar magnetometer (q.v.) and inclinometer (q.v.).

_Declination._--The changes in declination are obtained by means of a
magnet which is suspended by a long fibre and carries a mirror,
immediately below which a fixed mirror is attached to the base of the
instrument. Both mirrors are usually concave; if plane, a concave lens
is placed immediately before them. Light passing through a vertical
slit falls upon the mirrors, from which it is reflected, and two
images of the slit are produced, one by the movable mirror attached to
the magnet and the other by the fixed mirror. These images would be
short lines of light; but a piano-cylindrical lens is placed with its
axis horizontal just in front of the recording surface. In this way a
spot of light is obtained from each mirror. The recording surface is a
sheet of photographic paper wrapped round a drum which is rotated at a
constant speed by clockwork about a horizontal axis. The light
reflected from the fixed mirror traces a straight line on the paper,
serving as a base line from which the variations in declination are
measured. As the declination changes the spot of light reflected from
the magnet mirror moves parallel to the axis of the recording drum,
and hence the distance between the line traced by this spot and the
base line gives, for any instant, on an arbitrary scale the difference
between the declination and a constant angle, namely, the declination
corresponding to the base line. The value of this constant angle is
obtained by comparing the record with the value for the declination as
measured with a magnetometer. The value in terms of arc of the scale
of the record can be obtained by measuring the distance between the
magnet mirror and the recording drum, and in most observations it is
such that a millimetre on the record represents one minute of arc. The
time scale ordinarily employed is 15 mm. per hour, but in modern
instruments provision is generally made for the time scale to be
increased at will to 180 mm. per hour, so that the more rapid
variations of the declination can be followed. The advantages of using
small magnets, so that their moment of inertia may be small and hence
they may be able to respond to rapid changes in the earth's field,
were first insisted upon by E. Mascart,[1] while M. Eschenhagen[2]
first designed a set of magnetographs in which this idea of small
moment of inertia was carried to its useful limit, the magnets only
weighing 1.5 gram each, and the suspension consisting of a very fine
quartz fibre.

_Horizontal Force._--The variation of the horizontal force is obtained
by the motion of a magnet which is carried either by a bifilar
suspension or by a fairly stiff metal wire or quartz fibre. The upper
end of the suspension is turned till the axis of the magnet is at
right angles to the magnetic meridian. In this position the magnet is
in equilibrium under the action of the torsion of the suspension and
the couple exerted by the horizontal component, H, of the earth's
field, this couple depending on the product of H into the magnetic
moment, M, of the magnet. Hence if H varies the magnet will rotate in
such a way that the couple due to torsion is equal to the new value of
H multiplied by M. Since the movements of the magnet are always small,
the rotation of the magnet is proportional to the change in H, so long
as M and the couple, [theta], corresponding to unit twist of the
suspension system remain constant. When the temperature changes,
however, both M and [theta] in general change. With rise of
temperature M decreases, and this alone will produce the same effect
as would a decrease in H. To allow for this effect of temperature a
compensating system of metal bars is attached to the upper end of the
bifilar suspension, so arranged that with rise of temperature the
fibres are brought nearer together and hence the value of [theta]
decreases. Since such a decrease in [theta] would by itself cause the
magnet to turn in the same direction as if H had increased, it is
possible in a great measure to neutralize the effects of temperature
on the reading of the instrument. In the case of the unifilar
suspension, the provision of a temperature compensation is not so
easy, so that what is generally done is to protect the instrument from
temperature variation as much as possible and then to correct the
indications so as to allow for the residual changes, a continuous
record of the temperature being kept by a recording thermograph
attached to the instrument. In the Eschenhagen pattern instrument, in
which a single quartz fibre is used for the suspension, two magnets
are placed in the vicinity of the suspended magnet and are so arranged
that their field partly neutralizes the earth's field; thus the
torsion required to hold the magnet with its axis perpendicular to the
earth's field is reduced, and the arrangement permits of the
sensitiveness being altered by changing the position of the deflecting
magnets. Further, by suitably choosing the positions of the deflectors
and the coefficient of torsion of the fibre, it is possible to make
the temperature coefficient vanish. (See Adolf Schmidt, _Zeits. für
Instrumentenkunde_, 1907, 27, 145.) The method of recording the
variations in H is exactly the same as that adopted in the case of the
declination, and the sensitiveness generally adopted is such that 1
mm. on the record represents a change in H of .00005 C.G.S., the time
scale being the same as that employed in the case of the declination.

