With these may be placed another, which in lectures he frequently dwelt on--a simple doublet, as it is called, consisting of a point-source of fluid and an equal and closely adjacent point-sink. A short tube in an infinite mass of liquid, which is continually flowing in at one end and out at the other, may serve as a realisation of this arrangement. The lines of flow outside the tube are exactly analogous to the lines of force of a small magnet; and if at the same time there exist a uniform flow of the liquid in the direction of the length of the tube, the field of flow will be an exact picture of the field of force of the small magnet, when it is placed with its length along the lines of a previously existing uniform field. The flow in the doublet will be with or against the general flow according as the magnet is directed with or against the field. The paper on vortex-motion has been referred to above, and an indication given of the nature of the fluid-motion described by this title. There are, however, two cases of fluid-motion which are referred to as vortices, though the fundamental criterion of vortex-motion--the non-existence of a velocity-potential--is satisfied in only one of them. The exhibition of one of these was a favourite experiment in Thomson's ordinary lectures, as his old students will remember. If water in a large bowl is stirred rapidly with a teaspoon carried round and round in a circle about the axis of the bowl, the surface will become concave, and the form of the central part will be a paraboloid of revolution about the vertical through the lowest point, that is to say, any section of that part of the surface made by a vertical plane containing the axis will be a parabola symmetrical about the axis. The motion can be better produced by mounting the vessel on a whirling-table, and rotating it about the vertical axis coinciding with its axis of figure; but the phenomenon can be quite well seen without this machinery. In this case the velocity of each particle of the water is proportional to its distance from the axis, and the whole mass, when relative equilibrium is set up, turns, as if it were rigid, about the axis of the vessel. Each element of the fluid in this "forced vortex," as it is called, is in rotation, and, like the moon, makes one turn in one revolution about the centre of its path. This is, therefore, a true, though very simple, case of vortex-motion. On the other hand, what may be called a "free vortex" may exist, and is approximated to sometimes when water in a vessel is allowed to run off through an escape pipe at the bottom. The velocity of an element in this "vortex" is inversely proportional to its distance from the centre, and the form of the free surface is quite different from that in the other case. The name "free vortex" is often given to this case of motion, but there is no vortex-motion about it whatever.