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by saying that the magnetic field due to the earth in the
vicinity of the magnet is uniform.

Take a piece of gas-pipe a metre long and carefully freed
from magnetism. If 'it be held horizontally east and west,
either end of it will attract both the N-seeking and the
S-seeking pole of a magnetic needle. Gradually tilt it
into a vertical position. Its lower end will become a N
pole and will repel the N pole of the needle. Reverse it
and the lower end is again a N pole and the upper end a
S pole. Hold it vertically, or, better still, in the meridian
and inclined about 75 below the horizontal toward the
north, and strike it a sharp blow on the upper end with a
hammer. It has now acquired permanent magnetism with
the N pole at the lower end. This fact can be demon-
strated by holding the pipe horizontally east and west.
By reversing it and striking it on the other end the polar-
ity may be reversed, and by graduating the strength of the
blow the pipe may be nearly or quite demagnetized.

The earth acts inductively on the pipe, as any other
magnet does on a piece of iron, putting it under magnetic
stress. The vibration due to the blow gives a certain free-
dom of motion to the molecules, and they arrange them-
selves to some slight extent under the influence of the
earth's magnetic stress. With the molecules so arranged
the pipe becomes a magnet. Bars of iron or steel in a
vertical or in a horizontal north-and-south position acquire
magnetism by induction from the earth. This is especially



PttOPEKTIES OF MAGNETS. 325

true if they are subjected to frequent jarring. Drills, rail-
way iron, beams, and posts are illustrations.

Since opposite poles attract, it is evident that the north-
ern hemisphere of the earth has the polarity corresponding
to the S-seeking pole of a magnet. This south magnetic
pole does not correspond with the geographical pole of the
northern hemisphere. Sir J. C. Ross, in 1831, found it to
be situated in Boothia Felix, just within the Arctic Circle, in
latitude 70 5' N., and longitude 96 46' W. of Greenwich.
Schwatke concluded in 1879, from 'his observations, that
the pole had shifted to longitude 99 35' W. The magnetic
pole in the southern hemisphere has never been reached.

276. Magnetic Declination (B., 682). The magnetic
meridian is the vertical plane coinciding in direction with
the earth's field and containing, therefore, the axis of a
suspended magnetic needle. This meridian does not in
general coincide with the geographical meridian. The
angle between the two is called the magnetic declination.
The declination is east or west according as the N-seeking
pole of the needle points to the east or to the west of the
geographical meridian. The existence of magnetic decli-
nation was not known in Europe till the thirteenth century
and was first distinctly delineated on a map in 1436. To
Columbus belongs the undisputed discovery that the decli-
nation is different at different points of the earth's surface.
In 1492 he discovered a place of no declination in the
Atlantic Ocean north of the Azores.

Lines connecting points of equal declination are called
isogonic lines, and the line of no declination is an agonic
line. According to a chart constructed by the United States
Coast and Geodetic Survey, the agonic line in 1890
entered the United States from the Atlantic Ocean at



326 ELECTRICITY AND MAGNETISM.

Charleston, passed in a northwesterly direction through
Columbus, Ohio, about centrally through the lower penin-
sula of Michigan, across Grand Traverse Bay, Lake Michi-
gan, the upper peninsula, and Lake Superior.

The declination on the most easterly border of Maine is
now (1896) about 20 W., and on the extreme north-
western boundary of the State of Washington it is 23 E.
These values will not change much by the year 1900.

277. Variations in Declination. The earliest re-
corded declination is that of London in 1580. It was then
11 18' E. In 1657 it was zero at the same place. A
westerly declination then set in and attained a maximum
value of 24 27' W. about 1816 ; since then it has been
slowly diminishing to its present value (1896) of about 16
43' W. The needle will again point true north in London
about 1976, thus completing a half-cycle of changes in a
period of some 320 years.

Similar variations are in progress in other parts of the
earth. This change of long period is called the secular
variation of the declination. Besides it, there are the
diurnal and annual variations. In high latitudes the former
may reach 1, but in middle latitudes it has a mean value
of about 7J'. The annual variation is small, and is subject
to a periodicity corresponding apparently with the sun-spot
period of about eleven years.

Besides these variations, magnetic perturbations occur
during earthquakes, volcanic eruptions, and particularly
during auroral displays. The perturbations due to this last
cause sometimes reach a value as large as one or two
degrees. They are felt over wide areas, and are called
magnetic storms.



