By Conrad W. Cooke

We have in former articles described the highly interesting series of experimental researches of Dr. C. A. Bjerknes, Professor of Mathematics in the University of Christiania, which formed so attractive a feature in the Electrical Exhibition of Paris in 1881, and which constituted the practical development of a theoretical research which had extended over a previous period of more than twenty years. The experiments which we described in those articles were, as our readers will remember, upon the influence of pulsating and rectilinear vibrating bodies upon one another and upon bodies in their neighborhood, as well as upon the medium in which they are immersed. This medium, in the majority of Professor Bjerknes earlier experiments, was water, although he demonstrated mathematically, and to a small extent experimentally, that the phenomena, which bear so striking an analogy to those of magnetism, may be produced in air.

Our readers will recollect that in the spring of 1882 Mr. Stroh, by means of some very delicate and beautifully designed apparatus, was able to demonstrate a large number of the same phenomena in atmospheric air of the ordinary density; and about the same time Professor Bjerknes, in Christiania, was extending his researches to phenomena produced by a different class of vibrations, namely, those of bodies moving in oscillations of a circular character, such, for example, as a cylinder vibrating about its own axis or a sphere around one of its diameters; some of these experiments were brought by Professor Bjerknes before the Physical Society of London in the following June. Since that time, however, Professor Bjerknes, with the very important assistance of his son, Mr. Vilhelm Bjerknes, has been extending these experimental researches in the same direction, and with the results which it is the object of the present series of articles to describe.

The especial feature of interest in all Professor Bjerknes experiments has been the remarkably close analogy which exists between the phenomena exhibited in his mechanical experiments in water and other media and those of magnetism and of electricity, and it may be of some interest if we here recapitulate some of the more striking of these analogies.

(1.) In the first place, the vibrating or pulsating bodies, by setting the water or other medium in which they are immersed into vibration, set up in their immediate neighborhood a field of mechanical force very closely analogous to the field of magnetic force with which magnetized bodies are surrounded. The lines of vibration have precisely the same directions and form the same figures, while at the same time the decrease of the intensity of vibration by an increase of distance obeys precisely the same law as does that of magnetic intensity at increasing distances from a magnetic body.

(2.) When two or more vibrating bodies are immersed in a fluid, they set up around them fields of vibration, and act and react upon one another in a manner closely analogous to the action and reaction of magnets upon one another, producing the phenomena of attraction and repulsion. In this respect, however, the analogy appears to be inverse, repulsion being produced where, from the magnetic analogy, one would expect to find attraction, and vice versa.

(3.) If a neutral body, that is to say a body having no vibration of its own, be immersed in the fluid and within the field of vibration, phenomena are produced exactly analogous to the magnetic and diamagnetic phenomena produced by the action of a magnet upon soft iron or bismuth, its apparently magnetic or diamagnetic properties being determined by the specific gravity of the neutral body as compared to that of the medium in which it is immersed. If the neutral body be lighter than the medium, it exhibits the magnetic induction of iron with respect to polarity, but is nevertheless repelled; while if it be heavier than the medium, its direction is similar to that of diamagnetic bodies such as bismuth, but on the other hand exhibits the phenomena of attraction.

In this way Professor Bjerknes has been able to reproduce analogues of all the phenomena of magnetism and diamagnetism, those phenomena which may be classed as effects of induction being directly reproduced, while those which may be classed as effects of mechanical action, and resulting in change of place, are analogous inversely. This fact has been so much misunderstood both in this country and on the Continent that it will be well, before describing the experiments, to enter more fully into an explanation of these most interesting and instructive phenomena.

For the sake of clearness we will speak of magnetic induction as that property of a magnet by which it is surrounded by a field of force, and by which pieces of iron, within that field, are converted into magnets, and pieces of bismuth into diamagnets, and we will speak of magnetic action as the property of a magnet by which it attracts or repels another magnet, or by which it attacks or repels a piece of iron or bismuth magnetized by magnetic induction.

The corresponding hydrodynamic phenomena may be regarded in a similar manner; thus, when a vibrating or pulsating body immersed in a liquid surrounds itself with a field of vibrations, or communicates vibrations to other immersed bodies within that vibratory field, the phenomena so produced may be looked upon as phenomena of hydrodynamic induction, while on the other hand, when a vibrating or pulsating body attracts or repels another pulsating or vibratory body (whether such vibrations be produced by outside mechanical agency or by hydrodynamical induction), then the phenomena so produced are those of hydrodynamical action, and it is in this way that we shall treat the phenomena throughout this article, using the words induction and direct action in these somewhat restricted meanings.

In the hydrodynamical experiments of Professor Bjerknes all the phenomena of magnetic induction can be reproduced directly and perfectly, but the phenomena of magnetic action are not so exactly reproduced, that is to say, they are subject to a sort of inversion. Thus when two bodies are pulsating together and in the same phase (i.e., both expanding and both contracting at the same time), they mutually attract each other: but if they are pulsating in opposite phases, repulsion is the result. From this one experiment taken by itself we might be led to infer that bodies pulsating in similar phases are the hydrodynamic analogues of magnets having their opposite poles presented to one another, and that bodies pulsating in opposite phases are analogous to a presentation of similar magnetic poles; but it will be seen at once that this cannot be the case if three magnetic poles or three pulsating bodies be considered instead of only two. It is clear, on the one hand, that three similar magnet poles will all repel one another, while, on the other, of three pulsating bodies, two of them must always attract one another, while a third would be repelled; and, moreover, two similarly pulsating bodies set up around them the same lines of force as two similar magnetic poles, and two oppositely pulsating bodies produce lines of force identically the same as those set up by two magnets of opposite polarity.

Thus it will be seen that there is a break in the analogy between the hydrodynamical and the magnetic phenomena (if a uniform inversion of the effects can be called a break, for it is, as far as Professor Bjerknes' experiments go, without an exception); and if by any means this inversion could be reinverted, all the phenomena of magnetism and diamagnetism could be exactly reproduced by hydrodynamical analogues; there would thus be grounds for forming a theory of magnetism on the basis of mechanical phenomena, and a very important link in the chain of the correlation of the physical forces would be supplied.