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. [Illustration: FIG. 2.] 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.