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before, be directed to his right, that is, from B towards R'.

If the magnetic pole of which N N' is the line of direction be
a boreal or south pole, these directions will be reversed, each
line NN' and cc' being impelled to the left of the observer,
who looks from the other line. Thus, in such case, N N' will
be impelled by a force directed from A towards L, and c c' by
a force directed from B towards i/.

If the current ascend on the line c c', the directions of the
forces will be the reverse of those produced by a descending
current. Thus, when the current ascends, the line N N' will
be impelled to the left of the observer at c c' if the pole be
austral or north, and to his right if it be boreal or south ;
and in the same case the current c c' will be likewise impelled
to the left of the observer at N N' if the pole be austral or
north, and to his right if it be boreal or south.

To impress the memory with these various effects, it will be
sufficient to retain the directions of the forces produced be-
tween a descending current and a north magnetic pole. The
directions will be the same for an ascending current and a
south magnetic pole ; they will be reversed for a descending
current and south pole, or for an ascending current and north
pole.

Thus if the lines of direction of the current and the pole be
supposed to be both perpendicular to the surface of this paper,
and that the line of direction of the pole pass through the
paper at p, and that of the current at c, the directions of the
forces impressed on the lines of direction of the current and
the pole for a descending current and north magnetic pole, or
an ascending current and a south magnetic pole, are indicated
by the arrows \\\fig. 567., and their directions for a descending



308 VOLTAIC ELECTRICITY.

current and south magnetic pole, or an ascending current and
a north magnetic pole, are indicated in jig. 568.



p
Fig. 567. Fig. 568.

For example, if a current descend on a vertical wire, and the
austral or north pole of a magnet be placed so that its line of
direction shall be to the north of the current, the wire of the
current will be impelled by a force directed to the west, and the
line of direction of the magnetic pole by a force directed to the
east.

If the current ascend, or if the pole be a south pole, the wire
of the current will be impelled to the east, and the line of
direction of the pole to the west.

1919. Circular motion of magnetic pole round a fixed
current. If the line of direction of the current be fixed, and
that of the magnetic pole be movable, but so connected with
the line of the current as to remain always at the same distance
from it, the line of direction of the pole will be capable only of
moving round the surface of a cylinder whose axis is the direc-
tion of the current. In this case the force impressed by the
current on the line of direction of the pole, being always at
right angles to that line, and always on the same side of it as
viewed from the current, will impart to the line of direction of
the pole a motion of continued rotation round the current as an
axis. This rotation, as viewed on the side from which the
current flows, will be in the same direction as the motion of
the hand of a watch, where the pole is north, as represented in
fig. 569., and in the contrary direction as represented in fig.

570., where the pole is south.

1920. Circular motion of a current round a magnetic pole.
A similar motion of continued rotation will be imparted to
the wire conducting the current if the line of direction of the
magnetic pole be fixed, and the wire be similarly connected
with it. In this case the motion imparted by a north pole on



INFLUENCE OF CURRENTS AND MAGNETS. 309

a descending current is represented in Jig. 569., and that im-
pressed by a south pole \nfig. 570.





Fig. 569.

1921. Apparatus to illustrate experimentally these effects.
A great variety of apparatus and experimental expedients has
been contrived to illustrate and verify these laws.

1922. Apparatus to exhibit the direction of the force im-
pressed by a rectilinear current on a magnetic pole. To
demonstrate the direction of the force impressed by a rectilinear

current on a magnetic pole, let a light bar,
fig. 571., of ivory, or any other substance
not susceptible of magnetism, made flat at
the upper surface, be balanced like a compass
needle on a fine point, so as to be free to
move round it in an horizontal plane. Let a
magnetic needle, N s, be placed upon one
arm of it, so that one of the poles, the boreal s for example, be
exactly over the point of support ; and let a counterpoise, w, be
placed upon the other arm. Let the magnet be rendered
astatic, so as not to be affected by the earth's magnetism by
any of the methods already explained (1695).

Let the needle thus suspended be supposed to play round s,
Jig. 572., in the plane of the paper, and let a voltaic current
pass downwards along a wire perpendicular to the paper, c re-
presenting the intersection of such wire with the paper. The
needle, after some oscillations, will come to rest in the position




Fig. 571.