PROPERTIES OF MAGNETS. 327

278. Inclination or Dip. If a magnetic needle be
carefully balanced on an axis through its centre of gravity
before magnetization, its N-seeking pole after magnetization
will incline below the horizontal in the northern hemisphere
by an angle ranging from to 90. This angle is called
the inclination or dip. Norman, a London instrument-
maker who first measured it in 1576, constructed a dipping
needle, which is a magnetic needle free to turn about a
horizontal axis in a vertical plane, and is provided with a
graduated vertical circle. The dip in London in 1576 was
71 50'. It undergoes secular changes like those of the
declination. The dip in London for 1900 will be 67 9' and
in Washington, 70 18'. It reached its maximum value in
London in 1720 and has since been slowly diminishing. At
the magnetic pole in the northern hemisphere the needle
points vertically downwards.

279. Isoclinic Lines. Lines connecting points of
equal inclination on the earth's surface are isoclinic lines.
In the vicinity of the equator is a line of no inclination,
called the magnetic equator. It is a somewhat irregular
line and crosses the earth's equator at two

points, in longitude near 2 E. and 170
W. It veers as far south as lat. 16 and
as far north as lat. 10. The isoclinic
of 72 passes near Princeton, Pittsburgh,
Fort Wayne, Michigan City, Iowa City,
Helena, and Vancouver Island on the Pacific
coast.

280. Relations between Decimation,
Inclination, and Total Intensity. If 8 denotes the
angle of dip, then the total intensity of terrestrial mag-




328 ELECTRICITY AND MAGNETISM.

netism may be resolved into a vertical and a horizontal
component (Fig. 145) as follows:

<? = JsinS,



Hence tan 8 = -

C7O

Lines connecting places where the horizontal component
of terrestrial magnetic intensity is the same are called
isodynamic lines.

PROBLEMS.

1. A magnet whose strength of pole is 150 is placed in a mag-
netic field whose intensity is 0.18. What forces act on its poles ?

2. A bar magnet, 10 X 2 X 0.25 cms., was magnetized to a
strength of pole of 50. What was the intensity of magnetization

3. The horizontal component of the earth's magnetism at station
A was found to be 0.183 ; a magnet was oscillated at station A and
station B, and made 60 oscillations in 11 m. 24s. at the former and
in 12 m. 12 s. at the latter. Find the horizontal intensity at B.

4. A rectangular magnet, whose length was 15 cms. and strength
of pole 50, was set oscillating in a field whose horizontal intensity
was 0.18. It made 80 complete vibrations in 15m. 4s. Find its
moment of inertia.

5. When the magnet of problem 4 was made to oscillate at equal
distances from two magnets A and B successively, it made 80 com-
plete vibrations in 9m. 4s. and 10 m. 40s. respectively. Compare
the strength of pole of A and B.



MA(;. \ETlf DELATIONS OF A CURRENT, 329



CHAPTER XXI.

MAGNETIC RELATIONS OF A CURRENT.

281. Oersted's Discovery. The discovery by Oersted
at Copenhagen in 1819 was one of prime importance. He
observed that when a magnetic needle is brought near a
long straight wire conveying a current, the needle tends to
set itself at right angles both to the wire and to a perpen-
dicular drawn to it from the centre of the needle ; also that
the direction in which the needle turns depends on the




Fig. 146.

direction of the current through the conductor. A current
through a conductor therefore produces a magnetic field
about it. At this point the analogy between an electric
current and a stream of water flowing through a pipe fails,
for such a stream produces no effect in the region sur-
rounding the pipe.

Let a current flow through the conductor above the
needle NS from north to south as indicated (Fig. 146).
The X pole will turn toward the east. If the current be
reversed through this conductor, or if it pass from north to
south through the conductor under the needle, the N pole



330



ELECTRICITY AND MAGNETISM.



will turn toward the west. A current upward through a
vertical wire near the N pole of the needle will deflect it

in the direction of the arrows ;
that is, the N pole turns toward
the east.

If the wire be carried round
the needle in a rectangular
loop (Fig. 147), both branches
of it will contribute to the force
of deflection, and the N-seeking
pole at the left will turn to-
ward the east.




