VORTEX (Lat. a whirlpool). Till lately, it was a reproach to hydrodynamics that the theory of vortices or eddies in fluids had not been properly brought under the domain of mathematical analysis. Even now, the problem nas only been partially solved by the labors chiefly of Stokes (q.v.) and Helmholtz (q.v.), as their beautiful investigations apply only to perfect fluids, that is, fluids which oppose no frictional resistance to change of shape. In ordinary motions of perfect fluids, such as currents and waves, the instanta neous change of shape of a small spherical portion makes it an ellipsoid by simple exten .olons and compressions without rotation. The essential characteristic of vortex-motion is, that it involves rotation of some parts of the fluid. Helmholtz has shown that this rotational or vortex-motion remains with the parts of the fluid which first have it, and cannot be transferred. We can conceive no process by which vortex-motion could be given to, or taken from, a perfect fluid; for to our reason fluid friction (which does not exist in a perfect fluid) would seem to be indispensable. On such abstruse subjects we cannot of course enter here; but one result of Helmholtz's investigations is so curious that we must mention it. Wa are all familiar with those singular smoke-rings which are produced when a mortar is fired; or when, on a smaller scale, a bubble of pliosphur "ted hydrogen takes fire in air, or a smoker skillfully emits a puff of tobacco-smoke. A very simple mode of producing them, on even a large scale, is to bore a hole in one side of a box, remove the. opposite side, and substitute a cloth or sheet of india rubber for it. A slight blow on this membrane ejects a vortex-ring from the hole. To make this vor tex visible, we may burn phosphorus or moistened gunpowder in the box; or still better, sprinkle its interior with ammonia, and introduce a vessel containing common salt and sulphuric acid. The sal-ammoniac cloud which fills the box is admirably adapted to display the rings. Besides a progressive motion as a whole, the ring revolves about its owu central or medial line. Suppose two such rings to follow each other, with their planes parallel, and their centers moving in the same line, Helmholtz shows that (at least in a perfect fluid) the foremost will relax its speed, and spread out into a larger ring, while its follower will contract, and quicken its pace, till it passes through the other, which in turn becomes the pursuer, and so on. This very curious result may be realized
in a tea-cup, by drawing the half-immersed bowl of a tea-spoon along the surface of the tea for a short way, and withdrawing it. Two little whirlpools, or vortices, are then seen moving side by side. They are sections of the half vortex-ring which has been formed in the liquid by the spoon. A second half-ring may be at once sent after them by another stroke of the spoon, and the phenomenon above described will be obtained. "When, on the contrary, two such vortex-rinns meet, their centers moving in one line, they both spread out. and relax their speed indefinitely. This is obtained in a liquid by let ting the half vortex-ring impinge directly on the side of the vessel, when it spreads out, and relaxes its speed; just as if there were no boundary of the fluid, hut a second vortex. ring occupying the place of the image of the first which would be formed by a plane mirror substituted for the side of the vessel. When one vortex-ring impinges obliquely on another, it rebounds from it, and both are thrown into vibration, their form of equi librium being circular. They act in fact in this respect like solid India rubber rings. By forming them from an elliptic Apetture, they are produced in a state of vibration. A square aperture gives them in a different state of vibration.
The impossibility of producing or destroying vortex-rings in a perfect fluid—save by creative power—has led sir W. Thomson (q.v.) to regard the ultimate parts of matter as vortices of various kinds in a perfect fluid.
The word also come into use in connection with Descartes's once celebra ted theory of the universe, given in his Prineipia Philosophic. In this the rotation of the planets about the sun, the satellites about the planets, etc., were explained(!) by the hypothesis of vortices forever whirling about the central body. Descartes was a good mathematician, hut in natural philosophy he preferred metaphysics to experiment, and of course erred enormously. But he is not to be laughed at: mistakes more ridiculous than his are gravely propounded at the present day.