_Vertical Component._--To record the variations of the vertical
component use is made of a magnet mounted on knife edges so that it
can turn freely about a horizontal axis at right angles to its length
(H. Lloyd, _Proc. Roy. Irish Acad._, 1839, 1, 334). The magnet is so
weighted that its axis is approximately horizontal, and any change in
the inclination of the axis is observed by means of an attached
mirror, a second mirror fixed to the stand serving to give a base line
for the records, which are obtained in the same way as in the case of
the declination. The magnet is in equilibrium under the influence of
the couple VM due to the vertical component V, and the couple due to
the fact that the centre of gravity is slightly on one side of the
knife-edge. Hence when, say, V decreases the couple VM decreases, and
hence the north end of the balanced magnet rises, and vice versa. The
chief difficulty with this form of instrument is that it is very
sensitive to changes of temperature, for such changes not only alter M
but also in general cause the centre of gravity of the system to be
displaced with reference to the knife-edge. To reduce these effects
the magnet is fitted with compensating bars, generally of zinc, so
adjusted by trial that as far as possible they neutralize the effect
of changes of temperature. In the Eschenhagen form of vertical force
balance two deflecting magnets are used to partly neutralize the
vertical component, so that the centre of gravity is almost exactly
over the support. By varying the positions of these deflecting magnets
it is possible to compensate for the effects of changes of temperature
(A. Schmidt, loc. cit.). In order to eliminate the irregularity which
is apt to be introduced by dust, &c., interfering with the working of
the knife-edge, W. Watson (_Phil. Mag._, 1904 [6], 7, 393) designed a
form of vertical force balance in which the magnet with its mirror is
attached to the mid point of a horizontal stretched quartz fibre. The
temperature compensation is obtained by attaching a small weight to
the magnet, and then bringing it back to the horizontal position by
twisting the fibre.

The scale values of the records given by the horizontal and vertical
force magnetographs are determined by deflecting the respective
needles, either by means of a magnet placed at a known distance or by
passing an electric current through circular coils of large diameter
surrounding the instruments.

The width of the photographic sheet which receives the spot of light
reflected from the mirrors in the above instruments is generally so
great that in the case of ordinary changes the curve does not go off
the paper. Occasionally, however, during a disturbance such is not the
case, and hence a portion of the trace would be lost. To overcome this
difficulty Eschenhagen in his earlier type of instruments attached to
each magnet two mirrors, their planes being inclined at a small angle
so that when the spot reflected from one mirror goes off the paper,
that corresponding to the other comes on. In the later pattern a third
mirror is added of which the plane is inclined at about 30° to the
horizontal. The light from the slit is reflected on to this mirror by
an inclined fixed mirror, and after reflection at the movable mirror
is again reflected at the fixed mirror and so reaches the recording
drum. By this arrangement the angular rotation of the reflected beam
is less than that of the magnet, and hence the spot of light reflected
from this mirror yields a trace on a much smaller scale than that
given by the ordinary mirror and serves to give a complete record of
even the most energetic disturbance.

See also Balfour Stewart, _Report of the British Association_,
Aberdeen, 1859, 200, a description of the type of instrument used in
the older observatories; E. Mascart, _Traité de magnétisme terrestre_,
p. 191; W. Watson, _Terrestrial Magnetism_, 1901, 6, 187, describing
magnetographs used in India; M. Eschenhagen, _Verhandlungen der
deutschen physikalischen Gesellschaft_, 1899, 1, 147; _Terrestrial
Magnetism_, 1900, 5, 59; and 1901, 6, 59; _Zeits. für
Instrumentenkunde_, 1907, 27, 137; W. G. Cady, _Terrestrial
Magnetism_, 1904, 9, 69, describing a declination magnetograph in
which the record is obtained by means of a pen acting on a moving
strip of paper, so that the curve can be consulted at all times to see
whether a disturbance is in progress.

The effects of temperature being so marked on the readings of the
horizontal and vertical force magnetographs, it is usual to place the
instruments either in an underground room or in a room which, by means
of double walls and similar devices, is protected as much as possible
from temperature changes. For descriptions of the arrangements adopted
in some observatories see the following: U.S. observatories,
_Terrestrial Magnetism_, 1903, 8, 11; Utrecht, _Terrestrial
Magnetism_, 1900, 5, 49; St Maur, _Terrestrial Magnetism_, 1898, 3, 1;
Potsdam, _Veröffentlichungen des k. preuss. meteorol. Instituts_,
"Ergebnisse der magnetischen Beobachtungen in Potsdam in den Jahren
1890 und 1891;" Pavlovsk, "Das Konstantinow'sche meteorologische und
magnetische Observatorium in Pavlovsk," _Ausgabe der kaiserl. Akad.
der Wissenschaften zu St Petersburg_, 1895. (W. Wn.)

FOOTNOTES:

[1] _Report British Association_, Bristol, 1898, p. 741.

[2] _Verhandlungen der deutschen physikalischen Gesellschaft_, 1899,
1, 147; or _Terrestrial Magnetism_, 1900, 5, 59.

MAGNETOMETER, a name, in its most general sense, for any instrument used to measure the strength of any magnetic field; it is, however, often used in the restricted sense of an instrument for measuring a particular magnetic field, namely, that due to the earth's magnetism, and in this article the instruments used for measuring the value of the earth's magnetic field will alone be considered.

