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X L V I . Magnetic Figures illustrating Electrod!/narnicRelations.
B~/ SmVA~US P. TEOMPSON, _D.Sc., B.A., ~.R.A.S., _Pro-

[Plates ¥I. and VII.]
N a preliminary communication to the Physical Society in
February of the present year, the author announced a
method of studying and illustrating the known laws of the
mutual attractions or repulsions of conductors traversed b y
electric currents. The present paper is a complete statement
of the facts obtained in the experimental research which formed
the basis of that communication.
While preparing a set of magnetic currents to illustrate the
mutual actions of magnet-poles, it occurred to the writer that
the mutual attractions and repulsion of currents might be il-
lustrated in a similar manner by the figures formed with iron
filings. He was aware~ at that time that the lines of force of
a straight conductor carrying a current were a series of con-
centric circles lying in a plane to which the conductor was
normal. The series of figures now published originates, there-
fore, with the discovery of Faraday that the seat of the mutual
actions of currents and of magnets must be sought in the sur-
rounding medium. Since the communication of the prelimi-
nary notice, the writer has learned that one or two of the figures
had been previously and independently observed by Professor
F. Guthrie, but not published. Two others, ~os. 4 and 5 of
the present series, are imperfectly given by ]?araday in figures
18 and 19 of plate iii. in the third volume of his ' Experimental
Researches' (Series Twenty-ninth)S, and without reference to
the conclusions to be derived from their tbrms, which Faraday
apparently overlooked §.
The method employed for preserving the figures has been
uniform throughout the series. Plates of glass, 3½ inches long
by 3¼ inches broad, were coated with a solution of' gum-arabic
and gelatine, and were then carefully dried. When the ar-

I

fessor of Experimental P ]~ysicsin University College,Bristol*.

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* Communicated by the Physical Society.
See Faraday, ~Experimental Researches in Electricity,' voh iii. p.
400, § 3339, and plate iii. fig. 17 ; Guthrie, ~Magnetism and Electricity,'
p. 254, fig. 235~ Clerk-Maxwell, 'Electricity and Magnetism,' vol. ii.

~t. 477.

And ' Phil. Trans. 1853, p. 137.
~The attention of the writer has also been drawn to a statement in the
American Journal of Science for 1872, p. 263, by Professor A. M. Mayer,
that he has obtained magnetic "spectra" from electric currents in a manner
somewhat similar to thatnow described. The figures have, however, re-
mained unpublished and undescribed, so that the writer has no means of
learning how far the substance of the present communication may have
been anticipated.

Magnetic Figures illustrating Electrod~/namicRelations. 349

rangement of magnets or of conducting-wires had been made
for the particular case of the experiment, and the plate been
laid in a horizontal position~ fine filings of wrought iron pre-
viously sifted were dusted over the plate through muslin, and
the plate was tapped lightly with vertical blows from a piece
of thin glass rod. When the filings had arranged themselves,
and the plate was still in situ, a gentle current of steam was
allowed to play upon the plate, condensing upon the surface of
the gum and softening it, and thus allowing the filings to
embed themselves where they lay. After the gum had again
become hard, the prepared face was covered by a protecting
plate of glass, on which in certain cases were drawn the posi-
tions of the wires or magnets employed. The figures fixed in
this manner are suitable for projection with the lantern upon
the screen. They can be readily photographed for transpa-
rencies, or for paper prints; specimens of each of these
methods of photographic reproduction are exhibited to the
Society.
Figure 1 represents the condition of the magnetic field sur-
rounding the current in a straight conducting-wire, which was
carried vertically through a hole drilled in the plate. The
wire employed throughout the series was a silver one of about
"8 millim, in diameter. The battery power employed for this
experiment was that of 20 Cxrove's cells arranged in two series
of ten each. In some of the succeeding experiments a less
current was found sufficient.
But for the imperfections of the method of experiment~ these
curves would be perfect circles, and the distances between
two successive lines of force would be proportional to the
square of the distance from the centralpoint. The equipoten-
tial magnetic surfaces, being always normal to the magnetic
lines of force, would be represented by a system of radial lines
forming equal angles with one another. There appears to be
no recognized name for the closed curves traced out by the
lines of force around conductors carrying currents. With
great diffidence I therefore beg to speak of them as isodynamic
lines. They are theoretically disposed about a single straight
conductor in a perfectly concentric manner~ and at such dis-
tances apart as would be defined by the requirement that a
parallel conductor, carrying a like current of unit strengtb,
would do unit work in passing from one isodynamic line to the
next. The absolute value of an isodynamic line would of course
be determined (like magnetic and electrostatic potential) by
the work done by a like element of current in passing to any
point in that line from an infinite distance. No work is done
in moving an element of a parallel current along an isodyna-

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350

mie line, just as no work is done in moving a magnet-pole
along in an equipotential surface. The isodynamic lines
occupy, therefore, exactly the same relation to the element of
the circuit~ as do the equipotential surfaces to a magnet-pole
or to an electrified point.
Figure 2 represents the field above a horizontal wire carry-
ing a current~ and separated from the filings by the thickness
of the glass (about 1"7 millim.). The lines cross the wire at
right angles~ and are really the projections of a series of such
circles as exist in figure 1.
Figure 3 exhibits the form assumed by the filings when the
wire beneath the plate was coiled into a simple loop~ a small
piece of mica being inserted to prevent contact where it re-
crossed its path. The lines of the field within the loop run
longitudinally ; and. their projections on the surface are mere
points, as the fihngs show.
In figures 4 and 5, two wires pass vertically through the
plane of the figures~ carrying parallel currrents, which in
figure 4 are in the same direction, in figure 5 in opposite
directions. Amp~re's well-known law of the attraction in the
former cas% and of the repulsion in the latter, is well illus-
trated by the forms of the magnetic curves. In the former,
where the parallel currents attract, the outer isodynamic lines
are closed curves embracing both centres, the inner are dis-
torted ovals about each centre--the whole forming a system of
lemniscates, as would necessarily be the case, since the at-
traction at any point in the plate varies inversely as the square
of the distance i~om each current*.
In figure 5~ where the parallel currents repel each other,
the lines of force due to either current in no case enter or
coalesce with those of the other current. They form two series
of ovals of a peculiar form, flattened on the sides presented
towards the opposing series.
The conception of Faraday, " that the lines of magnetic
force tend to shorten themselves~ and that they repel each other
when placed side by side," has been shown by Clerk-Maxwell,
who thus concisely states it, to be perfectly consistent with the
theory that explains electromagnetic force as the result of a
state of stress in the medium filling the surrounding spacer.
Faraday also observes that " unlike magnetic lines, when end
on~ repel each other, as when similar poles are face to face,"
and that "like magnetic lines of force," when end on to each
other, coalesce. The terms "like " and "unlik%" as applied
See Thomson and Talt, Natural Philosophy~ art. 508~vol. i. p. 382.
t Clerk-Maxwell, ~Electricity and Magnetism,' vol. it. art. 645 ; Fara-
day~ ~Experimental R~earches~' 8266~3267~3268.

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Prof. S. P. Thompson on Magnetic Figures

illustrating F,lectrodynamic Relations.

351

to magnetic lines of force, refer, of course, to the two cases of
similarly or oppositely directed lines, the positive direction of
a line of force being reckoned as the direction in which a
north-seeking pole on it would tend to move*. The mutual
coalescence or repulsion exerted between the lines of force of
unlike or like magnetic poles is familiarly employed in the
experimental illustration of magnetic phenomena, so well known
since the researches of Professor Robison and Dr. Roger on
the magnetic curves, and appears to have been recognized long
beforet. It is believed that the present is the first distinct
attempt to apply similar considerations to the illustration of
electrodynamic relations between systems of conductors car-
rying currents, and between conductors of currents and mag-
net-poles.
The isodynamic lines, which are lines of magnetic force,
tend to shorten themselves. A very hasty inspection of fig. 4
will show that if any one of the system of lemniscates were to
"shorten itself," it would tend to bring the two centres nearer
together. Consider each isodyuamic line as a ring of some
elastic material (as, for example, an indiarubber ring) stretched
around a bundle of smooth wires~ the cross section of the bundle
having a perimeter corresponding in form to the isodynamic
line under consideration. The maximum shortening of such
an elastic ring would take place when the enclosed area was
made a circle. In other words, the lemniscate-form isodyna-
mics tend to become circles, and the two like parallel currents
are mutually urged towards each other.
In figure 5 the shortening of the isodynamic lines, and their
approach to the truly circular form, could only be accomplished
by the wider separation of the two conductors from each other.
Hence the mutual repulsion of two parallel conductors carry-
ing oppositely directed currents.
Figures 6 and 7 show the lines of force above the parallel
currents when these pass horizontally below the glass. In the
case of like currents the lines coalesce. In the case of unlike
currents they repel each other, and pass between the two wires
in a direction vertical to the plane of the glass, where their
characteristic form, as lines, is lost. The observation that the
filings adherent to wires carrying like parallel currents are
mutually attractive appears to'have been first made by Davy.
Figure 8 illustrates the law of currents crossing one another
at a point. In the two quadrants in which the currents both

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See Clerk-Maxwell, ' Electricity and Magnetism,' art. 489 i L. Cure-
ruing, cTheory of Electricitv~' p. ]94.
~" See Mus~henbroek, D~ssertatlo Phydea .Experimentalis de Magnate,
cap. iv. exp. cxvii., and tab. iv. figs. 4 & 6.

