"Juxtaposed coherent aggregates vibrating
in unison, or harmonic ratio, are mutually attracted."
Law of Repulsion
"Juxtaposed coherent aggregates vibrating
in discord are mutually repelled."
Hydrodynamic Analogies to Electricity and
Magnetism
by George Forbes, Paris, August 15, 1881
Nature
From a scientific and purely theoretical point of view there is no
object in the whole of the Electrical Exhibition at Paris of greater
interest than the remarkable collection of apparatus exhibited by R.
C[arl] A. Bjerknes of Christiana, and intended to show the fundamental
phenomena of electricity and magnetism by the analgous ones of
hydrodynamics. I will try to give a clear account of these experiements
and the apparatus employed; but no description can convey any idea of
the wonderful beauty of the actual experiments, whilst the mechanism
itself is also of most exquisite construction. Every result which is
thus shown by experiment had been previously predicted by Professor
Bjerknes as the result of his mathematical investigations.
It has long been known that if a tuning fork be struck and held
near to a light object like a balloon it attracts it. This is an old
experiment, and the theory of it has been worked out more than once.
Among others Sir William Thomson gave the theory in the Philosophical
Magazine in 1867. In general words the explanation is that the air in
the neighborhood of the tuning fork is rarefied by the agitation which
it experiences. Consequently the pressure of the air is greater as the
distance from the tuning fork increases. Thus the pressure on the far
side of the balloon is greater than that on the near side, and the
balloon is attracted.
Dr. Bjerknes has followed out the thory of this action until he has
succeeded in illustrating most of the fundamental phenomena of
electricity and magnetism. He causes vibrations to take place in a
trough of water about six inches deep. He uses a pair of cylinders
fitted with pistons which are moved in and out by a gearing which
regulates the length of stroke and also gives great rapidity. These
cylinders simply act alternately as air compressors and expanders, and
they can be arranged so that both compress and both expand the air
simultaneously, or in such a way that the one expands while the other
compresses the air, and vice versa. The cylinders are connected by thin
india rubber tubing, and fine metal pipes to the various instruments. A
very simple experiment consists in communicating pulsations to a pair
of tambours, and observing their mutual actions. They consist of a ring
of metal faced on both sides with india rubber and connected by a tube
with the air cylinders. One of them is held in the hand; the other is
mounted in the water in a manner which leaves it free to move. It is
then found that if the pulsations are of the same kind, i.e., if
both expand and both contract simultaneously, there is attraction. But if one expands while
the other contracts, and vice versa, there is repulsion.
In fact the phenomenon is the opposite of magnetical and electrical
phenomena, for here like poles attract and unlike poles repel.
Law of Attraction
"Juxtaposed coherent aggregates vibrating
in unison, or harmonic ratio, are mutually attracted." Keely
Law of Repulsion
"Juxtaposed coherent aggregates vibrating
in discord are mutually repelled." Keely
Instead of having the pulsations of a drum we may use the
oscillations of a sphere; and Dr. Bjerknes has mounted a beautiful
piece of apparatus by which the compressions and expansions of air are
used to cause a sphere to oscillate in the water. But in this case it
must be noticed that opposite sides of the sphere are in opposite
phases. In fact the sphere might be expected to act like a magnet; and
so it does. If two oscillating spheres be brought near each other,
then, if they are both moving to and from each other at the same time,
there is attraction; but if one of the spheres be turned round, so that
both spheres move in the same direction in their oscillations, then
there is repulsion. If one of these spheres be mounted so as to be free
to move about a vertical axis, it is found that when a second
oscillating sphere is brought near to it, the one which is free turns
round its axis and sets itself so that both spheres in their
oscillations are approaching each other or receding simultaneously. Two
oscillating spheres, mounted at the extremities of an arm, with freedom
to move, behave with respect to another oscillating sphere exactly like
a magnet in the neighborhood of another magnetic pole. I believe that
these directive effects are perfectly new, both theoretically and
experimentally. The professor mounts his rod with a sphere at each end
in two ways: (1) so that the oscillations are along the arm, and (2) so
that they are perpendicular. In all cases they behave as if each sphere
was a little magnet with its axis lying along the direction of
oscillation.
Dr. Bjerknes looks upon the water in his trough as being the
analogue of Faradays medium; and he looks upon these attractions and
repulsions as being due, not to the action of one body on the other,
but to the mutual action of one body and the water in contact with it.