Fig. 147



282. Ampere's Rule. All the movements of a mag-
netic needle under the influence of a current may be
summed up in one rule. That of Ampere is the follow-
ing: Conceive a man swimming with the electric current
through a conductor and facing the needle; then the
N-seeking pole will always be deflected in the direction
of his left hand. Since the action between the current
and the needle, like all others, is mutual, the conductor
will be urged toward his right.

A somewhat more convenient " rule of thumb " for most
cases is the following, due to Professor Moreland : Con-
ceive the current flowing in the direction of the extended
fingers of the outstretched right hand, with the palm turned
toward the needle ; then the N pole will be acted on by a
magnetic force in the direction of the extended thumb.

283. Maxwell's Rule. The rule suggested by Max-
well has the advantage that it expresses reciprocally the
relation between the direction of the current and the direc-
tion of the deflection. Consider a right-handed screw ; if




UELATIOX* OF A CUllllEXT. ool

the direction of the current be that of the forward motion
of the screw as it enters the nut, the positive direction of
the magnetic force is the di-
rection in which the screw
turns (Fig. 148). The same
relation is represented by the
circle and the arrow in Fig.
149. If the current Jews in

the direction of the long arrow, the resulting magnetic
force is with the arrows around -the circle ; conversely, if
,* x the current flows around the circle

with watch hands, the positive direc-
tion of the magnetic force,, or the di-
rection in which a N-seeking pole is
urged, is along the axis of the circle
away from the observer. If the fingers
of the closed right hand represent the
Fjg |49 circle with the current flowing out at

the finger tips, the outstretched thumb
points in the direction of the lines of force.

284. Magnetic Field about a "Wire. A
little consideration will show that if an observer
identifies himself with the conductor, the current
running from foot to head (Fig. 150), a single
isolated X -seeking pole would be urged round
him in a circle from right to left. The lines of
force due to a current are therefore concentric
circles about the conductor as a centre. Fig. 151
is made from the curves developed by iron filings
mi a sheet of cardboard whose plane was per- p . |50 +
pe nd ie ula r to the wire. The wire is seen end-on
in the figure. On gently tapping the paper the filings
arrange themselves in circles.





332



ELECTRICITY AND MAGNETISM.




Fig. 151.



This figure is a representation of what exists in any

plane perpendicular to
the wire. The entire
region about a con-
ductor conveying a
current is therefore
filled with these circu-
lar magnetic whirls.
They show that the
ether is under stress,
a n d therefore pos-
sesses potential en-
ergy. It is rather
m ore important to
direct the attention
to these magnetic

effects in the ether about the current than to what goes

on Avithin the conductor itself.

285. Magnetic Field, about a Current through a Cir-
cular Conductor. If the conductor be bent into a circle
or a loop (Fig. 152), the
space within it possesses
magnetic properties. All
the lines of force pass
through the loop so as to
urge the N-seeking pole of
a magnet downwards. The
current is flowing round
the loop, viewed from
above, in the direction of

Fig. 152.

watch hands (compare Fig.

149). Such a loop carrying a current acts like a magnetic




MAGNETIC RELATIONS OF A CURRENT. 333

; that is, one side of it attracts the N-seeking pole of
a magnet and the other repels it. A magnetic shell is
equivalent to a thin sheet made up of short bar magnets
placed side by side with their N poles forming one surface
of the plane or shell, and their S poles the other. It is
known as the lamellar distribution of magnetism. An
</lf ctric circuit is in every case equivalent to a magnetic
shell whose contour coincides with the circuit. The shell
is of such strength that the number of lines of force
coining from it is the same as the number due to the cur-
rent in the loop ; that is, the magnetic shell and the closed
circuit have in their vicinity identical magnetic fields.
The difference between them is that the shell is impervious
while the circuit is not.

286. Intensity of Field at Centre of Circular Coil.
- The intensity of the magnetic field at any point is the
force acting on a unit pole placed at the point. Faraday
showed that the magnetic intensity produced by a current
is proportional to the current, and Biot and Savart demon-
strated experimentally that for a current of indefinite
extent it is inversely proportional to the distance between
the conductor and the point. Laplace proved that this
latter result follows from the law of inverse squares as
applied to the mutual action between an element of the
circuit and the pole, thus confirming the law of Ampere.
Hence the intensity due to the current in an element ds of
the conductor, at a point P on a perpendicular from the
element, is

cr kids

& ^T~ 1

d~

where d is the distance between the current-element and
the point P, k is the force on unit pole due to unit current
at unit distance, and / is the strength of the current.



