Lord Kelvin: An account of his scientific life and work

by Andrew Gray

In Part II, the principal subjects treated are attractions, elasticity, such great hydrostatical examples as the equilibrium theory of the tides and the equilibrium of rotating liquid spheroids, and such problems of astronomical and terrestrial dynamics as the distribution of matter in the earth, with the bearing on this subject of the precession of the equinoxes, tidal friction, the earth's rigidity, the effects of elastic tides, the secular cooling of the earth, the age of the earth, and the "age of the sun's heat." Of these, with the exception of the age of the earth, we shall not attempt to give any account. The importance of the original contributions to elasticity contained in the book is indicated by the large space devoted to the Natural Philosophy in Professor Karl Pearson's continuation of Todhunter's History of Elasticity. The heavy task of editing Part II was performed mainly by Sir George Darwin, who made many notable additions from his own researches to the matter contained in the first edition.

In the next chapter an attempt will be made to present Thomson's views on the subject of the age of the earth. These, when they were published, attracted much attention, and received a good deal of hostile criticism from geologists and biologists, whose processes they were deemed to restrict to an entirely inadequate period of time.

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.