352

run to or from the central point, the lines of force tend to
coalesce. In the alternate quadrants they mutually repel each
other; and the angle of these quadrants tends to increase.
In figure 9 one current is carried horizontally below the glass,
the other traverses the plane of the figure normally. The dis-
symmetry of the resultant distribution of the lines reveals the
dissymmetrical nature of the force which tends to bring the
currents into parallelism. A n y shortening of the isodynamic
lines would tend to move the vertical current from that qua-
drant over which the lines are unbroken. Figures have also
been obtained with two currents crossing the plato in a vertical
plane of incidenc% but each at 45 ° to the normal. With some
distortion, these figures bear a general resemblance to figs. 4
and 5 in the two cases of the currents passing through the
plate in similar or in opposed directions. In the ibrmer case
their angular separation tends to diminish, in the latter to in-
crease.
Figures 10, 11, and 12 introduce the action of a vertical cur-
rent upon a small magnetic needle lying on the glass plate.
In the first case the needle lies in stable equilibrimn almost
tangentially to the isodynamic lines ; in the third its position
is reversed and unstable ; in the second case it is set at right
angles to the directive action of the current. The dissymme-
trical action of the forces on its poles produces a couple tend-
ing to turn it about its centre, as would be inferred from an
inspection of the lines of force of the figure.
Figures 13 and 14 illustrate a deduction from the theory of
the magnetic shell. A conductor carrying a current is acted
upon by a force urging it forward so as to make the number
of like lines of force included within it a maximum ~ ; that
is to say, a north-seeking pole is attracted into a circuit
on the side from which the positive current appears to circu-
late in a right-handed cyclical order (or in the same direction
as the hands of a clock). Similarly the circuit is urged back-
wards from a contrary pole, and tends to make the number of
unlike lines of force included within it a minimum. In the
figures a current ascends through the plane of the figure on
the left, and descends through it on the right, in a right-handed
cyclical order as seen from the magnet. Hence a north-
seeking pole is attracted, and a south-seeking pole repelled.
Figure 15 results from the action of two magnet-poles upon a
vertical conductor~ which in this case is attracted between the
poles.
Figure 16 illustrates the mutual tendency to rotation between
a magnet-pole and a conductor carrying a current parallel to
* Clerk-Maxwell, cElectricity and Magnetism,' art. 490.

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Prof. S. P. Thompson on Magnetic Figures

illustrating Electrodynamic Relations.

353

the axis of the magnet. In the figure, where the vertical cur-
rent passes upwards through the glass, the noighbouring south-
seeking pole (marked in position by a square dot) is urged
round the current with a couple tending in a right-handed
c~'T~'cllcalrotation. The couple is reversed, and acts in a left-
handed order, if either the current or the magnet-pole be
reversed. The contrasted dissymmetry so produced is very
curious, and the mutual displacement of the radial lines of
force of the pole and of the circular lines of the current is very
significant.
Figures 17 and 18 show lines of force arranged spirally in
the field. In these a current passes upwards through the glass,
while the pole of a magnet is placed vertically beneath : the
current, in fact, pusses through the magnet. The form of the
lines of force is remarkable. No work would be done on or
by an element of a vertical current in bringing it up to the
centre along one of the spiral lines ; for the work done by it
in bringing it in the spiral path across the successive circular
isodynamic lines of the current would be equal to that done
upon it in carrying it across the successive radial lines of force
of the magnet-pole. The equipotential surfaces of this field
are consequently another series of spirals of an opposite cy-
clical order. In figure 17 the current running up through a
south-seeking pole produced a right-handed spiral; in figure
18, with a north-seeking pole the spiral is of the opposite order.
Since the magnetic potential decreases from a magnet-polo
with the inverse square of the distance, and since the inducLive
action of the current on a point in the plane of the figure also
decreases according to the inverse square of the distance from
the current, each branch of the spirals would be described by a
moving point whose angular displacement from the arbitrary
zero is simply proportional to the distance from the central
point. The results of actual measurement of the spirals at
successive distances of whole millimetres from the centre show
as near an agreement with this supposition as the roughness
of the method of procuring the curves permits. The number
of branches of the spiral will clearly be proportional to the
strength of the magnet pole. The"obvious result of a "short-
ening" of the spiral lines would be to produce a rotational
move']nent, such-as we know to be produced on a free-magnet
pole under the influence of a current traversing it longitudi-
nally.
I am indebted to Mr. Robert Gillo, of Bridgwater, for the
admirable photographic copies of the various figures.
June 19, 1878.

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P]~il. M~g. S. 5. Vol. 6. No. 38. Nov. 1878.

2A

Fhl.Ma6. S 5 .Vol 6. Pl.VI.

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MACNETIC

ILLUSTRATING

FIGURES

ELECTRO-DYNAMIC

RELATIONS.

Phtl.Ma_~. S. 5 .Vol.6. ?I.VII

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MAGNETIC

ILLUSTRATING

FIGURES

ELECTRO-DYNAMIC

RELATIONS,
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