The elements which are actually measured when determining the value of the earth's field are usually the declination, the dip and the horizontal component (see MAGNETISM, TERRESTRIAL). For the instruments and methods used in measuring the dip see INCLINOMETER. It remains to consider the measurement of the declination and the horizontal component, these two elements being generally measured with the same instrument, which is called a unifilar magnetometer.

_Measurement of Declination._--The measurement of the declination
involves two separate observations, namely, the determination of (a)
the magnetic meridian and (b) the geographical meridian, the angle
between the two being the declination. In order to determine the
magnetic meridian the orientation of the magnetic axis of a freely
suspended magnet is observed; while, in the absence of a distant mark
of which the azimuth is known, the geographical meridian is obtained
from observations of the transit of the sun or a star. The geometrical
axis of the magnet is sometimes defined by means of a mirror rigidly
attached to the magnet and having the normal to the mirror as nearly
as may be parallel to the magnetic axis. This arrangement is not very
convenient, as it is difficult to protect the mirror from accidental
displacement, so that the angle between the geometrical and magnetic
axes may vary. For this reason the end of the magnet is sometimes
polished and acts as the mirror, in which case no displacement of the
reflecting surface with reference to the magnet is possible. A
different arrangement, used in the instrument described below,
consists in having the magnet hollow, with a small scale engraved on
glass firmly attached at one end, while to the other end is attached a
lens, so chosen that the scale is at its principal focus. In this case
the geometrical axis is the line joining the central division of the
scale to the optical centre of the lens. The position of the magnet is
observed by means of a small telescope, and since the scale is at the
principal focus of the lens, the scale will be in focus when the
telescope is adjusted to observe a distant object. Thus no alteration
in the focus of the telescope is necessary whether we are observing
the magnet, a distant fixed mark, or the sun.

The Kew Observatory pattern unifilar magnetometer is shown in figs. 1
and 2. The magnet consists of a hollow steel cylinder fitted with a
scale and lens as described above, and is suspended by a long thread
of unspun silk, which is attached at the upper end to the torsion head
H. The magnet is protected from draughts by the box A, which is closed
at the sides by two shutters when an observation is being taken. The
telescope B serves to observe the scale attached to the magnet when
determining the magnetic meridian, and to observe the sun or star when
determining the geographical meridian.

When making a determination of declination a brass plummet having the
same weight as the magnet is first suspended in its place, and the
torsion of the fibre is taken out. The magnet having been attached,
the instrument is rotated about its vertical axis till the centre
division of the scale appears to coincide with the vertical cross-wire
of the telescope. The two verniers on the azimuth circle having been
read, the magnet is then inverted, i.e. turned through 180° about its
axis, and the setting is repeated. A second setting with the magnet
inverted is generally made, and then another setting with the magnet
in its original position. The mean of all the readings of the verniers
gives the reading on the azimuth circle corresponding to the magnetic
meridian. To obtain the geographical meridian the box A is removed,
and an image of the sun or a star is reflected into the telescope B by
means of a small transit mirror N. This mirror can rotate about a
horizontal axis which is at right angles to the line of collimation of
the telescope, and is parallel to the surface of the mirror. The time
of transit of the sun or star across the vertical wire of the
telescope having been observed by means of a chronometer of which the
error is known, it is possible to calculate the azimuth of the sun or
star, if the latitude and longitude of the place of observation are
given. Hence if the readings of the verniers on the azimuth circle are
made when the transit is observed we can deduce the reading
corresponding to the geographical meridian.

The above method of determining the geographical meridian has the
serious objection that it is necessary to know the error of the
chronometer with very considerable accuracy, a matter of some
difficulty when observing at any distance from a fixed observatory.
If, however, a theodolite, fitted with a telescope which can rotate
about a horizontal axis and having an altitude circle, is employed, so
that when observing a transit the altitude of the sun or star can be
read off, then the time need only be known to within a minute or so.
Hence in more recent patterns of magnetometer it is usual to do away
with the transit mirror method of observing and either to use a
separate theodolite to observe the azimuth of some distant object,
which will then act as a fixed mark when making the declination
observations, or to attach to the magnetometer an altitude telescope
and circle for use when determining the geographical meridian.

The chief uncertainty in declination observations, at any rate at a
fixed observatory, lies in the variable torsion of the silk
suspension, as it is found that, although the fibre may be entirely
freed from torsion before beginning the declination observations, yet
at the conclusion of these observations a considerable amount of
torsion may have appeared. Soaking the fibre with glycerine, so that
the moisture it absorbs does not change so much with the hygrometric
state of the air, is of some advantage, but does not entirely remove
the difficulty. For this reason some observers use a thin strip of
phosphor bronze to suspend the magnet, considering that the absence of
a variable torsion more than compensates for the increased difficulty
in handling the more fragile metallic suspension.

