Fig. 40Fig. 40.
Imagine the earth to be stationary, and the sun and moon revolving round it. It was Gauss who found that the present action is the same as if the masses of the moon and sun were distributed allround their orbits. For instance, imagine the moon's mass distributed over her orbit in the form of a rigid ring of 480,000 miles diameter, and imagine less of it to exist where the present speed is greater, so that the ring would be thicker at the moon's apogee, and thinner at the perigee. Such a ring round the earth would be similar to Saturn's rings, which have also a precession of nodes, only Saturn's rings are not rigid, else there would be no equilibrium. Now if we leave out of account the earth and imagine this ring to exist by itself, and that its centre simply had a motion round the sun in a year, since it makes an angle of 5½° with the ecliptic it would vibrate into the ecliptic till it made the same angle on the other side and back again. But it revolves once about its centre in twenty-seven solar days, eight hours, and it will no longer swing like a ship in a ground-swell, but will get a motion of precession opposed in direction to its own revolution. As the ring's motion is against the hands of a watch, looking from the north down on the ecliptic, this retrogression of the moon's nodes is in the direction of the hands of a watch. It is exactly the same sort of phenomenon as the precession of the equinoxes, only with a much shorter period of 6798 days instead of 25,866 years.
I told you how, if we knew the moon's mass or the sun's, we could tell the amount of the forces, orthe torque as it is more properly called, with which it tries to tilt the earth. We know the rate at which the earth is spinning, and we have observed the precessional motion. Now when we follow up the method which I have sketched already, we find that the precessional velocity of a spinning body ought to be equal to the torque divided by the spinning velocity and by the moment of inertia[7]of the body about the polar axis. Hence the greater the tilting forces, and the less the spin and the less the moment of inertia, the greater is the precessional speed. Given all of these elements except one, it is easy to calculate that unknown element. Usually what we aim at in such a calculation is the determination of the moon's mass, as this phenomenon of precession and the action of the tides are the only two natural phenomena which have as yet enabled the moon's mass to be calculated.
I do not mean to apologize to you for the introduction of such terms asMoment of Inertia, nor do I mean to explain them. In this lecture I have avoided, as much as I could, the introduction of mathematical expressions and the use of technical terms. But I want you tounderstand that I am not afraid to introduce technical terms when giving a popular lecture. If there is any offence in such a practice, it must, in my opinion, be greatly aggravated by the addition of explanations of the precise meanings of such terms. The use of a correct technical term serves several useful purposes. First, it gives some satisfaction to the lecturer, as it enables him to state, very concisely, something which satisfies his own weak inclination to have his reasoning complete, but which he luckily has not time to trouble his audience with. Second, it corrects the universal belief of all popular audiences that they know everything now that can be said on the subject. Third, it teaches everybody, including the lecturer, that there is nothing lost and often a great deal gained by the adoption of a casual method of skipping when one is working up a new subject.
Some years ago it was argued that if the earth were a shell filled with liquid, if this liquid were quite frictionless, then the moment of inertia of the shell is allthatwe should have to take into account in considering precession, and that if it were viscous the precession would very soon disappear altogether. To illustrate the effect of the moment of inertia, I have hung up here a number of glasses—oneafilled with sand, anotherbwith treacle, a thirdcwith oil, the fourthdwith water,
Fig. 41Fig. 41.
and the fiftheis empty (Fig. 41). You see that if I twist these suspending wires and release them, a vibratory motion is set up, just like that of the balance of a watch. Observe that the glass with water vibrates quickly, its effective moment of inertia being merely that of the glass itself, and you see that the time of swing is pretty much the same as that of the empty glass; that is, the water does not seem to move with the glass. Observe that the vibration goes on for a fairly long time.
The glass with sand vibrates slowly; here there is great moment of inertia, as the sand and glass behave like one rigid body, and again the vibration goes on for a long time.
In the oil and treacle, however, there are longer periods of vibration than in the case of the water or empty glass, and less than would be the case if the vibrating bodies were all rigid, but the vibrations are stilled more rapidly because of friction.
Boiled (f) and unboiled (g) eggs suspended from wires in the same way will exhibit the same differences in the behaviour of bodies, one of which is rigid and the other liquid inside; you see how much slower an oscillation the boiled has than the unboiled.
