The Project Gutenberg eBook ofSpinning TopsThis ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Spinning TopsAuthor: John PerryRelease date: November 9, 2010 [eBook #34268]Most recently updated: January 7, 2021Language: EnglishCredits: Produced by Chris Curnow, Keith Edkins and the OnlineDistributed Proofreading Team at https://www.pgdp.net (Thisfile was produced from images generously made availableby The Internet Archive)*** START OF THE PROJECT GUTENBERG EBOOK SPINNING TOPS ***
This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.
Title: Spinning TopsAuthor: John PerryRelease date: November 9, 2010 [eBook #34268]Most recently updated: January 7, 2021Language: EnglishCredits: Produced by Chris Curnow, Keith Edkins and the OnlineDistributed Proofreading Team at https://www.pgdp.net (Thisfile was produced from images generously made availableby The Internet Archive)
Title: Spinning Tops
Author: John Perry
Author: John Perry
Release date: November 9, 2010 [eBook #34268]Most recently updated: January 7, 2021
Language: English
Credits: Produced by Chris Curnow, Keith Edkins and the OnlineDistributed Proofreading Team at https://www.pgdp.net (Thisfile was produced from images generously made availableby The Internet Archive)
*** START OF THE PROJECT GUTENBERG EBOOK SPINNING TOPS ***
The Earl of Pembroke to the Abbess of Wilton.
"Go spin, you jade! go spin!"
FrontispieceMAGNETISM, LIGHT, AND MOLECULAR SPINNING TOPS.Page 122.
Page 122.
BY
With an Illustrated Appendix on the Use of Gyrostats.
LONDONSOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE,Northumberland Avenue, W.C.; 43, Queen Victoria Street, E.C.Brighton: 129, North Street.NewYork: E.S.GORHAM.
1910
PUBLISHED UNDER THE DIRECTION OF THE GENERAL LITERATURE COMMITTEE
[Date of last impression, April 1908]
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 ejaculated 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.
JOHN PERRY.
JOHN PERRY.
At a Leeds Board School last week, the master said to his class, "There is to be a meeting of the British Association in Leeds. What is it all about? Who are the members of the British Association? 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 Association 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 otherElectro-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 theVril-yaignorance about the earth's rotation. Their knowledge of mechanics and dynamics was immense; no member attending the meeting of the British Association 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-SaxonKoom-Posherywas 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 neverhaving 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.
TheVril-yaignorance 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 nobody seemed able to spin, and there were others, wellprized objects, often studied in their behaviour and coveted as supremely valuable, that behaved well under the most unscientific treatment. And yet nobody, 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 accumulating 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 ofAsakusa in the Eastern capital of Japan, watching thetedzu-mashidirecting the evolutions of his heavily rimmedKoma. 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 Japan 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 natureare looked upon with tenderness; and perhaps it is from Japan 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 analogous 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 myhand, 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?
Fig. 1Fig. 1.
Here again is a ring of chain which is quite flexible. It seems ridiculous to imagine that thiscould 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).
Fig. 2Fig. 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 mass 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 notehow 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 glass 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.
Fig. 3Fig. 3.[3]
At the round hole in front of this box a rapid motion is given to a small quantity 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 yetto 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 actionsupon one another, and the study of these actions has given rise to Thomson's smoke-ring or vortex theory of the constitution of matter (Fig. 4).
Fig. 4Fig. 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 acuriously 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 quantities of fluid curious properties of elasticity, attraction and repulsion; that each of these entities 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 masses of earth and rock are rapidly disintegratedby 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 brass 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 termprecessionalfor any motion of this kind. Probably you will object more strongly to the great liberty I shall take presently, of saying that the caseprecesseswhen 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.
Fig. 5Fig. 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 doif 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. Andindeed there is a spiritual being inside, what the algebraic people call an impossible quantity, what other mathematicians call "an operator."
Fig. 6Fig. 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 assistant, 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 tothemselves that you onlypretendto 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 nobody 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 whateveras 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.
Fig. 7Fig. 7.
Fig. 8Fig. 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, aswith 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).
Fig. 9Fig. 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 assistant 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.
Fig. 10Fig. 10.
Fig. 11Fig. 11.