_Measurement of the Horizontal Component of the Earth's Field._--The
method of measuring the horizontal component which is almost
exclusively used, both in fixed observatories and in the field,
consists in observing the period of a freely suspended magnet, and
then obtaining the angle through which an auxiliary suspended magnet
is deflected by the magnet used in the first part of the experiment.
By the vibration experiment we obtain the value of the product of the
magnetic moment (M) of the magnet into the horizontal component (H),
while by the deflexion experiment we can deduce the value of the ratio
of M to H, and hence the two combined give both M and H.

In the case of the Kew pattern unifilar the same magnet that is used
for the declination is usually employed for determining H, and for the
purposes of the vibration experiment it is mounted as for the
observation of the magnetic meridian. The time of vibration is
obtained by means of a chronometer, using the eye-and-ear method. The
temperature of the magnet must also be observed, for which purpose a
thermometer C (fig. 1) is attached to the box A.

When making the deflection experiment the magnetometer is arranged as
shown in fig. 2. The auxiliary magnet has a plane mirror attached, the
plane of which is at right angles to the axis of the magnet. An image
of the ivory scale B is observed after reflection in the magnet mirror
by the telescope A. The magnet K used in the vibration experiment is
supported on a carriage L which can slide along the graduated bar D.
The axis of the magnet is horizontal and at the same level as the
mirror magnet, while when the central division of the scale B appears
to coincide with the vertical cross-wire of the telescope the axes of
the two magnets are at right angles. During the experiment the mirror
magnet is protected from draughts by two wooden doors which slide in
grooves. What is known as the method of sines is used, for since the
axes of the two magnets are always at right angles when the mirror
magnet is in its zero position, the ratio M/H is proportional to the
sine of the angle between the magnetic axis of the mirror magnet and
the magnetic meridian. When conducting a deflexion experiment the
deflecting magnet K is placed with its centre at 30 cm. from the
mirror magnet and to the east of the latter, and the whole instrument
is turned till the centre division of the scale B coincides with the
cross-wire of the telescope, when the readings of the verniers on the
azimuth circle are noted. The magnet K is then reversed in the
support, and a new setting taken. The difference between the two sets
of readings gives twice the angle which the magnetic axis of the
mirror magnet makes with the magnetic meridian. In order to eliminate
any error due to the zero of the scale D not being exactly below the
mirror magnet, the support L is then removed to the west side of the
instrument, and the settings are repeated. Further, to allow of a
correction being applied for the finite length of the magnets the
whole series of settings is repeated with the centre of the deflecting
magnet at 40 cm. from the mirror magnet.

Omitting correction terms depending on the temperature and on the
inductive effect of the earth's magnetism on the moment of the
deflecting magnet, if [theta] is the angle which the axis of the
deflected magnet makes with the meridian when the centre of the
deflecting magnet is at a distance r, then

r³H P Q
--- sin [theta] = 1 + --- + --- + &c.,
2M r r²

in which P and Q are constants depending on the dimensions and
magnetic states of the two magnets. The value of the constants P and Q
can be obtained by making deflexion experiments at three distances. It
is, however, possible by suitably choosing the proportions of the two
magnets to cause either P or Q to be very small. Thus it is usual, if
the magnets are of similar shape, to make the deflected magnet 0.467
of the length of the deflecting magnet, in which case Q is negligible,
and thus by means of deflexion experiments at two distances the value
of P can be obtained. (See C. Börgen, _Terrestrial Magnetism_, 1896,
i. p. 176, and C. Chree, _Phil. Mag._, 1904 [6], 7, p. 113.)

In the case of the vibration experiment correction terms have to be
introduced to allow for the temperature of the magnet, for the
inductive effect of the earth's field, which slightly increases the
magnetic moment of the magnet, and for the torsion of the suspension
fibre, as well as the rate of the chronometer. If the temperature of
the magnet were always exactly the same in both the vibration and
deflexion experiment, then no correction on account of the effect of
temperature in the magnetic moment would be necessary in either
experiment. The fact that the moment of inertia of the magnet varies
with the temperature must, however, be taken into account. In the
deflexion experiment, in addition to the induction correction, and
that for the effect of temperature on the magnetic moment, a
correction has to be applied for the effect of temperature on the
length of the bar which supports the deflexion magnet.