Even on the table here it is easy to show the difference between boiled and unboiled eggs.Roll them both; you see that one of them stops much sooner than the other; it is the unboiled one that stops sooner, because of its internal friction.
I must ask you to observe carefully the following very distinctive test of whether an egg is boiled or not. I roll the egg or spin it, and then place my finger on it just for an instant; long enough to stop the motion of the shell. You see that the boiled egg had quite finished its motion, but the unboiled egg's shell alone was stopped; the liquid inside goes on moving, and now renews the motion of the shell when I take my finger away.
It was argued that if the earth were fluid inside, the effective moment of inertia of the shell being comparatively small, and having, as we see in these examples, nothing whatever to do with the moment of inertia of the liquid, the precessional motion of the earth ought to be enormously quicker than it is. This was used as an argument against the idea of the earth's being fluid inside.
We know that the observed half-yearly and half-monthly changes of the precession of the earth would be much greater than they are if the earth were a rigid shell containing much liquid, and if the shell were not nearly infinitely rigid the phenomena of the tides would not occur, but in regard to the general precession of the earth there is nowno doubt that the old line of argument was wrong. Even if the earth were liquid inside, it spins so rapidly that it would behave like a rigid body in regard to such a slow phenomenon as precession of the equinoxes. In fact, in the older line of argument the important fact was lost sight of, that rapid rotation can give to even liquids a quasi-rigidity. Now here (Fig. 42a) is a hollow brass top filled with water. The frame is light, and the water inside has much more mass than the outside frame, and if you test this carefully you will find that the top spins in almost exactly the same way as if the water were quite rigid; in fact, as if the whole top were rigid. Here you see it spinning and precessing just like any rigid top. This top, I know, is not filled with water, it is only partially filled; but whether partially or wholly filled it spins very much like a rigid top.
Fig. 42Fig. 42.
This is not the case with a long hollow brass top with water inside. I told you that all bodies have one axis about which they prefer to rotate. The outside metal part of a top behaves in a way that is now well known to you; the friction of its peg on the table compels it to get up on its longer axis. But the fluid inside a top is not constrained to spin on its longer axis of figure, and as it prefers its shorter axis like all these bodies I showed you, it spins in its own way, and by friction and pressure against the case constrains the case to spin about the shorter axis, annulling completely the tendency of the outside part to rise or keep up on its long axis. Hence it is found to be simply impossible to spin a long hollow top when filled with water.
Fig. 44Fig. 44.
Fig. 43Fig. 43.
Here, for example, is one (Fig. 42b) that only differs from the last in being longer. It is filled, or partially filled, with water, and you observe that ifI slowly get up a great spin when it is mounted in this frame, and I let it out on the table as I did the other one, this one lies down at once and refuses to spin on its peg. This difference of behaviour is most remarkable in the two hollow tops you see before you (Fig. 43). They are both nearly spherical, both filled with water. They look so nearly alike that few persons among the audience are able to detect any difference in their shape. But one of them (a) is really slightly oblate like an orange, and the other (b) is slightly prolate like a lemon. I will give them both a gradually increasing rotation in this frame(Fig. 44) for a time sufficient to insure the rotation of the water inside. When just about to be set free to move like ordinary tops on the table, water and brass are moving like the parts of a rigid top. You see that the orange-shaped one continues to spin and precess, and gets itself upright when disturbed, like an ordinary rigid top; indeed I have seldom seen a better behaved top; whereas the lemon-shaped one lies down on its side at once, and quickly ceases to move in any way.
Fig. 45Fig. 45.
And now you will be able to appreciate a fourth test of a boiled egg, which is much more easily seen by a large audience than the last. Here is the unboiled one (Fig. 45b). I try my best to spin it as it lies on the table, but you see that I cannot give it much spin, and so there is nothing of any importance to look at. But you observe that it is quite easy to spin the boiledegg, and that for reasons now well known to you it behaves like the stones that Thomson spun on the sea-beach; it gets up on its longer axis, a very pretty object for our educated eyes to look at (Fig. 45a). You are all aware, from the behaviour of the lemon-shaped top, that even if, by the use of a whirling table suddenly stopped, or by any other contrivance, I could get up a spin in this unboiled egg, it would never make the slightest effort to rise on its end and spin about its longer axis.
