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been removed, and its place supplied by a towel tightly stretched. In order to make the air which is to be expelled from this box visible, we charge it first with ammoniacal gas, by sprinkling the bottom of the box with strong solution of ammonia. A certain quantity of ammoniacal gas has now been introduced into it, and we shall develop in addition a quantity of muriatic acid gas. This is done by putting into the box a dish containing common salt, over which I pour sulphuric acid of commerce. These two gases combine, and form solid sal-ammoniac, so that anything visible which escapes from the box is simply particles of sal

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ammoniac, which are so very small that they remain suspended by fluid-friction, like smoke in the air. Now notice the effect of a sudden blow applied to the end of the box opposite the hole. There you see a circular vortex-ring, moving on its own account through the room as if it were an independent solid.

I shall now try to show you the effect of one vortex-ring upon another, just as I showed it here to Thomson, when he at once formed his theory. You notice that when two vortex-rings impinge upon one another, they behave like solid elastic rings. They vibrate vehemently

after the shock, just as if they were solid rings of indiarubber. It is easy, as you now see (shows), to produce such vibration of a vortex-ring without any impact from another. All we have to do is to substitute an elliptical, or even a square, hole for the circular one we have hitherto employed. The circle is the equilibrium form of the simple vortex, and thus, if a simple vortex be produced of other than a circular form, it vibrates about that circular form as about a position of stable equilibrium. Another curious result which, as you see, is easily produced (shows), is to make one vortex-ring pass through another. Helmholtz showed theoretically that if two vortex-rings be moving with their centres in the same line, and their planes perpendicular to that line, then :first-if they are moving in the same direction, the pursuer contracts and moves faster, while the pursued expands and moves slower, so that they alternately penetrate one another :-second-if they are equal and moving in opposite directions, both expand indefinitely and move slower and slower, never reaching one another. In fact, the one behaves to the other like its image in a plane mirror. And this, as you now see, is the fate of a vortex-ring which impinges directly on a plane solid surface.

Now, the first vortex-ring which you saw sailing up through the class-room, contained precisely that particular portion of air, mixed with sal-ammoniac powder, which had been sent out of the box by the blow. It was not merely sal-ammoniac powder which was going through the air, but a certain definite portion of the smoky air, if we so may call it, from the inside of that box, which, in virtue of the vortex-motion which it had, became, as it were, a different substance from the

surrounding air, and moved through it very much like a solid body.

In fact, according to the result of Helmholtz's researches, if the air were a perfect fluid,-if there were no such thing as fluid-friction in air,-that vortex-ring would have gone on moving for ever. Not only so, but the portion of the fluid which contained the smoke, which was, as it were, marked by the smoke, would remain precisely the same set of particles of the fluid as it moved through the rest; so that those which were thus marked by the smoke were, by the fact of their rotation, distinguished or differentiated from all the rest of the particles of air in the room, and could not by any process, except an act of creative power, be made to unite with the fluid in the room.

That is a point which appears to me to be one of the most striking characteristics in the foundation of this suggestion of vortex-atoms. Granted that you have a perfect fluid, you could not produce a vortex-ring in it ; nor, if a vortex-ring were there, could you destroy it. No process at our command could enable us to do either, because in order to do it, fluid-friction is essentially requisite. Now, by the very definition of a perfect fluid, friction does not exist in it.

Thus, if we adopt Sir William Thomson's supposition that the universe is filled with something which we have no right to call ordinary matter (though it must possess inertia), but which we may call a perfect fluid; then, if any portions of it have vortex-motion communicated

1 Of course, in air, fluid-friction, which depends upon diffusion, soon interferes with this state of things. But, in the experiment as shown, the ring (of some six or eight inches in diameter) was not sensibly altered by such causes in the first twenty feet of its path.

to them, they will remain for ever stamped with that vortex-motion; they cannot part with it; it will remain with them as a characteristic for ever, or at least until the creative act which produced it shall take it away again. Thus this property of rotation may be the basis of all that to our senses appeals as matter.

The properties which Helmholtz showed that such a vortex-filament must possess are these-first, that every part of the core of the filament is essentially rotating. A vortex-filament may have infinitely many shapes besides the simple one which I showed you just

Unfortunately it appears impossible for us to form, even with an imperfect fluid like air or water, a vortex-filament of any more complex character than that simple circle. Theoretically, a vortex-filament can exist with any amount of knots and windings upon it, but then unfortunately we cannot devise an aperture by which to allow the smoky air to escape so as to give us such a knotted vortex. If we could devise the requisite form of aperture, and produce the vortex, then so long as the friction of the air did not seriously come into play, that vortex would retain its characteristics as completely as did the circular one which I sent out, and not only that, but it would possess that same elasticity about a definite form of equilibrium which you noticed the circular vortices possessed. They not merely keep their portion of air always in the vortex state, but they also have a definite form, in virtue of which they possess elasticity, so that when the form was altered for a moment by a sudden shock between two of them, each oscillated about its definite form, to which it finally settled down again.

In such a vortex-ring (as you will easily understand

by thinking how it came out of the round hole in the box), the motion of the particles of air is of this kind. Suppose it to be coming forward towards you, then every portion of the air on the inner side of the ring is moving forward, and every portion on the outer side is going backward, so that the whole is turning round and round its linear circular core. The air all about it is in motion according to a simple law which, however, I could not explain without mathematics-except in the particular case of that within the annulus, which is moving forward faster than the ring itself. I shall afford any of you who desire it (after the lecture)

an opportunity of convincing yourselves of the fact. Each of you will find that, if he places his face in the path of one of these large air vortex-rings, there is no sensation whatever until the vortex-ring is almost close to him, and when it reaches him he feels a sudden blast of wind flowing through the centre of it. Thus, this vortex-ring not only involves in itself rotating elements which are thereby distinguished altogether from the other elements of the fluid, but it also is associated necessarily with other movements through the nondifferentiated air, and especially a forward rapid current of air passing through its centre in the direction in which it is going.

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