From the collection of the z n T> T o Jrrelinger v iJibrary t P San Francisco, California 2006 DYNAMOS, ALTEKNATOKS, AND TKANSFOKMERS. DYNAMOS, ALTERNATORS, AND TRANSFORMERS: BY GISBEKT KAPP, M.lNST.C.E., M.lNST.E.E, ILLUSTRATED OF THE UNIVERSITY LONDON : BIGGS AND Co., 139-140, SALISBURY COURT, FLEET STREET, E.C, PREFACE. IN the present work it has been my object to place before the reader an exposition of the general principles underlying the construction of dynamo- electric apparatus, and to do this without the use of high mathematics and complicated methods of investigation. To avoid "mathematics altogether in a book treating of any engineering subject is, of course, impossible; but I have endeavoured to restrict the use of mathematics within such limits as will enable the average engineering student and the average practical engineer, even if he have no previous knowledge of electrical science, to follow the subject. GISBERT KAPP. 31, Parliament Street, Wesfiii^^ TJNIVERSITT CONTENTS. CHAPTER I. Definition Efficiency of Dynamo-Electric Apparatus Measurement of Electric Energy Principal Parts of Dynamo Distinction between Dynamo and Alternator Use and Power of these Machines. CHAPTER II. Scope of Theory The Magnetic Field Strength of Field Units of Measurement Physical and Mathematical Magnets Field of a Mathematical Pole. CHAPTER III. Magnetic Moment Measuring Weak Magnetic Fields Attractive Force of Magnets Practical Examples. CHAPTER IV. Action of Current upon Magnet Field of a Current- Unit Current Mechanical Force between Current and Magnet Practical Examples English System of Measurement. CHAPTER V. The Electromagnet The Solenoid Magnetic Per- meability Magnetic Force Line Integral of Magnetic Force Total Field Practical Example Extension of Theory to Solenoidal Electromagnets Magnetic Resistance. CHAPTER VI. Magnetic Properties of Iron Experimental Determi- nation of Permeability Hopkinson's Method Energy of Mag- netisation Hysteresis. CHAPTER VII. Induced Electromotive Force Cutting or Threading of Lines Value of Induced Electromotive Force C.G.S. Unit of Resistance Fleming's Rule Electromotive Force of Two- Pole Armature. CHAPTER VIII. Electromotive Force of Armature Closed-Coil Armature Winding Bi-polar Winding Multipolar Parallel Winding Multipolar Series Winding Multipolar Series and Parallel Winding. CHAPTER IX. Open-Coil Armatures The Brush Armature The Thomson-Houston Armature. CHAPTER X. Field Magnets Two-Pole Fields Muitipolar Fields- Weight of Fields Determination of Exciting Power Predeter- mination of Characteristics. CHAPTER XI. Static and Dynamic Electromotive Force Commuta- tion of Current Armature Back Ampere- Turns Dynamic Characteristic Armature Cross Ampere-Turns Sparkless Collection. CHAPTER XII. Influence of Linear Dimensions on the Output Very Small Dynamos Critical Conditions Large Dynamos Limits of Output Advantage of Muitipolar Dynamos. CHAPTER XIII. Loss of Power in Dynamos Eddy Currents in Pole- Pieces Eddy Currents in External Conductors Eddy Currents in the Armature Core Eddy Currents in the Interior of Ring Armatures Experimental Determination of Losses. CHAPTER XIV. Examples of Dynamos Ronald Scott's Dynamo Johnson and Phillips's Dynamo Oerlikon Dynamo Other Dynamos. CHAPTER XV. Elementary Alternator Measurement of Electro motive Force Fawcus and Cowan Dynamo Electromotive Force of Alternators Self-induction in Armatures of Alter- nators Clock Diagram Power in Alternating-Current Circuit Conditions for Maximum Power Application to Motors. CHAPTER XVI. Working Conditions Effect of Self -Induction Effect of Capacity Two Alternators Working on Same Circuit Armature Reaction Condition of Stability General Conclusions. CHAPTER XVII. Elementary Transformer Shell and Core Type- Effect of Leakage Open-Circuit Current Working Diagrams. CHAPTER XVIII. Examples of Alternators The Siemens Alternator The Ferranti Alternator Johnson and Phillips's Alternator The Electric Construction Corporation's Alternator The Gulcher Company's Alternator The Mordey Alternator The Kingdon Alternator. OF THE ' UNIVERSITT DYNAMOS, ALTERNATORS, AND TRANSFORMERS. CHAPTEE I. Definition. Efficiency of Dynamo-Electric Apparatus. Measurement of Electric Energy. Principal Parts of Dynamo. Distinction between Dynamo and Alternator. Use and Power of these Machines. In its broadest sense the term dynamo-electric machine denotes an apparatus in wjrich by the agency of electromagnetic induction mechanical energy of rotation is converted into the energy of an electric current, or inversely the energy of such currents is converted into mechanical energy of rotation. This definition holds good whether the current given out by the machine, when driven by power from a prime mover, is always flowing in the same direction or is alternately flowing in opposite directions ; it also holds good for a machine which is driven by a current sup- plied to it from some external source, whether the current is always flowing in the same direction or whether the direction of flow is periodically reversed. The qualification that the mechanical energy forming the starting or finishing point of the process must be energy of rotation is of importance in order to exclude a class of apparatus which have this in common with dynamo-electric machines, that their action is based on electromagnetic induction. Thus any ordinary electric B 10 DYNAMOS, ALTERNATORS, bell, a Morse telegraph apparatus, or the Timmis- Forbes electric railway brake, are all instruments in which the energy of electric currents is transformed into mechanical energy, but they are obviously not dynamo-electric machines. On the other hand, the Wimshurst electric machine is also excluded by the above definition, since in it the agency by which mechanical energy of rotation is converted into electric currents is not electromagnetic, but electrostatic induc- tion. The limits within which the term dynamo- electric machine is applicable are even with these restrictions still inconveniently wide, and for practical purposes a subdivision is necessary. The basis for this subdivision is twofold : first, whether the conversion is from mechanical into electric energy or the opposite ; secondly, whether the currents are direct that is, flow- ing always in the same direction or alternating, that is, flowing alternately in opposite directions. We obtain thus four classes of machines. These are : 1. The dynamo, in which mechanical energy of rotation is converted into the energy of a direct current. 2. The alternator, in which mechanical energy of rotation is converted into the energy of an alternating current. 3. The motor, in which the energy of a direct current is converted into mechanical energy of rotation. 4. The alternate current motor, in which the energy of one or more alternating currents is converted into mechanical energy of rotation. AND TEANSFOEMERS. 11 "Thus, either of these four types of apparatus has for its 'object the conversion of energy from one form into another form, and it is self-evident that the com- mercial value of the apparatus must depend, to a certain extent, on the efficiency of conversion that is, the ratio between the amount of energy supplied to the machine in one form and the amount obtained from it in the other form. The smaller the loss in- curred in the process of conversion the better is the' machine. That some loss must take place in dynamo- electric machines may be expected from analogy with other mechanical appliances, for there never has been any machine devised which works without loss, but in the class of apparatus we are now considering, the loss is smaller than in most other mechanical appliances. Thus it is by no means difficult to build dynamos which shall have an efficiency of 90 per cent., whereas the best centrifugal pumps scarcely reach 70 per cent, efficiency, and the best turbines 85 per cent., whilst in steam engines an efficiency of 75 per cent, is exceptionally high. If we except such simple mechanical devices as spur or belt gearing and the like appliances which serve for the transmission, as distinguished from the trans- formation of energy, then the dynamo- electric machine is unquestionably the most efficient apparatus at present known in mechanics. In this connection the question naturally arises how the efficiency of a dynamo or motor is to be determined. The efficiency is the ratio of two energies, that supplied, and that obtained from the machine. With one of the forms in which energy enters into the process every engineer is familiar, and there is no special difficulty in B 2 12 DYNAMOS, ALTERNATORS, accurately measuring it. If the dynamo is driven by a steam engine we can take full load and friction diagrams y and thus ascertain, with a fair amount of accuracy, what power is actually supplied to the dynamo, or better still, we can measure the power by some form of transmission dynamometer, and thus eliminate any slight error which might be due to the difference in engine friction when running light and loaded. Such measurements are perfectly familiar to mechanical engineers, but when we come to the electrical measurements required at the other end of the process we enter upon new ground. The interdependence of magneto-electric and purely mechanical forces will be considered in chapter IV., but for our present purpose it will suffice if we consider merely one method of measuring electric energy. If a current be sent through a wire we observe that the wire becomes heated. The -heat developed is due to the energy given off by the current in overcoming the resistance of the wire, and since the principle of the conservation of energy must hold good in electrical as well as in purely mechanical or thermo-dynamic processes, we conclude that the heat given off by the wire is an exact measure of the electric energy given off by the current. The heat developed per second can be measured in a calorimeter, and its mechanical equivalent in foot-pounds, kilo- gramme-metres, or horse-power ascertained, and the energy which we thus obtain must obviously be that given out by the current in the conductor. If at the same time we measure the current and the potential difference between the ends of the conductor, we find that with a direct and steady current the product of the AND TEANSFOEMEES. 13 two readings is proportional to the number of calories liberated per unit-time. We may therefore substitute for the somewhat cumbersome and difficult calorimetric method of measurement the far simpler electrical method, and say that the energy developed by a direct, steady current in a conductor is measured by the pro- duct of strength of current and difference of potential between the ends of the conductor. Thus the energy absorbed by a glow lamp would be found by multiplying the voltage at which the lamp is run by the current passing through it. In order that the measurement may be accurate, it is necessary that the conductor shall not be under any other electrodynamic influence. It must therefore not be moved in the neighbourhood of a magnet, nor must a magnet be moved near it. The reason is that such relative movement between a magnet and a conductor tends to set up in the latter a current which may either assist or retard the original current of which the energy is to be measured, and the measurement would therefore be erroneous by the amount of energy expended in or obtained by the movement. For the same reason the measurement of the energy of an alternating current cannot always be made in the simple manner above explained for direct currents. Under certain circumstances an alternating current acts upon its own conductor somewhat in the same way as a magnet in motion, and in such cases the product of voltage and current strength is greater than the true energy transformed into heat. To obtain the true energy when the current is alternating and the conductor has the property of reacting upon itself, a property commonly designated by the term " self- 14 DYNAMOS, ALTEBNATOES, induction," certain accessory measurements must be- made, but it is not necessary to enter into this matter at present, since it will be dealt with at some length in a subsequent chapter. Suffice it to say that for steady direct currents the product of potential difference and current strength is a true measure of the energy given off. Potential difference or electric pressure is meas- ured in volts, and current strength is measured in amperes, the produ'ct being volt-amperes, or waits. The interdependence of the watt and the other units of energy will be explained later on, for the present we need only note the following relations : One foot-pound per second = 1*36 watts. One kilogramme-metre ,, = 9'81 watts. One English horse-power -= 746 watts. One metric horse-power = 736 watts. Ity the aid of these equivalents we can therefore ex- press the power of a dynamo in any convenient system of mechanical units. We measure the electric energy in watts and convert the latter into horse-power if the energy supplied to the machine is given in that measure. For instance, let the current from a dynamo be measured by an ampere-meter placed in circuit. Let a voltmeter be connected close to the dynamo across the main wires, through which current is being supplied to a number of lamps, each lamp being also connected across the mains. Then by taking simul- taneous readings on the two instruments we can determine what energy is being used in the mains and lamps. The arrangement is diagrammatically shown in Fig. 1, where D represents the dynamo, which is AND TRANSFOKMERS. 15 connected by the conductors, B x B 2 , technically termed " brushes," with the main wires, M x M 2 . The main M 2 is interrupted and an ampere-meter, A, inserted into the gap, thus forcing the current to flow through the instrument and be thereby registered. A voltmeter, V, is connected by a couple of wires across the mains, and shows the pressure under which the current is being sent into the mains and through the group of lamps, L. Say the ampere-meter registers 140 amperes and the voltmeter 105 volts, then we conclude that the energy QL 0* FIG. 1. consumed in the circuit beyond the points 1 and 2 is 105 x 140 = 14,700 watts, or 19'72 horse-power. In the same way would be measured the energy supplied to a motor. In this case D would represent the motor receiving current from some source for instance, a set of batteries, which would take the place of the lamps, L ; and the energy which is being supplied to the motor in the form of electric current, flowing under a certain potential difference or pressure, can be com- puted from the indications of the two instruments A and V. We have here shown how the electric energy given 16 DYNAMOS, ALTERNATORS, off by a dynamo or supplied to a motor can be measured. To make such a measurement no know- ledge of the construction of the machine is required, the experimenter having simply to read the indications of two instruments and make a very simple calculation. We may, however, now enter upon the construction of these machines in a general way and give an account of their principal parts. For the sake of brevity, the description will be given with reference to dynamos, leaving it to be understood by the reader that the different parts are substantially the same in motors. Leaving aside for the present those parts which serve for purely mechanical purposes, there are in a dynamo four main parts serving electrical or magnetic purposes namely, field-magnets, armature, commutator, and brushes. The field-magnets and brushes are generally the fixed parts, whilst the armature with its com- mutator revolves. The currents are produced by the electromagnetic induction taking place in certain wires which are moved in front of magnet poles. These wires form part of the armature and are so intercon- nected that the single current impulses are added. They are also connected with the commutator upon which the brushes rub, and by this means the current is allowed to flow out of and return to the armature. The object and function of each of the four principal parts is, therefore, as follows : The field-magnets pro- duce the poles, which form the starting point of the process. In front of these poles or between them revolves the armature carrying wires in which currents are generated. These currents are grouped and directed by the commutator. The brushes finally have the AND TEANSFOEMEES. 17 office of establishing suitable connections between the fixed terminal points of the external circuit and the revolving commutator. The above description will be made clearer by reference to the drawing of a dynamo, -and for this purpose we select the "Victoria" machine represented in Fig. 2. This dynamo belongs to a class of machines usually comprised under the title " disc machines," on account of the fact that the armature is shaped somewhat like a disc or cylindrical ring of comparatively large diameter and small axial length. In the side elevation, Fig. 2, the armature is shown in section, A representing the core and W the winding. The core is composed of thin sheet iron strip, wound upon a stouter iron ring, B, which in its turn is supported by arms and hub, H, on the shaft. The torque is transmitted from the shaft to the wheel, H, by a\key in the usual way, and from the wheel to the core, A, by the flat arms which are arranged in halves and drawn together by screw bolts, thus pressing the core between them. For certain reasons, which need at present not be detailed, the core is formed not of one wide iron strip, but of several narrow strips wound side by side. When completed, the core is insulated over its whole surface, and the armature conductor, consisting of cotton covered wire, is wound on it, the convolutions passing round the out- side and through the inside between the flat arms. The armature winding forms a closed spiral which, for convenience of manufacture, is subdivided into sections, and the points of juncture between neighbouring sections are connected with neighbouring plates in the commutator C. These plates are insulated from each THE TT -NT T \"f T 1 . "R C T T "V 18 DYNAMOS, ALTERNATORS, AND TEANSFOEMERS. o I s- o" "20 DYNAMOS, ALTEBNATOBS, other, and form together a cylindrical body upon the outer surface of which the brushes rub for the purpose of bringing into and leading away from the armature the currents created in its convolutions when the latter pass in front of the pole pieces P P. These pole pieces form the inner ends of two sets of magnet bars placed on either side of the armature and connected at their outer ends by yoke castings Y. Coils of insulated copper wire, M and S, are placed over the magnet cores, and the currents circulating in these coils induces the magnetism which in its turn induces currents in the armature coils. Structurally an alternator does not greatly differ from a dynamo, though electrically there are points of radical difference between the two types of machines. This can best be seen by the changes required to transform the machine shown in Fig. 2 into an alternator. We would have to arrange the armature coils into four distinct groups corresponding with the four poles of the field-magnets. Coil 1 would be connected with coil 2, similarly coil 2 would be connected with coil 3, and coil 3 with coil 4, leaving the first wire of coil 1 and the last wire of coil 4 free. These free ends of the arma- ture circuit would be connected with two contact rings mounted on the spindle, but insulated from it and from each other. The current would be taken off these contact rings by brushes in the usual manner. It will now be seen in what particulars the dynamo differs from the alternator. We have a system of field-magnets in both machines, also an armature containing wire coils, but whereas in the dynamo these coils are numerous and each contains only a few turns, and in many cases AND TRANSFORMERS. 21 only one turn of wire, in the alternator the number of"} coils is only that of the field-magnet poles, but each coil contains a large number of turns of wire. In the dynamo the coils are continuously connected with each other and with the sections of the commutator. In the alternator there is no commutator, but merely a pair of contact rings forming the terminals of the armature circuit. In the dynamo one coil after another comes, so to speak, gradually into action and as gradually out of action, whereas in the alternator all the coils come simultaneously and more abruptly into and out of action. There are other differences between the two types of machines, but we must leave the con- sideration of these to future chapters, where we shall deal with the theory and practice of these machines more in detail. For the present it will suffice if we point out the various purposes for which dynamos and alternators are used. As regards the former they are used for electric lighting, electro-chemical work, thermo- electric work, and electric transmission of energy. Alternators are as yet principally used for lighting purposes, though the transmission of energy can also be affected by their agency. For electro-chemical work they have hitherto not been used, and as regards thermo- electric work, such as the manufacture of aluminium alloys, there is no reason to doubt that alternating currents could be successfully employed, though the bulk of the work has hitherto been done by direct currents. A point of considerable practical interest is that con- cerning the power of dynamos and alternators. It is scarcely ten years since engineers in this and other 22 DYNAMOS, ALTERNATORS, countries began to turn their attention to these ma- chines, and within that time there has been a steady growth in the size and power of them. Prior to the Paris Electrical Exhibition of 1881 there were but very few manufacturers of dynamo-electric machines, and the apparatus turned out by these few firms was rather of the kind suited for the laboratory than for the work- shop. The machines were of small power and imper- fect design, both electrically and mechanically; they were, in fact, made not by engineers, but by electricians accustomed to manufacture all kinds of small electrical apparatus, and who evidently did not in those days realise the magnitude of the mechanical forces with which they might have to deal in a properly designed dynamo. Yet the dynamo as a laboratory toy was then already an old invention. Shortly after Faraday had, in 1831, announced his great discovery of electro- magnetic induction, Pixii produced magneto-electric machines for alternating and for direct currents. He was followed by a large number of physicists and scientific instrument makers, whose improvements in matters of detail form an almost continuous record up to the year 1864, when Pacinotti made his great inven- tion of the closed armature circuit and commutator as now used ; Gramme in 1870 re-invented the same thing, and being a skilled workman was able to at once give practical shape to his invention in the dynamo which bears his name, and which has become the prototype of all dynamos with closed coil armatures. The Gramme machine was shown in 1873 at the Vienna Exhibition, where there were also on view alternators for use in lighthouses, but these machines attracted the attention AND TRANSFORMERS. 