CHAPTER I. General Principles-Lines of Force-Relations between Mechanical and Electrical Energy-Absolute Measurements-Ideal Motor and Transmission of Energy-Practical Units. A PROPER understanding of the principle of the conservation of energy, which exists throughout the whole of nature, must necessarily form the basis of all scientific investigation of mechanical or electrical problems, and of most of the improvements we might attempt to introduce in existing machinery and apparatus. In many cases, the fact that the original amount of energy remains unchanged, whilst the form in which it becomes manifest undergoes many alterations, is easily understood. For instance, if a locomotive engine draws a train behind it on a railway, we are at no loss to explain how the energy of fluid pressure of steam in the boiler is transformed into that of a steady pull overcoming the resistance of the train at a speed of so many miles per hour, and including all the so-called waste caused by deformation, friction, abrasion, and heating of the bodies through which the energy flows. The means by which, in this case, energy is transformed are, for the most part, purely mechanical, and sufficiently familiar to our imagination to allow us to form a mental picture of the different processes taking place. Even the transformation of heat into energy of fluid pressure, although we are not able to represent it by a mechanical model, has, through long familiarity with heat engines in one form or another, become comprehensible to us. With electrical energy, and with that of chemical action, this is not so. We can form no kind of mental picture of the process taking place in a voltaic cell where the energy of chemical action is transformed into that of an electric current, nor can we say what are the connecting links by the aid of which this current, after passing through hundreds of miles of wire, is made to impart mechanical energy to the armature of an electro-magnet, and thereby produce telegraphic signals. There is no mechanical connection between the sending key and the lever of the Morse instrument by which energy could be transmitted in the form of a pull, as is the case in our example of the coupling between a locomotive and its train, and yet energy is unmistakably transmitted. If we neglect waste, that is energy transformed in a way not immediately useful for the purpose in view, we find that the amount of electrical energy received at the distant station is proportional to the amount of chemical energy used up; and if we take the waste also into account, we shall find that the energy it represents, added to that received in the form of an electric current at the distant station, is again proportional to the amount of chemical energy developed in the voltaic cell. If we know the nature of the chemical process going on in the cell, we can always calculate, by the aid of electrochemical equivalents, what total amount of electrical energy can be obtained from a given weight of materials. Similarly there exists a definite and constant proportion between electrical and mechanical energy. The relation between the two is somewhat complicated by the development of heat, which, indeed, is inseparable from electric phenomena, but if we make due allowance for the energy wasted in heat, we shall find that a given amount of electrical energy will always produce the same amount of mechanical energy, irrespective of the time required, or the exact manner of transformation. Although we cannot say what are the connecting links between electric current and mechanical force, experiment shows that certain definite relations exist, and we can, on the basis of experimental facts, conceive a mental picture or model by the aid of which these relations are represented in a familiar form. Such a mental picture is the conception of magnetic lines of force, first introduced by Faraday. In adopting this method of rendering electro-mechanical phenomena tangible to our senses, we make no assumption whatever about the reality of the lines of force. Whether they actually exist is a matter of total indifference; but since all the experiments we can make are compatible with that conception, and since it enables us not only to explain experimental facts, but also to bring them within the region of actual measurement and calculation, it is convenient to make the theory of magnetic lines of force the basis of electro-mechanical investigations. If a sheet of paper be laid over a straight steel magnet having opposite poles at its ends, and sprinkled with iron filings, it will be found that these arrange themselves in curves, which we take to be the magnetic lines of force, Fig. 1. Each of these lines form a closed curve 1 1 A very convenient way of fixing these curves is by the aid of a sheet of glass, the surface of which has been coated with a thin layer of paraffin. The glass is laid over the magnet, then sprinkled, and carefully lifted off so as not to disturb the filings. It is then gently heated, when the paraffin melts, and upon cooling again the iron filings are fixed to the glass by the coating of paraffin. The glass plate may then be handled as if it were a drawing, and the curves can be reproduced by photography. The drawing in the text has been obtained in this manner. issuing from a point at one end of the magnet, and entering at a corresponding point at the other end. Some of the curves extend far out into space, beyond the surface of the paper, and as far as they are visible, they appear as open lines growing fainter the farther we go from the poles. They must, nevertheless, be considered to be closed lines, only so faint that we cannot trace them throughout their whole length. If the poles of our magnet were two mathematical points, all the curves would pass through those points, but since we Fig. 1. have to deal with a physical magnet, the poles of which are surfaces of some extension, the lines issue from all over these surfaces. To investigate the magnetic properties of these lines we can use a long thin magnetic needle (a magnetized knitting-needle answers very well) suspended vertically by a long thread, so that the lower end of the needle is within a short distance of the paper, and free to move all over it. We shall then find that the lower end of the needle will be repelled by one pole of the magnet and attracted by the other, and in following the combined action of these forces, it will move along that particular line of force upon which it was set on to the paper in the first instance, but it will never move across the lines. We conclude from this experiment that the lines of force are paths along which a free magnet pole is urged under the influence of the magnet. A free magnet pole of opposite sign would travel along the same lines, but in opposite direction, and, if of the same strength, it will be urged along with an equal force. If, instead of a long vertical needle, we take a very short one suspended horizontally in its centre close to the surface of the paper, the two opposite forces will tend to set the needle so as to form a tangent to the line of force passing through its centre, and as then the two forces are equal and opposite, no bodily shifting of the needle can take place. But on whatever point of any of the curves we set the needle, it will always swivel into such a position that its magnetic axis, that is a straight line joining its two poles, becomes a tangent to the curve. (Fig. 2.) It should here be remarked that unless the needle is very short in comparison to the magnet it will, when placed near one of the poles, be drawn right up to it, because in this case there would be a sensible difference in the distance of either of its poles from |