[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.
[Illustration: FIG. 1.--Unifilar Magnetometer, arranged to indicate
declination.]
_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.
[Illustration: FIG. 2.--Unifilar Magnetometer, arranged to show
deflexion.]
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.)