I hope you don't think that I have been speaking too long about astronomical matters, for there is one other important thing connected with astronomy that I must speak of. You see, I have had almost nothing practically to do with astronomy, and hence I have a strong interest in the subject. It is very curious, but quite true, that men practically engaged in any pursuit are almost unable to see the romance of it. This is what the imaginative outsider sees. But the overworked astronomer has a different point of view. As soon as it becomes one's duty to do a thing, and it is part of one's every-day work, the thing loses a great deal of its interest. We have been told by a great American philosopher that the only coachmen who ever saw the romance of coach-driving are those titled individuals who pay nowadays so largely for theprivilege. In almost any branch of engineering you will find that if any invention is made it is made by an outsider; by some one who comes to the study of the subject with a fresh mind. Who ever heard of an old inhabitant of Japan or Peru writing an interesting book about those countries? At the end of two years' residence he sees only the most familiar things when he takes his walks abroad, and he feels unmitigated contempt for the ingenuous globe-trotter who writes a book about the country after a month's travel over the most beaten tracks in it. Now the experienced astronomer has forgotten the difficulties of his predecessors and the doubts of outsiders. It is a long time since he felt that awe in gazing at a starry sky that we outsiders feel when we learn of the sizes and distances apart of the hosts of heaven. He speaks quite coolly of millions of years, and is nearly as callous when he refers to the ancient history of humanity on our planet as a weather-beaten geologist. The reason is obvious. Most of you know that theNautical Almanacis as a literary production one of the most uninteresting works of reference in existence. It is even more disconnected than a dictionary, and I should think that preparing census-tables must be ever so much more romantic as an occupation than preparing the tables of theNautical Almanac. And yeta particular figure, one of millions set down by an overworked calculator, may have all the tragic importance of life or death to the crew and passengers of a ship, when it is heading for safety or heading for the rocks under the mandate of that single printed character.
But this may not be a fair sort of criticism. I so seldom deal with astronomical matters, I know so little of the wear and tear and monotony of the every-day life of the astronomer, that I do not even know that the above facts are specially true about astronomers. I only know that they are very likely to be true because they are true of other professional men.
I am happy to say that I come in contact with all sorts and conditions of men, and among others, with some men who deny many of the things taught in our earliest school-books. For example, that the earth is round, or that the earth revolves, or that Frenchmen speak a language different from ours. Now no man who has been to sea will deny the roundness of the earth, however greatly he may wonder at it; and no man who has been to France will deny that the French language is different from ours; but many men who learnt about the rotation of the earth in their school-days, and have had a plentiful opportunity of observing the heavenly bodies, deny the rotation of the earth.They tell you that the stars and moon are revolving about the earth, for they see them revolving night after night, and the sun revolves about the earth, for they see it do so every day. And really if you think of it, it is not so easy to prove the revolution of the earth. By the help of good telescopes and the electric telegraph or good chronometers, it is easy to show from the want of parallax in stars that they must be very far away; but after all, we only know that either the earth revolves or else the sky revolves.[8]Of course, it seems infinitely more likely that the small earth should revolve than that the whole heavenly host should turn about the earth as a centre, and infinite likelihood is really absolute proof. Yet there is nobody who does not welcome an independent kind of proof. The phenomena of the tides, and nearly every new astronomical fact, may be said to be an addition to the proof. Still there is the absence of perfect certainty, and when we are told that these spinning-top phenomena give us a real proof of the rotation of the earth without our leaving the room, we welcomeit, even although we may sneer at it as unnecessary after we have obtained it.
Fig. 17Fig. 17.
You know that a gyrostat suspended with perfect freedom about axes, which all pass through its centre of gravity, maintains a constant direction in space however its support may be carried. Its axis is not forced to alter its direction in any way. Now this gyrostat (Fig. 17) has not the perfect absence of friction at its axes of which I speak, and even the slightest friction will produce some constraint which is injurious to the experiment I am about to describe. It must be remembered, that if there were absolutely no constraint, then, even if thegyrostat werenotspinning, its axis would keep a constant direction in space. But the spinning gyrostat shows its superiority in this, that any constraint due to friction is less powerful in altering the axis. The greater the spin, then, the better able are we to disregard effects due to friction. You have seen for yourselves the effect of carrying this gyrostat about in all sorts of ways—first, when it is not spinning and friction causes quite a large departure from constancy of direction of the axis; second, when it is spinning, and you see that although there is now the same friction as before, and I try to disturb the instrument more than before, the axis remains sensibly parallel to itself all the time. Now when this instrument is supported by the table it is really being carried round by the earth in its daily rotation. If the axis kept its direction perfectly, and it were now pointing horizontally due east, six hours after this it will point towards the north, but inclining downwards, six hours afterwards it will point due west horizontally, and after one revolution of the earth it will again point as it does now. Suppose I try the experiment, and I see that it points due east now in this room, and after a time it points due west, and yet I know that the gyrostat is constantly pointing in the same direction in space all the time, surely it is obvious that the room mustbe turning round in space. Suppose it points to the pole star now, in six hours, or twelve, or eighteen, or twenty-four, it will still point to the pole star.
