The modification of this arrangement by which Lord Kelvin explained the phosphorescence of such substances as luminous paint is also described, and will be recognised by some as an old friend. A number, two dozen or so, of straight rods of wood eighteen inches long are attached to a steel wire four or five inches apart, like steps on a ladder made with a single rope along the centres of the steps. The wire is so attached to each rod that the rod must turn with the wire if the latter is twisted round. Each rod is loaded with a piece of lead at each end to give it more moment of inertia about the wire. The wire, with this "ladder" attached to it, is rigidly attached to the centre of a cross-bar at the top, which can be made to swing about the wire as an axis and so impart twisting vibrations to the wire in a period depending on this driver. Sliding weights attached to the bar enable its moment of inertia to be changed at pleasure. The lower end of the wire carries a cross-bar with two vanes, immersed in treacle in a vessel below. When the period of the exciter was very long the waves of torsion did not travel down the "ladder," but when the period was made sufficiently short the waves travelled down and were absorbed in the treacle below. In the former case the vibrations persisted; the case was analogous to that of phosphorescence. [Illustration: FIG. 18.] Incidentally a full and very attractive account of the elastic solid theory is given in these lectures, accompanied as it is by characteristic digressions on points of interest which suggest themselves, and on topics on which the lecturer held strong opinions, such, for example, as the absurd British system of weights and measures. The book reads in many places like a report of some of the higher mathematical lectures which were given every session at Glasgow; and on that account, if on no other, it will be read by the old students of the higher class with affectionate interest. But the discussions of the great fundamental difficulty presented at once by dispersion--the fact, that is, that light of different wave lengths has different velocities in ordinary transparent matter--the discussions of the various theories of dispersion that have been put forward, the construction of the molecules, gyrostatic and non-gyrostatic, with all their remarkable properties, which Lord Kelvin invents in order to frame a dynamical mechanism which will imitate the action of matter as displayed in the complex manifestations of the optical phenomena, not only of isotropic matter, but of crystals, will ever afford instruction to every mathematician who has the courage to attack this subject, and remain as a monument to the extraordinary genius of their author.