I once showed some experiments on spinning tops to a coffee-drinking, tobacco-smoking audience in that most excellent institution, the Victoria Music Hall in London. In that music hall, things are not very different from what they are at any othermusic hall except in beer, wine, and spirits being unobtainable, and in short scientific addresses being occasionally given. Now, I impressed my audience as strongly as I could with the above fact, that if one wants to throw a quoit with certainty as to how it will alight, one gives it a spin; if one wants to throw a hoop or a hat to somebody to catch upon a stick, one gives the hoop or hat a spin; the disinclination of a spinning body to let its axis get altered in direction can always be depended upon. I told them that this was why smooth-bore guns cannot be depended upon for accuracy;[4]that the spin which an ordinary bullet took depended greatly on how it chanced to touch the muzzle as it just left the gun, whereas barrels are now rifled, that is, spiral grooves are now cut inside the barrel of a gun, and excrescences from the bullet or projectile fit into these grooves, so that as it is forced along the barrel of the gun by the explosive force of the powder, it must also spin about its axis. Hence it leaves the gun with a perfectly well-known spinning motion about which there can be no doubt, and we know too that Fig. 10 shows thekind of motion which it has afterwards, for, just like the hat or the biscuit, its spinning axis keeps nearly parallel to itself. Well, this was all I could do, for I am not skilful in throwing hats or quoits. But after my address was finished, and after a young lady in a spangled dress had sung a comic song, two jugglers came upon the stage, and I could not have had better illustrations of the above principle than were given in almost every trick performed by this lady and gentleman. They sent hats, and hoops, and plates, and umbrellas spinning from one to the other. One of them threw a stream of knives into the air, catching them and throwing them up again with perfect precision and my now educated audience shouted with delight, and showed in other unmistakableways that they observed the spin which that juggler gave to every knife as it left his hand, so that he might have a perfect knowledge as to how it would come back to him again (Fig. 11).It struck me with astonishment at the time that, almost without exception, every juggling trick performed that evening was an illustration of the above principle. And now, if you doubt my statement, just ask a child whether its hoop is more likely to tumble down when it is rapidly rolling along, or when it is going very slowly; ask a man on a bicycle to go more and more slowly to see if he keeps his balance better; ask a ballet-dancer how long she could stand on one toe without balancing herself with her arms or a pole, if she were not spinning; ask astronomers how many months would elapse before the earth would point ever so far away from the pole star if it were not spinning; and above all, ask a boy whether his top is as likely to stand upright upon its peg when it is not spinning as when it is spinning.
Fig. 12Fig. 12.
We will now examine more carefully the behaviour of this common top (Fig. 12). It is notspinning, and you observe that it tumbles down at once; it is quite unstable if I leave it resting upright on its peg. But now note that when it is spinning, it not only will remain upright resting on its peg, but if I give it a blow and so disturb its state, it goes circling round with a precessional motion which grows gradually less and less as time goes on, and the top lifts itself to the upright position again. I hope you do not think that time spent in careful observation of a phenomenon of this kind is wasted. Educated observation of the commonest phenomena occurring in our everyday life is never wasted, and I often feel that if workmen, who are the persons most familiar with inorganic nature, could only observe and apply simple scientific laws to their observations, instead of a great discovery every century we should have a great discovery every year. Well, to return to our top; there are two very curious observations to make. Please neglect for a short time the slight wobbling motions that occur. One observation we make is, that the top does not at first bow down in the direction of the blow. If I strike towards the south, the top bows towards the west; if I strike towards the west, the top bows down towards the north. Now the reason of this is known to all scientific men, and the principle underlying the top's behaviour is of very greatimportance in many ways, and I hope to make it clear to you. The second fact, that the top gradually reaches its upright position again, is one known to everybody, but the reason for it is not by any means well known, although I think that you will have no great difficulty in understanding it.
The first phenomenon will be observed in this case which I have already shown you. This case (Fig. 5),with the fly-wheel inside it, is called agyrostat. When I push the case it does not bow down, but slowly turns round. This gyrostat will not exhibit the second phenomenon; it will not rise up again if I manage to get it out of its upright position, but, on the contrary, will go precessing in wider and wider circles, getting further and further away from its upright position.
Fig. 13Fig. 13.
Fig. 14Fig. 14.
The first phenomenon is most easily studied in this balanced gyrostat (Fig. 13). You here see the fly-wheel G in a strong brass frame F, which is supported so that it is free to move about the vertical axis A B, or about the horizontal axis C D. The gyrostat is balanced by a weight W. Observe that I can increase the leverage of W or diminish it by shifting the position of the sleeve at A so that it will tend to either lift or lower the gyrostat, or exactly balance it as it does now. You must observe exactly what it is that we wish to study. If I endeavour to push F downwards, with the end of this stick (Fig. 14), it really moves horizontally to the right; now I push it to the right (Fig. 15), and it only rises; now push it up, and you see that it goes to the left; push it to the left, and it only goes downwards. You will notice that if I clamp the instrument so that it cannot move vertically, it moves at once horizontally; if I prevent mere horizontal motion it readily moves vertically when I push it. Leaving it free asbefore, I will now shift the position of the weight W, so that it tends continually to lift the gyrostat, and of course the instrument does not lift, it moves horizontally with a slow precessional motion. I now again shift the weight W, so that the gyrostat would fall if it were not spinning (Fig. 16), and it now moves horizontally with a slow precessional motion which is in a direction opposed to the last. These phenomena are easily explained, but,as I said before, it is necessary first to observe them carefully. You all know now, vaguely, the fundamental fact. It is that if I try to make a very quickly spinning body change the direction of its axis, the direction of the axis will change, but not in the way I intended. It is even more curious than my countryman's pig, for when he wanted the pig to go to Cork, he had to pretend that he was driving the pig home. His rule was a verysimple one, and we must find a rule for our spinning body, which is rather like a crab, that will only go along the road when you push it sidewise.