See also Stewart and Gee, _Practical Physics_, vol. 2, containing a
description of the Kew pattern unifilar magnetometer and detailed
instructions for performing the experiments; C. Chree, _Phil. Mag._,
1901 (6), 2, p. 613, and _Proc. Roy. Soc._, 1899, 65, p. 375,
containing a discussion of the errors to which the Kew unifilar
instrument is subject; E. Mascart, _Traité de magnétisme terrestre_,
containing a description of the instruments used in the French
magnetic survey, which are interesting on account of their small size
and consequent easy portability; H. E. D. Fraser, _Terrestrial
Magnetism_, 1901, 6, p. 65, containing a description of a modified Kew
pattern unifilar as used in the Indian survey; H. Wild, _Mém. Acad.
imp. sc. St Pétersbourg_, 1896 (viii.), vol. 3, No. 7, containing a
description of a most elaborate unifilar magnetometer with which it is
claimed results can be obtained of a very high order of accuracy; K.
Haufsmann, _Zeits. für Instrumentenkunde_, 1906, 26, p. 2, containing
a description of a magnetometer for field use, designed by M.
Eschenhagen, which has many advantages.

_Measurements of the Magnetic Elements at Sea._--Owing to the fact that the proportion of the earth's surface covered by sea is so much greater than the dry land, the determination of the magnetic elements on board ship is a matter of very considerable importance. The movements of a ship entirely preclude the employment of any instrument in which a magnet suspended by a fibre has any part, so that the unifilar is unsuited for such observations. In order to obtain the declination a pivoted magnet is used to obtain the magnetic meridian, the geographical meridian being obtained by observations on the sun or stars. A carefully made ship's compass is usually employed, though in some cases the compass card, with its attached magnets, is made reversible, so that the inclination to the zero of the card of the magnetic axis of the system of magnets attached to the card can be eliminated by reversal. In the absence of such a reversible card the index correction must be determined by comparison with a unifilar magnetometer, simultaneous observations being made on shore, and these observations repeated as often as occasion permits. To determine the dip a Fox's dip circle[1] is used. This consists of an ordinary dip circle (see INCLINOMETER) in which the ends of the axle of the needle are pointed and rest in jewelled holes, so that the movements of the ship do not displace the needle. The instrument is, of course, supported on a gimballed table, while the ship during the observations is kept on a fixed course. To obtain the _strength_ of the field the method usually adopted is that known as Lloyd's method.[2] To carry out a determination of the total force by this method the Fox dip circle has been slightly modified by E. W. Creak, and has been found to give satisfactory results on board ship. The circle is provided with two needles in addition to those used for determining the dip, one (a) an ordinary dip needle, and the other (b) a needle which has been loaded at one end by means of a small peg which fits into one of two symmetrically placed holes in the needle. The magnetism of these two needles is never reversed, and they are as much as possible protected from shock and from approach to other magnets, so that their magnetic state may remain as constant as possible. Attached to the cross-arm which carries the microscopes used to observe the ends of the dipping needle is a clamp, which will hold the needle _b_ in such a way that its plane is parallel to the vertical circle and its axis is at right angles to the line joining the two microscopes. Hence, when the microscopes are adjusted so as to coincide with the points of the dipping needle _a_, the axes of the two needles must be at right angles. The needle _a_ being suspended between the jewels, and the needle _b_ being held in the clamp, the cross-arm carrying the reading microscopes and the needle _b_ is rotated till the ends of the needle a coincide with the cross-wires of the microscopes. The verniers having been read, the cross-arm is rotated so as to deflect the needle _a_ in the opposite direction, and a new setting is taken. Half the difference between the two readings gives the angle through which the needle a has been deflected under the action of the needle _b_. This angle depends on the ratio of the magnetic moment of the needle _b_ to the total force of the earth's field. It also involves, of course, the distance between the needles and the distribution of the magnetism of the needles; but this factor is determined by comparing the value given by the instrument, at a shore station, with that given by an ordinary magnetometer. Hence the above observation gives us a means of obtaining the _ratio_ of the magnetic moment of the needle _b_ to the value of the earth's total force. The needle _b_ is then substituted for _a_, there being now no needle in the clamp attached to the microscope arm, and the difference between the reading now obtained and the dip, together with the weight added to the needle, gives the product of the moment of the needle _b_ into the earth's total force. Hence, from the two observations the value of the earth's total force can be deduced. In an actual observation the deflecting needle would be reversed, as well as the deflected one, while different weights would be used to deflect the needle _b_.

For a description of the method of using the Fox circle for
observations at sea consult the _Admiralty Manual of Scientific
Inquiry_, p. 116, while a description of the most recent form of the
circle, known as the Lloyd-Creak pattern, will be found in
_Terrestrial Magnetism_, 1901, 6, p. 119. An attachment to the
ordinary ship's compass, by means of which satisfactory measurements
of the horizontal component have been made on board ship, is described
by L. A. Bauer in _Terrestrial Magnetism_, 1906, 11, p. 78. The
principle of the method consists in deflecting the compass needle by
means of a horizontal magnet supported vertically over the compass
card, the axis of the deflecting magnet being always perpendicular to
the axis of the magnet attached to the card. The method is not
strictly an absolute one, since it presupposes a knowledge of the
magnetic moment of the deflecting magnet. In practice it is found that
a magnet can be prepared which, when suitably protected from shock,
&c., retains its magnetic moment sufficiently constant to enable
observations of H to be made comparable in accuracy with that of the
other elements obtained by the instruments ordinarily employed at sea.
(W. Wn.)

