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.
