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magnetic north and south, the force impressed on it will be
directed to the magnetic east and west, and will therefore be
also horizontal. It will be directed to the east, if the current
pass from north to south ; and to the west, if it pass from south
to north. Tiiis will be apparent, if it be considered that the
effect of the earth's magnetism is that of a south magnetic pole
placed below the current.

1990. Case of an horizontal current directed east and west.
If the current be horizontal and at right angles to the mag-
netic meridian, the force impressed on it will be directed north
and south in the plane of the magnetic meridian, and inclined
to the horizontal plane at an angle of 20 in this part of the
earth. This may be resolved into two forces, one vertical and
the other horizontal (154). The former will have a tendency to
remove the current from the horizontal plane, and the latter will
act in the horizontal plane in the direction of the magnetic
north and south. It will be directed from the south to the
north, if the current pass from west to east, and from the north
to the south, if the current pass from east to west. This will
also be apparent, by considering the effect produced upon a
horizontal current by a south magnetic pole placed below it.

1991. Case of a horizontal current in any intermediate
direction. If a horizontal current have any direction inter-
mediate between the magnetic meridian and a plane at right
angles to it, the force impressed on it, being still at right angles



356 VOLTAIC ELECTRICITY.

to the dipping-needle, and being inclined to the horizontal plane
at an angle less than 20, may be resolved into other forces
(154), one of which will be at right angles to the current, and
will be directed to the left of the current, as viewed from below
by an observer whose head is in the direction from which the
current passes (1918). '

1992. Effect of the earth's magnetism on a vertical current
which turns round a vertical axis. It follows, from what has
been here proved, that if a descending vertical rectilinear cur-
rent be so suspended as to be capable of turning freely round a
vertical axis, the earth's magnetism will impress upon it a force
directed from west to east in a plane at right angles to the
magnetic meridian ; and it will therefore move to such a posi-
tion, that the plane passing through the current and the axis
round which it moves shall be at right angles to the magnetic
meridian, the current being to the east of the axis.

If the current ascend, it will for like reasons take the position
in the same plane to the west of the axis, being then urged by
a force directed from east to west.

1993. Effect on a current which is capable of moving in a
horizontal plane. If a vertical current be supported in such a
manner that, retaining its vertical direction, it shall be capable
of moving freely in a horizontal plane in any direction what-
ever, as is the case when it floats on the surface of a liquid, the
earth's magnetism will impart to it a continuous rectilinear
motion in a direction at right angles to the plnne of the mag-
netic meridian, and directed eastward if the current descend,
and westward if it ascend.

If a horizontal rectilinear current be supported, so as to be
capable of revolving in the horizontal plane round one of its
extremities as a centre, the earth's magnetism will impart to it
a motion of continued rotation, since it impresses on it a force
always at right angles to the current, and directed to the same
side of it. If in this case the current flow towards the centre
round which it revolves, the rotation imparted to it will be
direct; if from the centre, retrograde, as viewed from above
(1920).

1994. Experimental illustrations of these effects. Pouillefs
apparatus A great variety of experimental expedients have
been contrived to verify these consequences of the principle of
the influence of terrestrial magnetism on currents.




INFLUENCE OF TERRESTRIAL MAGNETISM. 357

To exhibit the effects of the earth's magnetism on vertical
currents, M. Pouillet contrived an apparatus consisting of two
circular canals, represented in their vertical section in^. 626.,
one placed above the other, the lower canal
A o It' having a greater diameter than the upper.
In the opening in the centre of these canals
a metallic rod t is fixed in a vertical position,
supporting a mercurial cup c. A rod hh',
composed of a non-conducting substance, is
supported in the cup e by a point at its centre.
The vertical wires v v' are attached to the
ends of the rod hh', and terminate in points,
which are turned downwards, so as to dip
Fig. 626. into the liquid contained in the upper canal,

while their lower extremities dip into the
liquid contained in the lower canal. A bent wire connects
the mercury contained in the cup c with the liquid in the upper
canal.