23 of engineers to only a limited extent. It was after the invention of the glow lamp, and after the Paris Exhibitions of 1878 and 1881, when the engineering profession began to realise that there was an enormous .field for the commercial application of apparatus which had until then only been used for scientific purposes in the laboratory, or practically used in isolated instances, that engineers took up the manufacture of dynamos as a regular trade. The power of machines was at first very small, since they were generally required for iso- lated private electric light installations, which were naturally of a limited character. Gradually, however, when confidence in the electric light brought about its adoption in mills, factories, and other large establish- ments, the size of machines became larger, and this tendency has been further strengthened by the esta- blishment of central electric light stations. The power of modern dynamos and alternators is reckoned by hundreds of horse-power, and in some cases by thou- sands. Thus at the Deptford station Mr. Ferranti built alternators designed to give out 1,500 h.p. of electric energy, and still larger machines intended for an out- put of 10,000 h.p. were projected. In some of the Berlin central stations there are in use dynamos of 500 h.p., and it seems highly probable that for central stations generally machines of even larger power will in future be required. The power of machines required for other than lighting purposes is also constantly on the in- crease. As an instance, we may take the application of the dynamo to the transmission of energy. The transmission plant of 50 h.p., between Kriegstetten and Solothurn, Switzerland, which was erected some years 24 DYNAMOS, ALTERNATORS, ago, was then considered an undertaking of consider- able magnitude, but now there has been erected at Schaffhausen a plant of 600 h.p., whilst in America there are many generating stations for the supply of current to electric tramways and railways, the capacity of which is reckoned by many hundreds of horse-power. Similarly, we find that the machines required for electro-chemical and thermo-electric work are of con- siderable size. When storage batteries are used in central station lighting, the charging dynamos are seldom of less than 200 h.p. output, while large machines are also required in the manufacture of storage cells, the purification of copper and other pro- cesses. As regards thermo-electric work, it is interest- ing to note that the current required in the electric furnace represents a very considerable energy. Thus, at the Cowles Aluminium Works, at Milton, the energy necessary to work the furnace is about 400 h.p., whilst that required for the Heroult Furnace, at the Neu- hausen Works, is between 300 and 400 h.p. We see, therefore, that in all branches of heavy electrical engi- neering the tendency of the present time is in the direc- tion of large and powerful machines, such as can only be produced in engineering shops fitted with large tools and modern appliances. We also see that to turn out apparatus of such magnitude by the use of haphazard or rule of thumb methods of construction is out of the question. To ensure success the electrical engineer of our day must thoroughly understand the scientific principles involved in dynamo-electric machines, and must be careful to employ only the best materials and workmanship. CHAPTEE II. Scope of Theory. The Magnetic Field. Strength of Field. Units of Measurement. Physical and Mathe- matical Magnets. Field of a Mathematical Pole. General Scope of the Theory of Dynamo-Eleetrie Machines. The working of dynamos, alternators, and trans- formers is based on electromagnetic induction, and before we attempt to establish a working theory of any such machine it is necessary to investigate the general principles on which the theory must be based. We must for this purpose consider the interaction of magnets and electric currents, the general character and magnitude of the mechanical forces resulting from or causing such interaction, and the general relations existing between mechanical and electromagnetic forces and energies. It would be beyond the scope of the present book, which is primarily intended for practical engineers, to give a complete theory of electrodynamics. For this the reader must go to the works of Clerk Maxwell, Mascart and Joubert, Lord Kelvin, Lord Bayleigh, Oliver Lodge, Oliver Heaviside, Wiedemann, Wiillner, and others. No single author has treated the subject c 26 DYNAMOS, ALTERNATORS, completely, but by referring to the writings of several, the reader may be able to collect what may be called a tolerably complete theory of the subject. This would of course involve a considerable amount of labour, and would require a degree of mathematical skill not usually possessed by practical engineers. It is, how- ever, fortunately not necessary to establish or understand a theory in all its minute details in order to apply it to a useful purpose. Excellent steam engines have been and are being built by men who have never read a word of the writings of Carnot, Clapeyron, Clausius, Joule, or Helmholtz, but who have never- theless thoroughly grasped the chief thermo-dynamic principles, and have understood how to apply them. It is the same with electro-dynamics. Very few, if any, of the successful designers of dynamos have found it necessary to first master the writings of Maxwell before attempting the construction of machines. They nevertheless profited by the thoughts of Maxwell and similar men, but only after the information contained in their books had filtered down to them through the medium of more popular expounders of the theory aided by practical experiment. In attempting to establish a working theory of dynamo-electric machinery, or rather in setting forth the rules and formulae now used by the designers of such machines, we shall therefore not fol- low the lead of the pioneers in science so much as that of their more popular expounders and that of practical experience. The treatment will thus necessarily lack that mathematical elegance of which the scholastic mind is so fond, but on the other hand it will be more easily grasped and adopted by the practical engineer AND TRANSFORMERS. 27 who works as much by the aid of his mechanical instinct as by that of science. The Magnetic Field. If we lay a straight bar magnet upon the table and explore the space surrounding it by means of a compass needle, N, Fig. 3, we find that the needle takes up at every point in the vicinity of the magnet a perfectly definite position. In the diagram the north pole of the bar (that is, the end which, if the bar were freely suspended, would point to the geographical north) is c2 28 DYNAMOS, ALTERNATOKS, shaded, as is also the north pole of the needle. The- direction at which the needle sets itself in any point is. such as to make its south pole point more or less directly to the north pole of the bar, whilst its north pole points more or less directly to the south pole of the bar, the exact position being, so to speak, the best compromise the needle can make in order to satisfy the different attractions and repulsions. Let us assume the bar placed on a sheet of paper, and on the paper a line, a b, drawn in such a way that if the needle be shifted along that line its axis shall at all points be tangential to it. As it would be difficult to hit off the correct line without having anything to guide us, let us resort to the following device. Let us take a long and thin steel wire, W, magnetised north at its lower and south at its upper end, which is formed into a loop for con- venience of suspension by a thread. We shall now be able to let the lower end of the wire mark on the paper curves of the kind above mentioned. It is as though the magnetic forces of attraction and repulsion acted along these curves, which have therefore received the name of "lines of force." These lines will be found not only in the plane of the paper, but in the whole of the space surrounding the magnet, and their entirety is comprised under the name of " magnetic field." We therefore define the magnetic field as a space within which can be traced magnetic lines of force. The magnetic field of a steel magnet has an inner boundary formed by the surface of the magnet, but it has no definite outer boundary. The action on our exploring wire, W, becomes weaker and weaker as we go away from the magnet, but there is no definite limit within AND TEANSFOEMEES. 29 which lines of force could not be detected provided the -.exploring apparatus were delicate enough. Another method of rendering the lines of force visible consists in placing a sheet of paper over the magnet and sprinkling iron filings upon it. We then see that the filings FIG. 4. arrange themselves as in Fig. 4. They are densest near the poles and become more sparse at a distance from them. We find accordingly that the lower end of our exploring wire is strongly repelled when close to the north pole, and equally strongly attracted when close to the south pole of the magnet, whilst the forces acting on it in intermediate positions are smaller. The OF THE 30 DYNAMOS, ALTEENATOES, end of the wire in moving along the line, c d, is doing mechanical work, and the amount of work performed by a unit pole in the transition from one point of the curve to the other represents the difference of magnetic potential between these two points. It is useful to note that the amount of work is independent of the path traversed by the exploring pole. If the latter be con- strained to move in any circuitous route, work may be E H FIG. 5. absorbed and given off at different parts of its journey ; but if we deduct the work absorbed from that given off, we find that the difference represents exactly the work which would have been given off had w r e permitted the exploring pole to travel along the line of force on which it was originally set. Thus let, in Fig. 5, the exploring pole be set down on the point a in the line of force, N, a, d, e, S, and instead of allowing it to move along this line constrain it to move towards b, then to c, d, and finally to e. The journey a b will be performed against AND TEANSFOEMEES. 31 the repulsion of N upon the exploring pole, and work will therefore have to be done upon the latter. The journey b c, on the other hand, will yield work, for the point moves more or less in the direction in which it is impelled by the magnet. During the journey c d work is neither done upon the exploring pole nor given off by it, since it moves at right angles to all the lines of force which it passes. That this must be so can easily be seen from the consideration that work is the product of two factors namely, force and movement in the direction or exactly opposite to the direction of the force. In other words, in calculating the work we must only take account of that component of the motion which coincides at any moment with the direction of the force, and when the motion throughout takes place at right angles to all the forces, then the component which forms one factor in the work is zero, and therefore the whole work is zero. If no work is done or obtained in the transition between two points of the field, these two points must obviously have the same magnetic potential that is, must be equipotential points. We can imagine an infinite number of such points forming a surface which cuts all the lines of force at right angles, and an exploring pole moved in any way along such a surface will neither absorb nor give off work. Such a surface cutting all the lines of the field at right angles is called an equipotential surface. Thus, in a dynamo, the surface of the pole-piece or that of the armature core as far as it lies within the pole-piece are equipotential surfaces. We can move an exploring pole along either surface or along any inter- mediate surface equidistant from the polar or armature 32 DYNAMOS, ALTERNATORS, surface without receiving or doing work. If, however, we move the exploring pole from one surface to the other, we must either do work or obtain work. The space between the poles and armature core of a dynamo, even before the core is wound, is so confined that the experiment here described cannot easily be performed, to say nothing of the additional difficulty that in so intense a field the polarity of our exploring magnet would easily be reversed. In a somewhat more imper- fect or rough and ready manner the experiment can, however, on any dynamo be very easily performed as follows : Take a key or spanner in your hand, and approach with it the back of one of the pole-pieces. The piece of iron will be strongly attracted to the surface of the pole, and stick out from it self-sustained if allowed to actually come into contact. The piece of iron has become an exploring magnet, the end touching the pole-piece of the machine, assuming the opposite polarity to it, and the end pointing away the same polarity. If we rotate the iron bar about its point of contact, so as to bring its outer end nearer to the surface of the machine pole, we find that energy must be expended, which the bar will give out again if allowed to return into its natural position of sticking out straight from the surface. If, however, we displace the bar parallel to itself, we find that apart from friction there is no resistance to the movement. Either end of the bar is in this case moved along an equi- poteiitial surface, and consequently no work is being expended or received. Returning now to Fig. 5, we have seen that no work is performed in the journey from c to d. In the journey AND TEANSFOEMEES. 33 from d to e the exploring pole gives off work because moving along a line of force. Now it can easily be shown that the total amount of work given off by the exploring pole during its journey from a to e is inde- pendent of the particular route traversed, and only depends on the difference of magnetic potential between the two points a and e. We need for this purpose only imagine that a movement taken slantingly across the lines of force consists in a large number of minute steps taken alternately along and at right angles to the lines of force. The steps at right angles do not count as far as the performance of work is concerned, and the final result is the same as if all the steps had been taken along lines of force. Thus, the work done by the exploring pole in moving in a straight line from a to g is precisely the same as that which would be done if the pole were first to travel along the equipotential line af, and then from /to g along a line of force. If the exploring pole be of unit strength, this work repre- sents the difference of potential between a and g. Strength of Field. In exploring the field of a magnet, as shown in Fig. 3, we find that the forces acting upon the exploring pole vary with its position. The nearer the point of the wire, W, is to one of the poles or ends of the bar, M, the greater is the attractive force, and the nearer it is to the other end the greater is the repulsive force. Thus, although the exploring pole may travel from the north to the south pole of the bar along the same line of force, the actual amount of the force exerted upon it varies 34 DYNAMOS, ALTEENATOES, from point to point. If we investigate the variation of magnetic force with reference to Fig. 4, which shows the lines of force as revealed by the natural arrange- ment of iron filings, we find that the lines are densest in the neighbourhood of the poles, and the less dense the farther away we go from the poles. The density of the lines is, in fact, a measure for the force acting upon the exploring pole in different parts of the field. This relation between density of lines and magnetic force has led to the conclusion that the one is a function of the other ; and it has become usual to express the force exerted upon an exploring pole in a given part of a magnetic field as due to a density of so many lines of force per square centimetre of the cross-section taken at right angles to the flow of lines at that part of the field. When we define the strength of field between the poles and armature of a dynamo as 5,000 C.G.S. units, we mean thereby that through each square centi- metre of the intervening space there pass 5,000 times as many lines as pass through each square centimetre of a space in which unit force is exerted upon a unit ex- ploring pole. It is, therefore, only necessary to agree upon the units to be adopted, and we are at once able to numerically define the strength of a magnetic field at any point. In this connection it is, however, necessary to guard against a misconception which might arise from a too narrow or strictly literal interpretation of the lines of force theory. This theory, as far as it applies to magnetism, is due to Faraday, who adopted it as a natural and simple way of accounting for magnetic phenomena, without, however, ascribing to the lines any AND TEANSFOEMEES. 35 actual physical existence. With this reservation there is no danger of misconstruing Faraday's conception, but if we look upon lines of force as if each were a physical ntity, having a definite dimension, occupying a definitee position and exerting a definite force, the theory breaks down altogether. To show that this is so we have only to consider what must be the arrangement of lines in, say, a unit field. According to the theory there would in such a field be one line to each square centimetre of sectional area of the field, each line exerting unit me- chanical force upon unit pole placed on it. The unit pole being a mathematical point, and the line of force having no other dimension than length, mathematical precision would be required to get the pole exactly on to the line. To one such position of coincidence there is an. infinite number of positions in which the two will not coincide if we assume that the position of each line in space is fixed at the centre of its own square. Experiment shows that the magnetic force is exerted upon the pole not only at certain points, but at all points of the field, and to explain this we would have to assume that each line of force, though an entity and limited to its own square, is free to shift within that square in any way necessary to pick up our unit pole. This explanation, clumsy as it is, would suffice to account for the properties of the field if investigated by one unit pole only, but it breaks down if we imagine the investigation made by the aid of two poles less than one centimetre apart, for both poles are equally in- fluenced by the field. The idea that a line of force is a physical entity, pulling at a magnet pole as an elastic thread may pull at a heavy body, is therefore quite 36 DYNAMOS, ALTEENATOES, untenable, and if we wish to represent a magnetic field in some way by a mechanical model, we must abandon the idea of constructing such a model by means of threads to represent the lines of force. A more satisfactory, though by no means complete, mechanical representation of the magnetic field is by means of a liquid mass in motion. Imagine the magnet represented by a tube, in the centre of which there is a screw pump, and let the tube be immersed in water whilst the pump is rotated.' The water will issue at one end, flow in curved stream-lines and with varying velo- city round the tube, and enter it again at the other end. The unit exploring pole we replace by a disc of unit surface, which we place into various positions within the space surrounding the tube, and thus measure the force of the stream at any point. This analogy is im- perfect, because the force exerted by the water varies not as the velocity, but as the square of the velocity. Assuming, however, that the former be the case, then such a model can in a somewhat crude fashion be made to represent the magnetic field. We may think of the lines of force not as a definite number of fixed lines threading through the space which separates the two poles of the magnet, but as the stream-lines of a kind of magnetic fluid circulating through this space. Near the poles of the magnet the stream is contracted, and the velocity therefore great. In these places the force of impact of the magnetic fluid upon the exploring pole is a maximum, whilst farther away from the poles where the velocity, consequent upon the expansion of the stream, is less, the force of impact is also less. In .this manner can be explained the variation of magnetic AND TRANSFORMERS. 37 force as we move the exploring pole into different parts of the field, and the fact that a magnetic field taken by itself represents a definite amount of stored up energy. The conception of magnetic stream-lines is thus prefer- able to that of the rigid lines of force, and is indeed now generally adopted. Though we speak of a field of so many lines per square centimetre, we understand by this that the flow of force is so many times that exist- ing in a unit field, and the reader is asked to put this- interpretation upon the term "lines of force" where- ever this term occurs in this book. Units of Electro-Magnetic and Dynamic Measurements. Force. Every system of physical measurement must- be based upon the three fundamental units of mass,, length and time, and the different systems vary only in so far as the absolute magnitude of these fundamental units and their corresponding numerical values may differ. Thus, in the English system of measurement, a force of one pound is that force which if applied for one second to the mass of one pound will give it an accelera- tion equal to that of gravity, or, say, 32'2ft. per second. In the metric system the force of one kilogramme is similarly defined as that force which, if applied for one second to the mass of one kilogramme, will give it an acceleration equal to that of gravity, or, say, 9 '81 metres per second. In both systems the term force is similarly defined, but the units are of Different magni- tude, though identical in kind. For electro-dynamic measurements it is customary to reckon forces in a much smaller unit than either the pound or the kilo- 38 DYNAMOS, ALTEENATOES, gramme. This unit force is obtained by adopting the -centimetre as the fundamental unit of length, the gramme as the fundamental unit of mass, and the second as the fundamental unit of time. Measurements of forces and all other physical quantities which are based upon these fundamental units are said to be given in the centimetre, gramme, second, or, briefly, in the C.G.S. system. Thus, if we are told that a certain force has the value 20 in the C.G.S. system, we know that it is a force which, acting for one second upon the mass of 980 FIG. 6. one gramme, will give it an acceleration of 20 cetimetres per second, or, if acting for one second upon the mass of four grammes, will give it an acceleration of five centi- metres per second, or, if acting for the twentieth part of a second upon the mass of one gramme, will give it an acceleration of one centimetre per second. A force of one, or unit force, will similarly be defined as that force, which, acting upon the mass of one gramme for one second, will accelerate its velocity by one centimetre per second. Fig. 6 may serve to clearly explain this relation. Let a weight of 980 milligrammes slide abso- lutely without friction upon a table. Attach to this AND TBANSFOEMEES. 