Part 3 (2/2)

This is not the case with a long hollow bra.s.s 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.

[Ill.u.s.tration: FIG. 43.]

[Ill.u.s.tration: FIG. 44.]

Here, for example, is one (Fig. 42 _b_) that only differs from the last in being longer. It is filled, or partially filled, with water, and you observe that if {97} I 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 {98} (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 bra.s.s 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.

[Ill.u.s.tration: FIG. 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. 45 _b_). 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 boiled {99} egg, 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. 45 _a_). 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 t.i.tled individuals who pay nowadays so largely for the {100} privilege. 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 j.a.pan 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 the _Nautical Almanac_ is 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 the _Nautical Almanac_. And yet {101} a 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 pa.s.sengers of a s.h.i.+p, 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. {102} 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 n.o.body 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 welcome {103} it, even although we may sneer at it as unnecessary after we have obtained it.

[Ill.u.s.tration: FIG. 17.]

You know that a gyrostat suspended with perfect freedom about axes, which all pa.s.s through its centre of gravity, maintains a constant direction in s.p.a.ce 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 the {104} gyrostat were _not_ spinning, its axis would keep a constant direction in s.p.a.ce. 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 s.p.a.ce all the time, surely it is obvious that the room must {105} be turning round in s.p.a.ce. 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 lat.i.tude.

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. {106}

[Ill.u.s.tration: FIG. 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, {107} 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 lat.i.tude 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 lat.i.tude 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 parallel {108} to 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 compa.s.s needle (Fig. 50), although with an exceedingly slow swing.

[Ill.u.s.tration: FIG. 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 foundations {109} to get round towards the object of their adoration all the time they are in motion.

[Ill.u.s.tration: FIG. 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 observatory {110} about 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 s.p.a.ce, 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 way _weigh_ the 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.

[Ill.u.s.tration: FIG. 49.]

<script>