The liquid on the upper and lower canals is acidulated water
or mercury. If the liquid in the lower canal be put in com-
munication with the positive, and the rod t with the negative
pole, the current will pass from that canal up the two vertical
Avires v v', thence to the liquid in the upper canal, thence by
the connecting wire to the mercury in the cup c, and thence by
the rod t to the negative pole.

By this arrangement the two vertical currents vv', which
both ascend, are moveable round the rod t as an axis.

When this apparatus is left to the influence of the earth's
magnetism, the currents vv' will be affected by equal and
parallel forces directed westward at right angles to the mag-
netic meridian (1988). The equal and parallel forces being at
equal distances from the axis t, will be in equilibrium in all
positions (421), and the wires will therefore be astatic (1695).

If the point of the wire v' at h' be raised from the upper
canal, the current on v' will be suspended. In that case, the
wire t; being impelled by the terrestrial magnetism westward at
right angles to the magnetic meridian, the system will take a
position at right angles to that meridian, the wire on which the
current passes being to the west of the axis t. If the point at
h' be turned down so as to dip into the liquid, and the point at
h be turned up so as to suspend the current on h and establish



358 VOLTAIC ELECTRICITY.

that on h', the system will make half a revolution and will
place the wire h' on which the current runs to the west of t.

If by the reotrope the connexions with the poles of the bat-
tery be reversed, the currents on vv' will descend instead of as-
cending. In that case the system will be astatic as before, so
long as both currents are established on the wires v v'. But
if the connexion of either with the superior canal be removed,
the wire on which the remaining current passes being impelled
eastwards, the system will take a position in the plane of the
magnetic meridian, the wire on which the current runs being
east of the axis t.

When the currents on the wires v v' are both passing, the
system will be astatic only so long as the currents are equally
intense, and both in the same plane with the axis t. If while
the latter condition is fulfilled one of the wires be even in a
small degree thicker than the other, it will carry a stronger
current, and in that case it will turn to the magnetic east or
west, according as the currents descend or ascend, just as
though the current on the other wire were suppressed ; for in
this case the effective force is that due to the difference of the
intensities of the currents acting on that which is the stronger.

If the two wires be not in the same plane with the axis, the
forces which act upon them being equal, and parallel to the
plane of the magnetic meridian, the position of equilibrium will
be that in which the plane passing through them will be
parallel to the latter plane.

The position of equilibrium will be subject to an infinite
variety of changes, according as the plane of the wires vv',
their relative thickness, and their distances from the axis of
rotation are varied, and in this way a great number of inter-
esting experiments on the effects of the earth's magnetism may
be exhibited.

1995. Its application to show the effect of terrestrial mag-
netism on a horizontal current. To show experimentally
the effect of the earth's magnetism on a horizontal current,
M. Pouillet contrived an arrangement on a similar principle,
consisting of a circular canal, the ver-
tical section of which is represented in



fig. 627. A horizontal wire ab is sup-
ported by a point at its centre which
Fig. 627. regtg j n a mercur i a i CU p fixed upon a



INFLUENCE OF TERRESTRIAL MAGNETISM. 359

metallic rod, like t, fig. 626. Two points, a and b, project from
the wire and dip into the liquid in the canal, the small weights
c and d being so adjusted as to keep the wire a b exactly balanced.

If the central rod be connected with the positive, and the
liquid in the canal with the negative pole, the current will
ascend on the central rod, and will pass along the horizontal
wire in both directions from its centre to the points a and b, by
which it will pass to the liquid in the canal, and thence to the
negative pole. If by the reotrope the connexions be reversed
and the names of the poles changed, the current will pass from
a and b to the centre, and thence by the central rod to the
negative pole.

In the former case, the wire a b will revolve with retrograde,
and in the latter with direct rotation, in accordance with what
has been already explained (1918).

1996. Its effect on vertical currents shown by Ampere's
apparatus. If a rectangular current, such as that represented
injtf^. 595., be suspended in Ampere's frame, fig. 564., it will,
when left to the influence of terrestrial magnetism, take a
position at right angles to the magnetic meridian, the side on
which the current descends being to the east. For in this case
the horizontal currents which pass on the upper and lower sides
of the rectangle, being contrary in direction, will have a ten-
dency to revolve, one with direct, and the other with retrograde
motion round yy'\ These forces, therefore, neutralize each
other. The vertical descending current will be attracted to the
east, and the ascending current to the west (1992).