334 ELECTEICITY AND MAGNETISM.

If now P is at the centre of the circle around which the
current is flowing, then the intensity at the centre due to
the current in the entire circumference will be

cf kl^ds _ %7rrkl_ Z-jrkl

/ . o *~~~ *

r- r 2 r

If the unit current is so denned as to make k equal to unity,
we have



287. The Electromagnetic Unit of Current. - - The
electromagnetic system of electrical units in common use
is based on the magnetic effects of a current. If an element
of a conductor one centimetre long be bent into an arc of one
centimetre radius, then the current through it will have unit
strength when it exerts a force of one dyne on a unit pole at
the centre of the arc. This definition is equivalent to mak-
ing k equal to unity in the last article. If the field due
to unit current in unit length of the conductor is unity,
the field due to the whole circumference will be 2?r ; and
if the current is J, it will be ZirL If, further, the radius is
not unity, but r, the circumference will be 2?rr, and then



The ampere is one-tenth of this absolute or C.G.S. unit of
current. The unit of quantity in the electromagnetic
system is the quantity which passes any cross-section of a
conductor in one second when the current through it has
unit strength. The practical unit of quantity is the
coulomb ; it corresponds with the ampere, and is one-tenth
of an absolute unit.



MAGNETIC RELATIONS OF A CURRENT. 335

288. Galvanometers. We are now prepared to con-
sider in an elementary way several types of galvanometers
or instruments for measuring electric currents. When
their scales are graduated so as to read directly in amperes,
or when the readings reduce to amperes by the application
of a simple formula, galvanometers are called ammeters.

There are three general types of galvanometers : (1)
those in which the current flowing through a fixed coil of
wire causes the deflection of a suspended magnetic needle,
usually at the centre of the coil ; (2) those in which the
coil is movable around a vertical axis between the poles of
a fixed magnet. (3) These two kinds of galvanometers
are applicable to direct currents only. For both direct
and alternating currents another kind is employed, in which
both the fixed and the movable parts are coils. These are
called electrodynamometers.

289. The Tangent Galvanometer. The tangent gal-
vanometer consists of a short magnetic needle poised at
the centre of a large vertical coil with its plane in the
magnetic meridian. The radius of the coil must be large
in comparison with the length of the needle,

which turns about a vertical axis.

The magnetic field produced by the cur-
rent through the large coil is nearly uniform
near its centre, and is perpendicular to the
plane of the coil. For a short needle, there-
fore, the deflecting force is perpendicular * \
to the horizontal component of the earth's
magnetism, and its motion round a vertical s Fj |53
axis will not carry its poles into a magnetic
field of different strength. For equilibrium the moments
of these two forces are equal.




336 ELECTRICITY AND MAGNETISM.

Let N/S (Fig. 153) be the magnetic meridian, and the
trace of the plane of the coil with its centre at 0. Then
the two forces acting on the pole at A of strength m are
&8m in the magnetic meridian and Qjrml/r at right angles
to it ; r is the radius of the coil consisting of a single turn.
If I is the half-length of the needle AO, and 6 the angle
of deflection, then



or BSml sin = 2wml I cos 0.

r

Both m and I cancel out, and the deflection is independent
of the pole-strength. From this equation

I^-ffg^taaLB.

2-7T

For n turns of wire, where n is only a small number and
the n turns may be considered coincident,

2= SS - tan 0.



The fraction 2?r/r, or 2-Tm/r, is called the constant of the
galvanometer. It equals the strength of field produced at
the centre by unit current through the coil. If this con-
stant is denoted by 6r, the equation for the current may
be written simply

7=5? tan 0.
6r

/ is here expressed in C.G.S. units. In amperes,

/==i0^tan0.
&

For a uniform magnetic field the current is proportional to
the tangent of the angle of deflection. The chief objection




MAGNETIC RELATIONS OF A CURRENT. 337

to the use of this form of galvanometer is the variability
of 8

290. Nobili's Astatic Pair. For greater sensibility
the controlling couple of the earth's field on the movable
magnetic system must be reduced. This may be done by
means of a weak compensating magnet, either above or
below the movable magnetic needle, with its N-seeking pole
turned toward the north. The field produced by it at the
needle is then opposed to the earth's field.