Viewed in this light, his first experiment is equivalent to saying that
if a vibrating or oscillating body have its motions in the same
direction as the water, the body moves away from the centre of
disturbance, but if in the oppposite direction, towards it. This idea
gives us the analogy of dia- and para-magnetism. If, in the
neighborhood of a vibrating drum, we have a cork ball, retained under
water by a thread, the oscillations of the cork are greater than those
of the water in contact with it, owing to its small mass, and are
consequently relatively in the same direction. Accordingly we have
repulsion, corresponding to diamagnetism. If, on the other hand, we
hang in the water a ball which is heavier than water, its oscillations
are not so great as that of the water in its vicinity, owing to its
mass, and consequently the oscillations of the ball relatively to the
water are in the opposite direction to those of the water itself, and
there is attraction, corresponding to paramagnetism. A rod of cork and
another of metal are suspended horizontally by threads in the trough. A
vibrating drum is brought near to them; the cork rod sets itself
equatorially, and the metal rod axially.
If a pellet of iron be floated by a cork on water and two similar
poles (e.g. both north) be brought to its vicinity, one above and the
other below the pellet, the latter cannot remain exactly in the centre,
but will be repelled to a certain distance, beyond which however there
is the usual attraction. The reason is that when the pellet is nearly
in the line joining the two poles the north pole of the pellet
(according to our supposition) is further from this line than the south
one. The angle of action is less; so that although the north pole is
further away, the horizontal component of the north pole repulsion may
be greater than that of the south pole attraction. Dr. Bjerknes
reproduces this experiment causing two drums to pulsate in concord, the
one above the other. A pellet fixed to a wire, which is attached by
threads to two pieces of cork, is brought between the drums, and it is
found impossible to cause it to remain in the centre.
Dr. Bjerknes conceived further the beautiful idea of tracing out
the conditions of the vibrations of the water when acted on by
pulsating drums. For this purpose he mounted a sphere or cylinder on a
thin spring and fixed as fine paint brush to the top of it. This is put
into the water. The vibrations are in most cases so small that they
could not be detected, but by regulating the pulsations so as to be
isochronous with the vibrations of the spring, a powerful vibration can
be set up. When this is done a glass plate mounted on four springs is
lowered so as to touch the paint brush, and the direction of a
hydrodynamic line of force depicted. Thus the whole field is explored
and different diagrams are obtained according to the nature of the
pulsations. Using two drums pulsating concordantly, we get a figure of
two similar magnetic poles. If the pulsations are discordant it is like
the figure with two dissimilar poles. Three pulsating drums give a
figure identical with that produced by three magnetic poles. The
professor had previously calculated that the effects ought to be
identical, and I think the same might have been gathered from the
formulae in Sir William Thomsons "Mathematical Theory of Magnetism,"
but this only enhances the beauty of the experimental confirmation.
Physicists have been in the habit of looking upon magnetism as some
kind of molecular rotation. According to the present view it is a
rectilinear motion. Physicists have been accustomed to look upon the
conception of an isolated magnetic pole as an impossibility, but here,
while the oscillating sphere represents a magnetic molecule with north
and south poles, the pulsating drum represents an isolated pole. These
are new conceptions to the physicist, let us see whither they lead us.
The professor shows that if a rectilinear oscillation constitutes
magnetism, a circular oscillation must signify an electric current, the
axis of oscillation being the direction of the current. According to
this view what would be the action of a ring through which a current is
passing? If the ring were horizontal the inner parts of the ring would
all rise together and all fall together, they would vibrate and produce
the same effect as the rectilinear vibrations of a magnet. This is the
analogue of the Amperian currents.
To Illustrate the condition of the magnetic field in the
neighborhood of the electric currents, Dr. Bjerknes mounted two wooden
cylinders on vertical axis, connecting them by link-work, which enabled
him to vibrate them in the same or opposite ways. To produce enough
friction he was forced to employ syrup in place of water. The figures
which are produced on the glass plate are in every case the same as
those of electric currents, including the case of currents in parallel
and in opposite directions.
The theory is carried out a step further to explain the attraction
and subsequent repulsion after contact of an electrified and a neutral
substance and the passage of a spark. But it is extremely speculative,
and is not as yet experimentally illustrated, and I think that at
present it is better to pass it by.
I believe that the professor will exhibit his experiments and give
some account of his mathematical investigations, which have occupied
his time for five years, to the Academié des Sciences this afternoon.
His results have not been published before.