1997. Its effect on a circular current shown by Ampere's
apparatus. If a circular current, such as that represented in

fig. 594., be suspended in Ampere's frame, fig. 564., and sub-
mitted to the influence of terrestrial magnetism, each part of it
may be regarded as being compounded of a vertical and hori-
zontal component. The horizontal components in the upper
semicircle, flowing in a direction contrary to those in the lower
semicircle, their effects will neutralize each other. The vertical
components will descend on one side and ascend on the other.
That side on which they descend will be attracted to the east,
and that at which they ascend to the west ; and, consequently,
the current will place itself in a plane at right angles to the
magnetic meridian, its front being presented to the south.

1998. Its effect on a circular or spiral current shown by



360 VOLTAIC ELECTRICITY.

Delarive's floating apparatus. If a circular or spiral current
be placed on a floating apparatus, it will assume a like position
at right angles to the magnetic meridian, with its point to the
south ; and the same will be true of any circulating current.

1999. Astatic currents formed by Ampere's apparatus. To
construct a system of currents adapted to Ampere's frame,
which shall be astatic, it is only necessary so to arrange them
that there shall be equal and similar horizontal currents
running in contrary directions, and equal and similar vertical
currents in the same direction, and that the latter shall be at
equal distances from the axis on which the system turns; for in
that case the horizontal elements, having equal tendencies to
make the system revolve in contrary directions, will equilibrate,
and the vertical elements being affected by equal and parallel
forces at equal distances from the axis of rotation, will also
equilibrate.

By considering these principles, it will be evident that the
system of currents represented mfig. 628.,
adapted to Ampere's frame, fig. 564., is
astatic.

2000. Effect of earth's magnetism on
spiral currents shown by Ampere's appa-
ratus. If the arrangement of spiral
currents represented in fig. 605. be so dis-
posed that the current after passing through
one only of the two spirals shall return to
the negative pole, the earth's magnetism
Fig. 628. W JH affect it so as to bring it into such a

po ition that its plane will be at right angles to the magnetic
meridian. If the descending currents be on the side of the
spiral more remote from the axis of motion, the system will
arrange itself so that the spiral on which the current flows shall
be to the east of the axis. If the descending currents be on
the side nearer to the axis, the spiral on which the current
flows will throw itself to the west of the axis. In each case,
the front of the current is presented to the magnetic south, and
the descending currents are on the east side of the spiral.

If the current pass through both spirals in fig. 605., and
their fronts be on the same side, the earth's magnetism will
throw them into the plane at right angles to the magnetic me-
ridian, their fronts being presented te the south.




INFLUENCE OF TERRESTRIAL MAGNETISM. 361

If their fronts be on different sides, the system will be astatic,
and will rest in any position independent of the earth's mag-
netism, which in this case will produce equal and contrary
effects on the two spirals.

If the system of spiral currents represented in fig. 606. be
suspended in Ampere's frame, subject to the earth's magnetism,
the fronts of the currents being on the same side of the two
spirals, it will take such a position that the centres of the two
spirals will be in the magnetic meridian, their planes at right
angles to it, and the fronts of the currents presented to the
south. If in this case the fronts of the currents be on opposite
sides, the system will be astatic.

2001. Effect on an horizontal current shown by Pouillet's
apparatus. The rotation of the horizontal current produced
with the apparatus^. 627., may be accelerated, retarded, ar-
rested, or inverted by presenting the pole of an artificial magnet
above or below it, at a greater or less distance. A south
magnetic pole placed below it, or a north magnetic pole above,
producing forces identical in direction with those produced by
terrestrial magnetism, will accelerate the rotation in a greater
or less degree, according to the power of the artificial magnet,
and the greater or less proximity of its pole to the centre of
rotation of the current.

A north magnetic pole presented below, or a south pole above
the centre of rotation, producing forces contrary in their direction
to those resulting from the earth's magnetism,
will retard, arrest, or reverse the rotation ac-
cording as the forces exerted by the magnet are
less than, equal to, or greater than those im-
pressed by terrestrial magnetism.

