Spinning Tops Part 4

[Ill.u.s.tration: FIG. 50.]

This last as well as the other phenomena of which I have spoken is very suggestive. Here is a magnetic needle (Fig. 49), sometimes called a dipping needle from the way in which it is suspended. If I turn its {111} frame so that it can only move at right angles to the meridian, you see that it points vertically. You may reflect upon the a.n.a.logous properties of this magnetic needle (Fig. 50) and of the gyrostat (Fig. 47); they both, when only capable of moving horizontally, point to the north; and you see that a very frictionless gyrostat might be used as a compa.s.s, or at all events as a corrector of compa.s.ses.[10] I have just put before you another a.n.a.logy, and I want you to understand that, although these are only a.n.a.logies, they are not mere chance a.n.a.logies, for there is undoubtedly a dynamical connection between the magnetic and the gyrostatic phenomena. Magnetism depends on rotatory motion. The molecules of matter are in actual rotation, and a certain allineation of the axes of the rotations produces what we call magnetism. In a steel bar not magnetized the little axes of rotation are all in different directions. The process {112} of magnetization is simply bringing these rotations to be more or less round parallel axes, an allineation of the axes. A honey-combed ma.s.s with a spinning gyrostat in every cell, with all the spinning axes parallel, and the spins in the same direction, would--I was about to say, would be a magnet, but it would not be a magnet in all its properties, and yet it would resemble a magnet in many ways.[11]

[Ill.u.s.tration: FIG. 51.]

[Ill.u.s.tration: FIG. 52.]

Some of you, seeing electromotors and other electric contrivances near this table, may think that they have to do with our theories and explanations of magnetic phenomena. But I must explain that this electromotor which I hold in my hand (Fig. 51) is used by me merely as the {113} most convenient means I could find for the spinning of my tops and gyrostats. On the spindle of the motor is fastened a circular piece of wood; by touching this key I can supply the motor with electric energy, and the wooden disc is now rotating very rapidly. I have only to bring its rim in contact with any of these tops or gyrostats to set them spinning, and you see that I can set half a dozen gyrostats a-spinning in a few seconds; this chain of gyrostats, for instance. Again, this larger motor (Fig. 52), too large to move about in my hand, is fastened to the table, and I have used {114} it to drive my larger contrivances; but you understand that I use these just as a barber might use them to brush your hair, or Sarah Jane to clean the knives, or just as I would use a little steam-engine if it were more convenient for my purpose. It was more convenient for me to bring from London this battery of acc.u.mulators and these motors than to bring sacks of coals, and boilers, and steam-engines. But, indeed, all this has the deeper meaning that we can give to it if we like. Love is as old as the hills, and every day Love's messages are carried by the latest servant of man, the telegraph. These spinning tops were known probably to primeval man, and yet we have not learnt from them more than the most fractional portion of the lesson that they are always sending out to an un.o.bservant world. Toys like these were spun probably by the builders of the Pyramids when they were boys, and here you see them side by side with the very latest of man's contrivances. I feel almost as Mr. Stanley might feel if, with the help of the electric light and a magic-lantern, he described his experiences in that dreadful African forest to the usual company of a London drawing-room.

The phenomena I have been describing to you play such a very important part in nature, that if time admitted I might go on expounding and {115} explaining without finding any great reason to stop at one place rather than another. The time at my disposal allows me to refer to only one other matter, namely, the connection between light and magnetism and the behaviour of spinning tops.

You are all aware that sound takes time to travel. This is a matter of common observation, as one can see a distant woodchopper lift his axe again before one hears the sound of his last stroke. A destructive sea wave is produced on the coast of j.a.pan many hours after an earthquake occurs off the coast of America, the wave motion having taken time to travel across the Pacific. But although light travels more quickly than sound or wave motion in the sea, it does not travel with infinite rapidity, and the appearance of the eclipse of one of Jupiter's satellites is delayed by an observable number of minutes because light takes time to travel. The velocity has been measured by means of such observations, and we know that light travels at the rate of about 187,000 miles per second, or thirty thousand millions of centimetres per second. There is no doubt about this figure being nearly correct, for the velocity of light has been measured in the laboratory by a perfectly independent method.