310



VOLTAIC ELECTRICITY.



-"c

Fig. 572.



s N, so that its direction shall be at right angles to the line ON,
drawn from the current to the pole
P' N, and so that the centre s shall be

to the left of N as viewed from c.
\ It follows, from what has been

-fetf already explained, that the force ex-
\ erted by the current c on the pole N
I has the direction indicated by the
/' arrow from s to N. This force is
/' therefore directed to the right of N
as viewed from c.

If the wire carrying the current
be moved round the circle c c' c" c'",
the pole N will follow it, assuming

always such positions, N', N", N'", that SN', SN", s N w shall be
at right angles to c' N', C"N", c'" N'". It follows, therefore, that
whatever position may be given to the current, it will exert a
force upon the austral or north pole N of the magnet, the di-
rection of which will be at right angles to the line drawn from
the current to the pole, and to the right of the pole as viewed
from the current.

If the position of the needle be reversed, the pole N being
placed at the centre of motion, the
same phenomena will be manifested,
but in this case the needle will
place itself to the right of the pole s as
viewed from the current c, as repre-
sented in fig. 573. It follows there-
fore, in this case, that whatever po-
sition be given to the current, it will
exert a force upon the boreal or south
pole of the magnet, the direction of
which will be at right angles to the
line drawn from the current to the
pole, and to the left of the pole as viewed from the current.

The current has here been supposed to descend along the
wire. If it ascend the effects will be reversed. It will exert
a force on the austral pole directed to the left, and on the
boreal pole one directed to the right.

1923. Apparatus to measure intensity of this force. Having
indicated the conditions which determine the directions of the




INFLUENCE OF CURRENTS AND MAGNETS. 311

forces reciprocally exerted between magnetic poles and a cur-
rent, it is necessary to explain those which affect their intensity.
Let sx,Jig. 574., be an astatic needle affected by the current

c, whose direction is per-
pendicular to the- paper,
as already explained. If
, N be displaced it will 1
,W oscillate on the one side

~| "N"" || and the other of its po-

sition of rest, and its os-

Fig. 574. cillations will be governed

by the laws already explained in the case of the pendulum (256).
The intensity of the force impressed on it in the direction of
the arrows by the current c, will be proportional to the squares
of the number of vibrations per minute.

1924. Intensity varies inversely as the distance. If the
distance of c from N be varied, it will be found that the square
of the number of vibrations per minute will increase in the
same proportion as the distance CN is diminished, and vice versa.
It follows, therefore, that the force impressed by the current on
the pole is increased in the same ratio as the distance of the
current from the pole diminishes, and vice versa.

In the case here contemplated, the length of the wire carrying
the current being considerable, each part of it exercises a
separate force on N, and the entire force exerted is consequently
the resultant of an infinite number of forces, just as the weight
of a body is the resultant of the forces separately impressed by
gravity on its component molecules. LAPLACE has shown
that the indefinitely small parts into which the current may be
supposed to be divided, exert forces which are to each other
in the inverse ratio of the squares of their distances from the
pole, and that by the composition of these a resultant is pro-
duced, which varies in the inverse proportion of the distances
as indicated by observation.

From what has been stated, it is evident that if the current
^^ fig. 575. be placed at the centre s of the circle

round which the north pole of a magnet is free
to move, it will impart to the pole a continuous
7 motion of rotation in that circle. If the current
be supposed to move downwards, the pole N will
Fig. 575. t> e constantly driven to the right as viewed from



312 VOLTAIC ELECTRICITY.

the centre s (1918), and consequently the magnet will move in
the direction of the hand of a watch, as indicated by the arrows.
If the north pole N be placed at the centre, as in fig. 576.,
the current still descending, the force exerted on
the south pole s will be constantly directed to the
left as viewed from the centre, and the magnet
will accordingly move contrary to the hand of a
watch, as indicated by the arrows.

If the current ascend, these motions will be
reversed, the north pole moving contrary, and the
south according to the hand of a watch, as
indicated in figs. 577., 578.

