Page:Encyclopædia Britannica, Ninth Edition, v. 8.djvu/221

Rh E N F E N F 211 If a battery of electromotive force E maintain a current C in a conductor, and no other electromotive force exist in the circuit, the whole of the work done will be converted into heat, and the amount of work done per second will be EC. If R denote the resistance of the whole circuit, E = CR, and the heat generated per second is C 2 R. If the current drive an electromagnetic engine, the reaction of the engine will produce an electromotive force opposing the current. Suppose the current to be thus reduced to C. Then the work done by the battery per second will be EC or CC R, while the heat generated per second will be C 2 R, so that we have the difference (C - C )C R for the energy consumed in driving the engine. The ratio of this to the whole work done by the battery is ~, so that the efficiency is s. increased by diminishing C. If we could drive the engine so fast as to reduce C to zero, the whole of the energy of the battery would be available, no heat being produced in the wires, but the horse-power of the engine would be indefinitely small. The reason why the whole of the energy of the current is not available is that heat must always be generated in a wire in which a finite current is flowing, so that, in the case of a battery in which the whole of the energy of chemical affinity is employed in producing a current, the availability of the energy is limited only on account of the resistance of the conductors, and may be increased by diminishing this resistance. The availability of the energy of electrical separation in a charged Leyden jar is also limited only by the resistance of conductors, in virtue of which an amount of heat is necessarily produced, which is greater the less the time occupied in discharging the jar. The availability of the energy of magnetization is limited by the coercive force of the magnetized material, in virtue of which any change in the intensity of magnetization is accompanied by the production of heat. Since the motion of the centre of mass of a system is unaffected by any actions taking place between the parts of the system, it is plain that a system considered by itself cannot be said to possess energy in virtue of the motion of its centre of mass, and in estimating the energy of the system at any instant we may therefore treat this point as fixed, and consider only motions relative to it. Thus any motion of rotation we may consider to take place about an axis through the centre of mass. Now, if a system be not acted upon by any forces from without which have a moment about this axis, the product of the angular velocity of the sj 7 stem and of its moment of inertia about the axis of rotation will remain unchanged. Hence if we increase the moment of inertia we shall diminish the angular velocity in the inverse ratio, and therefore diminish the j energy of rotation in this ratio, since the latter is propor- j tional to the moment of inertia and the square of the angular velocity. If, then, we have a material system moving in the most general manner possible, we shall reduce its kinetic energy to a minimum by causing such actions to take place between the parts of the system as will make its moment of inertia about the invariable line as great as possible, and then changing the relative motions of the parts in such a manner that they move as if they were rigidly connected with one another. The motion of the system will then be a simple rotation with its kinetic energy as small as possible, and the greatest amount of energy will thus have been transformed. In all the cases we have examined there is a general tendency for other forms of energy to be transformed into heat on account of the friction of rough surfaces, the resistance of conductors, or similar causes, and thus to lose availability. In some cases, as when heat is converted into the kinetic energy of moving machinery or the potential energy of raised weights, there seems to be an | ascent of energy from the less available form of heat to the more available form of mechanical energy, but when this takes place there is always, accompanying it, a quantity of heat which passes from a body at a high temperature to one at a lower temperature, thus losing availability, so that on the whole there is a degradation of energy. Thus Thomson s second law T of thermodynamics, which states that &quot; it is impossible by means of inanimate material agency to obtain work by cooling matter below the temperature of the coldest body in the neighbourhood,&quot; appears to be generally true, except when this work is obtained at the expense of some other condition of advantage, as, for example, that possessed by air at a higher pressure than the surrounding atmosphere, or by different kinds of matter which are separate and tend to diffuse, and then the work having once been obtained, the system cannot be restored to its original condition without the degradation of energy from some other source, even though the heat converted into work be restored to the working bodies. It is sometimes important to consider the rate at which energy may be transformed into useful work, or the horse power of the agent. It generally happens that to obtain the greatest possible amount of work from a given supply of energy, and to obtain it at the greatest rate, are conflict ing interests. We have seen that the efficiency of an electromagnetic engine is greatest when the current is indefinitely small, and then the rate at which it works is also indefinitely small. Jacobi showed that for a given electromotive force in the battery the horse-power is greatest when the current is reduced to one-half of what it would be if the engine were at rest. A similar condition obtains in the steam-engine, in which a great rate of working necessitates the dissipation of a large amount of energy through the resistance of the steam-pipes, kc. The only way to secure a high degree of efficiency with a great horse-power in the case of the steam-engine is by increasing the section of the steam-pipes and the areas of the steam ports. The efficiency of an electromagnetic engine cannot be greater than one-half when it is working at its maximum horse-power, but we may obtain any fixed rate of working we please with a given degree of efficiency by diminishing the resistance of the battery and conductors until the maximum horse-power of the engine exceeds that at which it is to be worked by a sufficient amount. (w. G.) ENFANTIN, BAETHELEMY PBOSPEE [LE PERE EKFAN- TIN], (1796-1864), one of the founders of Saint-Sinionism, was born at Paris, February 8, 1796. He was the son of a banker of Dauphiny, and after receiving his early education at a lyceum, was sent in 1813 to the Ecole Polytechnique In March ISli he was one of the band of students who, on the heights of Montmartre and Saint- Chaumont, attempted resistance to the armies of the allies then engaged in the investment of Paris. In consequence of this outbreak of patriotic enthusiasm, the school was soon after closed by Louis XVIII., and the young student was compelled to seek some other career instead of that of the soldier. He first engaged himself to a country wine- merchant, for whom he travelled in Germany, Russia, and the Netherlands. In 1821 he entered a banking-house newly established at St Petersburg, but returned two years later to Paris, where he was appointed cashier to the Caisse Hypothecate. At the same time he became a member of the secret society of the Carbonari. In 1825 a new turn was given to his thoughts and his life by the friendship which he formed with Olinde Rodriguez, the favoured disciple of Saint-Simon. Introduced by Rodriguez to the master, who was then near his end, he ardently embraced his doctrines and schemes of social, political, and religious reformation. With Rodriguez he received the last in structions of Saint-Simon, and the two were entrusted