FOOTNOTES:

[1] _Annals of Electricity_, 1839, 3, p. 288.

[2] Humphrey Lloyd, _Proc. Roy. Irish Acad._, 1848, 4, p. 57.

MAGNETO-OPTICS. The first relation between magnetism and light was discovered by Faraday,[1] who proved that the plane of polarization of a ray of light was rotated when the ray travelled through certain substances parallel to the lines of magnetic force. This power of rotating the plane of polarization in a magnetic field has been shown to be possessed by all refracting substances, whether they are in the solid, liquid or gaseous state. The rotation by gases was established independently by H. Becquerel,[2] and Kundt and Röntgen,[3] while Kundt[4] found that films of the magnetic metals, iron, cobalt, nickel, thin enough to be transparent, produced enormous rotations, these being in iron and cobalt magnetized to saturation at the rate of 200,000° per cm. of thickness, and in nickel about 89,000°. The direction of rotation is not the same in all bodies. If we call the rotation positive when it is related to the direction of the magnetic force, like rotation and translation in a right-handed screw, or, what is equivalent, when it is in the direction of the electric currents which would produce a magnetic field in the same direction as that which produces the rotation, then most substances produce positive rotation. Among those that produce negative rotation are ferrous and ferric salts, ferricyanide of potassium, the salts of lanthanum, cerium and didymium, and chloride of titanium.[5]

The magnetic metals iron, nickel, cobalt, the salts of nickel and
cobalt, and oxygen (the most magnetic gas) produce positive rotation.

For slightly magnetizable substances the amount of rotation in a space
PQ is proportional to the difference between the magnetic potential at
P and Q; or if [theta] is the rotation in PQ, [Omega]_P, [Omega]_Q,
the magnetic potential at P and Q, then [theta] = R([Omega]_P -
[Omega]_Q), where R is a constant, called Verdet's constant, which
depends upon the refracting substance, the wave length of the light,
and the temperature. The following are the values of R (when the
rotation is expressed in circular measure) for the D line and a
temperature of 18° C.:--

Substance. R × 10^5. Observer.

Carbon bisulphide / 1.222 Lord Rayleigh[6] and Köpsel.[7]
\ 1.225 Rodger and Watson.[8]
Water / .377 Arons.[9]
\ .3808 Rodger and Watson.[8]
Alcohol .330 Du Bois.[10]
Ether .315 Du Bois.[10]
Oxygen (at 1 atmosphere) .000179 Kundt and Röntgen (_loc. cit._)
Faraday's heavy glass 1.738

The variation of Verdet's constant with temperature has been
determined for carbon bisulphide and water by Rodger and Watson (_loc.
cit._). They find if R_t, R0 are the values of Verdet's constant at
t°C and 0°C. respectively, then for carbon bisulphide R_t = R0 (1 -
.0016961), and for water R_t = R0 (1 - .0000305t - .00000305t²).

For the magnetic metals Kundt found that the rotation did not increase
so rapidly as the magnetic force, but that as this force was increased
the rotation reached a maximum value. This suggests that the rotation
is proportional to the intensity of magnetization, and not to the
magnetic force.

The amount of rotation in a given field depends greatly upon the wave
length of the light; the shorter the wave length the greater the
rotation, the rotation varying a little more rapidly than the inverse
square of the wave length. Verdet[11] has compared in the cases of
carbon bisulphide and creosote the rotation given by the formula

c² / di \
[theta] = mc[gamma] --------- ( c - [lamda] --------- )
[lambda]² \ d[lambda]/

with those actually observed; in this formula [theta] is the angular
rotation of the plane of polarization, m a constant depending on the
medium, [lambda] the wave length of the light in air, and i its index
of refraction in the medium. Verdet found that, though the agreement
is fair, the differences are greater than can be explained by errors
of experiment.

Verdet[12] has shown that the rotation of a salt solution is the sum of the rotations due to the salt and the solvent; thus, by mixing a salt which produces negative rotation with water which produces positive rotation, it is possible to get a solution which does not exhibit any rotation. Such solutions are not in general magnetically neutral. By mixing diamagnetic and paramagnetic substances we can get magnetically neutral solutions, which, however, produce a finite rotation of the plane of polarization. The relation of the magnetic rotation to chemical constitution has been studied in great detail by Perkin,[13] Wachsmuth,[14] Jahn[15] and Schönrock.[16]

The rotation of the plane of polarization may conveniently be regarded as denoting that the velocity of propagation of circular-polarized light travelling along the lines of magnetic force depends upon the direction of rotation of the ray, the velocity when the rotation is related to the direction of the magnetic force, like rotation and translation on a right-handed screw being different from that for a left-handed rotation. A plane-polarized ray may be regarded as compounded of two oppositely circularly-polarized rays, and as these travel along the lines of magnetic force with different velocities, the one will gain or lose in phase on the other, so that when they are again compounded they will correspond to a plane-polarized ray, but in consequence of the change of phase the plane of polarization will not coincide with its original position.

