Spinning Tops Part 1

Spinning Tops.

by John Perry.

PREFACE.

This is not the lecture as it was delivered. Instead of two pages of letterpress and a woodcut, the reader may imagine that for half a minute the lecturer played with a spinning top or gyrostat, and occasionally e.j.a.c.u.l.a.t.ed words of warning, admonition, and explanation towards his audience. A verbatim report would make rather uninteresting reading, and I have taken the liberty of trying, by greater fullness of explanation, to make up to the reader for his not having seen the moving apparatus. It has also been necessary in a treatise intended for general readers to simplify the reasoning, the lecture having been delivered to persons whose life experiences peculiarly fitted them for understanding scientific things. An "argument" has been added at the end to make the steps of the reasoning clearer.

JOHN PERRY.

SPINNING TOPS.

At a Leeds Board School last week, the master said to his cla.s.s, "There is to be a meeting of the British a.s.sociation in Leeds. What is it all about?

Who are the members of the British a.s.sociation? What do they do?" There was a long pause. At length it was broken by an intelligent shy boy: "Please, sir, I know--they spin tops!"[1]

Now I am sorry to say that this answer was wrong. The members of the British a.s.sociation and the Operatives of Leeds have neglected top-spinning since they were ten years of age. If more attention were paid to the intelligent examination of the behaviour of tops, there would be greater advances in mechanical engineering and a great many industries. There would be a better general knowledge of astronomy. Geologists would not make mistakes by millions of years, and our knowledge of Light, and Radiant Heat, and other {10} Electro-magnetic Phenomena would extend much more rapidly than it does.

I shall try to show you towards the end of the lecture that the fact of our earth's being a spinning body is one which would make itself known to us even if we lived in subterranean regions like the coming race of an ingenious novelist.[2] It is the greatest and most persistent cause of many of the phenomena which occur around us and beneath us, and it is probable that even Terrestrial Magnetism is almost altogether due to it. Indeed there is only one possible explanation of the _Vril-ya_ ignorance about the earth's rotation. Their knowledge of mechanics and dynamics was immense; no member attending the meeting of the British a.s.sociation can approach them in their knowledge of, I will not say, _Vril_, but even of quite vulgar electricity and magnetism; and yet this great race which expresses so strongly its contempt for Anglo-Saxon _Koom-Poshery_ was actually ignorant of the fact that it had existed for untold generations inside an object that spins about an axis.

Can we imagine for one instant that the children of that race had never spun a top or trundled a hoop, and so had had no chance of being led to the greatest study of nature? No; the only possible explanation lies in the great novelist's never {11} having done these things himself. He had probably as a child a contempt for the study of nature, he was a baby Pelham, and as a man he was condemned to remain in ignorance even of the powers of the new race that he had created.

The _Vril-ya_ ignorance of the behaviour of spinning bodies existing as it does side by side with their deep knowledge of magnetism, becomes even more remarkable when it comes home to us that the phenomena of magnetism and of light are certainly closely connected with the behaviour of spinning bodies, and indeed that a familiar knowledge of the behaviour of such bodies is absolutely necessary for a proper comprehension of most of the phenomena occurring in nature. The instinctive craving to investigate these phenomena seems to manifest itself soon after we are able to talk, and who knows how much of the intellectual inferiority of woman is due to her neglect of the study of spinning tops; but alas, even for boys in the pursuit of top-spinning, the youthful mind and muscle are left with no other guidance than that which is supplied by the experience of young and not very scientific companions. I remember distinctly that there were many puzzling problems presented to me every day. There were tops which n.o.body seemed able to spin, and there were others, well {12} prized objects, often studied in their behaviour and coveted as supremely valuable, that behaved well under the most unscientific treatment. And yet n.o.body, even the makers, seemed to know why one behaved badly and the other well.

I do not disguise from myself the fact that it is rather a difficult task to talk of spinning tops to men who have long lost that skill which they wonder at in their children; that knowingness of touch and handling which gave them once so much power over what I fear to call inanimate nature. A problem which the child gives up as hopeless of solution, is seldom attacked again in maturer years; he drives his desire for knowledge into the obscure lumber-closets of his mind, and there it lies, with the acc.u.mulating dust of his life, a neglected and almost forgotten instinct.

Some of you may think that this instinct only remains with those minds so many of which are childish even to the limit of life's span; and probably none of you have had the opportunity of seeing how the old dust rubs off from the life of the ordinary man, and the old desire comes back to him to understand the mysteries that surround him.

But I have not only felt this desire myself, I have seen it in the excited eyes of the crowd of people who stand by the hour under the dropping cherry-blossoms beside the red-pillared temple of {13} Asakusa in the Eastern capital of j.a.pan, watching the _tedzu-mashi_ directing the evolutions of his heavily rimmed _Koma_. First he throws away from him his great top obliquely into the air and catches it spinning on the end of a stick, or the point of a sword, or any other convenient implement; he now sends it about quite carelessly, catching it as it comes back to him from all sorts of directions; he makes it run up the hand-rail of a staircase into a house by the door and out again by the window; he makes it travel up a great corkscrew. Now he seizes it in his hands, and with a few dexterous twists gives it a new stock of spinning energy. He makes it travel along a stretched string or the edge of a sword; he does all sorts of other curious things with his tops, and suddenly sinks from his masterful position to beg for a few coppers at the end of his performance.