39 weight a perfectly weightless and flexible cord, which is taken over a pulley, E, and to the lower end of the cord attach a weight of one milligramme. Let the pulley have no mass, and turn without friction. The only force acting upon the system is that of gravity, which tends to pull the small weight down and the large weight forward on the table. If the large weight were not attached to the cord, the small weight would fall with an acceleration of 981 centimetres per second, but as the total mass to be set in motion is 981 times as great, the acceleration will only be one centimetre per second. Now let us increase both weights in the same proportion, namely, the large weight from 980 milligrammes to 1,000 milligrammes that is, to one gramme and the small weight from one milligramme to 1,000; 980 = 1*0204 milligrammes. By the propor- tional increase of both weights we have not altered the acceleration, which is still one centimetre, and as the force which produces this acceleration in the large weight passes through the cord, we find that the tension in this cord represents exactly unit force in the C.G.S. system. Engineers are in the habit of expressing forces, not as the cause of acceleration in a given mass, but simply as so many pounds, or grammes, or tons whichever unit is most convenient. To express the magnitude of unit force in our cord in this manner, we have only to ascertain how much of the small weight is actually transmitted in the shape of a pull in the cord. It is obvious that the whole of the small weight cannot be so transmitted unless the small weight is at rest, but as the small weight is moving downwards with an 40 DYNAMOS, ALTEENATORS, accelerated speed, the force corresponding to the ac- celeration is, so to speak, taken off the cord, and only the difference between the weight and the force required to- accelerate that weight is transmitted. The small weight is T0204 milligrammes, and its acceleration is one centimetre per second, whilst that due to gravity is 981 centimetres per second. The force which reaches the cord is therefore that corresponding to an accelera- tion of 980 centimetres, or QQf) 1-0204 x = 1-019359 millirammes. We thus find that in a locality where the acceleration of gravity is 981 centimetres, unit force may be repre- sented by the weight of 1*019359 milligrammes. The reference to gravity is necessary, as can easily be seen if we go through a calculation similar to the above, but made on the supposition that the acceleration due ta gravity is different. As a matter of fact, such differ- ences exist even on our planet, but the differences are small. Suppose, however, that there were on this earth a spot in which the acceleration of gravity is only half that assumed in our previous calculation. This would not alter the magnitude of unit force as defined by unit mass and unit acceleration, and which could be recorded in precisely the same manner by a spring balance at all points of the earth, but it would alter the equivalent weight. We should find that unit force in this case would be represented by the downward pull of a weight of 2 '038718 milligrammes, that is twice the weight as before. In expressing unit force as the dead weight of 1 '019359 milligrammes, it is therefore necessary to remember that the relation only holds AND TEANSFOEMEES. 41 good for those localities in which the acceleration of gravity is 981 centimetres per second. Unit force as thus defined is called a "DYNE," and we may therefore say that the force of a dyne is in our latitudes represented by the weight of T019359 milli- grammes, or approximately by a weight by two per cent greater than that of a milligramme. From this we find the following relations : One gramme ... = 981 dynes. One kilogramme = 981,000 dynes. One pound ... = 444,980 dynes. One ton - 996,752,240 dynes. Activity or Power. Having now defined the unit of force, we must next go through a similar process to define the unit of activity or power. Obviously, unit work is done if the force of one dyne acts through the distance of one centimetre, and if this work be performed in unit time that is, in one second we have unit rate of doing work. For this we use the term unit energy. The name given to the unit of work is the " EEG," representing the work performed in overcoming a force of one dyne through a distance of one centimetre, and if this be done in one second we have the unit of power or activity. Some very simple arithmetical operations, which need not be given in detail, show that the following relations exist : 1 gramme-centimetre per sec = 981 ergs per sec. 1 kilogrammetre ,, ,, = 98, 100, 000 ergs ,, ,, 1 foot-pound ... ,, ,, = 13,562,859 ergs ,, ,, 1 English horse-power =7,459,571,687 ergs ,, ,, 1 metric horse-power =7,357,500,000 ergs D 42 DYNAMOS, ALTEENATOES, These figures are inconveniently large, and for practical work a larger unit than the erg-second is generally adop- ted. This is called the "WATT," and is equivalent to 10,000,000 ergs. By introducing this, unit we have the following relations : One English horse-power = 745'957168, or very nearly 746 watts. One metric horse-power = 735 '75, or very nearly 736 watts. In future, when speaking of horse-power, it will be understood that the horse-power is reckoned as equiva- lent to 746 watts. Work. We have yet to define the unit of work. This as already stated is the erg, and is of course to be considered irrespectively of the time in which it has been performed, but as engineers are more familiar with the idea of power than work, unit work is sometimes defined with reference to unit power. Unit work is obviously represented by the work done by unit power in unit time. This unit is also inconveniently small, and for practical purposes it is customary to employ a unit 10,000,000 times as great namely, the "WATT- SECOND" or "JOULE." If we raise a weight from the floor and place it upon the table we have done work, and the amount of this work is independent of the time it has taken us to raise the weight. The rate at which the work has been done (that is, the power or activity) is inversely proportional to the time, but the work itself is a constant, and may be expressed as the product of the weight and the height to which the AND TEANSFORMEES. 43 weight has been raised. We may thus express the work by using the foot-pound or the kilogrammetre as a unit, but as these terms are generally also used to express rate of doing work or activity, it is pre- ferable to adopt another way of reckoning work. We can for this purpose use the thermo-dynamic equivalent and reckon work not as so many foot- pounds, but as so many heat units. Thus, if we lift 772 Ib. 1ft. we have done 772 foot-pounds, or the work represented by one British heat unit. Simi- larly, if we raise one kilogramme to a height of 424 metres we have done the work which is equivalent to one calorie. The calorie is the heat required to raise the temperature of one kilogramme of water by one deg. C. Adopting the thermo-dynamic equivalent as the basis for reckoning work, we find by a simple arith- metical operation, which need not be given at length, that the following relations exist : One British Fahrenheit heat unit = 1,047*053 joules or watt-seconds. One calorie = 4,159*44 joules or watt-seconds. The use of these units may be illustrated by the fol- lowing example : Glow lamps are often used under water for decorative purposes. Assume that a lamp absorbing energy at the rate of 60 watts is placed into a vessel containing one litre or, say, one kilogramme of water at 20 deg. C. Supposing the energy which in the lamp is transformed into heat is all communicated to the water and that there is no radiation of heat How long will it take until the water is raised to boiling point ? Boiling point will be reached when 80 D 2 44 DYNAMOS, ALTERNATORS, calories have been given to the water. This will be the- case when the lamp has dissipated into the mass of water surrounding it 80 x 4,159'44 = 332,755 joules. Since 60 joules are given off by the lamp in one second, or 3,600 joules in one minute, it will take 92'43 min- utes, or, say, about one and a half hour, to bring the water to boiling point. In reality it will take some- what longer, as we are not able to entirely prevent radiation from the vessel containing the water. Mathematical and Physical Poles. In the same manner as we distinguish between mathematical and physical points must we also distinguish between mathematical and physical magnet poles. The magnets shown in Figs. 3, 4, and 5 have physical poles that is, poles of finite dimensions. The poles are those parts of the magnet from which lines of force emanate, and as shown in the figures those parts occupy some space. In Fig. 4 it is, in fact, difficult to distinguish between the poles and other parts of the bar, since the lines of force emanate from almost the whole of its surface. They are, however, densest at the ends, and we therefore call the ends of the bar conventionally its poles without fixing any very definite limits to their extent. This indefinite arrangement of lines is obviously inconvenient for mathematical treatment, and in order to get over the difficulty we imagine the physical magnet replaced by an imaginary or mathe- matical magnet, consisting of a middle part wholly free from lines and two mathematical points for its poles from which all the lines of force emanate. A single pole is impossible in nature, but by making our AND TRANSFOEMEES. 45 imaginary magnet long enough we can separate its two poles sufficiently far to obtain round each almost the same effects as might be expected from single poles. The strength of a magnet, whether it be a physical or mathematical magnet, can be expressed as the product of its length that is, the distance between its poles and the amount of free magnetism at either pole. This product is called the " MAGNETIC MOMENT." We assume that in each pole there is concentrated a definite amount of what may be called magnetic matter, from which the flow of force emanates. This matter, though of the same kind at both poles, must be supposed to differ in its sign. At one end of the magnet we have positive or north magnetic matter, and at the other end we have negative or south magnetic matter. Supposing the flow of force to be taken as proceeding from the north pole to the south pole through air, we can also say that the north magnetic matter sends out and the south magnetic matter absorbs the stream-lines of magnetic force. We take in this definition the direction of the stream-line to be that in which a free north pole would be urged through the field. Whether such a thing as magnetic matter actually exists or not is of no practical importance. The term magnetic matter is merely a convenient way of expressing a certain property of magnet poles, and may be retained without in the slightest degree contradicting experimental facts. Under this conception the attractive force of a magnet must be assumed to be proportional to the amount of magnetic matter, or, as we may also say, to the amount of free magnetism concentrated in its poles, and simi- larly the strength of field must be assumed to be directly 46 DYNAMOS, ALTEENATOES, proportional to the amount of free magnetism at the: poles. The Magnetic Field of a Mathematical Pole. Let, in Fig. 7, M represent the north pole of a mathematical magnet of such length that we may leave its south pole out of consideration. Let the quantity of magnetic matter concentrated in this pole be also- FIG. 7. denoted by M, and place another north pole containing in .units of magnetism at the distance r 2 from M. Ac- cording to a well-known law the repulsion between the i i XT . m M 4*^ ^ -, two poles is given by the expression - Now des- T 2 cribe with radius, r 2 a sphere, S 2 , round M, and imagine the pole m placed at various points on this sphere, then the repulsion between M and m, though varying in direction, will for all these positions have the same AND TEANSFOEMEBS. 47 magnitude. The sphere, S 2 , is, in fact, a surface of con- stant magnetic potential. The lines of force constitu- ting the field of M are radii cutting S 2 at right angles. Now move the pole m from its position on the equi- potential surface S 2 to the position m l on the equipo- tential surface S^ The work done upon m in transit is obviously f i\ M m _ /I 1 \ / -9 d r = - M m I - J r 2 r 2 \r 1 rj the negative sign denoting that such work has been expended. This expression gives the difference of magnetic potential between any two points of the sur- faces Si and S 2 if we suppose the pole m to contain unit of magnetism. Now let r 2 be infinitely large as compared with r l9 or, in other words, let the pole be brought from a point as far away from M as to be beyond its field, then the work done upon unit pole in bringing it to a point on the sphere Sj is obviously and this expression gives the potential of the surface S r We may thus define magnetic potential at any point of a magnetic field as the work which must be done upon unit pole to bring it from a place beyond the field where the potential is zero to that point of the field. The numeric value of the magnetic potential must naturally depend upon the units we choose for expressing it. We define unit magnetism as that amount of magnetic matter which, if concentrated in a point, will repel an equal amount of magnetic matter concentrated in another point one centimetre distant with the force of one dyne. E 48 DYNAMOS, ALTEKNATOKS, Thus let, in Fig. 7, both M and m be poles containing unit magnetism, or, briefly, unit poles, and let r T be one centimetre. Imagine the poles tied at that distance to the ends of a cord, then the tension in that cord will be one dyne, and this tension will be the same if m is moved to any point of the sphere Sj. Now we have previously denned unit strength of field as that flow of magnetic lines which will exert unit of mechanical force upon unit pole. The unit of mechanical force is the dyne, and the unit of field strength is a density of one line per square centimetre. In order to obtain unit of repulsive force there must therefore pass such a flow of magnetic force through the sphere Sj as can be expressed by a density of one line of force per square centimetre. Now a sphere of the radius 1 has a surface of 4?r square centimetres, and we find therefore that the pole M is sending out a total of 4 TT lines of force. A pole of twice the strength will obviously send out twice as many lines, and generally a pole of the strength M will send out 4 TT M lines. Calling F the total field strength, expressed as the number of lines of force, or, as it is also termed, the total induction, emanating from a pole containing M units of magnetic matter, we have therefore the following relation between these quantities F = 47rM . . .. . (I) 7 F M-2* 4 7T CHAPTEE III. Magnetic Moment. Measuring Weak Magnetic Fields. Attractive Force of Magnets. Practical Examples. Magnetic Moment. It has already been mentioned that the magnetic moment of a magnet is the product of the strength of pole, M, and length, L. Replacing M by its equivalent value here given, we have T T^ Magnetic moment = -j Now F is the number of unit lines of force going out at one end and in at the other end of the bar. If we denote by B the number of lines flowing through each square centimetre of cross-section of bar and by A the area of cross-section, we may also write TVT 4-' Magnetic moment = The symbol B indicates the density of lines within the bar and is commonly called the " specific induction," or, briefly, the " induction." Since LA is the volume of the bar, we can also say that the magnetic moment of a straight bar magnet is equal to the volume multiplied by the specific induction and divided by 4 TT. Now 50 DYNAMOS, ALTERNATORS, imagine our bar magnet suspended in a magnetic field, in which the induction is H, and let the lines of this field be all horizontal and at right angles to the axis of the bar. The north pole of the bar will be jpulled for- ward that is, in the direction in which the lines of the field flow and the south pole will be pulled in the opposite direction, the two forces producing a certain torsional moment, which is given by the expression Torque = M L H. LABH Torque = - 4 TT The torque is of course here given in dyne-centimetres. To obtain it in gramme-centimetres we have to divide by 981. An example may serve to give an idea of the kind of forces we have to deal with in magnetism. Let us suppose that we magnetise a large steel bar and suspend it in the field of the earth, in fact, that we make a gigantic compass needle and measure the tor- sional moment which is required to keep this compass needle in an east-west position. Let the magnet be one metre long and ten centimetres square. If strongly magnetised by suitable means we shall be able to con- centrate on each square centimetre of end face about 400 units of magnetic matter, corresponding to an induction of about 5,000 lines per square centimetre of cross-section. The field of the earth may be taken as 18 C.G.S. units. Inserting these values in the above equation, we find that the field of the earth will exert upon our bar magnet a torque of 730 gramme-centi- metres. To keep the bar in its east to west position we must therefore apply to one end of it a force of AND TEANSFOEMEES. 51 14*60 grammes, or, say, a little over half an ounce. This, it will be seen, is a very small force for so large an apparatus, the dead weight of which would be about 1801b., but then it must be remembered that though the magnet taken by itself is powerful, the field in which it is placed is very weak. Had the strength of field, H, been such as can easily be produced in air by means of coils of wire through which currents pass, the torque exerted by the bar would have been enormously greater. A field of 500 C.G-.S. units can easily be pro- duced between two coils placed parallel to each other at a distance about equal to their radius. Now, if we suspend our steel magnet in such a field the torque in gramme-centimetres will be Torque = 100 x 100 x x 500 x - = 2,030,000. To reduce this to kilogrammetres we divide by 1,000 x 100 = 100,000, since the kilogramme contains- 1,000 grammes and the centimetre is the hundredth part of the metre. We thus obtain Torque = 20*3 kilogrammetres. To keep the bar in its position parallel to the plane of the coils we would, therefore, have to apply at each end a force of 20'3 kilogrammes, or 451b., the direction of these forces being at right angles to the axis of the bar. Measuring Weak Magnetic Fields. The calculation here given is only correct under the supposition that the magnetism of the bar remains un- altered when the bar is placed into the field. In reality, 52 DYNAMOS, ALTEKNATOKS, however, this is not the case when the field is strong. A field of 500 C.G.S. units is already a very strong field, and would alter the magnetisation of the bar even if the latter be made of the very hardest steel. The calculation of torque must therefore be taken as being only an approximation, and has been given merely to show the kind of forces coming into play in such cases. In a weak field the magnetism of a strongly magnetised steel bar is not changed, and is, in fact, what it professes to be by name, that is "permanent." The magnetic moment of the bar may therefore be regarded as constant for all its positions in the weak field, and this fact is made use of in the determination of the strength of magnetic fields. It might appear at a first glance that we if knew the magnetic moment of the bar, the strength of the field could be easily found by measuring the mechanical couple required to keep the bar at right angles to the lines of the field, but such a measurement could not be made with any accuracy. In the first place, the couple with a bar of moderate dimensions and a weak field is exceedingly small, and therefore difficult to determine exactly, and, in the second place, the determination of the magnetic moment is in itself a more difficult operation than the determina- tion of the strength of a magnetic field, which, indeed, generally precedes it. The method commonly used for the determination of weak magnetic fields, and more especially for the field of the earth, consists in making two distinct tests with the same magnet. In the first test the magnet is so placed as to deflect a compass needle, and from the relative position and distance between needle and magnet, and the deflection of the AND TEANSFOEMEES. 53' former, the ratio between M, the magnetic moment of the latter, and H, the field strength, can be calculated. TT We thus obtain^; Next we set the magnet swinging, and note the time of vibration. According to a well- known law, the time of vibration is proportional to the square root of the moment of inertia (which for a cylindrical bar can be easily calculated), and inversely proportional to the square root of M H, the force under the influence of which the bar swings. By multiplying the two values we obtain H 2 , and by dividing one by the other we obtain M 2 , so that the two observations suffice for the determination of the strength of field as the magnetic moment of the bar. As this method is to be found described in every text-book on magnetism it is not necessary to enter into its details in this place, the more so as for the determination of the strong fields with which the electrical engineer is mostly concerned, it is only of value in so far as it gives us a point of comparison. Strong fields are generally measured by another method based upon electromagnetic induction, the apparatus used consisting of wire coils and a ballistic galvanometer. One of the wire coils is placed under the influence of the field of the earth, and the other under that of the field to be measured, whilst the deflection of the galvanometer in both cases enables us to compare the two fields. The subject must, however, be left to a later chapter, in which we shall deal with the interaction between magnetic fields and electric currents. The Attractive Force of Magnets. The formulae given in the preceding and present 54 DYNAMOS, ALTERNATORS, chapter enable us to calculate the mechanical force in dynes, or grammes, or pounds with which magnets attract each other, or a magnet attracts a piece of iron it has magnetised by induction. When the distance between the attracting (or repelling) poles is large in comparison with the dimensions of the magnets, the problem is simple enough. We can in this case imagine the physical magnets replaced by their equiva- lent mathematical magnets with their poles concen- trated in mathematical points, and by applying the law of inverse squares, in the manner to be found in every text-book on magnetism, obtain perfectly definite ex- pressions for the forces acting between the poles and the resulting couples. The problem in this form has, however, no interest for the designer of dynamos, and need, therefore, not be further considered in this place. What interests the dynamo builder is the attraction between magnetised surfaces of large extent, as com- pared with their distance apart, and in these cases the law of inverse squares ceases to be applicable. When investigating the attraction between the pole-pieces of a dynamo and the surface of its armature, we are not dealing with magnetism concentrated in mathematical points, but with magnetism distributed over definite surfaces. The forces resulting from this may become under certain conditions very considerable, and as they must directly affect the armature shaft, bearings, and other parts, it is necessary to investigate the matter so as to be able to take these forces into consideration in- designing the mechanical portion of the machine. Before proceeding to the theoretical consideration of the subject, it will be useful to show its practical bear- AND TEANSFOEMEES. 