_Reflection from a Magnet._--Kerr[17] in 1877 found that when plane-polarized light is incident on the pole of an electromagnet, polished so as to act like a mirror, the plane of polarization of the reflected light is rotated by the magnet. Further experiments on this phenomenon have been made by Righi,[18] Kundt,[19] Du Bois,[20] Sissingh,[21] Hall,[22] Hurion,[23] Kaz[24] and Zeeman.[25] The simplest case is when the incident plane-polarized light falls normally on the pole of an electromagnet. When the magnet is not excited the reflected ray is plane-polarized; when the magnet is excited the plane of polarization is rotated through a small angle, the direction of rotation being opposite to that of the currents exciting the pole. Righi found that the reflected light was slightly elliptically polarized, the axes of the ellipse being of very unequal magnitude. A piece of gold-leaf placed over the pole entirely stops the rotation, showing that it is not produced in the air near the pole. Rotation takes place from magnetized nickel and cobalt as well as from iron, and is in the same direction (Hall). Righi has shown that the rotation at reflection is greater for long waves than for short, whereas, as we have seen, the Faraday rotation is greater for short waves than for long. The rotation for different coloured light from iron, nickel, cobalt and magnetite has been measured by Du Bois; in magnetite the direction of rotation is opposite to that of the other metals. When the light is incident obliquely and not normally on the polished pole of an electromagnet, it is elliptically polarized after reflection, even when the plane of polarization is parallel or at right angles to the plane of incidence. According to Righi, the amount of rotation when the plane of polarization of the incident light is perpendicular to the plane of incidence reaches a maximum when the angle of incidence is between 44° and 68°, while when the light is polarized in the plane of incidence the rotation steadily decreases as the angle of incidence is increased. The rotation when the light is polarized in the plane of incidence is always less than when it is polarized at right angles to that plane, except when the incidence is normal, when the two rotations are of course equal.

_Reflection from Tangentially Magnetized Iron._--In this case Kerr[26] found: (1) When the plane of incidence is perpendicular to the lines of magnetic force, no rotation of the reflected light is produced by magnetization; (2) no rotation is produced when the light is incident normally; (3) when the incidence is oblique, the lines of magnetic force being in the plane of incidence, the reflected light is elliptically polarized after reflection, and the axes of the ellipse are not in and at right angles to the plane of incidence. When the light is polarized in the plane of incidence, the rotation is at all angles of incidence in the opposite direction to that of the currents which would produce a magnetic field of the same sign as the magnet. When the light is polarized at right angles to the plane of incidence, the rotation is in the same direction as these currents when the angle of incidence is between 0° and 75° according to Kerr, between 0° and 80° according to Kundt, and between 0° and 78° 54´ according to Righi. When the incidence is more oblique than this, the rotation of the plane of polarization is in the opposite direction to the electric currents which would produce a magnetic field of the same sign.

The theory of the phenomena just described has been dealt with by Airy,[27] C. Neumann,[28] Maxwell,[29] Fitzgerald,[30] Rowland,[31] H. A. Lorentz,[32] Voight,[33] Ketteler,[34] van Loghem,[35] Potier,[36] Basset,[37] Goldhammer,[38] Drude,[39] J. J. Thomson,[40] and Leatham;[41] for a critical discussion of many of these theories we refer the reader to Larmor's[42] British Association Report. Most of these theories have proceeded on the plan of adding to the expression for the electromotive force terms indicating a force similar in character to that discovered by Hall (see MAGNETISM) in metallic conductors carrying a current in a magnetic field, i.e. an electromotive force at right angles to the plane containing the magnetic force and the electric current, and proportional to the sine of the angle between these vectors. The introduction of a term of this kind gives rotation of the plane of polarization by transmission through all refracting substance, and by reflection from magnetized metals, and shows a fair agreement between the theoretical and experimental results. The simplest way of treating the questions seems, however, to be to go to the equations which represent the propagation of a wave travelling through a medium containing ions. A moving ion in a magnetic field will be acted upon by a mechanical force which is at right angles to its direction of motion, and also to the magnetic force, and is equal per unit charge to the product of these two vectors and the sine of the angle between them. For the sake of brevity we will take the special case of a wave travelling parallel to the magnetic force in the direction of the axis of z.