Fig. 15Fig. 15.
Fig. 16Fig. 16.[5]
Fig. 10Fig. 10.
As an illustration of this, consider the spinning projectile of Fig. 10. The spin tends to keep its axis always in the same direction. But there is a defect in the arrangement, which you are now in aposition to understand. You see that at A the air must be pressing upon the undersurface A A, and I have to explain that this pressure tends to make the projectile turn itself broadside on to the air. A boat in a current not allowed to move as a whole, but tied at its middle, sets itself broadside on to the current. Observe this disc of cardboard which I drop through the air edgewise, and note how quickly it sets itself broadside on and falls more slowly; and some of you may have thrown over into the water at Aden small pieces of silver for the diving boys, and you are aware that if it were not for this slow falling of the coins with a wobbling motion broadside on, it would be nearly impossible for any diving boy to get possession of them. Now all this is a parenthesis. Thepressure of the air tends to make the projectile turn broadside on, but as the projectile is spinning it does not tilt up, no more than this gyrostat does when I try to tilt it up, it really tilts out of the plane of the diagram, out of the plane of its flight; and only that artillerymen know exactly what it will do, this kind ofwindageof the projectile would give them great trouble.
You will notice that an experienced child when it wants to change the direction of a hoop, just exerts a tilting pressure with its hoop-stick. A man on a bicycle changes his direction by leaning over so as to be out of balance. It is well to remind you, however, that the motion of a bicycle and its rider is not all rotational, so that it is not altogether the analogue of a top or gyrostat. The explanation of the swerving from a straight path when the rider tilts his body, ultimately comes to the same simple principle, Newton's second law of motion, but it is arrived at more readily. It is for the same reason—put briefly, the exercise of a centripetal force—that when one is riding he can materially assist his horse to turn a corner quickly, if he does not mind appearances, by inclining his body towards the side to which he wants to turn; and the more slowly the horse is going the greater is the tendency to turn for a given amount of tilting of one's body. Circus-riders, when galloping in a circle, assist their horses greatly by the position of their bodies; it isnot to save themselves from falling by centrifugal force that they take a position on a horse's back which no riding-master would allow his pupil to imitate; and the respectable riders of this country would not scorn to help their horses in this way to quick turning movements, if they had to chase and collect cattle like American cowboys.
Very good illustrations of change of direction are obtained in playingbowls. You know that a bowl, if it had nobias, that is, if it had no little weight inside it tending to tilt it, would roll along the level bowling-green in a straight path, its speed getting less and less till it stopped. As a matter of fact, however, you know that at the beginning, when it is moving fast, its path is pretty straight, but because it always has bias the path is never quite straight, and it bends more and more rapidly as the speed diminishes. In all our examples the slower the spin the quicker is the precession produced by given tilting forces.
Now close observation will give you a simple rule about the behaviour of a gyrostat. As a matter of fact, all that has been incomprehensible or curious disappears at once, if instead of speaking of this gyrostat as moving up or down, or to the right or left, I speak of its motions about its various axes. It offers no resistance to mere motion of translation. But when I spoke of its movinghorizontally, I ought to have said that it moved about the vertical axis A B (Fig. 13). Again, what I referred to as up and down motion of F is really motion in a vertical plane about the horizontal axis C D. In future, when I speak of trying to give motion to F, think only of the axis about which I try to turn it, and then a little observation will clear the ground.
Fig. 18Fig. 18.
Fig. 17Fig. 17.