Now the most interesting physical work done since Newton's time is the outcome of the experiments of Faraday and the theoretical deductions of {116} Thomson and Maxwell. It is the theory that light and radiant heat are simply electro-magnetic disturbances propagated through s.p.a.ce. I dare not do more than just refer to this matter, although it is of enormous importance. I can only say, that of all the observed facts in the sciences of light, electricity, and magnetism, we know of none that is in opposition to Maxwell's theory, and we know of many that support it. The greatest and earliest support that it had was this. If the theory is correct, then a certain electro-magnetic measurement ought to result in exactly the same quant.i.ty as the velocity of light. Now I want you to understand that the electric measurement is one of quant.i.ties that seem to have nothing whatever to do with light, except that one uses one's eyes in making the measurement; it requires the use of a two-foot rule and a magnetic needle, and coils of wire and currents of electricity. It seemed to bear a relations.h.i.+p to the velocity of light, which was not very unlike the fabled connection between Tenterden Steeple and the Goodwin Sands. It is a measurement which it is very difficult to make accurately. A number of skilful experimenters, working independently, and using quite different methods, arrived at results only one of which is as much as five per cent.

different from the observed velocity of light, and some of them, {117} on which the best dependence may be placed, agree exactly with the average value of the measurements of the velocity of light.

There is then a wonderful agreement of the two measurements, but without more explanation than I can give you now, you cannot perhaps understand the importance of this agreement between two seemingly unconnected magnitudes.

At all events we now know, from the work of Professor Hertz in the last two years, that Maxwell's theory is correct, and that light is an electro-magnetic disturbance; and what is more, we know that electro-magnetic disturbances, incomparably slower than red-light or heat, are pa.s.sing now through our bodies; that this now recognized kind of radiation may be reflected and refracted, and yet will pa.s.s through brick and stone walls and foggy atmospheres where light cannot pa.s.s, and that possibly all military and marine and lighthouse signalling may be conducted in the future through the agency of this new and wonderful kind of radiation, of which what we call light is merely one form. Why at this moment, for all I know, two citizens of Leeds may be signalling to each other in this way through half a mile of houses, including this hall in which we are present.[12]

{118}

I mention this, the greatest modern philosophical discovery, because the germ of it, which was published by Thomson in 1856, makes direct reference to the a.n.a.logy between the behaviour of our spinning-tops and magnetic and electrical phenomena. It will be easier, however, for us to consider here a mechanical ill.u.s.tration of the rotation of the plane of polarized light by magnetism which Thomson elaborated in 1874. This phenomenon may, I think, be regarded as the most important of all Faraday's discoveries. It was of enormous scientific importance, because it was made in a direction where a new phenomenon was not even suspected. Of his discovery of induced currents of electricity, to which all electric-lighting companies and transmission of power companies of the present day owe their being, Faraday himself said that it was a natural consequence of the discoveries of an earlier experimenter, Oersted. But this magneto-optic discovery was quite unexpected. I will now describe the phenomenon.

Some of you are aware that when a beam of light is sent through this implement, called a Nichol's Prism, it becomes polarized, or one-sided--that is, all the light that comes through is known to be propagated by vibrations which occur all in one plane. This rope (Fig. 53) hanging from the ceiling {119} ill.u.s.trates the nature of plane polarized light. All points in the rope are vibrating in the same plane. Well, this prism A, Fig. 54, only lets through it light that is polarized in a vertical plane. And here at B I have a similar implement, and I place it so that it also will only allow light to pa.s.s through it which is polarized in a vertical plane. Hence most of the light coming through the polarizer, as the first prism is called, will pa.s.s readily through the a.n.a.lyzer, as the second is called, and I am now letting this light enter my eye. But when I turn the a.n.a.lyzer round through a right angle, I find that I see no light; there was a gradual darkening as I rotated the a.n.a.lyzer. The a.n.a.lyzer will now only allow light to pa.s.s through which is polarized in a horizontal plane, and it receives no such light.

[Ill.u.s.tration: FIG. 53.]

[Ill.u.s.tration: FIG. 54.]

