The fourth dimension

82 THE FOURTH DIMENSION

find the corresponding movement about a plane in four space.

Now, of all the movements which take place in fluids, the most important from a physical point of view is vortex motion.

A vortex is a whirl or eddy—it is shown in the gyrating wreaths of dust seen on a summer day; it is exhibited on a larger scale in the destructive march of a cyclone.

A wheel whirling round will throw off the water on it. But when this circling motion takes place in a liquid itself it is strangely persistent. There is, of course, a certain cohesion between the particles of water by which they mutually impede their motions. But in a liquid devoid of friction, such that every particle is free from lateral cohesion on its path of motion, it can be shown that a vortex or eddy separates from the mass of the fluid a certain portion, which always remain in that vortex.

The shape of the vortex may alter, but it always consists of the same particles of the fluid.

Now, a very remarkable fact about such a vortex is that the ends of the vortex cannot remain suspended and isolated in the fluid. They must always run to the boundary of the fluid. An eddy in water that remains half way down without coming to the top is impossible.

The ends of a vortex must reach the boundary of a fiuid—the boundary may be external or internal—a vortex may exist between two objects in the fluid, terminating one end on each object, the objects being internal boundaries of the fluid. Again, a vortex may have its ends linked together, so that it formsa ring. Circular vortex rings of this description are often seen in puffs of smoke, and that the smoke travels on in the ring is a proof that the vortex always consists of the same particles of ai: