Two vortex-rings projected one after the other also act on one another in a very curious manner. Their planes are perpendicular to the direction of motion, and the fluid is moving round the circular core of the ring. There is irrotational cyclic motion of the fluid through the ring in one direction and back outside, as shown in Fig. 13, which can be detected by placing a candle flame in the path of the centre. The first ring, in consequence of the existence of that which follows it, moves more slowly, and opens out more widely, the following ring hastens its motion and diminishes in diameter, until finally it overtakes the former and penetrates it. As soon as it has passed through it moves ahead more and more slowly, until the one which has been left behind begins to catch it up, and the changes which took place before are repeated. The one penetrating becomes in its turn the penetrated, and so on in alternation. Great care and skill are, however, necessary to make this interesting experiment succeed. We have not space to deal here with other hydrodynamical investigations, such as the contributions which Thomson made to the discussion of the many difficult problems of the motion of solids through a liquid, or to his very numerous and important contributions to the theory of waves. The number and importance of his hydrodynamical papers may be judged from the fact that there are no less than fifty-two references to his papers, and thirty-five to Thomson and Tait's _Natural Philosophy_ in the latest edition of Lamb's Hydrodynamics, and that many of these are concerned with general theorems and results of great value. CHAPTER X THE ENERGY THEORY OF ELECTROLYSIS--ELECTRICAL UNITS--ELECTRICAL OSCILLATIONS ELECTROLYSIS AND ELECTRICAL UNITS In December 1851 Thomson communicated an important paper to the _Philosophical Magazine_ on "The Mechanical Theory of Electrolysis," and "Applications of Mechanical Effect to the Measurement of Electromotive Forces, and of Galvanic Resistances, in Absolute Units." In the first of these he supposed a machine of the kind imagined by Faraday, consisting of a metal disk, rotating uniformly with its plane at right angles to the lines of force of a uniform magnetic field, and touched at its centre and its circumference by fixed wires, to send a current through an electrochemical apparatus, to which the wires are connected. A certain amount of work W was supposed to be spent in a given time, during which a quantity of heat H was evolved in the circuit, and a certain amount of work M spent in the chemical apparatus in effecting chemical change. If H be taken in dynamical units, W = H + M. The work done in driving the disk, if the intensity of the field is I, the current produced c, the radius of the disc r, and the angular velocity of turning w, is ½Ir²cw.