Here is a gyrostat (Fig. 17), suspended in gymbals so carefully that neither gravity nor any frictional forces at the pivots constrain it; nothing that I can do to this frame which I hold in my hand will affect the direction of the axis E F of the gyrostat. Observe that I whirl round on my toes like a ballet-dancer while this is in my hand. I move it about in all sorts of ways, but if it was pointing to the pole star at the beginning it remains pointing to the pole star; if it pointed towards the moon at the beginning it still pointstowards the moon. The fact is, that as there is almost no frictional constraint at the pivots there are almost no forces tending to turn the axis of rotation of the gyrostat, and I can only give it motions of translation. But now I will clamp this vertical spindle by means of a screw and repeat my ballet-dance whirl; you will note that I need not whirl round, a very small portion of a whirl is enough to cause this gyrostat (Fig. 18) to set its spinning axis vertical, to set its axis parallel to the vertical axis of rotation which I give it. Now I whirl in the opposite direction, the gyrostat at once turns a somersault, turns completely round and remains again with its axis vertical, and if you were to carefully note the direction of the spinning of thegyrostat, you would find the following rule to be generally true:—Pay no attention to mere translational motion, think only of rotation about axes, and just remember that when you constrain the axis of a spinning body to rotate, it will endeavour to set its own axis parallel to the new axis about which you rotate it; and not only is this the case, but it will endeavour to have the direction of its own spin the same as the direction of the new rotation. I again twirl on my toes, holding this frame, and now I know that to a person looking down upon the gyrostat and me from the ceiling, as I revolved in the direction of the hands of a clock, the gyrostat is spinning in the direction of the hands of a clock; but if I revolve against the clock direction (Fig. 19) the gyrostat tumbles over so as again to be revolving in the same direction as that in which I revolve.
Fig. 19Fig. 19.
This then is the simple rule which will enable you to tell beforehand how a gyrostat will movewhen you try to turn it in any particular direction. You have only to remember that if you continued your effort long enough, the spinning axis would become parallel to your new axis of motion, and the direction of spinning would be the same as the direction of your new turning motion.
Now let me apply my rule to this balanced gyrostat. I shove it, or give it an impulse downwards, but observe that this really means a rotation about the horizontal axis C D (Fig. 13), and hence the gyrostat turns its axis as if it wanted to become parallel to C D. Thus, looking down from above (as shown by Fig. 20), O E was the direction of the spinning axis, O D was the axis about which I endeavoured to move it, and the instantaneous effect was that O E altered to the position O G. A greater impulse of the same kind would have caused the spinning axis instantly to go to O H or O J, whereas an upward opposite impulse would have instantly made the spinning axis point in the direction O K, O L or O M, depending on how great the impulse was and the rate of spinning. When one observes these phenomena for the first time, one says, "I shoved it down, and it moved to the right; I shoved it up, and it moved to the left;" but if the direction of the spin were opposite to what it is, one would say, "I shoved it down, and it moved to the left; I shoved it up, and it moved to the right." The simplestatement in all cases ought to be, "I wanted to rotate it about a new axis, and the effect was to send its spinning axis towards the direction of the new axis." And now if you play with this balanced gyrostat as I am doing, shoving it about in all sorts of ways, you will find the rule to be a correct one, and there is no difficulty in predicting what will happen.
Fig. 20Fig. 20.
If this rule is right, we see at once why precession takes place. I put this gyrostat (Fig. 13) out of balance, and if it were not rotating it would fall downwards; but a force acting downwards really causes the gyrostat to move to the right, and so you see that it is continually moving in this way, for the force is always acting downwards, and the spinning axis is continually chasing the new axes about which gravity tends continually to make it revolve. We see also why it is that if the want of balance is the other way, if gravity tends to lift the gyrostat, the precession is in the opposite direction. And in playing with this gyrostat as I do now, giving it all sorts of pushes, one makes other observations and sees that the above rule simplifies them all; that is, it enables us to remember them. For example, if I use this stick to hurry on the precession, the gyrostat moves in opposition to the force which causes the precession. I am particularly anxious that you should remember this. At present the balance-weight is so placed that the gyrostat would fall if it were not spinning. But it is spinning, and so it precesses. If gravity were greater it would precess faster, and it comes home to us that it is this precession which enables the force of gravity to be inoperative in mere downward motion. You see that if the precession is hurried, it is more than sufficient to balance gravity,and the gyrostat rises. If I retard the precession, it is unable to balance gravity, and the gyrostat falls. If I clamp this vertical axis so that precession is impossible, you will notice that the gyrostat falls just as if it were not spinning. If I clamp the instrument so that it cannot move vertically, you notice how readily I can make it move horizontally; I can set it rotating horizontally like any ordinary body.
In applying our rule to this top, observe that the axis of spinning is the axis E F of the top (Fig. 12). As seen in the figure, gravity is tending to make the top rotate about the axis F D, and the spinning axis in its chase of the axis F D describes a cone in space as it precesses. This gyrostat, which is top-heavy, rotates and precesses in much the same way as the top; that is, if you apply our rule, or use your observation, you will find that to an observer above the table the spinning and precession occur in the same direction, that is, either both with the hands of a watch, or both against the hands of a watch. Whereas, a top like this before you (Fig. 21), supported above its centre of gravity, or the gyrostat here (Fig. 22), which is also supported above its centre of gravity, or the gyrostat shown in Fig. 56, or any other gyrostat supported in such a way that it would be in stable equilibrium if it were not spinning; in all thesecases, to an observer placed above the table, the precession is in a direction opposite to that of the spinning.