Lord Kelvin: An account of his scientific life and work

by Andrew Gray

Gyrostatic Action

Thomson in his lectures and otherwise gave a great deal of attention to the motion of gyrostats, and to the effect of the inclusion of gyrostats in a system on its properties. Reference has been made to the treatment of "gyrostatic domination" in "Thomson and Tait." A gyrostat consists of a disk or wheel with a massive rim, which revolves within a case or framework, by which the whole arrangement can be moved about, or supported, without interfering with the wheel. The ordinary toy consisting of wheel with a massive rim, and a light frame, is an example. But much larger and more carefully made instruments, in which the wheel is entirely enclosed, give the most interesting experiments. The body seems to have its properties entirely altered by the rotation of the wheel, and of course the case prevents any outward change from being visible.

Fig. 15.

Figure 15 shows one form of gyrostat mounted on a horizontal frame, held in the hands of an experimenter. The axis of the fly-wheel is vertical within the tubular part of the case; the fly-wheel is within the part on which is engraved an arrow-head to show the direction of rotation. Round the case in the plane of the wheel is a projecting rim sharpened to an edge, on which the gyrostat can be supported in other experiments. To the rim are screwed two projecting pivots, which can turn in bearings on the two sides of the frame as shown. The centre of mass of the wheel is on the level of these pivots, so that the instrument will remain with either end of the axis up.

If the fly-wheel be not in rotation, the experimenter can carry the arrangement about, and the fly-wheel and case move with it as if the gyrostat were merely an ordinary rigid body. But now remove the gyrostat from the frame, and set the wheel in rotation. This is done by an endless cord wrapped round a small pulley fast on the axle (to which access is obtained by a hole just opposite in the case) and passed also round a larger pulley on the shaft of a motor. When the motor is started the cord must be tightened only very gently at first, so that it slips on the pulley, otherwise the motor would be retarded, and possibly burned by the current. The fly-wheel gradually gets up speed, and then the cord can be brought quite tight so that no slipping occurs. When the speed is great enough the cord is cut with a stroke from a sharp knife and runs out.

The gyrostat is now replaced on its pivots in the frame, with its axis vertical, and moved about as it was before. If the experimenter, holding the frame as shown, turns round in the direction of the arrow, which is that of rotation, nothing happens. If, however, he turns round the other way, the gyrostat immediately turns on its pivots so as to point the other end of the axis up. If the experimenter continues his turning motion, the gyrostat is now quiescent: for it is being carried round now in the direction of rotation. Thus, with no gravitational stability at all (since the centre is on a level with the pivots) the gyrostat is in stable equilibrium when carried round in the direction of rotation, but is in unstable equilibrium when carried round the opposite way.

Thus, if the observer knew nothing of the rotation of the fly-wheel, and could see and feel only the outside of the case, the behaviour of the instrument might well appear very astonishing.

This is a case of what Thomson and Tait call "gyrostatic domination," which is treated very fully in their Sections 345 (vi) to 345 (xxviii) of Part I. It may be remarked here that this case of motion may be easily treated mathematically in an exceedingly elementary manner, and the instability of the one case, and the stability of the other, made clear to the beginner who has only a notion of the composition of angular momenta about different axes.

A year or two ago it was suggested by Professor Pickering, of Harvard, that the fact that the outermost satellite of Saturn revolves in the direction opposite to the planet's rotation, may be due to the fact that originally Saturn rotated in the direction of the motion of this moon, but inasmuch as his motion round the sun was opposite in direction to his rotation, he was turned, so to speak, upside down, like the gyrostat! The other satellites, it is suggested, were thrown off later, as their revolution is direct. Professor Pickering refers to an experiment (similar to that described above) which he gives as new. Thomson had shown this experiment for many years, as an example of the general discussion in "Thomson and Tait," and its theory had already been explicitly published.[21]

Many other experiments with gyrostats used to be shown by Thomson to visitors. Many of these are indicated in "Thomson and Tait." The earth's precessional motion is a gyrostatic effect due to the differential attraction of the sun, which tends to bring the plane of the equator into coincidence with the ecliptic, and so alters the direction of the axis of rotation. Old students will remember the balanced globe—with inclined material axis rolling round a horizontal ring—by which the kinematics of the motion could be studied, and the displacement of the equinoxes on the ecliptic traced.

Fig. 16.