If the system of currents represented in
fig. 629. be suspended on Pouillet's apparatus,
represented in^. 626., it will receive a motion
of continued rotation from the influence of the
Fig. 629. earth's magnetism. In this case the vertical
currents being in the same direction will be in equilibrium
(1994) ; and the horizontal currents passing either from the
centre of the upper horizontal wire to the extremities, or vice
versa, according to the mode of connexion, will receive a mo-
tion of rotation direct or retrograde (1995). This motion of
rotation may be affected in the manner above described by the

II. K




362 VOLTAIC ELECTRICITY.

pole of a mngnet applied in the centre of the lower circular
canal, fig. 626.

2002. Effect of terrestrial magnetism on an heliacal current
shown by Amperes apparatus. An heliacal current such as
that represented in Jig. 608., being mounted on Ampere's
frame, or arranged upon a floating apparatus, fig. 609., will be
acted on by the eai'th's magnetism. The several convolutions
will, like a single circulating current, take a position at right
angles to the magnetic meridian, their fronts being presented
to the south. The axis of the helix will consequently be di-
rected to the magnetic north and south ; and it will, in fine,
exhibit all the directive properties of a magnetic needle, the
end to which the front of the currents is directed being its
south pole.

If such a current were mounted on a horizontal axis at right
angles to the plane of the magnetic meridian, it would, under
the influence of the earth's magnetism, take the direction of the
dipping-needle, the front of the currents corresponding in
direction to the south pole of the needle.

2003. The dip of a current illustrated by Amperes rectangle.
The phenomenon of the dip may also be experimentally
illustrated by Ampere's electro-magnetic rectangle, fig. 630.,
which consists of a horizontal axis xv, which is a tube of wood
or other non-conductor, at right angles to which is fixed a




Fig. 630.



RECIPROCAL INFLUENCE OF CURRENTS. 363

lozenge-shaped bar az, composed also of a non-conductor.
Upon this cross is fixed the rectangle ABDC, composed of wire.
The rectangle rests by steel pivots at M and N on metallic
plates, which communicate by wires with the mercurial cups at
s and K. These latter being placed in connexion with the
poles of a voltaic battery, the current will pass from the positive
cup s up the pillar and round the rectangle, as indicated by the
arrows. At x it passes along a wire through the tube xv to v,
and thence by the steel point, the plate M, and the pillar, to the
negative cup R.

The axis MN being placed at right angles to the magnetic
meridian, and the connexions established, the rectangle will be
immediately affected by the earth's magnetism, and after some
oscillations, will settle into a position at right angles to the
direction of the dipping-needle.

In this case the forces impressed by the earth's magnetism on
the parts of the current forming the sides AC and BD, will pass
through the axis MN, and will therefore be resisted. The forces
impressed on AB and CD will be equal, and will act at the middle
points a and z, at right angles to AB and CD, and in a plane at
right angles to the direction of the dip. These forces will
therefore be in directions exactly opposed to each other when
the line az takes the direction of the dip, and will therefore be
in equilibrium.



CHAP. VIII.

RECIPROCAL INFLUENCE OF VOLTAIC CURRENTS.

2004. Results of Ampere's researches. The mutual attrac-
tion and repulsion manifested between conductors charged with
the electric fluids in repose, would naturally suggest the in-
quiry whether any analogous reciprocal actions would be mani-
fested by the same fluids in motion. The experimental analysis
of this question led Ampere to the discovery of a body of phe-
nomena which he had the felicity of reducing to general laws.
The mathematical theory raised upon these laws has supplied the
means by which phenomena, hitherto scattered and unconnected,

R 2



364



VOLTAIC ELECTRICITY.



and ascribed to a diversity of agents, are traced to a common
source.

Although the limits within which a treatise so elementary as
this manual is necessarily confined excludes any detailed ex-
position of these beautiful physico-mathematical researches,
they cannot be altogether passed over in silence. We shall
therefore give as brief an exposition of them as is compatible
with their great importance, and that clearness without which
all exposition would be useless.