Descending current acting on north pole
(fid- 575.).

p. 5 _ Descending current acting on south pole

g * (fig. 576.).

Ascending current acting on south pole




Ascending current acting on north pole
(fig. 578.).

Fig. 578.

1925. Case in which the current is icitkin, but not at the
centre of the circle in which the pole revolves. If the current
be within the circle described by the free pole, but not at its
centre, the pole will still revolve ; but the force which impels it
will not be uniform, as it is when the current is at the centre.
Since the force exerted by the current on the pole is inversely
as its distance from the pole, that force will be necessarily
uniform when the current is at the centre, the distance of the
pole from it being always the same. But when the current is
within the circle at a point c,fig. 579., different from the centre,

the distance CN will vary, and the force ex-
erted on N will vary in the inverse proportion,
increasing as the distance is diminished, and
decreasing as the distance is increased. The
rotation will nevertheless equally take place,
and in the same direction as when the current
c is at the centre.

1926. Action of a current on a magnet, both poles being free.
Having thus explained the mutual action of the current, and




INFLUENCE OF CURRENTS AND MAGNETS. 313

each pole of the needle separately, we shall now consider the
case in which a magnetic needle suspended as usual on its
centre is exposed to the action of the current.

1927. Case in which the current is outside the circle described
by the poles. Let G,figs. 580, 581., as before, be a descending
current placed outside the circle in which the poles of the needle
NS play. The forces exerted by the current on the two poles
N and s have in this case opposite effects on the needle, and
consequently it will turn in the direction of that which has the
greater effect, and will be in equilibrium when the effects are
equal.

If the poles be placed at N' and s', fig. 580., the force exerted
on them will move N' towards N, and s' towards s, and the
needle will turn in the direction of the arrows by the combined
effects of both forces. When N' arrives at N", the force being
in the direction ON" will be ineffective ; but the force acting on
s", the opposite pole, will continue to turn the needle towards
the position NS, where it is at right angles to co. After
passing N", the force on N is effective in opposition to that on
s, but in a very small degree, so that the effect on s prepon-
derates until the needle arrives at the position SN. Here, the
poles N and s being equally distant from c, the forces are equal,




and being equally inclined to SN, have equal effects in opposite
directions. The needle is therefore held in equilibrium. If the
needle be moved beyond this position, the effect of the force
on N predominating over that of the force on s, the needle
will be brought back to the position SN, and will oscillate on
the one side and the other of this direction, showing that it
is the position of stable equilibrium (299).

If the pole s be placed at s',fig. 581., the effects on the two



314



VOLTAIC ELECTRICITY.



poles s' and N' will, as before, combine to turn the needle as
indicated by the arrows, moving the south pole towards s, and
the north towards N.

It follows, therefore, that a downward current c acting as in
figs. 580, 581. outside the circle described by the poles, will
throw the needle into a direction SN at right angles to the line
CO drawn from the current to the centre of the needle, the
north pole being on the right as viewed from the current.

An ascending current will produce the contrary effects, the
north pole being thrown to the left as viewed from the
current.

1928. Case in which the current passes through the circle.
If the current pass through the circle described by the poles,
the needle will rest indifferently in any direction that may be
given to it. In this case, fig. 582., let c be the current. The
forces it exerts on s and N being in the in-
verse ratio of the distances, that which affects
s will be to that which affects N as CN is to
cs. The moment of the force on s will
therefore be CNXCS, and the moment of the
force on N will be CSXCN. These moments
being equal, the forces must be in equilibrium
(426), and the needle will therefore remain
at rest whatever position be given to it.

1929. Case in which the current passes

within the circle. Let the current pass within the circle
described by the poles. In this case the effects of the current on
the two poles s and N is opposite in every position. If the pole be
at t*\jig. 583., the point of the circle nearest
to c, the force on N' being greater than the
force on s' in the ratio of cs' to CN'(1923),
the effect of the force on N' will predomi-
nate, and N' will be moved towards N, and
s' towards s. The effects on N will continue
to predominate until they arrive at the
position NS, where the effects become equal
and the needle is in equilibrium ; for here
the distances of s and N from C being equal, the forces are equal ;
and since they are equally inclined to the needle, they have
equal effects to turn it in contrary directions. After passing N,
the effect on s predominates ; the needle will be brought back





Fig. 583.