Now it is not easy to obtain so frictionless a gyrostat that it will maintain a good spin for such a length of time as will enable the rotation of the room to be made visible to an audience. But I will describe to you how forty years ago it was proved in a laboratory that the earth turns on its axis. This experiment is usually connected with the name of Foucault, the same philosopher who with Fizeau showed how in a laboratory we can measure the velocity of light, and therefore measure the distance of the sun. It was suggested by Mr. Lang of Edinburgh in 1836, although only carried out in 1852 by Foucault. By these experiments, if you were placed on a body from which you could see no stars or other outside objects, say that you were living in underground regions, you could discover—first, whether there is a motion of rotation, and the amount of it; second, the meridian line or the direction of the true north; third, your latitude. Obtain a gyrostat like this (Fig. 46) but much larger, and far more frictionlessly suspended, so that it is free to move vertically or horizontally. For the vertical motion your gymbal pivots ought to be hard steel knife-edges.
Fig. 46Fig. 46.
As for the horizontal freedom, Foucault used a fine steel wire. Let there be a fine scale engraved crosswise on the outer gymbal ring, and try to discover if it moves horizontally by means of a microscope with cross wires. When this is carefully done we find that there is a motion,but this is not the motion of the gyrostat, it is the motion of the microscope. In fact, the microscope and all other objects in the room are going round the gyrostat frame.
Now let us consider what occurs. The room is rotating about the earth's axis, and we know the rate of rotation; but we only want to know for our present purpose how much of the total rotation is about a vertical line in the room. If the room were at the North Pole, the whole rotation would be about the vertical line. If the room were at the equator, none of its rotation would be about a vertical line. In our latitude now, the horizontal rate of rotation about a vertical axis is about four-fifths of the whole rate of rotation of the earth on its axis, and this is the amount that would be measured by our microscope. This experiment would give no result at a place on the equator, but in our latitude you would have a laboratory proof of the rotation of the earth. Foucault made the measurements with great accuracy.
If you now clamp the frame, and allow the spinning axis to have no motion except in a horizontal plane, the motion which the earth tends to give it about a vertical axis cannot now affect the gyrostat, but the earth constrains it to move about an axis due north and south, and consequently the spinning axis tries to put itself parallelto the north and south direction (Fig. 47). Hence with such an instrument it is easy to find the true north. If there were absolutely no friction the instrument would vibrate about the true north position like the compass needle (Fig. 50), although with an exceedingly slow swing.
Fig. 47Fig. 47.
It is with a curious mixture of feelings that one first recognizes the fact that all rotating bodies, fly-wheels of steam-engines and the like, are always tending to turn themselves towards the pole star; gently and vainly tugging at their foundationsto get round towards the object of their adoration all the time they are in motion.
Fig. 48Fig. 48.
Now we have found the meridian as in Fig. 47, we can begin a third experiment. Prevent motion horizontally, that is, about a vertical axis, but give the instrument freedom to move vertically in the meridian, like a transit instrument in an observatoryabout its horizontal axis. Its revolution with the earth will tend to make it change its angular position, and therefore it places itself parallel to the earth's axis; when in this position the daily rotation no longer causes any change in its direction in space, so it continues to point to the pole star (Fig. 48). It would be an interesting experiment to measure with a delicate chemical balance the force with which the axis raises itself, and in this wayweighthe rotational motion of the earth.[9]
Now let us turn the frame of the instrument G B round a right angle, so that the spinning axis can only move in a plane at right angles to the meridian; obviously it is constrained by the vertical component of the earth's rotation, and points vertically downwards.
Fig. 50Fig. 50.
Fig. 49Fig. 49.