55 ing with reference to a definite case. Fig. 8 represents diagrammatically the field, F, and armature core, A, of an ordinary dynamo of the so-called "upright" type. The flow of lines takes place from the left, or north pole-piece, IS^NN^ through the small air space, a lt a 2 , into the armature core, A, then out on the other side, where the flow of force again leaps across the air space, b l b. 2 , and enters the pole-piece, Si S S 2 , returning by the yoke, Y, to the north pole-piece, and thus forming 56 DYNAMOS, ALTEBNATOKS, a closed magnetic circuit. Two such circuits are shown in the figure by dotted lines, the direction of flow being indicated by arrows. It has already been pointed out in the previous chapter that the surface of the pole-piece and that of the armature must be equi- potential surfaces, a fact easily verified by experiment. The lines of force between these surfaces must there- fore stand at right angles to them in every point, or, in other words, be radial with reference to the centre, 0, of the armature. Near the edges of the polar surfaces their true radial direction will naturally be somewhat disturbed, but we deliberately neglect the effect of this disturbance. Imagine a unit exploring pole placed at N 2 , and it will be repelled from the surface of this pole-piece in a radial direction, whilst at the same time it will be attracted in the same direction, by the surface of the armature, the force acting upon the pole being the sum of repulsion and attraction. On the other side, a unit exploring pole placed on the surface of the armature opposite S will be repelled by the armature and attracted by the field pole. Now let, in the first case, the exploring pole be rigidly fastened to the surface of the field pole at N 15 or, better still, let it be part and parcel of the latter. This assumption is equivalent to saying that we consider the forces acting upon an element of the polar surface, N x N N 2 , of such extent that it contains unit quantity of magnetic matter. Obviously this element of surface cannot be repelled from the rest of the surface, since it forms an integral part of it ; and one of the forces which we found above as acting upon a free unit pole is now eliminated. The other force, that of attraction to- AND TBANSFOEMEES. 57 wards the surface of the armature, remains, however, unchanged. Each element of the polar surface is thus attracted towards the armature, and since action and reaction must be equal and opposite, the armature as a whole is attracted by the polar surface. The same reasoning applies to the other side of the machine. If we imagine the unit exploring pole to form part and parcel of the armature surface opposite Sj, we find that although the repulsion towards the right has ceased, the attraction towards the right remains, and as this applies to every element of armature surface within the pole-piece, Sj S 2 S, the armature as a whole experiences an attraction to the right. If the arrangement of the armature in the field is perfectly symmetrical, the attraction to the left balances the attraction to the right, and there is no side thrust on the bearings, though there may be up or down thrust, if the arrange- ment is unsymmetrical with reference to the diameter, N S. Imagine, for instance, the upper half of both pole-pieces removed. The armature would in this case be attracted by the north pole-piece, not only to the left, but also downwards. Similarly, the attraction on it from the south pole-piece would be to the right and downwards. The two horizontal components balance each other, but the vertical components are added, and produce a down thrust on the bearings in addition to the thrust due to the weight of the arma- ture. The same effect, but to a lesser degree, must result from any minor inequality between the upper and lower halves of the pole-pieces, and as it is not always practicable to ensure absolute symmetry in all directions, it becomes important to be able to calcu- 58 DYNAMOS, ALTEENATOES, late the mechanical forces and strains resulting from such want of symmetry. We now proceed to investi- gate this matter from a more general point of view. FIG. 9. r ^"Let,[in Fig. 9, N N and S S represent the polar end faces of two straight magnets, of so great a length that the influence -Jof their other poles upon an exploring pole FIG. 10. placed into the gap at A may be neglected ; or let N S be the poles of a magnet bent into ring form as shown in Fig. 10. In such a magnet the only accessible field r ml V AND TEANSFOEMEES. 59 is that existing in the narrow gap between the poles, and an exploring pole placed in this space cannot be affected by any other lines of force but those leaping across the gap. The amount of magnetic matter con- tained on each polar surface, divided by the surface, is, in a straight bar magnet, obviously equal to the mag- netic moment divided by the volume, and is called the intensity of magnetisation. In a curved magnet this definition does, however, not hold good, as can easily be seen if we imagine the originally straight magnet bent into a circle until the poles nearly touch. The magnetic moment, which is the product of pole strength and distance between the poles, has now decreased, but the amount of magnetic matter on each pole has not decreased. To make the definition fit the case of bent magnets, we must consider not the ratio between the magnetic moment of the magnet taken as a whole and divided by its whole volume, but the magnetic moment of a cubic centimetre cut out and separated from the rest of the mass. It is, however, more simple to abstract altogether from the idea of intensity of magne- tisation and substitute that of " density of magnetic matter." Thus we may assume that the magnetic matter is uniformly spread over the polar surfaces with a density m, meaning thereby that on each square centimetre of surface there are m absolute or C.G-.S. units of magnetic matter. Each particle of magnetic matter on the surface N N repels the point A according to the law of inverse squares, but the direction of these forces and their intensity varies. The total force is found by integrating the elementary forces, as we now proceed to show. E2 60 DYNAMOS, ALTERNATORS, The horizontal component, d P, of the force exerted by an elementary particle, a-, of the polar surface at D, upon the unit pole placed at A, is evidently g - 2 cos - a > an ^ if we imagine a complete ring, D D, a T x of such elementary particles of width, d a, the force exerted by the ring is ,-P. m 2 TT a d a d P = -- o --- o cos. a. ic 2 + a 2 It will be seen from the diagram that a = x tan. a, and for d a we can therefore write x - - ; so that the cos. a above expression for the horizontal force becomes , -P. m 2 TT a d P = 7-5 - ^r - 5- # cos. a a a. cos. 2 a But since (# 2 + a 2 ) cos. 2 a = # 2 , we have also d P = m 2 TT - cos. a d a. x . a sin. a Since - = - we find x cos. a cZ P = 2 TT m sin. a d a, and by integrating between the limits a = 0, and a = a} we find the total repulsive force exerted by the polar surface upon a unit pole, P = 2 TT m (1 cos. a). Now imagine the surface very large in comparison with the distance x of the point A. In this case the lines joining A with the edges of the polar surface AND TEANSFOEMEES. 61 will be sensibly parallel to it. We have therefore a = ~-. Since the cosine of ~ is 0, we have A _j P = 2 TT m . . . . . . (2) The unit pole is not only repelled by the surface N N, but it is at the same time attracted by the surface S S, and a similar calculation shows that the attractive force of this surface upon it is also 2 TT m, so that the total force exerted upon the unit pole in the gap between N N and S S is 2 P = 4 TT m. This expression enables us to calculate the strength of the field within the gap. It has been previously stated that, according to a conventionally adopted measure, we call that a unit strength of field in which there is unit flow of force per square centimetre, or in which a unit pole is impelled with the force of 1 dyne. If the impelling force is 4 TT m dynes, the flow of force per square centimetre is 4 TT m. This is commonly called the "induction," and denoted by the symbol |i. We thus find that ^ = 4 TT m. Let S denote the number of square centimetres in each polar surface, then S is the total flow of force or field strength, F, expressed in number of unit lines of force ; and S m is the total pole strength, or amount of magnetic matter, M, spread over each of the polar surfaces. We find therefore F = 4<7r M. 62 DYNAMOS, ALTEENATOES, that is to say, the total field is 4 TT times the total pole strength, a result which has already been obtained in the previous chapter for a single pole. In that case, however, the field surrounded the pole on all sides, and it was not immediately obvious that the expression would also hold good in cases where the field is, so to speak, one sided that is, emanating from the pole in one direction only. This we now see is the case, and the formula F = 4 TT M is universally applicable. Returning now to formula (2) we have seen that the repulsion of the surface NN upon unit north pole placed close to it is 2 TT m. Had the exploring pole been a unit south pole, we would have found the same expression, but with a negative sign, showing that the force was one of attraction that is, opposite in direc- tion. Now let it be part of the surface of the south pole, and we see immediately that every unit of magnetic matter spread over the surface S S is attracted by N N with a force of 2 TT m dynes ; and since there are m s such units on this surface, the total force is 2 -TT m 2 s. It will be convenient to bring this expression into another form by introducing the induction, IP. IS II 2 Since m = j , we have w 2 = 2 , and O 7T This formula, it should be remembered, is only correct if the distance between the polar surfaces is so small in comparison with their extent that the dis- turbance near the edges, where the upper limit for the angle a is less than ~, may be neglected ; or where,. AND TRANSFORMERS. 63 though the distance between the polar faces is sensible, as in dynamo machines, one of the surfaces extends considerably beyond the other. When the surfaces are in actual contact as for instance, in a magnet and its keeper the formula may be applied without correc- tion, but when the distance is sensible and the surfaces are small, a certain allowance for the influence of the edges must be made. For practical purposes it is, however, not generally necessary to calculate the attractive force with very great accuracy, and the formula, s ^ Attractive force in dynes = ^ (3) O 7T may be used as a fair approximation. It will be useful to show the application of this for- mula by a few examples. Let, in Fig. 11, M represent a magnet provided with a keeper, K. The magnet limbs are 3 centimetres square, and the induction is ^ = 20,000. The attractive force of each limb on the keeper . 9 x 20,000 2 m ; . . ... , ., in dynes is therefore 5 5-2-3 To obtain it in kilo- o x o'14 grammes we divide by 981,000 and find the attractive f *V\rt.r t! 9 x 400 x 10 6 force of both limbs = ^u x 981,000 : Q = 292 kilogrammes. A magnet of the dimensions here given would weigh a little under 2 kilogrammes, so. that its attractive force is approximately 150 times its dead weight. As another example we may take the dynamo shown in Fig. 8. Let the armature core be 30 cm. (nearly 64 DYNAMOS, ALTEBNATOES, 12in.) diameter, and 40 cm. (nearly 16in.) long. Let the angle embraced by the pole-pieces on each side be 120 deg., and assume a mean induction of |i = 5,000 across the polar diameter, N S. It will be shown later on that the induction is not constant over the whole extent of air gap, but that it has a greater than M FIG. 11. its mean value below and a smaller than its mean value above the polar diameter. The reason for this variation cannot be given now, as it has to do with the inter- action between electric currents and magnets, which will be treated in subsequent chapters. For the present we shall simply assume that such a difference exists, and that numerically it may be expressed by saying AND TKANSFOEMEES. 65 ihat the mean field induction above the polar diameter is 4,800 and below it 5,200 C.G.S. units. The attrac- tion on the upper right-hand quarter of the armature may, with a polar angle of 120 deg., be represented by FIG. 8. a force acting at 30 deg. to the polar diameter, and its vertical component is obviously sin. 30 deg. = '5 of its numerical value. Similarly with the left-hand upper quarter. The total vertical force acting upwards upon the upper half of the armature is therefore equal to the 66 DYNAMOS, ALTEENATOES, attraction of the upper half of one pole-piece. In the same way we find the total vertical force acting down- wards upon the lower half of the armature equal to the attraction of the lower half of one pole-piece. The difference between these two forces represents the down thrust upon the bearings in addition to that due to dead weight. Inserting the numbers into equation (3) we find: which is about 100 kilogrammes. A dynamo of the dimensions here given would be a machine of about 40 or 50 h. p., and it will readily be seen that in such a machine an extra load of Icwt. per bearing is quite unimportant and may be neglected in the design. There are, however, cases in which the magnetic pull may become important, and provision must be made to withstand it. As an example may be cited a class of dynamo known under the name of disc machines. In these machines the armature core is not of cylin- drical shape, but has the form of a flat disc revolving between circular rows of poles on either side of it. When carefully adjusted, the width of the gaps on either side is equal, and the attractive forces are balanced. The armature is kept in this position by a thrust bearing on its shaft, and as long as there is no wear the load on the thrust bearing is very small. If, however, wear takes place, or from some other cause the armature be allowed to run nearer to one ring of pole faces than the other, the field on that side is stronger, and a considerable magnetic pull is the result. AND TRANSFOEMEES. 67 Let, in a 100-h.p. machine, the sum of the polar surfaces on one side of the disc be 2,000 square centimetres, and let the induction for which the machine was originally built be 4,600, the air gap being on either side 20 mm., a little over fin. Now, suppose that from some cause the armature is allowed to shift by 2 mm., then, roughly speaking, the induction on the side of the reduced gap will have become 5,000, and that on the side of the widened gap 4,200. We shall then have an unbalanced magnetic thrust of 2,000 x (5,000*-4,20QS) ^ 25-12x981,000 or, say, about 600 kilogrammes, which is a force of sufficient magnitude to be taken into account when designing the mechanical details of the machine. CHAPTEK IV. Action of Current upon Magnet Field of a Current. Unit Current Mechanical Force between Current and Magnet Practical Examples English System of Measurement. Directive Action of a Current upon a Magnet. If we lay a case containing a compass needle on the table and stretch a wire across the top of it, we find that upon sending a current through the wire the needle tends to set itself at right angles to the wire. If the needle is not under the influence of any other force, or if the current is very strong, the position assumed is exactly perpendicular to the wire, and if other forces act on the needle, the position assumed by it indicates the direction of the resultant of these other forces and the deflecting force due to the current. We are thus able by observing the degree to which the needle is deflected to form an estimate of the deflecting force exerted by the^current. We find in this way that the force is diminished if we raise the wire parallel to itself a certain distance from the needle, also that the direction of this force is reversed if we place the wire below instead of above the needle, and that for all positions the force increases with the current. AND TEANSFOEMEES. 69 The Magnetic Field of a Current. It will be obvious from these experiments that a wire carrying a current is surrounded by circular lines^of force over its whole length, and that the lines are Densest near the wire and less dense at a distance. FIG. 12. FIG. 13. There is, in fact, a kind of magnetic whirl round the wire, as shown in Fig. 12, the lines forming concentric rings. This will be more clearly seen in Fig. 13, where the wire is supposed to pierce a sheet of paper on which the lines are traced. According to Ampere's well- known rule, the direction in which the north pole of a 70 DYNAMOS, ALTERNATORS, needle is deflected can be ascertained in the following manner : Imagine a man swimming in and with the current^and looking at the north pole of the needle, then] the latter will be deflected to the left of the swimmer. We have in a previous chapter defined the FIG. 14. direction of flow of force in a magnetic field as that in which a free north pole is urged to travel, and this definition, combined with Ampere's rule, enables us at once to determine the sense in which the magnetic whirl takes place. If the current flows upwards through the wire, Fig. 13, the flow of force must be in the sense as AND TRANSFORMERS. 71 shown by the arrows; or, to put it in another way, if we look in the direction in which the current flows, the flow of force is clockwise. That the lines offeree arrange themselves in concentric circles can easily be shown by a modification of the experiment with iron filings, which we described in connection with the field of a magnet. We take a glass plate, Fig. 14, and drill a hole through its centre. The plate is covered with a thin film of paraffin, and a wire is threaded through the hole. Now send a current through the wire, and sprinkle iron filings, at the same time gently tapping the plate to facilitate the arrangement of the filings. The latter will assume the position shown in the diagram. To retain the filings we have only to gently heat the plate, when the paraffin melts, and the iron filings become embedded, and are thus fixed in position after the plate has cooled again. Strength of Field Produced by a Current. Having thus found that a current is surrounded by a magnetic whirl, constituting the field of the current, the next thing to do is to ascertain the strength of field at any point in the space surrounding the wire. From the circular arrangement of the iron filings we at once conclude that the force at any point is exerted at right angles to the plane laid through that point and the part of the wire, the influence of the current in which we desire to measure. It is, however, impossible to measure by itself the force exerted upon an exploring pole by the current in a short bit of wire, since the current must be brought to and led from this short bit by other wires, the current in which must also influence our pole, and 72 DYNAMOS, ALTEKNATOBS, thus mask the effect of the particular piece investigated.- We can only obtain a current in a closed circuit, and the exploring pole must necessarily be under the influence of the whole of the circuit. To investigate the law experimentally, it is therefore necessary to take a circuit of such simple shape that the observed effects due to the whole circuit may enable us to draw a con- clusion as to the effect of any single part. The most simple imaginable arrangement is that of a circular current with the exploring pole placed in the plane and centre of the circle. In this case, however, all parts of the circuit are equidistant from the pole, and the direc- tion of the current in any element of the circuit is at right angles to the line joining the element and the pole. The results obtained with such an apparatus will therefore not be applicable without further verification to circuits in which the elements are not equidistant from the pole and form other than right angles with the lines joining them to the pole. By using a circular current we find that the force exerted upon unit pole placed in the centre of the circle is proportional to the circumference of the circle, to the current strength, and inversely proportional to the square of the radius of the circle. We may thus reasonably conclude that the force exerted by an element is proportional to the length of this element, the current, and inversely pro- portional to the square of the distance of the element from the unit pole, but only if the element forms a right angle with the line joining it to the pole. Where this condition is not fulfilled the experiment leaves us with- out information. Here it is necessary to make an assumption, and to verify it by a subsequent experiment.. AND TEANSFOEMEES. 73 The assumption we make is that if the element forms an angle of less than 90 deg. with the line joining it with the pole that is, when the element is not seen in its full length, or, so to speak, broad side on from the pole the force is diminished in the ratio of one to the sine of the angle. In other words, instead of taking the length of the element itself, we take that of its pro- jection in the line of view from the pole. An element lying wholly in that line will therefore exert no force on the pole. Whether our assumption is correct can be verified by experiment, and for this purpose we chose an infinite straight current flowing down the wire, W W, Fig. 15. In reality we can, of course, not have an infinitely long wire, but by taking a wire of considerable length as compared with the distance of the pole N from the wire, we shall approach very closely to the theoretical condition, especially if we take care to carry the other parts of the circuit as far away from the pole as pos- sible. The current, c, in the element A B exerts a force which in absolute measure is given by the expression c A B ; and that exerted by the element C D is accord- a 2 - . cCE. mg to our assumption given by the expression , 2 If we now integrate these elementary forces over the whole length of the wire, and find that the resulting force is that found by experiment, we naturally con- clude that oar assumption was correct. It is for this purpose not even necessary to make a quantitative experiment, that is, actually weigh the force, since the absolute magnitude of such forces has already been found by the experiment with the circular current. F 74 DYNAMOS, ALTEKNATOKS, All we now care to know is the law according to which the force varies with the distance a, and this can be found by a very simple experiment. Let, in Fig. 16, W N FIG. 15. WW again represent the wire, and suppose there is suspended round it a ring-shaped wooden disc, D, on which we place a magnet, IS! S, in any position. We AND TEANSFOEMEES. 75 iind that there is no tendency for the disc to rotate, though the magnet taken by itself tends, as we have already seen, to set itself at right angles to the wire. With the direction of current as indicated by the arrow, w FIG. 16. the north pole of the magnet will tend to move forward in clockwise direction, as seen from above, whilst the south pole will tend to move in the opposite direction ; and since each force taken by itself would produce rota- tion of the disc, we conclude that the corresponding F2 76 DYNAMOS, ALTEENATOES, turning moments exerted upon the disc are equal and opposite. The forces exerted upon the poles must therefore be inversely as their distances, a lt a 2 , from the wire ; and if we find that the integration of the elementary forces in Fig. 15 give us this result, we naturally conclude that our assumption was correct. In this figure, the force exerted by the element A B tends to lift the pole N out of the plane of the paper, and the same* is true for DC and any other element. If N be a unit pole, the force due to the current, c, in the element C D is If we denote the distance between the elements, A B and C D, by x, and make the length of the element C D so small that it may be considered an infinitely small increment, dx, of this distance, we have: -i 7 a d a x = a cotg. a and d x = . 9C . . sin 2 2 a d x sm3 a c sm^ a b* d x . sin 3 a . c ~~ 2 a . d a . sin 3 a . c a 2 sin 2 a c sin a d a a which, integrated over the whole length of the wire that is, from a = to a = TT, gives the total force AND TRANSFOEMEES. 