How tame all this must seem to you who more than half forget your childish initiation into the mysteries of nature; but trust me, if I could only make that old top-spinner perform those magical operations of his on this platform, the delight of the enjoyment of beautiful motion would come back.

Perhaps it is only in j.a.pan that such an exhibition is possible; the land where the waving bamboo, and the circling hawk, and the undulating summer sea, and every beautiful motion of nature {14} are looked upon with tenderness; and perhaps it is from j.a.pan that we shall learn the development of our childish enthusiasm.

The devotees of the new emotional art of beautiful motion and changing colour are still in the main beggars like Homer, and they live in garrets like Johnson and Savage; but the dawn of a new era is heralded, or rather the dawn has already come, for Sir William Thomson's achievements in the study of spinning tops rank already as by no means the meanest of his great career.

If you will only think of it, the behaviour of the commonest spinning top is very wonderful. When not spinning you see that it falls down at once, I find it impossible to balance it on its peg; but what a very different object it is when spinning; you see that it not only does not fall down, it offers a strange resistance when I strike it, and actually lifts itself more and more to an upright position. Once started on scientific observation, nature gives us facts of an a.n.a.logous kind in great plenty.

Those of you who have observed a rapidly moving heavy belt or rope, know that rapid motion gives a peculiar quasi-rigidity to flexible and even to fluid things.

Here, for example, is a disc of quite thin paper (Fig. 1), and when I set it in rapid rotation you observe that it resists the force exerted by my {15} hand, the blow of my fist, as if it were a disc of steel. Hear how it resounds when I strike it with a stick. Where has its flexibility gone?

[Ill.u.s.tration: FIG. 1.]

Here again is a ring of chain which is quite flexible. It seems ridiculous to imagine that this {16} could be made to stand up like a stiff hoop, and yet you observe that when I give it a rapid rotation on this mandril and let it slide off upon the table, it runs over the table just as if it were a rigid ring, and when it drops on the floor it rebounds like a boy's hoop (Fig. 2).

[Ill.u.s.tration: FIG. 2.]

Here again is a very soft hat, specially made for this sort of experiment.

You will note that it collapses to the table in a shapeless ma.s.s when I lay it down, and seems quite incapable of resisting forces which tend to alter its shape. In fact, there is almost a complete absence of rigidity; but when this is spun on the end of a stick, first note {17} how it has taken a very easily defined shape; secondly, note how it runs along the table as if it were made of steel; thirdly, note how all at once it collapses again into a shapeless heap of soft material when its rapid motion has ceased.

Even so you will see that when a drunken man is not leaning against a wall or lamp-post, he feels that his only chance of escape from ignominious collapse is to get up a decent rate of speed, to obtain a quasi-sobriety of demeanour by rapidity of motion.

The water inside this gla.s.s vessel (Fig. 3) is in a state of rapid motion, revolving with the vessel itself. Now observe the piece of paraffin wax A immersed in the water, and you will see when I push at it with a rod that it vibrates just as if it were surrounded with a thick jelly. Let us now apply Prof. Fitzgerald's improvement on this experiment of Sir William Thomson's. Here is a disc B stuck on the end of the rod; observe that when I introduce it, although it does not touch A, A is repelled from the disc.

Now observe that when I twirl the disc it seems to attract A.

[Ill.u.s.tration: FIG. 3.[3]]

At the round hole in front of this box a rapid motion is given to a small quant.i.ty of air which is mixed with smoke that you may see it. That smoke-ring moves through the air almost like a solid body for a considerable distance unchanged, and I am not sure that it may not be possible yet {18} to send as a projectile a huge poisoned smoke-ring, so that it may destroy or stupefy an army miles away. Remember that it is really the same air all the time. You will observe that two smoke rings sent from two boxes have curious actions {19} upon one another, and the study of these actions has given rise to Thomson's smoke-ring or vortex theory of the const.i.tution of matter (Fig. 4).

[Ill.u.s.tration: FIG. 4.]

It was Rankine, the great guide of all engineers, who first suggested the idea of molecular vortices in his explanations of heat phenomena and the phenomena of elasticity--the idea that every particle of matter is like a little spinning top; but I am now speaking of Thomson's theory. To imagine that an atom of matter is merely a {20} curiously shaped smoke-ring formed miraculously in a perfect fluid, and which can never undergo permanent alteration, looks to be a very curious and far-fetched hypothesis. But in spite of certain difficulties, it is the foundation of the theory which will best explain most of the molecular phenomena observed by philosophers.