Then supposing that all the ions are of the same kind, and that there
are _n_ of these each with mass _m_ and charge _e_ per unit volume,
the equations representing the field are (see ELECTRIC WAVES):--

dX0 d[xi] d[beta]
K0 --- + 4[pi]ne ----- = -------;
dt dt dz

dX[0] d[beta]
----- = -------;
dz dt

dY0 d[eta] d[alpha]
K0 --- + 4[pi]ne ------ = - --------
dt dt dz

dY0 d[alpha]
--- = - --------;
dz dt

d²[xi] d[xi] / 4[pi] \ d[eta]
m ------ + R1 ----- + a[xi] = ( X0 + ----- ne[xi] ) e + He ------
dt² dt \ 3 / dt

d²[eta] d[eta] / 4[pi] \ d[xi]
m ------- + R1 ------ + a[eta] = ( Y0 + ----- ne[eta] ) e - He -----;
dt² dt \ 3 / dt

where H is the external magnetic field, X0, Y0 the components of the
part of the electric force in the wave not due to the charges on the
atoms, [alpha] and [beta] the components of the magnetic force, [xi]
and [eta] the co-ordinates of an ion, R1 the coefficient of resistance
to the motion of the ions, and [alpha] the force at unit distance
tending to bring the ion back to its position of equilibrium, K0 the
specific inductive capacity of a vacuum. If the variables are
proportional to [epsilon]^[l(pt - qz)] we find by substitution that q
is given by the equation

4[pi]ne²p²P 4[pi]ne³Hp³
q² - K0p² - ----------- = ± -----------,
P² - H²e²p² P² - H²e²p²

where

P = (a - (4/3)[pi]ne²) + R1[iota]p - mp²,

or, by neglecting R, P = m(s² - p²), where s is the period of the free
ions. If, q1², q2² are the roots of this equation, then corresponding
to q1 we have X0 = [iota]Y0 and to q2 X0 = -[iota]Y0. We thus get two
oppositely circular-polarized rays travelling with the velocities p/q1
and p/q2 respectively. Hence if v1, v2 are these velocities, and v the
velocity when there is no magnetic field, we obtain, if we neglect
terms in H²,

1 1 4[pi]ne³Hp
--- = -- + ------------,
v1² v² m²(s² - p²)²

1 1 4[pi]ne³Hp
--- = -- - ------------.
v2² v² m²(s² - p²)²

The rotation r of the plane of polarization per unit length

/ 1 1 \ 2[pi]ne³Hp²v
= ½p ( --- - --- ) = -------------.
\ v1 v2 / m²(s² - p²)²

Since 1/v² = K0 + 4[pi]ne²/m(s² - p²), we have if µ is the refractive
index for light of frequency p, and v0 the velocity of light in vacuo.

µ² - 1 = 4[pi]ne²v²0 / m(s² - p²) (1)

So that we may put

r = (µ² - 1)²p²H / s[pi]µne v0³ (2)

Becquerel (_Comptes rendus_, 125, p. 683) gives for r the expression

e H dµ
½ --- ---- ---------,
m v0 d[lambda]

where [lambda] is the wave length. This is equivalent to (2) if µ is
given by (1). He has shown that this expression is in good agreement
with experiment. The sign of r depends on the sign of e, hence the
rotation due to negative ions would be opposite to that for positive.
For the great majority of substances the direction of rotation is that
corresponding to the negation ion. We see from the equations that the
rotation is very large for such a value of p as makes P = 0: this
value corresponds to a free period of the ions, so that the rotation
ought to be very large in the neighbourhood of an absorption band.
This has been verified for sodium vapour by Macaluso and Corbino.[43]

If plane-polarized light falls normally on a plane face of the medium
containing the ions, then if the electric force in the incident wave
is parallel to x and is equal to the real part of A[epsilon]^[l(pt -
qz)], if the reflected beam in which the electric force is parallel to
x is represented by B[epsilon]^[l(pt + qz)] and the reflected beam in
which the electric force is parallel to the axis of y by
C[epsilon]^[l(pt + qz)], then the conditions that the magnetic force
parallel to the surface is continuous, and that the electric forces
parallel to the surface in the air are continuous with Y0, X0 in the
medium, give

A B [iota]C
----------------- = ----------- = ----------
(q + q1) (q + q2) (q² - q1q2) q(q2 - q1)

or approximately, since q1 and q2 are nearly equal,

[iota]C q(q2 - q1) (µ² - 1)pH
------- = ---------- = ------------.
B q² - q1² 4[pi]µne V0²

Thus in transparent bodies for which µ is real, C and B differ in
phase by [pi]/2, and the reflected light is elliptically polarized,
the major axis of the ellipse being in the plane of polarization of
the incident light, so that in this case there is no rotation, but
only elliptic polarization; when there is strong absorption so that µ
contains an imaginary term, C/B will contain a real part so that the
reflected light will be elliptically polarized, but the major axis is
no longer in the plane of polarization of the incident light; we
should thus have a rotation of the plane of polarization superposed on
the elliptic polarization.