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 itsframe so that it can only move at right angles to the meridian, you see that it points vertically. You may reflect upon the analogous 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 compass, or at all events as a corrector of compasses.[10]I have just put before you another analogy, and I want you to understand that, although these are only analogies, they are not mere chance analogies, 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 processof magnetization is simply bringing these rotations to be more or less round parallel axes, an allineation of the axes. A honey-combed mass 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]
Fig. 51Fig. 51.
Fig. 52Fig. 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 themost 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 usedit 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 accumulators 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 unobservant 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 andexplaining 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 Japan 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 ofThomson and Maxwell. It is the theory that light and radiant heat are simply electro-magnetic disturbances propagated through space. 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 quantity as the velocity of light. Now I want you to understand that the electric measurement is one of quantities 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 relationship 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,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 passing now through our bodies; that this now recognized kind of radiation may be reflected and refracted, and yet will pass through brick and stone walls and foggy atmospheres where light cannot pass, 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]
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 analogy between the behaviour of our spinning-tops and magnetic and electrical phenomena. It will be easier, however, for us to consider here a mechanical illustration 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 ceilingillustrates 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 pass 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 pass readily through the analyzer, as the second is called, and I am now letting this light enter my eye. But when I turn the analyzer round through a right angle, I find that I see no light; there was a gradual darkening as I rotated the analyzer. The analyzer will now only allow light to pass through which is polarized in a horizontal plane, and it receives no such light.
Fig. 53Fig. 53.
Fig. 54Fig. 54.
You will see in this model (Fig. 55) a good illustration of polarized light. The white, brilliantly illuminated thread M N ispulled 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 encumbrance. A vertical slot at A, through which the thread passes, 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 illustration 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 pass through it, and B also allows up and down motion to pass through. But now, as B is turned round, it lets less and less of the up and down motion pass 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 pass 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 vibrationpassing through, to obtain the information. Hence, as in the light case, we may call A a polarizer of vibrations, and B an analyzer.
Fig. 55Fig. 55.
Now if polarized light is passing from A to B (Fig. 54) through the air, say, and we have the analyzer 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 assume 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 illustration I am indebted to Professor Silvanus Thomson, and the next piece of apparatus which I shall show also belongs to him.
I have here (seeFrontispiece) a powerful armour-clad coil, or electro-magnet. There is a central hole through it, through which a beam of light may be passed from an electric lamp, and I have a piece of Faraday's heavy glass nearly filling this hole. I have a polarizer at one end, and an analyzer at the other. You see now that thepolarized light passes through the heavy glass and the analyzer, and enters the eye of an observer. I will now turn B until the light no longer passes. 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 passes, and if your eye were here you would see that there is light passing through the analyzer. The magnetism has done something to the light, it has made it capable of passing where it could not pass before. When I turn the analyzer a little I stop the light again, and now I know that what the magnetism did was to convert the glass 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 analyzer this disc of Professor Silvanus 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 passed through the analyzer 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 magneticfield in the glass. 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.
Fig. 56Fig. 56.
Fig. 57Fig. 57.
As an illustration of what occurs between polarizer and analyzer, 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 insuch 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 thesubstance 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 illustration 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.
Fig. 58Fig. 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 iseverywhere horizontal. Now it is very important not to have any illustration 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 illustration, 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 glass 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 importantparticular the gyrostat analogue must follow the magnetic method, and not the sugar method. We must regard this model, then, the analogue 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 simpleways 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 superstitious 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 space 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 tothem perhaps at every footfall, at the flapping of every coat-tail.
Imagine the following question set in a school examination paper of 2090A.D.—"Can you account for the crass 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 pennyas 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, fashion and luxury, power and fame—these fire the ambitions of men, and attract myriads of eager worshippers; 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.