2005. Reciprocal action of rectilinear currents. If two
rectilinear currents be parallel, they will attract or repel each
other according as they flow in the same or opposite directions.

This is verified experimentally by the apparatus represented
\nftg. 631., which is on the principle of Ampere's frame. The
mercurial cup marked + receives
the current from the positive pole.
The current passes as indicated by
the arrows upwards on the pillar t,
and thence to the cup x, from
which it flows round the rectangle,
returning to the cup y, and thence
to the pillar v, by which it de-
scends to the cup, which is con-
nected with the negative pole.

If the rectangle thus arranged be
placed with its plane at any angle
Fl S- 631> -with the plane of the pillars t and

v, upon which the ascending and descending currents pass, it
will turn upon its axis until its plane coincides with the plane
of the pillars t and v, the side of the rectangle de on which the
current ascends being next the pillars t, on which it ascends.
If by means of the reotrope (1911) the connexion be reversed, so
that the current shall descend on *and de, and shall ascend on v
and be, it will still maintain its position. But if the connexions
at x and y be reversed, the connexions of the cups + and
remaining unchanged, the current will descend on ed while it
ascends on t, and will ascend on be while it descends on v. In
this case t will repel de and attract be, and v will repel be and
attract de, and accordingly the rectangle will make a half revo-
lution, and be will place itself near t, and de near v.

2006. Action of a spiral or heliacal current on a rectilinear




RECIPROCAL INFLUENCE OF CURRENTS. 365



current A sinuous, spiral, or heliacal current, provided its
convolutions are not considerable in magnitude, impresses on
another current in its neighbourhood the same force as a straight
current would produce, whose direction would coincide with
the axis of the sinuous or spiral current. This is proved ex-
perimentally by the fact that a spiral current which has a re-
turning straight current passing along its axis, will exercise no
force either of attraction or repulsion on a straight current
parallel to it. Now since on suspending the spiral current the
straight current will attract or repel a parallel straight current,
it follows that the spiral current exactly neutralizes the effect of
the straight current flowing in the opposite direction, and con-
sequently it will be equivalent to a straight current flowing in
the same direction.

2007. Mutual action of diverging or converging rectilinear
currents. Rectilinear currents which diverge from or con-
verge to a common point mutually attract. Those, one of which
diverges, and the other converges, mutually repel ; that is to

c say, if two rectilinear
currents cc' and cc',
fig. 632., which inter-
sect at o, both flow to-
wards or from o, they
will mutually attract ;
Fig- 632 - but if one flow towards,

and the other from o, they will mutually repel. The currents,
being supposed to flow in the direction of the arrows, oc and o<?
will mutually attract, as will also oc' andoc'; while oc' and oc
will repel, as will also oc and oc'.

If the wires conducting the currents were moveable on o as a
pivot, they would accordingly close, the
angle coc diminishing until they would
coincide.

2008. Experimental illustration of
this. This may be experimentally illus-
trated by the apparatus represented in
fig. 633. in plane, and in fig. 634. in sec-
tion, consisting of a circular canal filled
with mercury or acidulated water sepa-
rated into two parts by partitions at a
Fig. 633. an( j _ Two wires cd and ef, suspended





366 VOLTAIC ELECTKICITY.

on a central pivot, move freely one over and independent of
the other, like the hands of a watch, the points being at right
angles, so as to dip into the canal. The
mercurial cup x being supposed to be con-
nected with the positive, and y with the
Fig. 634. negative pole, the current passing to the

liquid will flow along the wires as indicated by the arrows from
the liquid in one section to that of the other, and will pass to the
negative cup y. When the wires cd and efihus carrying the
current are left to their mutual influence, the angle they form
will close, and the directions of the wires will coincide, so that
the currents shall flow in the same direction upon them.

In these and all similar experiments, the phenomena will
necessarily be modified by the effects produced by the earth's
magnetism. In some cases the apparatus can be rendered
astatic (1695); and in others, the effect due to the terrestrial
magnetism being known, can be allowed for, so that the phe-
nomena under examination may be eliminated.

2009. Mutual action of rectilinear currents which are not in
the same plane. If two rectilinear currents be not in the same



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