INFLUENCE OF CURRENTS AND MAGNETS. 315

to the position NS, and will oscillate on the one side and the
other, indicating stable equilibrium (299).

If the needle be placed with the pole s' at the point nearest
toe, fig. 584., the effect on s' predominating,
s' will be moved towards s, and N' towards
N, and the needle will attain the same
position as in the former case.

It follows, therefore, that when a de-
scending current passes within the circle
described by the poles, as represented in
figs. 583, 584., the needle will be thrown
into a direction SN at right angles to the line CO drawn from
the current to the centre of the needle, the north pole pointing
to the left as viewed from the current.

An ascending current will produce the contrary effect,
throwing the north pole to the right.

It will be observed that the direction of the poles, when the
current is within the circle, is opposite to its direction when
it is outside the circle.

1930. Apparatus to illustrate electro-magnetic rotation.
A variety of interesting and instructive apparatus has been
contrived to illustrate experimentally the reciprocal forces
manifested between currents and magnets. These may be
described generally as exhibiting a magnet revolving round a
current, or a current revolving round a magnet, or each
revolving round the other, impelled by the forces which the
current and the poles of the magnet exert upon each other. It
will be conducive to brevity in describing these effects to
designate a motion of rotation which is from left to right, or
according to that of the hand of a watch, as direct rotation,
and the contrary as retrograde rotation. It will therefore
follow from what has been explained, that if N and s express
the north and south poles of the magnet, and A and D express
an ascending and descending current, the rotation of each
round the other in every possible case will be as follows :



'



j Retrograde.



We shall classify the apparatus according to the particular
manner in which they exhibit the action of the forces.
p 2



316



VOLTAIC ELECTRICITY.



1931. To cause either pole of a magnet to revolve round a
fixed voltaic current. Let two bar magnets be bent into the
form shown 'mfig. 585., so that a small
part at the middle of their length shall
be horizontal. Under this part an
agate cap is fixed, by which the mag-
net is supported on a pivot. Above
the horizontal part a small cup contain-
ing mercury is fixed. The magnets
are thus free to revolve on the pivots.
A small circular canal of mercury sur-
rounds each magnet a little below the
rectangular bend, into which the amal-
gamated point of a bent wire dips.
These wires are connected with two
vertical rods, which, turning at right
angles above, terminate in a small cup
Two similar mercurial cups communicate
If the upper cup be put




Fig. 585.



containing mercury.

with the circular mercurial canals.

in communication with the positive pole of a battery, and the

lower cups with the negative pole, descending currents will be

established on the vertical rods ; and if the upper cup be put

in communication with the negative, and the lower with the

positive, the currents will ascend. The two magnets may be

placed either with the same or opposite poles uppermost. The

currents pass from the vertical rods to the mercury in the

circular canals, thence to the lower cups, and thence to the

negative poles.

When the descending current passes on the rods, the north
pole of the magnet revolves with direct, and the
south pole with retrograde motion. When the cur-
rent ascends, these motions are reversed.

1932. To cause a moveable current to revolve
round the fixed pole of a magnet. Let a glass
vessel,^. 586., be nearly filled with mercury. Let
a metallic wire suspended from a hook over its
centre be capable of revolving while its end rests
upon the surface of the mercury. A rod of metal
enters at the bottom of the vessel, and is in con-
tact with a magnetic bar fixed vertically in the
Fig. 586. centre of the vessel. When one of the poles of the.




INFLUENCE OF CURRENTS AND MAGNETS. 317

battery is put in communication with the moveable wire, and
the other with the fixed wire connected with the magnet, a
current will pass along the moveable wire, either to the mer-
cury or from it, according to the connexion made with the
poles of the battery ; and the moveable wire will revolve round
the magnet, touching the surface of the mercury with a motion
direct or retrograde, according as the current descends or
ascends, and according to the name of the magnetic pole fixed
in the centre (1930).

