are situated upon one of the curves which can be drawn in each section of the ring, are indissolubly tied down to their circular paths, and can never quit them; so that the whole mass of the vortex ring will be always formed of the same particles. This theorem was proved by Helmholtz in 1858. This eminent physicist has analyzed the vortex motions which would exist in a perfect fluid free from all friction. He has proved that in such a medium vortex rings, bounded by a system of vortex lines, are formed of an invariable quantity of the same liquid molecules, so that the rings can move, and even change their form, without the connection of their constituent parts ever being broken. They will continue to revolve, and nothing will be able to separate them, divide them, or destroy them. Those existing in the liquid will exist there for ever, and new ones can only be excited in it by a creative act.
The smoke-rings, of which we have spoken above, would give a perfect representation of these liquid vortex rings if they were formed and moved in a perfect fluid. They are not so; but such as can be formed can serve for the demonstration of some properties of matter in vortex motion. They are endowed with elasticity and can change their form. The circle is their position of equilibrium, and, when their form is altered, they oscillate round this position, and finally reassume the circular form. But, if we try to cut them, they recede before the knife, or bend round it, without allowing themselves to be injured. They give, therefore, a representation of something which would be indivisible. And when two rings meet each other, they behave like two solid elastic bodies; after the impact they vibrate energetically. It is a singular fact that when two rings are moving in the same direction, so that their centers are situated upon the same line, and their planes perpendicular to this line, the hinder ring contracts continually, while its velocity increases; the ring in advance, on the contrary, expands, and its velocity decreases until the other has passed it, when the same action recommences, so that the rings alternately pass through each other. But, through all these changes of form and velocity, each preserves its own individuality, and these two circular masses of smoke move through the air as if they were something perfectly distinct and independent. These curious experiments were made in England.
Helmholtz, therefore, has discovered the fundamental properties of matter in vortex motion, and Sir William Thomson has stated, "This perfect medium and these vortex rings which move through it, represent the universe." A fluid fills all space, and what we call matter are portions of this fluid which are animated with vortex motion. There are innumerable legions of very small fractions or portions, but each of these portions is perfectly limited, distinct from the entire mass, and distinct from all others, not only in its own substance, but in its mass and its mode of motion—qualities which it will preserve for ever. These portions are atoms. In the perfect medium which contains them all, none of them can change or disappear, none of them can be formed spontaneously. Everywhere atoms of the same kind are constituted after the same fashion, and are endowed with the same properties. It is well known, in fact, that the atoms of hydrogen vibrate exactly in the same periods, whether we heat them in a Geissler's tube, observe them in the sun, or in the most distant nebulæ.Such is, in a few words, the conception of vortex atoms. It accounts, in a satisfactory manner, for some properties of matter, and of all the hypotheses upon the nature of atoms it appears to be the most probable. We see also that it permits the revival of the ancient hypothesis of the unity of matter, and in a more acceptable form than that of Prout's hypothesis. Is the idea absolutely new? No; it was originally conceived by Descartes. So far is it true that, when the perpetual, and perhaps insolvable, problem of the constitution of matter is discussed, the human mind seems to turn in a circle, the same ideas lasting for ages, and being presented under fresh forms to the highest intellects who have endeavored to solve this problem. But is there no difference among these great intellects in their manner of working? Most certainly: some, more powerful, perhaps, but bolder, have proceeded by intuition; others, better armed and stricter, by induction. Here lies the progress and the superiority of modern methods, and it would be unjust to pretend that the important efforts, of which we have had striking testimony, have not made an advance in this difficult problem which was impossible to Lucretius and even to Descartes.
The Skin in Health and Disease. By L. Duncan Bulkley, M. D. Philadelphia: Presley Blakiston. Pp. 148. Price, 50 cents.
We have here an excellent contribution to the series of "American Health Primers." It is as good as its predecessors, which is no slight praise. There are many popular books on that important subject, "The Skin," and several of them meritorious, but this is no reason why Dr. Bulkley should not have made another—because, in the first place, this interesting organ of the body is very important in relation to health, and there are but few people who are at all aware of it. They have not only to be taught, but the lessons must be hammered into them by ceaseless repetition. Hence the need of fresh and unremitting inculcations. Dr. Bulkley's book is to be welcomed on this ground; but it has also a special merit which we have
- "Wirbelfëden und Wirbellinien."
- P. G. Tait. "Lectures on some Recent Advances in Physical Science." London, 1876.