You will see in this model (Fig. 55) a good ill.u.s.tration of polarized light. The white, brilliantly illuminated thread M N is {120} pulled by a weight beyond the pulley M, and its end N is fastened to one limb of a tuning-fork. Some ragged-looking pieces of thread round the portion N A prevent its vibrating in any very determinate way, but from A to M the thread is free from all enc.u.mbrance. A vertical slot at A, through which the thread pa.s.ses, determines the nature of the vibration of the part A B; every part of the thread between A and B is vibrating in up and down directions only. A vertical slot in B allows the vertical vibration to be communicated through it, and so we see the part B M vibrating in the same way as A B. I might point out quite a lot of ways in which this is not a perfect ill.u.s.tration of what occurs with light in Fig. 54. But it is quite good enough for my present purpose. A is a polarizer of vibration; it only allows up and down motion to pa.s.s through it, and B also allows up and down motion to pa.s.s through. But now, as B is turned round, it lets less and less of the up and down motion pa.s.s through it, until when it is in the second position shown in the lower part of the figure, it allows no up and down motion to pa.s.s through, and there is no visible motion of the thread between B and M. You will observe that if we did not know in what plane (in the present case the plane is vertical) the vibrations of the thread between A and B occurred, we should only have to turn B round until we found no vibration {122} pa.s.sing through, to obtain the information. Hence, as in the light case, we may call A a polarizer of vibrations, and B an a.n.a.lyzer.

[Ill.u.s.tration: FIG. 55.]

Now if polarized light is pa.s.sing from A to B (Fig. 54) through the air, say, and we have the a.n.a.lyzer placed so that there is darkness, we find that if we place in the path of the ray some solution of sugar we shall no longer have darkness at B; we must turn B round to get things dark again; this is evidence of the sugar solution having twisted round the plane of polarization of the light. I will now a.s.sume that you know something about what is meant by twisting the plane of polarization of light. You know that sugar solution will do it, and the longer the path of the ray through the sugar, the more twist it gets. This phenomenon is taken advantage of in the sugar industries, to find the strengths of sugar solutions. For the thread ill.u.s.tration I am indebted to Professor Silva.n.u.s Thomson, and the next piece of apparatus which I shall show also belongs to him.

I have here (_see_ Frontispiece) a powerful armour-clad coil, or electro-magnet. There is a central hole through it, through which a beam of light may be pa.s.sed from an electric lamp, and I have a piece of Faraday's heavy gla.s.s nearly filling this hole. I have a polarizer at one end, and an a.n.a.lyzer at the other. You see now that the {123} polarized light pa.s.ses through the heavy gla.s.s and the a.n.a.lyzer, and enters the eye of an observer. I will now turn B until the light no longer pa.s.ses. Until now there has been no magnetism, but I have the means here of producing a most intense magnetic field in the direction in which the ray pa.s.ses, and if your eye were here you would see that there is light pa.s.sing through the a.n.a.lyzer. The magnetism has done something to the light, it has made it capable of pa.s.sing where it could not pa.s.s before. When I turn the a.n.a.lyzer a little I stop the light again, and now I know that what the magnetism did was to convert the gla.s.s into a medium like the sugar, a medium which rotates the plane of polarization of light.

In this experiment you have had to rely upon my personal measurement of the actual rotation produced. But if I insert between the polarizer and a.n.a.lyzer this disc of Professor Silva.n.u.s Thomson's, built up of twenty-four radial pieces of mica, I shall have a means of showing to this audience the actual rotation of the plane of polarization of light. You see now on the screen the light which has pa.s.sed through the a.n.a.lyzer in the form of a cross, and if the cross rotates it is a sign of the rotation of the plane of polarization of the light. By means of this electric key I can create, destroy, and reverse the magnetic {124} field in the gla.s.s. As I create magnetism you see the twisting of the cross; I destroy the magnetism, and it returns to its old position; I create the opposite kind of magnetism, and you see that the cross twists in the opposite way. I hope it is now known to you that magnetism rotates the plane of polarization of light as the solution of sugar did.

[Ill.u.s.tration: FIG. 56.]

[Ill.u.s.tration: FIG. 57.]

As an ill.u.s.tration of what occurs between polarizer and a.n.a.lyzer, look again at this rope (Fig. 53) fastened to the ceiling. I move the bottom end sharply from east to west, and you see that every part of the rope moves from east to west. Can you imagine a rope such that when the bottom end was moved from east to west, a point some yards up moved from east-north-east to west-sou'-west, that a higher point moved from north-east to south-west, and so on, the direction gradually changing for higher and higher points?

