The gyrostat is an instrument designed by Lord Kelvin (Natural Philosophy, § 345) to illustrate the more complicated state of motion of a spinning body when free to wander about on a horizontal plane, like a top spun on the pavement, or a hoop or bicycle on the road. It consists essentially of a massive fly-wheel concealed in a metal casing, and its behaviour on a table, or with various modes of suspension or support, described in Thomson and Tait, Natural Philosophy, serves to illustrate the curious reversal of the ordinary laws of statical equilibrium due to the gyrostatic domination of the interior invisible fly-wheel, when rotated rapidly (fig. 5).

The toy shown in figs. 6 and 7, which can be bought for a shilling, is acting as a gyroscope in fig. 6 and a gyrostat in fig. 7.

Fig. 3.Fig. 4.

The gyroscope, as represented in figs. 2 and 3 by Maxwell’s dynamical top, is provided with screws by which the centre of gravity can be brought into coincidence with the point of support. It can then be used to illustrate Poinsot’s theory of the motion of a body under no force, the gyroscope being made kinetically unsymmetrical by a setting of the screws. The discussion of this movement is required for Jacobi’s theorems on the allied motion of a top and of a body under no force (Poinsot, Théorie nouvelle de la rotation des corps, Paris, 1857; Jacobi, Werke, ii. Note B, p. 476).

To imitate the movement of the top the centre of gravity is displaced from the point of support so as to give a preponderance. When the motion takes place in the neighbourhood of the downward vertical, the bicycle wheel can be made to serve again mounted as in fig. 8 by a stalk in the prolongation of the axle, suspended from a universal joint at O; it can then be spun by hand and projected in any manner.

Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.Fig. 9.

The first practical application of the gyroscopic principle was invented and carried out (1744) by Serson, with a spinning top with a polished upper plane surface for giving an artificial horizon at sea, undisturbed by the motion of the ship, when the real horizon was obscured. The instrument has been perfected by Admiral Georges Ernest Fleuriais (fig. 9), and is interesting theoretically as showing the correction required practically for the rotation of the earth. Gilbert’s barogyroscope is devised for the same purpose of showing the earth’s rotation; a description of it, and of the latest form employed by Föppl, is given in the Ency. d. math. Wiss., 1904, with bibliographical references in the article “Mechanics of Physical Apparatus.” The rotation of the fly-wheel is maintained here by an electric motor, as devised by G. M. Hopkins, and described in the Scientific American, 1878. To demonstrate the rotation of the earth by the constancy in direction of the axis of a gyroscope is a suggestion that has often been made; by E. Sang in 1836, and others. The experiment was first carried out with success by Foucault in 1851, by a simple pendulum swung in the dome of the Pantheon, Paris, and it has been repeated frequently (Mémoires sur le pendule, 1889).

A gyroscopic fly-wheel will preserve its original direction in space only when left absolutely free in all directions, as required in the experiments above. If employed in steering, as of a torpedo, the gyroscope must act through the intermediary of a light relay; but if direct-acting, the reaction will cause precession of the axis, and the original direction is lost.

The gyrostatic principle, in which one degree of freedom is suppressed in the axis, is useful for imparting steadiness and stability in a moving body; it is employed by Schlick to mitigate the rolling of a ship and to maintain the upright position of Brennan’s monorail car.