In the theory of dynamical systems there are as many velocities as there are coordinates and the kinetic energy is a homogeneous quadratic function of these velocities, in which in general not only the squares but also the products of the velocities appear. When we have one or more circuits carrying electric currents, we can distinguish in the kinetic energy one part that depends on the material velocities only, and this is the kinetic energy of ordinary mechanics, and a second part containing only the velocities corresponding to the internal coordinates; this is the magnetic energy that manifests itself in so many ways. Now, is this all? There would certainly be a third part of the kinetic energy if an electric current consisted in a real motion of some substance along the conducting wire, for if the wire were moving, say in the direction of its length, with the velocity _v_ and if _v'_ were the internal velocity proportional to the current, the total velocity of the moving substance would be _v_ + _v'_ and in its square we should have the term 2_vv'_. One is led to a similar conclusion on other less simple assumptions and so, independently of an special conception, the question arises whether any part of the kinetic energy consists of products of ordinary velocities and strengths of electric currents. Maxwell thinks this question to be of great importance and deems it "desirable that experiments should be made on the subject with great care." He then proceeds to examine different ways in which the terms in question might be made to reveal themselves, the first of which he explains as follows: If any part of the kinetic energy depends on the product of an ordinary velocity and the strength of a current, it will probably be most easily observed when the velocity and the current are in the same or in opposite directions. We therefore take a circular coil of a great many windings, and suspend it by a fine vertical wire, so that its windings are horizontal, and the coil is capable of rotating about a vertical axis, either in the same direction as the current in the coil, or in the opposite direction. We shall suppose the current to be conveyed into the coil by means of the suspending wire, and, after passing round the windings, to complete its circuit by passing downwards through a wire in the same line with the suspending wire and dipping into a cup of mercury. A vertical mirror is attached to the coil to detect any motion in azimuth.