Whatever be the value of the theory, you see from these experiments that motion does give to small quant.i.ties of fluid curious properties of elasticity, attraction and repulsion; that each of these ent.i.ties refuses to be cut in two; that you cannot bring a knife even near the smoke-ring; and that what may be called a collision between two of them is not very different in any way from the collision between two rings of india-rubber.

Another example of the rigidity given to a fluid by rapid motion, is the feeling of utter helplessness which even the strongest swimmers sometimes experience when they get caught in an eddy underneath the water.

I could, if I liked, multiply these instances of the quasi-rigidity which mere motion gives to flexible or fluid bodies. In Nevada a jet of water like the jet from a fireman's hose, except that it is much more rapid, which is nearly as easily projected in different directions, is used in mining, and huge ma.s.ses of earth and rock are rapidly disintegrated {21} by the running water, which seems to be rather like a bar of steel than a jet of water in its rigidity.

It is, however, probable that you will take more interest in this box of bra.s.s which I hold in my hands. You see nothing moving, but really, inside this case there is a fly-wheel revolving rapidly. Observe that I rest this case on the table on its sharp edge, a sort of skate, and it does not tumble down as an ordinary box would do, or as this box will do after a while, when its contents come to rest. Observe that I can strike it violent blows, and it does not seem to budge from its vertical position; it turns itself just a little round, but does not get tilted, however hard I strike it. Observe that if I do get it tilted a little it does not fall down, but slowly turns with what is called a precessional motion (Fig. 5).

You will, I hope, allow me, all through this lecture, to use the term _precessional_ for any motion of this kind. Probably you will object more strongly to the great liberty I shall take presently, of saying that the case _precesses_ when it has this kind of motion; but I really have almost no option in the matter, as I must use some verb, and I have no time to invent a less barbarous one.

[Ill.u.s.tration: FIG. 5.]

When I hold this box in my hands (Fig. 6), I find that if I move it with a motion of mere translation in any direction, it feels just as it would do {22} if its contents were at rest, but if I try to turn it in my hands I find the most curious great resistance to such a motion. The result is that when you hold this in your hands, its readiness to move so long as it is not turned round, and its great resistance to turning round, and its unexpected tendency to turn in a different way from that in which you try to turn it, give one the most uncanny sensations. It seems almost as if an invisible being had hold of the box and exercised forces capriciously. And {23} indeed there is a spiritual being inside, what the algebraic people call an impossible quant.i.ty, what other mathematicians call "an operator."

[Ill.u.s.tration: FIG. 6.]

Nearly all the experiments, even the tops and other apparatus you have seen or will see to-night, have been arranged and made by my enthusiastic a.s.sistant, Mr. Shepherd. The following experiment is not only his in arrangement; even the idea of it is his. He said, you may grin and contort your body with that large gyrostat in your hands, but many of your audience will simply say to {24} themselves that you only _pretend_ to find a difficulty in turning the gyrostat. So he arranged this pivoted table for me to stand upon, and you will observe that when I now try to turn the gyrostat, it will not turn; however I may exert myself, it keeps pointing to that particular corner of the room, and all my efforts only result in turning round my own body and the table, but not the gyrostat.

Now you will find that in every case this box only resists having the axis of revolution of its hidden flywheel turned round, and if you are interested in the matter and make a few observations, you will soon see that every spinning body like the fly-wheel inside this case resists more or less the change of direction of its spinning axis. When the fly-wheels of steam-engines and dynamo machines and other quick speed machines are rotating on board ship, you may be quite sure that they offer a greater resistance to the pitching or rolling or turning of the ship, or any other motion which tends to turn their axes in direction, than when they are not rotating.

Here is a top lying on a plate, and I throw it up into the air; you will observe that its motion is very difficult to follow, and n.o.body could predict, before it falls, exactly how it will alight on the plate; it may come down peg-end foremost, or hindmost, or sideways. But when I spin it (Fig. 7), and now throw it up into the air, there is no doubt whatever {25} as to how it will come down. The spinning axis keeps parallel to itself, and I can throw the top up time after time, without disturbing much the spinning motion.

[Ill.u.s.tration: FIG. 7.]

[Ill.u.s.tration: FIG. 8.]

If I pitch up this biscuit, you will observe that I can have no certainty as to how it will come down, but if I give it a spin before it leaves my hand there is no doubt whatever (Fig. 8). Here is a hat. I throw it up, and I cannot be sure as to how it will move, but if I give it a spin, you see that, as {26} with the top and the biscuit, the axis about which the spinning takes place keeps parallel to itself, and we have perfect certainty as to the hat's alighting on the ground brim downwards (Fig. 9).

[Ill.u.s.tration: FIG. 9.]

I need not again bring before you the very soft hat to which we gave a quasi-rigidity a few minutes ago; but you will remember that my a.s.sistant sent that off like a projectile through the air when it was spinning, and that it kept its spinning axis parallel to itself just like this more rigid hat and the biscuit.

[Ill.u.s.tration: FIG. 10.]