Sympathetic Vibratory Physics - It’s a Musical Universe
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The following article lends support to
Keelys Laws of Attraction and Repulsion:
 
Law of Attraction
"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 AcademiČ des Sciences this afternoon. His results have not been published before.

George Forbes, Paris, August 15, 1881
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