Some of you, knowing what I have done, may be able to imagine it. We should have what we want if this rope were a chain of gyrostats such as you see figured in the diagram; gyrostats all spinning in the same way looked at from below, with frictionless hinges between them. Here is such a chain (Fig. 56), one of many that I have tried to use in this way for several years. But although I have often believed that I saw the phenomenon occur in {126} such a chain, I must now confess to repeated failures. The difficulties I have met with are almost altogether mechanical ones. You see that by touching all the gyrostats in succession with this rapidly revolving disc driven by the little electromotor, I can get them all to spin at the same time; but you will notice that what with bad mechanism and bad calculation on my part, and want of skill, the phenomenon is completely masked by wild movements of the gyrostats, the causes of which are better known than capable of rectification. The principle of the action is very visible in this gyrostat suspended as the bob of a pendulum (Fig. 57). You may imagine this to represent a particle of the {127} substance which transmits light in the magnetic field, and you see by the trickling thin stream of sand which falls from it on the paper that it is continually changing the plane of polarization. But I am happy to say that I can show you to-night a really successful ill.u.s.tration of Thomson's principle; it is the very first time that this most suggestive experiment has been shown to an audience. I have a number of double gyrostats (Fig. 58) placed on the same line, joined end to end by short pieces of elastic. Each instrument is supported at its centre of gravity, and it can rotate both in horizontal and in vertical planes.

[Ill.u.s.tration: FIG. 58.]

The end of the vibrating lever A can only get a horizontal motion from my hand, and the motion is transmitted from one gyrostat to the next, until it has travelled to the very end one. Observe that when the gyrostats are not spinning, the motion is {128} everywhere horizontal. Now it is very important not to have any ill.u.s.tration here of a reflected ray of light, and so I have introduced a good deal of friction at all the supports. I will now spin all the gyrostats, and you will observe that when A moves nearly straight horizontally, the next gyrostat moves straight but in a slightly different plane, the second gyrostat moves in another plane, and so on, each gyrostat slightly twisting the plane in which the motion occurs; and you see that the end one does not by any means receive the horizontal motion of A, but a motion nearly vertical. This is a mechanical ill.u.s.tration, the first successful one I have made after many trials, of the effect on light of magnetism. The reason for the action that occurs in this model must be known to everybody who has tried to follow me from the beginning of the lecture.

And you can all see that we have only to imagine that many particles of the gla.s.s are rotating like gyrostats, and that magnetism has partially caused an allineation of their axes, to have a dynamical theory of Faraday's discovery. The magnet twists the plane of polarization, and so does the solution of sugar; but it is found by experiment that the magnet does it indifferently for coming and going, whereas the sugar does it in a way that corresponds with a spiral structure of molecules. You see that in this important {129} particular the gyrostat a.n.a.logue must follow the magnetic method, and not the sugar method. We must regard this model, then, the a.n.a.logue to Faraday's experiment, as giving great support to the idea that magnetism consists of rotation.

I have already exceeded the limits of time usually allowed to a popular lecturer, but you see that I am very far from having exhausted our subject.

I am not quite sure that I have accomplished the object with which I set out. My object was, starting from the very different behaviour of a top when spinning and when not spinning, to show you that the observation of that very common phenomenon, and a determination to understand it, might lead us to understand very much more complex-looking things. There is no lesson which it is more important to learn than this--That it is in the study of every-day facts that all the great discoveries of the future lie.

Three thousand years ago spinning tops were common, but people never studied them. Three thousand years ago people boiled water and made steam, but the steam-engine was unknown to them. They had charcoal and saltpetre and sulphur, but they knew nothing of gunpowder. They saw fossils in rocks, but the wonders of geology were unstudied by them. They had bits of iron and copper, but not one of them thought of any one of the fifty simple {130} ways that are now known to us of combining those known things into a telephone. Why, even the simplest kind of signalling by flags or lanterns was unknown to them, and yet a knowledge of this might have changed the fate of the world on one of the great days of battle that we read about. We look on Nature now in an utterly different way, with a great deal more knowledge, with a great deal more reverence, and with much less unreasoning superst.i.tious fear. And what we are to the people of three thousand years ago, so will be the people of one hundred years hence to us; for indeed the acceleration of the rate of progress in science is itself accelerating. The army of scientific workers gets larger and larger every day, and it is my belief that every unit of the population will be a scientific worker before long. And so we are gradually making time and s.p.a.ce yield to us and obey us. But just think of it! Of all the discoveries of the next hundred years; the things that are unknown to us, but which will be so well known to our descendants that they will sneer at us as utterly ignorant, because these things will seem to them such self-evident facts; I say, of all these things, if one of us to-morrow discovered one of them, he would be regarded as a great discoverer. And yet the children of a hundred years hence will know it: it will be brought home to {131} them perhaps at every footfall, at the flapping of every coat-tail.

