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, §§ 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