Another example of the gyrostatic domination discussed in "Thomson and Tait" is given in the very remarkable address entitled "A Kinetic Theory of Matter," which Sir William Thomson delivered to Section A of the British Association at Montreal, in 1884. Figure 16 shows an ordinary double "coach spring," the upper and lower members of which carry two hooked rods as shown. If the upper hook is attached to a fixed support, and a weight is hung on the lower, the spring will be drawn out, and the arrangement will be in equilibrium under a certain elongation. If the weight be pulled down further and then left to itself, it will vibrate up and down in a period depending upon the equilibrium elongation produced by the weight. The same thing will happen if a spiral spring be substituted for the coach spring. A spherical case, through which the hooked rods pass freely, hides the internal parts from view.

Fig. 17.

Figure 17 shows two hooked rods, as in the former case, attached by swivels to two opposite corners of a frame formed of four rods jointed together at their ends. Each of these is divided in the middle for the insertion of a gyrostat, the axis of which is pivoted on the adjacent ends of the two halves of the rod. A spherical case, indicated by the circle, again hides the internal arrangement from inspection, but permits the hooked rods to move freely up and down. The swivels allow the frame, gyrostats and all, to be turned about the line of the hooks.

If now the gyrostats be not in rotation, the frame will be perfectly limp, and will not in the least resist pull applied by a weight. But if the gyrostats be rotated in the directions shown by the circles, with arrowheads drawn round the rods, there will be angular momentum of the whole system about the line joining the hooks, and if a weight or a force be applied to pull out the frame along that line, the pull will be resisted just as it was in the other case by the spring. Moreover, equilibrium will be obtained with an elongation proportional to the weight hung on, and small oscillations will be performed just as if there were a spring in the interior instead of the gyrostats.

According as the frame is pulled out, or shortened, the angular momentum of the gyrostats about the line joining the hooks is increased or diminished, and the frame, carrying the gyrostats with it, turns about the swivels in one direction or the other, at the rate necessary to maintain the angular momentum at a constant value. But this will not be perceived from without.

The rotation of the fly-wheels thus gives to the otherwise limp frame the elasticity which the spring possesses; without dissection of the model the difference cannot be perceived. This illustrates Thomson's idea that the elasticity of matter may be due to motion of molecules or groups of molecules of the body, imbedded in a connecting framework, deformed by applied forces as in this model, and producing displacements which are resisted in consequence of the motion.

And here may be mentioned also Thomson's explanation of the phenomenon, discovered by Faraday, of the rotation of the plane of a beam of polarised light which is passed along the lines of force of a magnetic field. This rotation is distinct altogether from that which is produced when polarised light is passed along a tube filled with a solution of sugar or tartaric acid. If the ray be reflected after passage, and made to retraverse the medium, the rotation is annulled in the latter case, it is doubled in the former. This led Thomson to the view that in sugar, tartaric acid, quartz, etc., the turning is due to the structure of the substance, and in the magnetic field to rotation already existing in the medium. He used to say that a very large number of minute spiral cavities all in the same direction, and all right-handed or all left-handed, in the sugar or quartz, would give the effect; on the other hand, the magnetic phenomenon could only be produced by some arrangement analogous to a very large number of tops, or gyrostats, imbedded in the medium with their axes all in one direction (or preponderatingly so) and all turning the same way. The rotation of these tops or gyrostats Thomson supposed to be caused by the magnetic field, and to be essentially that which constitutes the magnetisation of the medium.

Let the frame of the gyrostatic spring-balance described above, turn round the line joining the hooks so as to exactly compensate, by turning in the opposite direction, the angular momentum about that line given by the fly-wheels; then the arrangement will have no angular momentum on the whole; and a large number of such balances, all very minute and hooked together, will form a substance without angular momentum in any part. But now by the equivalent of a magnetic force along the lines of the hooks, let a different angular turning of the frames be produced; the medium will possess a specific angular momentum in every part. If a wave of transverse vibrations which are parallel to one direction (that is, if the wave be plane-polarised) enter the medium in the direction of the axes of the frames, the direction of vibration will be turned as the wave proceeds, that is, the plane of polarisation will be turned round.

More recent research has shown an effect of a magnetic field on the spectrum of light produced in the field, and viewed with a spectroscope in a direction at right angles to the field—the Zeeman effect, as it is called—and the explanation of this effect by equations of moving electric charges, which are essentially gyrostatic equations, is suggestive of an analogy or correspondence between the systems of moving electrons which constitute these charges, and some such gyrostatic molecules as Thomson imagined. It has been pointed out that the Zeeman effect, in its simple forms at least, can be exactly imitated by the motion of an ordinary pendulum having a gyrostat in its bob, with its axis directed along the suspension rod.[22]