Imagine the following question set in a school examination paper of 2090 A.D.--"Can you account for the cra.s.s ignorance of our forefathers in not being able to see from England what their friends were doing in Australia?"[13] Or this--"Messages are being received every minute from our friends on the planet Mars, and are now being answered: how do you account for our ancestors being utterly ignorant that these messages were occasionally sent to them?" Or this--"What metal is as strong compared with steel as steel is compared with lead? and explain why the discovery of it was not made in Sheffield."

But there is one question that our descendants will never ask in accents of jocularity, for to their bitter sorrow every man, woman, and child of them will know the answer, and that question is this--"If our ancestors in the matter of coal economy were not quite as ignorant as a baby who takes a penny {132} as equivalent for a half-crown, why did they waste our coal?

Why did they destroy what never can be replaced?"

My friends, let me conclude by impressing upon you the value of knowledge, and the importance of using every opportunity within your reach to increase your own store of it. Many are the glittering things that seem to compete successfully with it, and to exercise a stronger fascination over human hearts. Wealth and rank, fas.h.i.+on and luxury, power and fame--these fire the ambitions of men, and attract myriads of eager wors.h.i.+ppers; but, believe it, they are but poor things in comparison with knowledge, and have no such pure satisfactions to give as those which it is able to bestow. There is no evil thing under the sun which knowledge, when wielded by an earnest and rightly directed will, may not help to purge out and destroy; and there is no man or woman born into this world who has not been given the capacity, not merely to gather in knowledge for his own improvement and delight, but even to add something, however little, to that general stock of knowledge which is the world's best wealth.

{133}

ARGUMENT.

1. _Introduction_, pages 9-14, showing the importance of the study of spinning-top behaviour.

2. _Quasi-rigidity induced even in flexible and fluid bodies by rapid motion_, 14-21.

Ill.u.s.trations: Top, 14; belt or rope, 14; disc of thin paper, 14; ring of chain, 15; soft hat, 16; drunken man, 16; rotating water, 16; smoke rings, 17; Thomson's Molecular Theory, 19; swimmer caught in an eddy, 20; mining water jet, 20; cased gyrostat, 21.

3. _The nature of this quasi-rigidity in spinning bodies is a resistance to change of direction of the axis of spinning_, 21-30.

Ill.u.s.trations: Cased gyrostat, 21-24; tops, biscuits, hats, thrown into the air, 24-26; quoits, hoops, projectiles from guns, 27; jugglers at the Victoria Music Hall, 26-30; child trundling hoop, man on bicycle, ballet-dancer, the earth pointing to pole star, boy's top, 30.

4. _Study of the crab-like behaviour of a spinning body_, 30-49.

Ill.u.s.trations: Spinning top, 31; cased gyrostat, 32; balanced gyrostat, 33-36; windage of projectiles from {134} rifled guns, 36-38; tilting a hoop or bicycle, turning quickly on horseback, 38; bowls, 39; how to simplify one's observations, 39, 40; the ill.u.s.tration which gives us our simple universal rule, 40-42; testing the rule, 42-44; explanation of precession of gyrostat, 44, 45; precession of common top, 46; precession of overhung top, 46; list of our results given in a wall sheet, 48, 49.

5. _Proof or explanation of our simple universal rule_, 50-54.

Giving two independent rotations to a body, 50, 51; composition of rotations, 52, 53.

6. _Warning that the rule is not, after all, so simple_, 54-66.

Two independent spins given to the earth, 54; centrifugal force, 55; balancing of quick speed machinery, 56, 57; the possible wobbling of the earth, 58; the three princ.i.p.al axes of a body, 59; the free spinning of discs, cones, rods, rings of chain, 60; nodding motion of a gyrostat, 62; of a top, 63; parenthesis about inaccuracy of statement and Rankine's rhyme, 63, 64; further complications in gyrostatic behaviour, 64; strange elastic, jelly-like behaviour, 65; gyrostat on stilts, 66.

7. _Why a gyrostat falls_, 66, 67.

8. _Why a top rises_, 67-74.

General ignorance, 67; Thomson preparing for the mathematical tripos, 68; behaviour of a water-worn stone when spun on a table, 68, 69; parenthesis on technical education, 70; simple explanation of why a top rises, 70-73; behaviour of heterogeneous sphere when spun, 74.