1.Introduction, pages9-14, 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.Illustrations: 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.Illustrations: 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.Illustrations: Spinning top,31; cased gyrostat,32; balanced gyrostat,33-36; windage of projectiles fromrifled guns,36-38; tilting a hoop or bicycle, turning quickly on horseback,38; bowls,39; how to simplify one's observations,39,40; the illustration 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 principal 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,74.9.Precessional motion of the earth,74-91.Its nature and effects on climate,75-80; resemblance of the precessing earth to certain models,80-82; tilting forces exerted by the sun and moon on theearth,82-84; how the earth's precessional motion is always altering,85-88; the retrogression of the moon's nodes is itself another example,88,89; an exact statement made and a sort of apology for making it,90,91.10.Influence of possible internal fluidity of the earth on its precessional motion,91-98.Effect of fluids and sand in tumblers,91-93; three tests of the internal rigidity of an egg, that is, of its being a boiled egg,93,94; quasi-rigidity of fluids due to rapid motion, forgotten in original argument,95; beautiful behaviour of hollow top filled with water,95; striking contrasts in the behaviour of two tops which are very much alike,97,98; fourth test of a boiled egg,98.11. Apology for dwelling further upon astronomical matters, and impertinent remarks about astronomers,99-101.12. How a gyrostat would enable a person living in subterranean regions to know,1st, that the earth rotates;2nd, the amount of rotation;3rd, the direction of true north;4th, the latitude,101-111.Some men's want of faith,101; disbelief in the earth's rotation,102; how a free gyrostat behaves,103,104; Foucault's laboratory measurement of the earth's rotation,105-107; to find the true north,108; all rotating bodies vainly endeavouring to point to the pole star,108; to find the latitude,110; analogies between the gyrostat and the mariner's compass and the dipping needle,110,111; dynamical connection between magnetism and gyrostatic phenomena,111.13. How the lecturer spun his tops, using electro-motors,112-114.14.Light,magnetism,and molecular spinning tops,115-128.Light takes time to travel,115; the electro-magnetictheory of light,116,117; signalling through fogs and buildings by means of a new kind of radiation,117; Faraday's rotation of the plane of polarization by magnetism, with illustrations and models,118-124; chain of gyrostats,124; gyrostat as a pendulum bob,126; Thomson's mechanical illustration of Faraday's experiment,127,128.15.Conclusion,129-132.The necessity for cultivating the observation,129; future discovery,130; questions to be asked one hundred years hence,131; knowledge the thing most to be wished for,132.
1.Introduction, pages9-14, 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.
Illustrations: 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.
Illustrations: 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.
Illustrations: Spinning top,31; cased gyrostat,32; balanced gyrostat,33-36; windage of projectiles fromrifled guns,36-38; tilting a hoop or bicycle, turning quickly on horseback,38; bowls,39; how to simplify one's observations,39,40; the illustration 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 principal 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.
9.Precessional motion of the earth,74-91.
Its nature and effects on climate,75-80; resemblance of the precessing earth to certain models,80-82; tilting forces exerted by the sun and moon on theearth,82-84; how the earth's precessional motion is always altering,85-88; the retrogression of the moon's nodes is itself another example,88,89; an exact statement made and a sort of apology for making it,90,91.
10.Influence of possible internal fluidity of the earth on its precessional motion,91-98.
Effect of fluids and sand in tumblers,91-93; three tests of the internal rigidity of an egg, that is, of its being a boiled egg,93,94; quasi-rigidity of fluids due to rapid motion, forgotten in original argument,95; beautiful behaviour of hollow top filled with water,95; striking contrasts in the behaviour of two tops which are very much alike,97,98; fourth test of a boiled egg,98.
11. Apology for dwelling further upon astronomical matters, and impertinent remarks about astronomers,99-101.
12. How a gyrostat would enable a person living in subterranean regions to know,1st, that the earth rotates;2nd, the amount of rotation;3rd, the direction of true north;4th, the latitude,101-111.
Some men's want of faith,101; disbelief in the earth's rotation,102; how a free gyrostat behaves,103,104; Foucault's laboratory measurement of the earth's rotation,105-107; to find the true north,108; all rotating bodies vainly endeavouring to point to the pole star,108; to find the latitude,110; analogies between the gyrostat and the mariner's compass and the dipping needle,110,111; dynamical connection between magnetism and gyrostatic phenomena,111.
13. How the lecturer spun his tops, using electro-motors,112-114.
14.Light,magnetism,and molecular spinning tops,115-128.
Light takes time to travel,115; the electro-magnetictheory of light,116,117; signalling through fogs and buildings by means of a new kind of radiation,117; Faraday's rotation of the plane of polarization by magnetism, with illustrations and models,118-124; chain of gyrostats,124; gyrostat as a pendulum bob,126; Thomson's mechanical illustration of Faraday's experiment,127,128.
15.Conclusion,129-132.
The necessity for cultivating the observation,129; future discovery,130; questions to be asked one hundred years hence,131; knowledge the thing most to be wished for,132.