77 We see, therefore, that the force tending to lift the pole, N, out of the plane of the paper is indeed inversely proportional to a, the distance of the pole from the wire, and that, therefore, our above assump- tions are correct. Definition of Unit Current. Since the force exerted upon unit pole is in the C.G.S. system equal to the induction in air, or the strength of field, H, we can also write and say that the induction at a point of the field of a current flowing along a very long straight wire is two times the current divided by the distance of the point from the wire. This relation gives us at once the definition of unit current. It is that current ivhich, flowing along a straight wire of infinite length, produces a field of 2 C.G.S. units at all points 1 centimetre from the wire, or unit field strength at a distance of 2 centimetres from the wire. This definition, although perfectly correct, is not the one generally given in text-books. It is customary to define unit current in relation to a circular conductor of 1 centimetre radius. Obviously the force exerted by a current, c, upon a unit pole placed in the centre of the circle is 2 TT c, and if the current is unity the force is 2 TT. Hence we may also define unit current as that current which, flowing in a thin wire forming a circle of 1 centimetre radius, acts upon a unit pole placed in ihe centre with a force of 2 TT dynes. The unit of cur- 78 DYNAMOS, ALTEENATOES, rent thus defined, although of convenient magnitude, has not been adopted in practice. It is customary to measure currents in a unit only one-tenth the magnitude of that here defined, and to call this practical unit the AMPEEE. Thus a current of 25 amperes is the same as a current of 2*5 units in the C.G.S. system. Mechanical Forces between Currents and Magnets. To a certain extent we have already in the preceding paragraphs considered the mechanical forces between conductors and magnets, but this was done principally with the object of determining the properties of the magnetic field of a current. We must now approach the subject more from the engineer's point of view, and consider in detail the mechanical forces between conductors carrying currents and magnet poles or magnetic fields. It will at once be evident that if in our previous investigations we had assumed the strength of the exploring pole to be M instead of unity, all the forces would have been M times larger. Similarly, if the radius of the coil had been r centimetres instead of 1 centimetre, the force exerted upon the pole would have been smaller in the ratio of 1 to r. Let, in Fig. 17, N S represent a magnet of the pole strength, M, and place the north end into the centre of a circular wire of radius, r, which is supplied with a current, c, from a, cell, C. Let the magnet be so long that the influence of the current upon its south pole may be neglected, then the force with which the north pole will be drawn to the left is given by the expression AND TEANSFOEMEES. 79 From the pole N, lines of force emanate in all direc- tions, and, as was shown in Chapter II., equation (1), the whole flow of force is 4 TT M. FIG. 17. Imagine a sphere of radius, r, laid round the pole : then the density of lines on the surface of this sphere is 4-TrM M mi , , ,, , ,. | 2 = ~T The whole of the circular wire lies, M therefore, in a field of the strength ' for which we write the symbol fi, meaning thereby the induction or flow of force through the space close round the wire. It is customary to use the symbol P for the induction through iron, as will be shown later on, and to express the strength of a field by the symbol H. But as we shall use this symbol to denote the line integral 80 DYNAMOS, ALTEENATOES, of magnetic force, it will be best to retain the symbol $1 in all cases where we deal with induction or flow of force per square centimetre, whether this flow takes place through iron or any other substance. In the present case the substance is air, and the lines of force cut the wire in every point of it at a right angle, and the force produced in every point is parallel to the axis of the magnet that is to say, at right angles both to the lines of the field and to the direction of the current. That a mechanical force must act on the wire is evident from the consideration that we can have no action on the magnet without an equal and opposite reaction on the wire. We have seen that if the coil is fixed, the magnet will be drawn to the left. Now, if we imagine the magnet to be fixed, the tendency will be to draw the coil to the right. We thus see that a wire through which a current passes has, when placed into a mag- netic field, the tendency to move parallel to itself and at right angles to the lines of the field. The force pro- ducing this tendency is, in the case represented by Fig. 17, given by the equation Now, 27rris the length, Z, of the circular wire, and we find, therefore, that the mechanical force in dynes acting upon the wire is given by the product of current strength, length of conductor within the influence of the field, and strength of field, or in symbols P = Zc|i ...... (7) In this expression the current is, of course, given in C.G.S. measure. If it be given in amperes we have AND TBANSFOBMEBS. 81 To get the forces in kilogrammes we divide by 981,000 P kilogrammes = gj^~ ... (8) Or for convenience P kilogrammes = 101937 Ic & 10" 8 (9) Practical Examples. Thus, a wire carrying 100 amperes, and passing for the length of 1 metre through a field of 1,000 C.G.S. units, is acted upon with a force of l'01937kg., or very nearly 2^1b. It is this mechanical force due to the interaction of magnetic fields and electric currents which in dynamos has to be overcome by the power of the prime mover, and in motors gives the turning moment or torque to the spindle of the armature. This will be clearly seen from Fig. 18, which is a 'diagrammatic representation of a motor or dynamo. For the sake of simplicity only one loop of wire, A B C D, is shown on the armature, and the field magnets are shown in dotted lines. Through the narrow space included between the inner surface of the pole-pieces and the outer surface of the armature core (variously called air space, interpolar space, air gap, etc.) there exists a strong magnetic field that is to say, the space is traversed by lines of force, all flowing radially inwards from the north pole-piece into the armature core, and radially outwards from the armature core to the south pole-piece on the other side. An element of the armature conductor, A B, is therefore in exactly the same relation to the lines emanating from the north pole-piece as in an 82 DYNAMOS, ALTEKNATOKS, element of the circular conductor, Fig. 17, in relation to the lines emanating from N. Each element of this circular conductor, and therefore the whole conductor, is pushed to the right (the right hand of a swimmer in the current looking at the north pole, so that the lines would pierce him in front) , and if we imagine a swimmer FIG. 18. in the conductor A B it is easy to see that the ten- dency will be to push the conductor upwards, giving the armature a counter clockwise rotation, as seen from the end at which the current enters. If, in Fig. 17,. we reverse the magnet so that the south pole, S, occupies the centre of the circle, and imagine, again, a man swimming in and with the current whilst looking AND TEANSFOEMEES. 83 to the south pole, so that the lines of force pierce him at the back, then the conductor will be pushed to the left. By applying the same reasoning to the conductor C D, in Fig. 18, we find that it will be pushed down- wards, which will also produce a counter clockwise rotation. The application of formula (9) may be shown by the following example : In modern dynamos and motors the strength of field in the interpolar space may be taken as about 5,000 C.G-.S. units. Assume that a cur- rent of 100 amperes flows through the wire AB, in Fig. 18, then the force acting upon, say, 10 centi- metres of wire is given by formula (9) as *5097 of a kilogramme, or l'121b. This corresponds in English measure to about 3*41b. per foot of wire if the current is 100 amperes. We may thus say that with the strength of field customary in ordinary dynamos and motors every foot of wire under the influence of the field is subjected to a force of a little less than 3 Jib. when the current passing through the wire is 100 amperes. With larger or smaller currents this force will, of course, be proportionately larger or smaller. The English System of Measurement. The metric system of measurement, which we have up to the present employed, although the most rational and simple for purely scientific work, is not always convenient for the workshop, and for such purposes another system, which has received the name of the English system of measurement, is often employed. In this system we reckon forces in pounds, lengths in 84 DYNAMOS, ALTEENATOES, inches, and magnetic induction in a unit 6,000 times as great as the corresponding C.G.S. unit. This par- ticular relation of 1 to 6,000 has been adopted on account of certain calculations required in the design of dynamos, as will be explained in a later chapter. For the present it suffices to note that a total flow of force of 6,000 C.G.S. lines is equivalent to a total flow .of force represented by one English line ; that 120,000 C.G.S. lines are equivalent to 20 English lines and so on. The induction per square centimetre, or what is briefly called "induction," in the C.G.S. system can be expressed by its equivalent in the English system as a density of so many English lines per square inch. Calling B the induction in English measure, and ^ the induc- tion in the C.G.S. measure, we find by a simple calcu- lation that the two are related as follows By introducing this term and substituting inches for centimetres in equation (9), we find P pounds = 531 c I BlQ- 6 . . . (11) By the aid of equations (9) or (11), we can at once find the torque or turning moment of an armature of the kind represented in Fig. 18. Let, by way of example, the diameter of the armature measured to the centre of the conductors be 12in. and its length 20in. Assume that there are 120 conductors on the outside of the armature, and let the pole-pieces embrace an angle of 120 deg. on each side. Then there will be under Ms> e *c., then we can establish the following equations : Mi M2 ^ 7 c 3 % _ TT 7 1 63. Ms By adding these equations we obtain l 2 + l 3+ ). . (12) Line Integral of Magnetic Force. It will be seen that the term on the right of this equation is simply the work which must be done upon 96 DYNAMOS, ALTEKNATOKS, unit pole in bringing it from one end to the other of our chain of cylinders. Nothing would have been altered in our reasoning if instead of a field of straight lines we had assumed one of curved lines, provided we had suitably altered the shape of our cylindrical spaces. w The spaces filled by materials of different permeability might in this case form a complete chain closed on itself, and our exploring pole would then start from and arrive at the same point, but the journey could no longer be taken along any arbitrary route. It must now AND TBANSFORMERS. 97 be taken along a path, looping once round the conductor, the current in which produces the field, and for conve- nience we may choose a route along the lines of force. The work done is therefore the line integral of the magnetic force taken once round the closed magnetic circuit, and if we divide this quantity by the term ( + _?_ + -1- + . . . J we obtain the induction. An Vi M 2 M 3 x example will make this matter clear. Let, in Fig. 21, WW be a straight wire of very great length, through which flows a current, c, in the direction indicated by the arrow. Define round this wire a ring-shaped space, B, of section A and radius a. The flow of magnetic force within this space, as seen from above, has a clockwise direc- tion, so that if we carry a unit north pole once round the ring in a counter clockwise direction we must per- form work. It has been shown in equation (5) that the induction in air or the strength of field of such a cur- 2c rent is , which represents the force resisting the QJ movement of the exploring pole at every point of its journey. To find the work done in carrying the pole once round the ring we multiply this force with the distance traversed, which is 2 TT &, and find Line integral of magnetic force = 4 TT c. . (13) The induction can now be found from equation (12) . . . . . (14) l_ + 2_ +_3 -J- . ' . Ml M2 M3 whilst the total field strength of flow of lines is F = AW. 98 DYNAMOS, ALTERNATORS, It should be noted that the radius of the ring has vanished from the equation. It is implicitly contained in the terms which denote the lengths of the different sections, for the larger the radius the larger will also be these terms, but except in this way the radius has no influence on the induction. We conclude from this fact that the true circular shape of the ring is not essential, FIG, 22. and that a ring of any shape would give the same induc- tion provided the length of the different sections were the same as in the circular ring. This conclusion also follows from the fact that the work done upon unit pole- is independent of the exact route traversed, provided this route loops once round the conductor, the current in which produces the field. Instead of grouping our materials so as to form a truly circular ring round the conductor, we may therefore group them in any other way, the only essential condition being that they shall AND TEANSFOEMEES. 9S form a closed circuit round it. An arrangement, such as is shown in Fig. 22, will therefore be magnetically equivalent to that shown in Fig. 21. We have here the field-magnet system and armature of a dynamo, v/hich form together a closed magnetic circuit round the wire, W W, through which the current, c, flows. If the cross-section of the magnetic circuit were the same at every point, formula (14) could at once be used to determine the induction across the armature in this dynamo, but for reasons which will be explained later on, it is not customary to make the cross-section of the different parts in a machine the same, and before we can use the formula in this case, we must alter it so as to be applicable to magnetic circuits of varying cross-section. Total Field. Let A!, A 2 , A 3 , etc., denote the cross-sections of the various parts, and 1P 1? 1P 2 , P 3 , etc., the corresponding inductions, then the total flow of lines, which must obviously be a constant for the whole magnetic circuit, is given by the expressions A : 2, ^2 1^ e ^c. Formula (11), which we have brought into the form M HZ ~~' can now also be written as follows : 100 DYNAMOS, ALTERNATORS, And by adding these equations we obtain The term on the right is, as shown above, the line integral of the magnetic force emanating from the current in the wire, W W, and is given by the expres- sion 4 -TT c, so that we obtain for the total flow of lines the expression F- . . " , . (15) (16) Practical Example. The application of formula (16) caD best be shown by an example. For this purpose we take a dynamo having an armature of 30 centimetres diameter and 50 centi- metres length. We wish to find what strength of current will be required in the straight wire, W W, Fig. 22, in order to obtain a total flow of 1,000 English lines (6 . 10 6 C.G.S. lines) through the armature. The magnetic circuit may be divided into three parts namely, the field magnets the air spaces, and the armature the lengths of which we assume to be respec- tively 140, 2x2 = 4, and 30 centimetres. The length of each air space we take as 2 centimetres, but as there are two such spaces we must double this figure. Let the cross-sectional area of the field magnets be AND TEANSFOEMEES. 101 800 square centimetres, that of the air spaces 1,800 square centimetres, and that of the armature 500 square centimetres. The permeability of the armature core we assume as 1,000, and that of the field magnets as 2,000. The permeability of the air space we take as unity. Inserting these values in equation (16), we find 6x10- 140 30 1800 800x2000 500x1000 if c is to be given in amperes. We find from this in round numbers c = 11,400 amperes. If we lay a long straight wire through the limbs of the field magnets of this machine, and send a current of 11,400 amperes through this wire, we shall obtain the desired total field of six million C.G.S. lines. It would of course be quite impracticable to employ such an enormous current to excite the field magnets, and to get over this difficulty we would naturally employ, not a single conductor carrying the whole of the current, but a large number of conductors laid side by side, each carrying a portion of the total current. We might, further, loop the ends of the different conductors to- gether so that the same current shall traverse them successively, and by making the loops as short as possible, so as to save wire and reduce the resistance of the coil, arrive at the usual form of field-magnet coils. Instead of a straight current of 11,400 amperes we would thus have a coil of 11,400 ampere-turns. Now,, however, the question presents itself whether such a 102 DYNAMOS, ALTEENATOES, coil, wound closely round the magnets, is really equiva- lent to the long straight wire passing between the limbs. At first sight this would not seem to be the case, because the equation (5), on which we had based our calculations, is, strictly speaking, only correct for a wire infinitely long, a condition not even approximately fulfilled by a coil of finite perimeter. Before we can accept equation (16) for the calculation of dynamos we must, therefore, verify it in reference to the usual form of field-magnet coils. Extension of Theory to Solenoidal Electromagnets. We have seen that a solenoid provided with an iron core becomes an electromagnet as soon as we send FIG. 23. a current through the wire coils of the solenoid. Hitherto we have supposed the core to be straight, and of about the same length as the solenoid, but as in dynamos we must have a closed magnetic circuit, we AND TEANSFOEMEES. 103 shall now suppose the core bent so as to form a ring interlinked with the ring formed by the wire coil. This arrangement is shown in Fig. 23, where W represents the coil of insulated wire receiving current in the direction indicated by the arrows from some source, and E> a ring which may be composed of Fm. 24. different sections of different permeabilities. One of these sections may be an air gap, G, in which the permeability is 1, and this corresponds in a dynamo to the spaces between the polar and armature sur- faces. The problem now is to find the line integral of magnetic force due to the current in the coil, W, the integration being performed once round the magnetic circuit, R. Let, in Fig. 24, W W be the section through one turn 104 DYNAMOS, ALTEENATOES, of wire in the coil, taken at right angles to its plane, and let a be the radius of the coil. The magnetic whirl round the wire consist of lines which cut the plane of the coil at right angles. The plane of the coil must therefore be an equipotential surface, and no work is performed in moving an exploring pole over the plane surface encircled by the wire, either within or without. We require to find the line integral of mag- netic force along a loop taken once round any part of the wire. It can be shown that any path, of whatever shape, will give the same line integral, provided it loops round the wire. Thus the work which must be done to carry the unit exploring pole once round the oblong path, 2 3 , shown in a dotted line, must be exactly the same as that required to carry it from 0, away to the right into infinity, then round through an infi- nitely large semi-circle to the left, and back again to the starting point. To understand this clearly we have only to follow the pole through the various stages of its journey. No work is done in transit from 2 to 0, since both points lie on an equipotential surface. The journey from to infinity absorbs work, whilst no work is absorbed in any movement which the exploring pole makes at an infinite distance. Thus the quarter circle through which we must carry the pole until it meets the plane O 2 3 absorbs no work, and as this plane is itself an equipotential surface, we find that the magnetic potential at O 3 is exactly the same as that at a point on the line Oi at an infinite distance from 0. To carry our unit exploring pole from to infinity to the right requires, therefore, exactly the same amount of work as to carry it from 2 to 3 along the finite path shown by AND TBANSFORMEKS. 105 the dotted line. Similarly, to carry it from infinity on the left back to requires the same amount of work as is consumed in the second part of the dotted circuit namely, from O 3 to 2 . As the same reasoning applies to any closed circuit looping round the wire we see that the line integral along any such circuit is equal to that found for the journey of unit pole from an infinite distance on the left through the circle W W, and out to an infinite distance to the right. This integral can easily be found as follows : Assume the pole arrived at the point Oj. An element, I, of the conductor acts upon it with a force, Q= - 4 d 2 in the direction 1 Q. The horizontal component of this is P = -? sin a, a 2 and as this equation applies to every element, we find the total force due to the whole circular conductor sin a d 2 since d = , we have also sin a a The work done in a small displacement, dx, of the exploring pole is sin' 5 adx. a H 106 DYNAMOS, ALTEENATOES, Now x = a cotg. a and d x = - . a , which inserted sin 2 a gives P dx= 2 TTC sin a da. Integrating this equation between the limits of a = and a = TT we find Line integral of magnetic force = 4 ?r c . . (17) exactly the same expression as we found in (13) for the straight conductor infinitely long. We thus find that the expression (16) (16) is also applicable to solenoidal electromagnets. It is obviously immaterial whether the coil in Fig. 24 consists of only one circular wire, or of a wire making many turns, since neither the diameter nor the thickness of the coil enter into equation (17), and the integral has been taken over a line in- finitely long. We may thus subdivide the whole current into a number of wires lying either closely side by side, or spread over a certain length of coil, and the result will be the same, provided we take the magnetic circuit through all the turns of the coil. We see, therefore, that the magnetic effect is independent of the shape of the coil. If the coil consists of several wires the magnetic effect will of course be due to the product of the number of turns and the current passing through each turn; it will, in fact, be due to the ampere-turns. Let, now, c be the current in each wire, AND TRANSFORMERS. 107 and T the number of turns in the coil, then equation (16) must be written as follows : It must not be forgotten that the current in this formula is to be taken in C.G.S. units. If it is taken in amperes we must divide by 10, and have . . ,' . . (19) This expression may conveniently be brought into another form. Suppose the magnetic circuit is com- posed of three sections of different length, area, and permeability, which we distinguish by the indices 1, 2, .and 3, then w r e can also write In 1 In - (20) The term on the left is the line integral of the mag- netic force taken once round the magnetic circuit, or the total difference of magnetic potential under which the flow of force, F, is produced ; the terms on the right show how this total potential difference is divided .between the different sections of the magnetic circuit. They are of the character : flow multiplied by an ex- pression which contains the length of the section in the nominator, and the product of area and permeability in the denominator. H2 108 DYNAMOS, ALTERNATORS, It will be at once apparent that a very remarkable analogy exists between formula (20) as expressing the property of a magnetic circuit and Ohm's law express- ing the property of an electric circuit. To see this clearly, we have only to substitute for the flow of magnetic force strength of current, for the permeability the specific conductivity or the reciprocal of the specific resistance, and for 'kirc r the electromotive force. According to this analogy the terms of the form must be regarded as the magnetic resistances of those parts of the magnetic circuit to which they refer, and we may translate Ohm's law from the electric into the magnetic circuit as follows : The magnetomotive force (line integral of the magnetic force) is equal to the pro- r \ duct of the total flow of magnetic force multiplied with the total magnetic resistance. The conception of magnetic resistance is a very con- venient one, and helps to greatly simplify the calculation of dynamo-electric apparatus ; but on strictly scientific grounds it is open to some objections. As we shall in future make frequent use of the term magnetic resist- ance, it is desirable to at once state what these objections are, and how far they are justified. The principal objections are that the overcoming of magnetic resistance, unlike that of electric resistance, does not necessitate the expenditure of energy, and that the magnetic resistance is not constant, but varies with the degree of induction that is, with the total flow of magnetism. As regards the first objection, this no doubt is justified. If we apply an electromotive force to the ends of a conductor in such way as to cause a AND TEANSFOEMEES. 