fly wheels pivoted on some or on all of the links.  The imitation is not confined to cases of equilibrium.  It holds also for vibration produced by disturbing the system infinitesimally from a position of stable equilibrium and leaving it to itself.  Thus we may make a gyrostatic system such that it is in equilibrium under the influence of certain positive forces applied to different points of this system; all the forces being precisely the same as, and the points of application similarly situated to, those of the stable system with springs.  Then, provided proper masses (that is to say, proper amounts and distributions of inertia) be attributed to the links, we may remove the external forces from each system, and the consequent vibration of the points of application of the forces will be identical.  Or we may act upon the systems of material points and springs with any given forces for any given time, and leave it to itself, and do the same thing for the gyrostatic system; the consequent motion will be the same in the two cases.  If in the one case the springs are made more and more stiff, and in the other case the angular velocities of the fly wheels are made greater and greater, the periods of the vibrational constituents of the motion will become shorter and shorter, and the amplitudes smaller and smaller, and the motions will approach more and more nearly those of two perfectly rigid groups of material points moving through space and rotating according to the well known mode of rotation of a rigid body having unequal moments of inertia about its three principal axes.  In one case the ideal nearly rigid connection between the particles is produced by massless, exceedingly stiff springs; in the other case it is produced by the exceedingly rapid rotation of the fly wheels in a system which, when the fly wheels are deprived of their rotation, is perfectly limp.

[Footnote 1:  Paper on “Vortex Atoms,” Proc.  R.S.E.  February. 1867:  abstract of a lecture before the Royal Institution of Great Britain, March 4, 1881, on “Elasticity Viewed as possibly a Mode of Motion”; Thomson and Tait’s “Natural Philosophy,” second edition, part 1, Sec.Sec. 345 viii. to 345 xxxvii.; “On Oscillation and Waves in an Adynamic Gyrostatic System” (title only), Proc.  R.S.E.  March, 1883.]

The drawings (Figs. 1 and 2) before you illustrate two such material systems.[1] The directions of rotation of the fly-wheels in the gyrostatic system (Fig. 2) are indicated by directional ellipses, which show in perspective the direction of rotation of the fly-wheel of each gyrostat.  The gyrostatic system (Fig. 2) might have been constituted of two gyrostatic members, but four are shown for symmetry.  The inclosing circle represents in each case in section an inclosing spherical shell to prevent the interior from being seen.  In the inside of one there are fly-wheels, in the inside of the other a massless spring.  The projecting hooked rods seem as if they are connected