Nobili's astatic pair is another method
in common use. It consists of a pair of
needles (Fig. 154) mounted in the same
vertical plane, but with their similar poles
turned in opposite directions. If their
magnetic axes were rigorously in the same
plane, their lengths equal, and their poles of the same
strength, such a system would stand indifferently in any
azimuth. In practice neither condition is exactly met, but
the system has a small directive force tending to set it in
the plane of the magnetic meridian..

If both needles are surrounded with coils so connected
that the current flows round them in opposite directions,
the two forces of deflection will turn the system in the
same direction, while the opposing controlling force is re-
duced to a small value.

291. The Astatic Mirror Galvanometer. In Fig. 15";
the coils are swung open to expose to view the astatic sys-
tem. It consists of minute pieces of magnetized watch-
spring at the centres of the coils above and below. They
are mounted on an aluminium wire, and midway between
them is a small round mirror fco reflect a beam of lio-ht



338



ELECTRICITY AND MAGNETISM.



which serves as a long pointer. The lower set of magnets

has a slightly greater magnetic moment than the upper one.

The four coils are
so joined in series
that the current
through them oper-
ates to turn the
whole system in
the same direction.
The control mag-
net in this particu-
lar instrument is
under the base. It
is movable around
a vertical axis, and
its effective mag-
netic moment can
be varied by turn-
ing the milled
screw jS. The
screw turns two
soft- iron nuts

Fig |55 threaded on the

magnet so as to

partly close its magnetic circuit, and thus alter its external

field of force.




292. The d'Arsonyal Galvanometer. It is imma-
terial from a magnetic point of view whether the coil or
the magnet of a galvanometer is made movable, since the
action between them is reciprocal. The great advantage
of the d'Arsonval galvanometer is that it has a strong field
of its own, which is only, slightly affected by the earth's



MAGNETIC RELATIONS OF A CURRENT.



339



magnetism or by iron or other magnetic materials in its
neighborhood. It is also possible to so shape the pole-
pieces of the permanent magnet in it that the deflection
si nil! be strictly proportional to
the current through a wide
range. The well-known Weston
instruments are of this type.

Fig. 156 is a d'Arsonval gal-
vanometer of the ordinary pat-
tern. The coil swings in the
strong field between the poles
of the upright magnet and the
cylindrical soft-iron core inside
of it. It is suspended by a fine
wire or thin phosphor-bronze
strip, through which the cur-
rent enters the coil, while a
straight wire or a helix con-
veys it out at the bottom.

The Ayrton-Mather form of
this galvanometer has a single ring magnet with only a

narrow vertical opening between
its poles (Fig. 157). Iiithis open-
ing is placed a tube containing a
long narrow coil without any iron
core. It is suspended as in the
other form. Its plane must be
parallel to the lines of force in the

narrow gap in which it hangs.

*^~

293. Potential Galvanome-
ters. Galvanometers used for the purpose of determining
the potential difference between two points of a circuit




Fig. 156





340 ELECTRICITY AND MAGNETISM.

must be of high resistance. If they are graduated to read
in volts they are called voltmeters. They are always con-
nected as a shunt. Thus, if the galvanometer 6r (Fig. 158)
is connected to the points A and B as a shunt to the resist-
ance s, and if its resistance is high in comparison with s,
so that no appreciable part of the whole current passes
through the galvanometer, then the small current that
does pass through it is strictly de-
pendent on the potential difference
between A and B. Any sensitive
galvanometer may be used as a volt-
meter by adding a sufficiently large
resistance in series with it. Unless
the resistance of a voltmeter is high,
the application of its terminals to two
points of a circuit, so as to put it in parallel with a resist-
ance through which a current is flowing, will diminish
the potential difference which it is desired to measure.

If the galvanometer resistance is 99 times that of the
shunted resistance s, then one per cent of the current goes
through the galvanometer, and the potential difference
between the terminals of s is reduced one per cent.

294. Electromagnetic Units. It will be convenient
for reference to bring together the several electrical units
expressed in magnetic measure in the C.G.S. system.

Unit Strength of Current. A current has unit strength
when a length of one centimetre of its circuit, bent into an
arc of one centimetre radius, exerts a force of one dyne on
a unit magnetic pole (264) at its centre (287).

Unit Quantity of Electricity. It is the quantity conveyed
by unit current in one second.

Unit Potential Difference. Unit potential difference, or



SITY




MAGNETIC RELAtoW28]&r CURRENT. 341



unit electromotive force, exists between two points when
the transfer of unit quantity of electricity from one point


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