109 current to flow, the conductor becomes heated, and under no conceivable arrangement can the correspond- ing loss of energy be avoided. With the magnetic circuit the case is quite different. It is true that the exciting coil through which we pass the magnetising current must have some resistance, and to that extent energy will be required to make the current flow through it, but we can reduce this energy to any desired extent by making the wire of large size, without in any way altering the magnetic flow. Moreover, we can produce such a flow without the use of any wire coil at all if we chose, as the source of magnetism, a perma- nent steel magnet. It is therefore necessary, when speaking of magnetic resistance, to always bear in mind that it is not a resistance in the ordinary sense of the word that is, one which can only be overcome by the expenditure of energy but rather of the nature of that resistance which bodies offer to forces tending to produce deformation. The second objection mentioned above is not so well founded, because the electric resistance of a circuit is also liable to vary with the current passing through it. The specific resistance of all metals increases with temperature, and as the temperature rises as the current is increased, it follows that the larger the current the higher will be the electric resistance of those parts of the circuit which are of metal. This is precisely the relation between flow of magnetism and magnetic resistance. The greater the flow the smaller is the permeability, and the greater its reciprocal, which is a measure for the magnetic resistance, so that in this respect there is only a difference in degree, 110 DYNAMOS, ALTEENATOES, but not one in kind between the electric and magnetic circuit. From the structure of formula (20), it will at once be apparent that the total magnetomotive force, acting in a given magnetic circuit, is the sum of the magneto- motive forces required in the different parts of the circuit, and that, in fact, Ohm's law applies not only to the circuit as a whole, but also to every part of it. We may therefore establish the general proposition : " The flow of magnetism through any section of a magnetic circuit is the quotient of the magnetomotive force in that section (difference of magnetic potential between the beginning and the end of the section) and its magnetic resistance." From this proposition it follows that where several paths are offered to the flow of magnetism under the same magnetomotive force, the flow will divide amongst them in the inverse ratio of their magnetic resistances. Thus, in a dynamo, there is between the pole-pieces a multiplicity of paths for the flow of magnetism. One path is through the armature, and the lines taking this path are the only lines of use in the working of the machine. In addition, there are, however, other lines which take a path through air from one pole-piece to the other, and these lines, although, like the others, created by and passing through the exciting coils, are lost to the purpose for which the machine is con- structed. We shall revert to this subject when we come to deal with the leakage or waste field of dynamo machines. For the practical application of formula (20), it is convenient to bring it into a slightly different form by AND TEANSFOEMEES. Ill dividing both sides by *4 TT, so as to obtain directly the exciting power in ampere-turns l\ / ' l-25d AJ/* 1-256 A 2M2 1'256 or, briefly, c T = F E . . . *. . (22) where K-2-I- 'i V . (23) 1'256 A./UL which we conventionally call the sum of all the mag- netic resistances. When, in future, speaking of mag- netic resistance, it will be understood that the term given in equation (23) is meant. In equation (21) the flow of lines is given in the C.G.S. system, the lengths are in centimetres, and the areas in square centimetres. For the use in the workshop it is, however, convenient to give dimensions in inches, and to employ the English unit for the flow of magnetism. Let Z be the flow in English measure, and I be given in inches, and A in square inches, then a simple arithmetical operation shows that formula (21) becomes cr = Z (1880 ^ - + 1880 A - + 1880 -} . (24) A! fr A 2 yu 2 A 3 fat In the English system of measurement the magnetic resistance is therefore given by the expression E = 21880 li . . / , . (25) A/* When the permeability is 1, as in the interpolar space of a dynamo or motor, this formula becomes Ea = 1880 1 ..... (26) A 112 DYNAMOS, ALTEENATOES, / where we use the index a to show that the resistance refers to air and not to iron. The coefficient 1880 is only valid if the permeability of the copper, which partly fills the interpolar space, is equal to that of air, which is unity. Commercial copper is sometimes slightly magnetic, and then a somewhat smaller co- efficient must be used. It should also be noted that the area A is not only the area of the pole-piece, but this area with an addition of a certain fringe due to the spreading of the lines near the edges of the pole- piece, a subject to which we shall return in a later chapter. CHAPTEE VI. Magnetic Properties of Iron Experimental Deter- mination of Permeability Hopkinson's Method- Energy of Magnetisation Hysteresis. Magnetic Properties of Iron. According to the definition given on page 93, mag- netic permeability is a numerical coefficient denoting the ratio in which the presence of iron multiplies the number of lines of force previously existing in a magnetic field. This multiplying power is different with different samples of iron, and it also varies for the same sample with the strength of the original field, or, what comes to the same thing, with the magnetising force, and therefore also with the induction produced. It is customary to state the permeability as a function of the induction, or of the magnetising force, and thus the magnetic quality of any sample of iron can be expressed in the shape of a table or a curve. These curves may be constructed to represent the following relations : Magnetising force and permeability. Induc- tion and permeability, or magnetising force and induc- tion. The latter is the most directly obtainable and useful curve. If the magnetising force be removed the iron does 114 DYNAMOS, ALTEENATOES, not return to its original state that is, to the state in which it was before any magnetising force had been applied ; but it retains a certain amount of magnetisa- tion called the "residual magnetisation," and which may be numerically expressed by the corresponding in- duction. To each magnetising force and consequent induction corresponds, therefore, a definite residual in- duction, which can also be represented by a curve. If the magnetising forces be plotted as abscissae and the inductions as ordinates, the curve of residual induction is found to have a similar shape with the curve of in- duction, but to lie wholly below it. It may here be mentioned that if the sample, whilst being tested for its magnetic properties, is subjected to mechanical vibrations or strains, the curve of induction is slightly raised and the curve of residual induction is consider- ably lowered. Another point which should be noted is the difference between an ascending and a descending curve of mag- netisation. If we first test a sample by applying gradually higher and higher magnetising forces, taking care to determine the induction at each step, and plot the results, we obtain an ascending curve of magnetisa- tion. As the induction becomes larger its increment for equal increments of magnetising force becomes smaller and smaller, the curve becoming more and more flat, until a point is reached when no increase of mag- netising force produces any increase in the induction. When in this condition the iron is said to have attained a point of saturation, its permeability being reduced to zero. In what follows we assume that the magnetisation has not been carried so far, but only to a certain point. AND TEANSFOEMEES. 115 If we now gradually reduce the magnetising force, and again plot the induction at each step, we obtain a descending curve of magnetisation, which lies wholly outside of the former curve, and passes through the axis of ordinates (corresponding to zero magnetising force) at a point above the centre of co-ordinates. The distance of this point of intersection from the centre of co-ordinates represents the induction which is still left, in the sample after the magnetising force has been gradually reduced to zero, and this induction is called the " retentiveness " of the sample. Now suppose that when the magnetising force has been gradually brought down to zero, we reverse it so as to demagnetise the sample beyond its point of retentiveness, and gradually increase the magnetising force which is now acting in a negative direction, until the previous induction but in the reverse sense is reached, we obtain the ascend- ing negative branch of the curve of magnetisation. Decreasing now the negative or reverse magnetising force to zero, and reversing it a second time so as to make it positive, and gradually increasing it to the pre- vious value, will give us, first, the descending negative, and, finally, the ascending positive branch of the curve of magnetisation, which brings us again to the point from which the descending curve of magnetisation starts. We have thus carried the iron through a complete cycle of magnetisation from a certain positive induc- tion, through zero to an equal negative induction, and back through zero to the starting point. The closed curve representing this cycle cuts the axis of co- ordinates in four points namely, the axis of ordinates above and below the centre in points, which give the 116 DYNAMOS, ALTEENATOES, retentiveness of the sample, and the axis of abscissae in points to the right and left of the centre, which show what amount of reversed magnetising force is required to reduce the induction of the sample to zero. Dr. Hopkinson, in his celebrated paper on the " Magnetisa- tion of Iron," read before the Eoyal Society in 1885, has suggested that this reverse magnetising force should be called the " coercive force " of the sample, if the curves have been obtained by extreme magnetising forces in both directions. -16000 -100 25. It will be convenient to illustrate the various terms here introduced by a diagram. Let, in Fig. 25, the curve, C, represent the magnetising curve of a certain sample of iron which has not previously been subjected to any magnetising force. Arrived at C, we gradually AND TRANSFORMERS. 117 reduce the magnetising force to zero, and obtain the portion, C B, of the positive descending curve of magnetisation. We next reverse the magnetising force until it has reached the negative value, A, when the remainder, B A, of the positive descending curve of magnetisation is obtained. By still further increasing the negative magnetising force we obtain the negative ascending curve of magnetisation, AC 1 , and by gradually reducing the magnetising force to zero and increasing it to A 1 , we can plot the negative descending curve of magnetisation, C 1 A 1 . A further increase of mag- netising force gives us, finally, the ascending curve of magnetisation, A 1 C. The diagram gives us now B = B 1 = Eetentiveness. A = O A 1 = Coercive force. It is especially the latter quantity which plays an important part in dynamo machines and similar appa- ratus, since upon the coercive force depends to a certain degree the energy which is transformed into heat when the iron undergoes a cyclic change of magnetisation, a point to which we shall return later on. Experimental Determination of Permeability. In the above description of the magnetic behaviour of a sample of iron we have assumed that the magne- tising force and corresponding induction are known at every instant, and it will therefore now be necessary to show how this knowledge is obtained, or, in other words, how the relations between magnetic force,, induction, and permeability can be experimentally determined. Various methods have been used for this 118 DYNAMOS, ALTEENATOES, purpose. In some of the earlier methods the sample was in the form of a short rod or piece of straight wire inserted into a solenoid and there magnetised. A mag- netometer was used to determine the magnetic moment of the sample corresponding to each magnetising current, the precaution having been used to either separately determine and allow for the action of the solenoid itself on the magnetometer, or to compensate for it by the use of certain compensating coils so arranged as to produce an exactly equal but opposite magnetic effect. The deflection of the magnetometer could then be used to calculate the magnetic moment, intensity of magnetisation, and in- duction of the sample. This method has been used with good effect by Prof. J. A. Ewing, who described it, as well as other methods, in his paper, " Experi- mental Researches in Magnetism," presented to the Royal Society in 1885. Ewing points out that the method is only reliable, especially as regards the deter- mination of retentiveness, if the sample be very long in comparison with its diameter. Where this is not the case the free magnetism at the ends exercises a self-demagnetising force upon the interior and middle parts of the bar or wire, so that the induction deter- mined for short bars is lower than that determined for long bars. The same difficulty accompanies, of course, all methods in which the sample experimented on is in the form of a short bar with free ends ; and with a view to eliminate the error likely to arise from the action of the ends, which cannot be exactly estimated, Stoletow and Rowland used samples formed into closed rings, and the latter also straight bars of very great length. AND TEANSFOEMEES. 119 Ewing found that if the length of the bar is over 300 diameters the demagnetising effect of the free ends becomes negligible. With samples of the closed ring form the use of any magnetometer method is, however, excluded, since there is, or, at least, should not be any free magnetism to affect the magnetometer. Another method of measuring the induction must therefore be adopted. The most generally used is the ballistic method, which is based upon the fact that any change in the total flow of lines within the sample produces an electro- motive force in a coil of wire surrounding the sample. This so-called " exploring coil " is connected with a ballistic galvanometer, the deflection of which in- dicates the integral of electromotive force multiplied by time ; and since this integral is proportional to the variation in the total number of lines of force passing through the coil, the deflection of the ballistic galvano- meter is also proportional to the variation in the induc- tion of the sample of iron under experiment. A consideration in detail of the apparatus required in these experiments, and of the corrections to be made and precautions to be observed, would be beyond the scope of this book. Suffice it to say that from the resistance of exploring coil and ballistic galvanometer, the period and logarithmic decrement of the latter and other electrical data, the change of induction corre- sponding to any observed deflection can be calculated. The constant of the ballistic galvanometer can also be found experimentally by the use of what Ewing terms an " earth coil." This is a flat coil of known area and number of turns connected with the ballistic galvano- 120 DYNAMOS, ALTERNATORS, meter. The earth coil is laid upon a horizontal table and then suddenly turned over. During this move- ment the vertical component of the earth's lines of force are, so to speak, first withdrawn (when the earth coil gets into a vertical position) and then reinserted in the opposite direction when this coil again becomes horizontal. We have thus a change in the total flow of lines amounting to twice the number of vertical lines of force passing through the coil when it is horizontal. This number can be calculated from the dimensions of the earth coil and the intensity of the vertical com- ponent of the earth's magnetism, which latter can be determined by a 'magnetometer, as explained in Chapter III., p. 52. Having thus experimentally determined the relation between a given change in the flow of force and the corresponding deflection of the ballistic galvanometer, this relation is used to deter- mine the change in the flow of force corresponding to other observed deflections. Hopkinson's Method of Investigating the Magnetic Properties of Metals. From a practical point of view it is important to determine the magnetic properties of different brands of iron on samples which are of such a shape that they may be readily obtained and not differ in their properties from the bulk of the metal, the properties of which they are supposed to represent. Assume, for instance, that we wish to test a certain brand of wrought iron for its suitability for field magnets. In such a case it would be useless to draw the iron into wire and experiment upon samples of this wire, since the very manipulation AND TEANSFOEMEES. 121 of wire-drawing may have so altered the iron as to make the subsequent magnetic tests misleading. What we would do in this case is to make a small forging and treat it (as to annealing and machining) as much as possible in the same manner as we would treat the real field- magnet forging. A method of testing which satisfies the requirements of practical engineers has been devised by Dr. John Hopkinson. This apparatus is adapted for the testing of samples in the shape of bars which are cast or forged, and then turned up true to a diameter FIG. 26. of Jin. The length of the bars need only be moderate,, as by the peculiar arrangement to be described presently there is no free magnetism at the ends. Samples of this shape are easily obtained, and accuracy of diameter ensured, by using the ordinary gauges found in all engi- neering workshops. The apparatus itself is very simple. It consists of a block, A, Fig. 26, of annealed wrought iron 18in. long, Gin. wide, and 2in. deep. In the middle a space is cut out as shown to receive the magnetising coils, Cj C 2 , and an exploring coil, E, which is connected with the ballistic galvanometer, not shown in the drawing. The 122 DYNAMOS, ALTEENATOES, ends of the block are bored to receive the sample rods, B! B 2 , the diameter of the holes being just sufficiently larger than that of the rods to give an easy fit. The magnetising current is measured, and from its observed value, together with the number of turns in the magne- tising coils and the dimensions of the apparatus, the magnetising force can be calculated. Two sample bars are used which meet with their accurately turned end faces at or near the centre of the apparatus, and one of the bars can be suddenly withdrawn by means of the shackle shown. The exploring coil is in this case set free and pulled suddenly out of its position by a spring. Thus there is a sudden change from a certain induction through the exploring coil to zero induction, and the throw of the galvanometer can be used to indicate what the induction was the moment before the sample bar and coil were withdrawn. Part of the magnetising force is required to drive the lines of force through the sample bars and part to drive them through the block, the arrangement representing a case to which formula (20), page 107, applies. If the magnetising current, c, be measured in amperes, and r represent the number of effective turns of wire in both magnetising solenoids, we have where the index 1 refers to the sample bars and the index 2 to the block. The latter being of soft annealed iron, /* 2 has a high value. At the same time the cross - section of the block A 2 is very great in comparison with that of the sample bar, so that the fraction 2 AND TEANSFOEMEES. 123 has a very small value and may be altogether neglected, so that the above formula becomes Ft Since the area of the sample bar is known, we can 'calculate the induction, "p, from the total flow of lines, F, and also the permeability. The magnetising force is H = -' and this is calculated from the magnetising current. The total flow of force, F, is found from the throw of the ballistic galvanometer, and by dividing by the area of the sample bar, we find the induction, |i, and finally we find the permeability by dividing induc- tion by magnetising force i|; ' -. | . p Dr. Hopkinson has in the paper already mentioned, " Magnetisation of Iron," givsn the result of experi- ments upon a great variety of samples of iron. The most important are of course annealed wrought iron and grey <3ast iron, because these materials are used in dynamo machines. The curves in Figs. 27 and 28 give average values compiled from Dr. Hopkinson' s tables and diagrams. It should be noted that each brand of iron, although it may be generally classified as annealed wrought iron or grey cast iron, may, and generally does, show curves differing somewhat from the curves here given, and the latter must therefore be regarded merely as convenient approximations. It should also be noted that no distinction is made between the i2 124 DYNAMOS, ALTEENATOES, D/n 1000 c as u ftits * *- en 0* ascending and the descending curves of magnetisation r for the simple reason that with dynamo machines, for AND TEANSFOEMEES. B />? lOOOc g.s.units 125 ihe calculation of which these curves are primarily in- tended, we reach a certain induction as often with an 126 DYNAMOS, ALTERNATORS, increasing as with a decreasing magnetising force, and that therefore the mean between the two curves will give on the whole the most accurate results. The mechanical vibrations to which a dynamo is subjected when working also tends to diminish the interval be- tween the ascending and descending curve of magnetisa- tion. On each diagram two curves of induction are shown, the ratio of abscissae of these being as 1 : 10.. This has been done in order to render the early part of the curves better visible. The abscissae for the lower curve are figured below, and those for the higher curve are figured above. The curve sloping to the right on each diagram represents by its abscissae the permeability, the ordinates being induction. The permeability is a simple numeric given in the diagram for cast iron by the tenfold value of the lower or the simple value of the upper figures on the axis of the abscissae. In the diagram for wrought iron the permeability is given by the hundredfold value of the lower or tenfold value of the upper figures. The use of these curves in the design- ing and testing of dynamo machines will be explained in a subsequent chapter. Energy of Magnetisation. It was pointed out in Chapter V. that no energy is required to maintain a magnetic field when once it is established. We have compared the flow of magnetic lines of force to the stream-lines of a liquid in motion, and here also there is, apart from friction, no energy required to keep the liquid in motion. Energy is, however, required to set the liquid in motion, and this energy is stored in the liquid, and can be re- AND TEANSFOEMEES. 