Let zz',fig. 587., represent a section of a circular trough
containing mercury, having an opening at the
centre, in which is inserted a metallic rod,
terminating at the top in a mercurial cup c.
A. wire at a b b' a' is bent so as to form three
sides of a rectangle, the width b b' correspond-
ing with the diameter of the circular trough
z z' . A point is attached to the middle of b b 1 ,
which rests in the cup c, so that the rectangle
is balanced on the rod t, and capable of re-
Fig. 587. volving on the pivot as a centre.

If the mercury in the circular trough be
connected by a wire with the negative, while the cup c is
connected with the positive pole of a battery, descending
currents will be established along the vertical wires b a and
b' a'; and if the connexions be reversed, these currents will
ascend.

If, when these currents are established, the pole of a magnet
be applied under the centre P, it will act upon the vertical
currents, and will cause the rectangular wire at abb' a' to
revolve round c, with a motion direct or retrograde, according
to the direction of the current and the name of the magnetic
pole (1920).

The points of contact of the revolving wires with the
mercury may be multiplied by attaching the ends a a' of the
wires to a metallic hoop, the edge of which will rest in contact
with the metal ; or the wires a b and a' b' may be altogether
replaced by a thin copper cylinder balanced on a point in the
cup at c.

Another apparatus for illustrating this is represented in
fig. 588. A bar magnet is fixed vertically in the centre of a
circular trough containing mercury. A light and hollow cy-



318




VOLTAIC ELECTRICITY.

linder of copper is suspended on a point rest-
ing in an agate cup placed on the top of the
magnet, and having a vertical wire proceed-
ing from it, which terminates in a small mer-
curial cup p at the top. Another wire con-
nects the mercury in the trough with a
mercurial cup N. When the cups p and N
are put in communication with the poles of
the battery, a current is established on the
sides of the copper cylinder c c, and rotation
takes place as already described.

A double apparatus of this kind, erected on
the two poles of a horse-shoe magnet, is re-
presented in fig. 589.







Fig. 58!).



Fig. 590.



1933. Amperes method. Ampere adopted the following
method of exhibiting the revolution of a current round a
magnet. A double cylinder of copper, c C,Jig. 590., about 2^-
in. diameter and 2iy in. high, is supported on the pole of a
bar magnet by a plate of metal passing across the upper orifice
of the inner cylinder. A light cylinder of zinc z z, supported
on a wire arch A, is introduced between the inner and outer
cylinders of copper, a steel point attached to the wire arch
resting upon the plate by which the copper cylinders are sup-
ported. On introducing dilute acid between the copper cy-
linders, electromotive action takes place, the current passing
from the zinc to the acid, thence to the copper, and thence



INFLUENCE OF CURRENTS AND MAGNETS. 319

through the pivot to the zinc. The zinc being in this case free
to revolve, while the copper is fixed, and the current descending
on the former, the rotation will be direct or retrograde accord-
ing as the magnetic pole is north or south.

If the copper were free to revolve as well as the zinc, it would
turn in the contrary direction, since the current ascends upon
it, while it descends on the zinc. Mr. J. Marsh modified Am-
pere's apparatus, so as to produce this effect by substituting a
pivot, resting in a cup at the top of the magnet, for the metallic
arch by which, in the former case, the copper vessel was
sustained.

A double arrangement of this kind is given in fig. 591.,
where the double cylinders are supported on pivots on the two
poles of a horse-shoe magnet. The rotation of the corresponding
cylinders on the two opposite magnetic poles will be in con-
trary directions.





Fig. 591.



Fig. 592.



1934. To make a magnet turn on its own axis by a current
parallel to it. The tendency of the conductor on which a
current passes to revolve round a magnet will not the less exist,
though the current be so fixed to the magnet as to be in-
capable of revolving without carrying the magnet with it. In
fig. 592., the magnet M is sunk by a platinum weight p ; its
upper end being fixed to the copper cylinder ww, a current
passing from p to N causes the cylinder to rotate, carrying with
it the magnet.

v 4



320



VOLTAIC ELECTRICITY.



Since a magnetic bar is itself a conductor, it is not necessary
to introduce any other ; and a current passing
along the bar will give rotation to it. An ap-
paratus for exhibiting this effect is represented



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