127 covered by arresting again its motion. If our analog} 7 between a liquid in motion and a magnetic field is generally correct, we should expect to find that a mag- netic field can only be established by the expenditure of a definite amount of mechanical energy which remains, so to speak, stored in the field, and can be recovered by allowing the field to vanish again. This is indeed the case, as can easily be shown. It has been explained in Chapter V. that the line integral of magnetic force or difference of magnetic potential between two points of a magnetic field is the energy which must be expended or can be obtained by moving unit pole from one to the other of these points. If these two points are 1 centimetre apart, the difference of magnet potential between them is H, the magnetic force. Imagine now a space of 1 cubic centimetre, delineated in the field in such a position that the lines of force pass at right angles through two opposite sides of the cube, and let the induction be uniform over their surfaces, its value in absolute measure being denoted by IP. The value of !& will of course depend upon the permeability of the substance which fills our cube. If the substance be air or another non-mag- iietic material, the induction will be H ; if it be iron of permeability JUL, it will be = //, H. Whatever the material occupying the field, there will be a definite induction for each magnetising force. Now assume that we increase the magnetising force by an infini- tesimal amount. The induction will in this case also increase by an infinitesimal amount d^. Previous to the change the amount of magnetic matter on the end faces of our cube was After the change it will be 47T 128 DYNAMOS, ALTERNATORS, <3jg /7 "at? + ?; that is to say, units of magnetic matter 4 7T 4 7T 4 7T have been transferred from one end face of the cube to the other under a magnetic force which varied during the process from H to H + d H. We may neglect the term d H as infinitely small, and compute the energy d ! represented by the transfer as H 5. We may now 4 7T imagine the magnetic force again increased by an infinitely small step, and the process repeated an infinite number of times until a finite increase of magnetic force and induction has been obtained. The total energy will obviously be the integral of the above expression taken between the limits of induction pro- duced, or in symbols Ergs=f 'H*?, ', 4 ^ if by 1^ and |i 2 we denote the limits between which the induction has been altered. The total energy of 1 cubic centimetre of the magnetised substance raised to the induction is obtained by adopting zero as one and IP as the other limit, or in symbols Total energy in ergs = / H 1 J 4 7T (27) The application of this formula to the magnetisation of iron will be clear from Fig. 29. The curve shown represents the relation between magnetic force and in- duction. Let A x A 2 represent two conditions of the AND TKANSFOEMEKS. 129 magnetisation sufficiently near each other to be attri- buted without any great error to the same magnetic force H, and let 1 2 represent the corresponding values of the induction. The increment of magnetic matter transferred under the magnetic force, H, is graphically represented by the length of the line |^ $ 2 divided by 4?r, and the corresponding energy by the .area Aj A 2 |i 2 1, divided by 4 TT. FIG. 29. The total energy in ergs represented by the mag- netisation of 1 cubic centimetre of iron from the induction zero to the induction *$, is therefore given by the area contained between the axis of ordinates and the curve of magnetisation divided by 4 TT. This is the shaded area, A $, in the diagram. It will thus be seen that if the curve of magnetisation of any particular brand of iron is known, the energy which can be magnetically stored in a given volume, or 130 DYNAMOS, ALTEKNATORS, weight of this iron at different inductions, can readily be calculated. Hysteresis. The theory of energy of magnetisation which has been here given, is of practical importance in two res- pects. One is the construction of choking coils for use with alternating currents, and the other alternating- current apparatus generally. A choking coil consists of an iron core surrounded by a solenoid, which is inserted into an alternate-current circuit. During the growth of the current from zero to its maximum value, a certain amount of energy is magnetically stored in the iron core, and thus prevented from reaching the lamp or other apparatus upon which the current operates. During the period of decline of current, the energy is again given off, and opposes to a certain extent the reversal of current, and thus the choking coil acts as a kind of elastic buffer between the source of current and the lamp, reducing the effective electro- motive force at the terminals of the latter. It is not necessary to enter in this place more minutely into the theory and construction of choking coils, and we have only mentioned these appliances to show that the seemingly abstruse calculations concerning the energy of a magnetic field are by 110 means without practical value in electrical engineering. The other application mentioned at the beginning of this paragraph is even of more importance. It concerns alternate-current apparatus generally, and is known under the name of "hysteresis," given to it by Pro- fessor Ewing, who has made a special study of the AND TEANSFOEMEES. 131 subject. The name implies a lagging behind, and refers more particularly to the lag of induction behind magnetic force, as shown by the difference between the ascending and descending curves of magnetisation,. Fig. 25. -12000 -14000 -16000 -100 -60 -60 -40 -20 20 40 60 SO 100 FIG. 25. Starting with a magnetic force of zero, and increasing it to its maximum positive value, we obtain the curve B 1 A 1 C. When the point C has been reached each cubic centimetre of iron has absorbed an amount of energy, which is given in ergs, by the area enclosed between the curve B 1 A 1 C and B 1 c on the axis of ordi- nates divided by 4 TT. If we now decrease the magnetic force again to zero, we ought to recover the whole of the energy previously absorbed if the iron acted as a perfect 132 DYNAMOS, ALTEENATOES, storing appliance. This, however, is not the case. We only obtain the energy corresponding to the area com- prised between B C and c B. The difference namely, the energy represented by the area of the figure B 1 A 1 C B B 1 has been lost, or, rather, transformed into heat, which is dissipated. The same reasoning applies to i50(X / i * 10000 5000 / / \ / 1 i / J (s 1 / 1 1 / r. 1 \ / * I 1 / / i 1 / ^ i / k WPO - / | 'vxm L-^ s y ^ ' \ ^ <* *' cgs Unit ** .o" 5 *** IVr * """* B in English Measure FIG. 30. negative magnetic forces, with the result that if we carry the iron once through a complete magnetic cycle we waste an amount of energy, which is given in ergs, by the area of the distorted lozenge-shaped figure, C B A C 1 B 1 A 1 C, divided by 4 TT. The energy thus lost in hysteresis not only reduces the efficiency of alternate- AND TEANSFOEMEES. ro co <=> _n c> -n ^3 C ji >> to ; = V." [ ve T 7 'ro ' I'/t 6 % 5 3 r A- be the angle embraced by each pole-piece, and assume the induction uniform over that portion of the armature defined by this angle. The induction in the inter- OF THE UNIVERSITY 148 DYNAMOS, ALTEENATOES, mediate portions we assume to be zero. Strictly speaking, this is not correct. In reality there is no abrupt change in the induction at the edges of the pole- pieces, but a gradual shading off. For the determina- tion of the electromotive force a knowledge of the exact distribution of the field is, however, not required, since we are not concerned in knowing the electromotive force in each wire, but its sum computed from all the wires, and if in consequence of an uneven distribution of field one wire does less than its proper share of the work, another wire must do more, leaving the total electromotive force exactly the same as if the distribu- tion of field were as above assumed. The number of active wires under the influence of one pole-piece is at any time ( T. The electromotive force in volts gene- 2 7T rated in each of these wires is by formula (30) I ^ a TT D 10~ 8 , where we write TT -^ for v, the linear 60 60 speed of the wires across the lines of the field. The total electromotive force is therefore Now, the term a> P a I is the total flow of lines or 2 strength of field, F, in C.G.S. measure, which can be determined from the constructive data of the machine AND TKANSFOEMERS. 149* and the exciting power applied according to formula (19) r . Chapter V. Inserting this value we have E = Fr^lO-8. . . . (32) bU Calling Z the strength of field in English measure (one English line of force is equivalent to 6,000 C.G.S. lines, Chapter IV.) we also obtain (33) CHAPTEK VIII. Electromotive Force of Armature Closed-Coil Armature Winding Bi-Polar Winding 1 Multipolar Parallel Winding Multipolar Series Winding Multipolar Series and Parallel Winding. Electromotive Force of Armature. At the end of the preceding chapter a formula was given for the electromotive force of an armature taken as a whole. The formula was obtained on the sup- position that the field is absolutely uniform, or, in other words, that the induction through the inter- polar space (the space between the iron of the arma- ture and that of the pole faces) is constant. It was also stated that this supposition is not correct, but that any variation in the induction between one part and another part of the interpolar space may be left out of account, as the excess of electromotive force in some wires would be counterbalanced by the deficiency of electromotive force in others, and thus the electro- motive force of the armature taken as a whole would be the same. as if the field were absolutely uniform. This is a plausible explanation, but not a scientific proof, and before proceeding further it will be expedient to give the strict proof for formulae (32) and (33) . Fig. 36 represents a transverse section through an armature AND TEANSFOEMEES. 151 and its field poles, N S. The distribution of magnetic lines of force within the interpolar space depends on so many circumstances that we cannot possibly map out the field merely by drawing, but if we wanted to know the distribution of magnetism we would have to determine it experimentally by means of an exploring coil, or iron filings, or in some other way. It is, how- B FIG. 36. ever, for our present purpose, not at all necessary that we should know the exact distribution of lines offeree; all we need know is the total magnetic flux which enters the armature on the left of the neutral line, A B, and issues from it on the right of that line. The winding on the armature is so arranged that the elec- tromotive forces induced in all the wires lying to one side of the line of commutation, A B, add up, and that 152 DYNAMOS, ALTEENATOES, the total electromotive force on the left of this line is equal to the total electromotive force on the right. Eetaining the previous notation, we have r active conductors on the armature, and the total electro- motive force induced is that due to ^ wires in series. a If we number the conductors from the top right and left 1, 2, 3, and so on, and consider the centre line of each, we can imagine the total magnetic flux, F, sub- divided into as many parts as there are conductors on each side, and say that the flux between the top of the armature and centre of conductor 1 is A F x ; the flux between centre of conductor 1 and centre of conductor 2 is A F 2 , and so on. The total flux, F, is thus the sum of all the A F taken over the left or right half of the armature. Now let us consider two successive positions of the armature separated by an angle equal to that corresponding to the distance between two successive conductors. In being shifted from one to the other position, conductor 1 will cut all the lines of force passing between 1 and 2, conductor 2 will cut all the lines of force passing between 2 and 3, and so on. The electromotive force created in conductor 1 is, therefore, A ~T71 A "T71 ?, that in wire 2 is ?, and so on, t being the time t t in which the armature rotates through the small angle corresponding to the distance of one conductor to its neighbour. The total electromotive force generated in the conductors on one side of the diameter ot 2t X A "F 1 TT commutation, A B, is therefore - = . t t AND TEANSFOEMEES. 153 Let D be the diameter of the armature in centi- metres and n the number of revolutions per second, then the circumferential speed is TT D, and the dis- 60 tance between two neighbouring conductors is ^ T ' Hence t TT D = _ 60 T ' and = r t 60* which, inserted into the above equation, gives The electromotive force is here given in C.G-.S. units. To obtain it in volts we must divide by 10~ 8 , and have E = F T 10~ 8 .... (32) which is the same expression as was given in the pre- ceding chapter. We see, therefore, that the electro- motive force depends simply on the total flux, F, but is quite independent of the more or less regular distribu- tion of the flux throughout the interpolar space. The total flux is of course that emanating from one pole-piece. We have thus proved that the formulas (32) and (33), given at the end of the last chapter, are rigorously correct, but as they refer only to bi-polar machines we must yet investigate what modification, if any, will be required in the formula for armature electromotive force in order to become applicable to L 154 DYNAMOS, ALTERNATORS, multipolar machines. Take, for instance, a machine with four poles, as shown in Fig. 37. The flux emanating from each pole divides so as to reach the two neighbouring poles, as shown by the dotted lines. If we assume that each pole supplies a flux of F lines, FIG. 37. there will be four bands of induction through the arma- F ture, each carrying lines. In order to facilitate the comparison with a bi-polar machine, let us assume that we have in Fig. 37 the same armature as in Fig. 36. The number of conductors under the influ- ence of each pole is now instead of as formerly; 4t ^j but if we assume that the total flux from each of the four poles is the same as that emanating from each of the AND TEANSFOEMEES. 155 two poles in Fig. 36, then the number of lines passing between neighbouring conductors will be greater than it is in the two-pole machine. In other words, although now we have fewer A F, each A F, taken individually, represents more lines, and the induction within the interpolar space is stronger. By adopting the same reasoning as before, we find that also in the case of a multipolar machine the total electromotive force of the conductors under the influence of one pole-piece is represented by T E = FT^C.G.S. units, 60 and is therefore the same as in a bi-polar machine. It is important to note that the formula here found refers to the electromotive force of that part of the armature which lies between two successive points of commutation, and which for brevity we shall call armature sections. In a bi-polar machine these points are diametrically opposite, and the electromotive force is that due to one-half the armature conductors on either side of the diameter of commutation. In this case there are two armature sections coupled in parallel, and the electromotive force of one section is the same as that of the armature taken as a whole. If we had to do with a machine having a four-pole field the armature winding would have to be con- sidered as consisting of four sections, each embracing 90 deg. If the machine had six poles there would be L2 156 DYNAMOS, ALTERNATORS, six armature sections, each embracing 60 deg., and so on. The formula E = F r 10~ 8 volts/ . . . (32), 60 gives the electromotive force of each section, and although in a bi-polar machine this is the same as the electromotive force of the armature taken as a whole,, this is not necessarily the case in a multipolar machine. It will be the case if the winding of the armature is such that all the sections are coupled in parallel, but if a method of winding be employed whereby two, three, or more sections are coupled in series, then the electromotive force of the armature taken as a whole will be two, three, or more times that given by formula (32). Thus in a four-pole machine with series-wound armature the total electromotive force will be twice that of a bi-polar machine with equal field strength and equal number of armature conductors. In a six-pole machine with series-wound armature the electromotive force will be three times that of a bi-polar machine, and so on. The current given by a bi-polar machine is twice the current passing through each armature conductor. In a four-pole machine with parallel-wound armature the current is four times that passing through each arma- ture conductor ; in a six-pole machine with parallel- wound armature it is six times that passing through each armature conductor, and so on. The following table will render the relations between number of poles, electromotive force, current, and output clear. AND TEANSFOEMEES. 157 In this table, E represents the electromotive force of C one armature section as given by formula (32), and 2 is the current in each armature conductor. Number of Poles. Total E.M.F. Total Current. Total Output. Parallel winding. Series winding. Parallel winding. Series winding. Parallel or series wind- ing. 2 4 -6 8 271 E E E E E E 2E 3E 4E n E C 2C 3C 4C nC O C C c c EC 2EC 3EC 4EC n~& C This table shows that the output obtainable with any given size and weight of armature increases as the number of poles is increased, and it would thus appear that multipolar machines must, under all circum- stances, be better than bi-polar machines. It should, however, be borne in mind that the electromotive force of one armature section depends on the strength of the field, and if we put more magnets round a given armature each pole-piece will become smaller, and we must either provide for a vastly greater density of lines in the interpolar space which, for reasons that will be -explained later on, is not always feasible or we must be satisfied with a weaker field, and this may counteract the advantage which would otherwise result from the multipolar arrangement. Generally speaking, an arma- ture designed for a bi-polar field will probably not 158 DYNAMOS, ALTEKNATOBS, work well in a multipolar field, and when designed for a multipolar field will certainly work badly in a bi-polar field ; but if we are free to vary the dimensions and winding of the armature to suit either one or the other type of field, then we find that the bi-polar field is best for small and the multipolar for large machines. This point will be found fully considered in Chapter XI. For the present we are only concerned with the electromotive force that may be obtained with a given armature winding and field. If we have to do with a multipolar machine the winding of the armature may, as already stated, be on the parallel or series system. It is, how- ever, also possible to adopt a combination of the two methods and to wind, for instance, a 12-pole armature in such way that three sections are coupled in series and four in parallel. Armature Windings. It is now necessary to explain some of the methods- of winding by which armature sections may be put in series or in parallel.* Bi-polar machines of the open- coil armature type have the sections coupled in series, and these will be found described in Chapter IX. In bi-polar machines of the closed- coil type the parallel arrangement is the only feasible one, and, for the sake * Space permits only to give some of the windings more generally used. Those who require more detailed information on the subject should consult Dr. Arnold's excellent little book, " Die Ankerwickelungen der Gleichstrom Dynamomaschinen "; Berlin, Julius Springer, 1891. Dr. Arnold treats the subject in a most comprehensive manner, and shows how any given winding can be represented and new windings discovered by the use of algebraical formulae and diagrams. If I do not follow Arnold's- method it is not that I underestimate its scientific merit, but simpl} 7 - because I think that within the limited space at my disposal explanation by means of examples and winding tables are more easily given. AND TEANSFOEMEES. 159 of simplicity, we shall begin the investigation with them. We shall then proceed to the consideration of multi- polar windings, taking the parallel arrangement first, the series arrangement next, and finally, the combina- tion of the two. Bi-polar Winding. Let, in Fig. 38, the circle represent the cross-section FIG. 38. of the armature revolving clockwise between the field poles, N S, and the 16 small circles on the circumference the conductors. Applying Fleming's rule of Chapter VII., we find that in all the con- ductors between the armature and the N pole-piece an electromotive force will be induced downwards that 160 DYNAMOS, ALTERNATORS, is, away from the observer and in all the conductors under the influence of the S pole-piece the electro- motive force will be upwards, or towards the observer. We represent the latter direction by a dot in the middle of the wire, being the point of the arrow which denotes the direction of the current. Similarly a down- ward current may be represented by an arrow flying away from the observer, who will then see, not its point, but its wings at the back. We therefore repre- sent the downward current by a small cross inscribed in the wire. This method of representing the direction of cur- rents, or electromotive force, in wires seen end on is used throughout this book. In winding this armature we first divide the circumference into 16 equal parts, and mark out on the cylindrical surface 16 lines parallel to the axis. Let us begin to wind at line 16, laying the wire on along this line from the front end to the back end. Arrived at the back end, we stretch the wire across the back face of the armature, as shown by the dotted line 16-7, and wind along line 7 to the front. Next we stretch the wire along the front end, as shown by the full line 7-14, and wind down line 14. Then across, back, and up line 5, and so on, until we close the winding on itself with the front connection 9-16. It is characteristic for this winding, commonly known under the term " drum winding," that we complete each turn, not with the next, but the next but one wire to that with which the turn has begun. This winding may be represented by the following winding table, in which the numbers in the columns headed D represent wires wound downwards, and those in the columns AND TBANSFOEMEKS. 161 marked U wires wound upwards, the letters B and F representing back and front connections respectively. WINDING TABLE FOR DRUM ARMATURE WITH SIXTEEN ACTIVE CONDUCTORS. F D B U F D B U F D B U F D B U 16 8 16 7 15 14 6 5 13 12 4 3 11 10 a 1 9 The number of columns in the table is quite immaterial, and we could also arrange the table as follows : F. D. B. U. 16 7 14 5 12 3 10 1 8 15 6 13 4 11 2 9 16 7 This method of representing the winding is prefer- able to a diagram on account of its greater clearness, especially if the number of conductors is large, as in this case the diagram becomes confused on account of the many lines crossing each other. We must now investigate the distribution of electro- motive force between the different armature wires. It 162 DYNAMOS, ALTERNATORS, will be seen from the diagram that the electromotive force is as follows in the different wires : 15, 16, 1 noE.M.F. 2, 3, 4, 5, 6 downward E.M.F. 7, 8, 9, noE.M.F. 10, 11, 12, 13, 14 upward E.M.F. The brushes are shown touching the wires at the diameter of commutation, B being the negative brush, where the current enters, and + B the positive brush, where it leaves the armature. In reality, the brushes do not touch the wires directly, but a commutator, the plates of which (numbering in this case eight) are attached to each alternate wire. For clearness of illustration, the commutator has, however, been omitted from the figure. For the sake of simplicity, let us assume that the same electromotive force is generated in each of the wires 2 to 6 and 10 to 14, and let us call this the unit of electromotive force, and designate it by 1. Let us also assume the absolute potential of - B to be 0. Then the absolute potential of wire 1 and of the back connection 1-10 will be zero, but that of the front con- nection 11-3 will be 1, 10 being an active wire, in which an electromotive force of 1 is produced. When we reach the back end of 3 another unit of electro- motive force has been added, so that the absolute potential of the back connection 3-12 will be 2. Similiarly the absolute potential of the front connection 12-5 will be 3, and so on. We may represent this accumulation of potential in our winding table by inserting under the columns B and F, instead of the AND TRANSFORMERS. dash representing the back or front connections, numbers denoting the units of potential in each of these connections. We arrive thus at the following table : F. D. B. U. 5 16 5 7 5 14 4 b 12 2 3 1 10 . 1 tf-B 8 15 6 1 13 i 4 3 11 4 2 5 9 -5+B 16 5 7 The negative brush is in contact with the front con- nection 8-1, and the positive brush with the front connection 16-9, and by reference to the table we find that the total difference of potential between the two brushes is 5 units. We also see that the differ- ence of potential between adjacent wires in the neigh- bourhood of the points of commutation is 5 units i.e., the full electromotive force of the machine. This is an important point in the practical construction of armatures, and in order to bring it more fully into light a winding table is here given for a machine with a larger number of armature conductors. We have in the previous examples assumed that the machine has only 16 armature conductors, in order that the winding diagram may not become too complicated, but in actual practice the number of conductors is much larger, and it is expedient to 164 DYNAMOS, ALTEENATORS, study the distribution of potential in a machine as actually built. For this purpose we take a 200-volt machine, having 100 conductors on the armature that is, 50 on each side of the diameter of com- mutation. Of these there will be about 40 under the influence of each pole-piece, so that the unit of electro- motive force that is, the electromotive force in each wire will be 5 volts. In passing from one wire to the next we have, therefore, to add 5 volts at each step. This progression of electromotive force from wire to wire is clearly shown by the figures inserted in the columns B and F. Some of the numbers in these columns are underlined, and these represent the connections which are attached to those commutator bars that are in con- tact with the brushes. Thus, when the brushes touch two commutator segments on each side, the current enters the winding at the front ends of wires 49, 51, 98, and 100, and leaves it at the front ends of 48, 50, 99, and 1. It runs, therefore, down in the former and up in the latter wires. An instant later, when the armature has turned through a small angle, the commutator segment connected with 51 and 100 has passed beyond the brush, and the direction of current in these two wires is upwards, whilst the current in 50 and 1 is similarly reversed, running now downwards. By reference to the winding table, it will be seen that there is no electromotive force acting in any of these eight wires, and if the brushes were set as represented by the table, the change in the direction of the current would have to take place in each wire suddenly upon its emerging from under the brush. AND TEANSFOEMEES. WINDING AND POTENTIAL TABLE FOR DRUM ARMATURE. 100 Conductors, 200 Volts, 5 Volts per Active Conductor. 165 F. D. B. u. F. D. B. u. F. D. B. u. F. 100 49 98 47 96 45 0- 94 43 5 92 10 41 15 90 20 39 25 25 88 30 37 35 86 40 35 45 84 50 33 55 55 82 60 31 65 80 70 29 75 78 80 27 85 85 76 90 25 95 74 100 23 105 72 110 21 115- 115 70 120 19 125 68 130 17 135 66 140 15 145 145 64 150 13 155 62 160 11 165 60 170 9 175 175 58 180 7 185 56 190 5 195 54 200 3 200 200 52 200 1 200 50 200 99 200 48 200 97 200 200 46 200 95 200 44 195 93 190 42 135 91 180 150 40 175 89 170 38 165 87 160 36 155 85 150 150 34 145 83 140 32 135 81 130 30 125 79 120 120 28 115 77 110 26 105 75 100 24 95 73 90 90 22 85 71 80 20 75 69 70 18 65 67 60 60 16 55 65 50 14 45 63 40 12 35 61 30 30 10 25 59 21 8 15 57 10 6 5 55 4 53 2 51 100 Idle wires, 94 to 4 and 45 to 53 ; 5 volts down in each of the wires 5 to 44 ; 5 volts up in each of the wires 54 to 93. This would lead to sparking, and to avoid this fault the brushes must be shifted slightly forward, so that a slight electromotive force may act in the wires under commutation, whereby the previous current is gradu- ally stopped and the reverse current as gradually induced, even before the wire emerges from under the brush. This point will be found more fully dealt with in Chapter XI. For the present, it interests us only to study the distribution of electromotive force between the different wires which is not materially affected by a slight displacement of the brushes ; and on reference to the table it will be seen that there is a potential difference of 200 volts between adjacent 166 DYNAMOS, ALTERNATORS, wires in the neighbourhood of the points of com- mutation. This can be shown more clearly by writing the wires down, not in their order of winding as in the table, but in the order of their numerical succession, and writing under each pair the average potential difference as extracted from columns B and F of the table. We select for this purpose the quarter of the armature containing wires 100 to 50, the distribution of potential in the other quarters being symmetrical. We thus obtain the following : Wires 100 1 2 3 4 5 6 Potential difference 200 200 200 200 192J 185 Wires 6 7 8 9 1C) 11 Potential difference 175 165 155 145 135 Wires 11 12 13 14 15 16 Potential difference 125 115 105 1)5 85 Wires../ 16 17 18 19 20 21 Potential difference 75 65 55 45 35 Wires 21 22 23 24 25 Potential difference 25 15 5 5 This table shows clearly that the full voltage stress comes on the insulation of the idle wires, and that as we pass along the active wires to the polar diameter this stress is gradually reduced. As, however, all the wires must successively pass through the region of commutation, it is necessary that the insulation be- tween every wire and its neighbour should be good enough to sustain the full voltage of the machine. It need hardly be mentioned that each coil wound on the AND TRANSFORMERS. 167 armature may consist, not only of one turn, as in our present example, but of any number >of turns. Thus we might, for instance, use five turns for each coil, and in this case the total electromotive force of the machine would become 1,000 volts, and we should have to insulate neighbouring coils for a pressure of 1,000 volts. This is a somewhat difficult matter, and presents a certain risk of breakdown, so that the drum winding is not used for very high voltages. The limit at which this type of winding is yet safe may be taken at 1,000 FIG. 39. volts in certain exceptional cases, but more generally at about 600 volts. One means for preventing the strain on the insu- lation between neighbouring wires which has been employed by C. E. L. Brown and others is to put the winding on in two layers, separated by a stout sheet of insulating material, as shown in Fig. 39. Here all the wires of even number are first placed on the arma- ture core all round, the ends which are to form the return winding being left projecting at the back. Then 168 DYNAMOS, ALTEBNATOKS, a sheet of specially strong insulation, ss, is put on, and the wires are brought forward ovsr it to form the con- ductors of odd numbers. In this manner the voltage difference between adjacent wires is kept down to a very moderate amount, whilst that between super- imposed wires, although equal to the full voltage of the machine, can be safely borne owing to the extra insulation of the insertion, s s. FIG. 40. Another point which requires careful attention in drum armatures is the arrangement and insulation of the end connections. A glance at Fig. 38 will show that the wires at the end faces of the armature cross each other at various angles. Now, it is comparatively easy to insulate two wires laid parallel side by side, but when the wires cross there is great risk of the insula- AND TEANSFOBMBE8. 169 tion being cut through, to avoid which the insertion of strong felt or other insulating material becomes necessary. In larger machines, which are not wound with wire but with bars, the end connections are generally formed by specially-shaped plates so arranged as to avoid any large difference of potential between adjacent plates. Such constructions will be found more fully described in the examples of machines given later on. Another method of winding two-pole armatures is shown in Fig. 40. This is known under the term ring winding, or Gramme winding, although first used by Pacinotti in his electromotor. In this arrange- ment the core of the armature forms a hollow cylinder, and the winding is carried spirally round it, being, of course, closed on itself. In the figure there are shown 16 conductors. Starting the winding at the top, we would wind down 16, then up 1', through the interior, then down 1, up 2', down 2, up 3', and so on. The winding table is in this case simple. Writing 1', 2', 3' for the inner turns of coils 1, 2, 3, we have F. D B. U. F. D. B. U. F. D. B. U. 16 1' __ 1 _ 2' 2 3' 3 4' 4 5' 5 6' , 6 r 7 8' 8 9' 9 10' 10 11' 11 12' 12 13' 13 14' 14 15' 15 16' 16 ~ In this case the back and front connections are much shorter than in the drum armature, their length being, 170 DYNAMOS, ALTERNATORS, in fact, only slightly greater than the radial depth of the armature core, or, say, about one-third the diameter, whilst in drum armatures the length of the end connections is from 1 to If times the diameter. This is a distinct advantage of the ring winding ; but, on the other hand, the greater number of wires is a disadvantage as compared with the drum winding. On comparing the above winding table with that given on page 161, it will be seen that of those wires which are parallel to the iron there are twice as many, and of end connections there are also twice as many. It is, of course, advantageous to produce the required voltage with as short a length of wire as possible, not only on account of the saving in material, but also because the resistance of the armature will thereby be reduced. In comparing, therefore, the merits of two methods of winding arma- tures, one of the points to be taken into account is the length of wire required to produce a given voltage, or, in other words, the ratio of the length of wire under the influence of the field magnet to the total length of wire in the winding. In both kinds of winding only the outer conductors are under the influence of the field poles, and are, therefore, producing electromotive force ; the end connections in ring and drum, and the internal wire in the ring winding, do not con- tribute to the electromotive force, and must, therefore, be regarded as idle wires. The ratio of useful to total winding depends, of course, on the general proportions of the wire and on the skill with which the designer contrives to arrange the wires with the least waste of space. The latter consideration depends AND TKANSFOEMEES. 171 again on the size, speed, and voltage of the machine, as there will obviously be less waste of space where the machine is large and the wires stout, than where the machine is small and has to be wound with fine wire, the space occupied by insulation being in the latter case large in proportion to the space occupied by copper. Taking, however, average condition of winding, we can make a rough comparison between the ring and drum type of armature, assuming for this purpose that the end con- nections in the ring are '4 of the diameter of the core, and in the drum T6. We must also assume a certain proportion between the diameter and length of <;ore. If, for instance, the length is equal to the diameter, we would have in the ring each turn equal to 2*8 times the diameter, and the efficiency of the winding would be ='356. In the drum each 2*8 turn would be 5 '2 times the diameter of the core, and o the efficiency of winding = '385. The following DA table shows the efficiency of winding calculated in this manner for different ratios of length to diameter of core : Length Efficiency of Winding for Diameter. Ring. Drum. 5 1-0 1-5 2-0 278 356 395 416 238 385 484 555 UNIVERSITY 172 DYNAMOS, ALTERNATORS, This table shows clearly that the longer the arma- ture in comparison with its diameter, the better is the total length of winding utilised. It also shows that for all but very short armatures the drum winding is more efficient than the ring winding, though for the usual proportions, when the length is from one to 1J times the diameter, the difference between the efficiency of the two windings is not very great. There is, however, another point in favour of drum winding which does not appear in the above table. This table gives simply the length of useful winding, but says nothing as to resistance of winding. When an arma- ture is wound with wire the total armature resistance is, of course, directly proportional to the length of wire comprised in the winding, but when a bar winding is used the section of its different parts (outer bars, cross- connections, and inner bars, if any) can be made different, so as to utilise the available winding space in the best possible way, or reduce the armature resist- ance as far as possible. Now, in a ring, the part where the winding is most difficult to house is the inside, as the space there is necessarily limited, and for this reason it is hardly ever found possible to increase the section of the inside bars as compared to that of the outside or active bars. On the other hand, with a drum, the winding space at the ends is not so restricted, and we can generally manage to use cross-connections of larger area than that of the active bars. We thus find that not only does the drum have a shorter winding circuit than the ring, but parts of this circuit may be made of larger section than is possible in the ring, with the result that the resistance is sensibly AND TEANSFOEMEES. 173 reduced. A lower resistance means, of course, that we may pass a larger current through the armature, and obtain a larger output from a given weight and size of armature. In practice it is found that this increase of output amounts to from 30 to 50 per cent. Thus far the advantage would seem to lie entirely with the drum winding, but this is to some extent balanced by the greater difficulty of the insulation and support of the coils. In small armatures which are wound with wire, the coils are more difficult to hold in place when wound drum fashion than when wound ring fashion, as in the latter case the inner turns and short end connections help to keep the outer turns in their position. The same thing applies to large machines for high voltage, with the additional difficulty of insulating neighbouring coils, which is absent in ring armatures. By referring to Fig. 40, it will be seen that the current passes successively through coil after coil in the order in which the coils succeed each other, so that the difference of potential between adjacent coils is equal to the electromotive force generated in one coil. It is therefore an easy matter to insulate the coils against each other, and on account of this advantage we find that for machines of high voltage the ring winding is generally preferred. In medium- sized and large machines of moderate voltage, the difficulties above mentioned can, however, easily be met, and in these cases the drum winding is certainly preferable to the ring winding. Multipolar Parallel Winding. .We have now to enquire how either method of 174 DYNAMOS, ALTEENATOES, winding may be extended to multipolar machines. The simplest case is a parallel-wound ring armature,, and this we take first. Fig. 41 shows such an arma- ture in a six-pole field. It will be seen that the winding is carried spirally round the armature core in -B FIG. 41. precisely the same manner as would be adopted in a two-pole machine. The direction in which the electro- motive force is induced in the different wires is shown by dots and crosses as before. In each group of seven wires under the N poles the direction is downwards, in AND TEANSFOEMEES. 175 each group under the S poles it is upwards. Assuming each of the conductors to generate 1 volt and the current to enter at the brush - B to the left of the uppermost N pole, where we may regard the absolute value of the potential to be zero, there will be an absolute potential of 7 volts in wire 9. From wire 10 onwards the electromotive force is upwards that is to say, we have to deduct 1 volt for each successive wire, so that by the time we arrive at 17 the absolute potential has again been reduced to zero. The two brushes marked - B in the diagram are, therefore, at the same potential, and may be joined by an external conductor. The same consideration applies to the rest of the armature and to the positive brushes, so that we may connect externally the three negative brushes together and the three positive brushes together. The voltage between the negative and positive brushes is, of course, that due to one section of the armature winding, and the total current is six times that pass- ing through each conductor. In the type of winding shown in Fig. 41, we require, therefore, six brushes spaced equally round the com- mutator. This is with certain constructions of machine an inconvenient disposition, and has the further dis- advantage that we have to adjust six brushes instead of two. It is, however, possible to reduce the number of brushes to two by adding to the winding internal cross- connections. The figure represents an armature with 48 wires, and in the position shown the three negative brushes connect coils 1, 17, and 33, whilst at the same time the three positive brushes connect coils 9, 25, and 41. Now, it will be clear that if we wish to remove 176 DYNAMOS, ALTERNATORS, four out of the six brushes, we must replace the external connections made between the two sets of three brushes by internal connections made between the two sets of three coils above mentioned. This would, of course, have to be done for all sets of three coils, and might be represented by the following wind- ing table, in which the vertical columns, read down- wards, represent the successive spirals of the usual ring winding, and the horizontal lines between the columns the internal cross-connections. Those of the latter which at the moment are in immediate connec- tion with the brushes are shown by thicker lines. Fig. 42 represents diagrammatically a four-pole cylinder armature with cross-connections. In order to keep the illustration clear, the armature is supposed to have only 16 coils, and the cross-connections are shown in concentric circles, though in practice they are generally arranged spirally round a cylindrical sleeve behind the commutator, or they are housed within the commutator. Cross-connections of this kind have first been used by Mr. Mordey, in his Victoria dynamos. WINDING TABLE FOR PARALLEL SIX-POLE RING ARMATURE WITH INTERNAL CROSS-CONNECTIONS. 1 _ 17 _ 33 _ 10 26 42 2 18 34 11 27 43 3 19 35 12 28 _ 44 4 20 36 13 29 45 5 21 37 14 30 46 _ 6 22 38 15 31 47 7 23 39 16 32 48 8 24 40 17 _ 33 MI 1 _ 9 25 41 The advantages of the multipolar ring winding are AND TRANSFORMERS. 177 that we can use conductors of smaller section, which an be more easily handled, and that the commutated currents are smaller, so that the danger of sparking at the brushes can be more easily avoided. There is also the further advantage that no great difference of poten- tial can ever exist between adjacent coils. On the other FIG. 42. hand, there is the danger of internal currents, heating, and waste of power due to the following cause : Suppose that, owing to careless lining out in the erection of the machine, or to wear in the bearings, the armature is not quite in the centre of the field, but a little lower, the air space between its core and the three lower field poles will 178 DYNAMOS, ALTEENATOES, be less, and that between the core and the three upper field poles, Fig. 41, will be more than the normal amount. It will be obvious that the total flux of lines depends, amongst other things, on the air space ; being greater for a small and smaller for a large air space. The eccentric positicn of the armature results, there- fore, in an inequality of magnetic flux from the different pole - pieces with the consequence that the electro- motive force of each individual coil in the lower half of the armature will be greater than in the upper half. Let us assume, for the sake of illustration, that the difference is only 10 per cent. The absolute potential of wire 2 would be 1 volt, and that of wires 18 and 34 would be I'l volt. That of wire 3 would be 2 volts, and that of wires 19 and 35, joined to it by the cross- connections, would be 2*2 volts, and so on with the other wires. This difference of voltage must produce currents circulating internally through the coils and their cross-connections, which currents will be the greater, and, therefore, the more harmful, the lower the resistance of the winding that is, the more perfect the armature is in other respects. The resistance of an armature can easily be brought down to such a value that the loss of pressure at full output is only from 3 to 3J per cent, of the total electromotive force. It such an armature should be out of centre to the extent assumed (i.e., producing a difference of flux of 10 per cent.), then the wasteful internal currents would be about 1J times as strong as the normal currents, and being, as it were, superimposed on the latter, the result would be that those coils which are in the strong field would carry 2J times the normal current, and AND TEANSFOEMEES. 179 those coils which are in the weak field would carry a negative current of half the normal strength. Owing to armature reaction, the inequality in the current in the different coils will, in reality, not be so great as here indicated, but even if we assume that the arma- ture reactions would entirely prevent any reversal of FIG. 43. current in the top coils, this would still leave double- the normal current to be carried by the lower coils,, and consequently there would be double the voltage- loss over the armature. There would also be a great tendency to sparking, owing to the want of symmetry in the field and the one-sided load on the armature. 180 . DYNAMOS, ALTEKNATOKS, For these various reasons it is important, if a parallel method of winding be employed, to take great care to have the armature properly centred, and the field poles all of the same strength. This applies, of course, equally to multipolar drums. We have now to investigate the parallel method of drum winding for multipolar machines, and for this purpose we take a four-pole armature having 24 conductors, Fig. 43. Electrically, such an armature FIG. 44. is equivalent to a pair of armatures, each having 12 conductors, and each taking half the total current. In order to find the winding for the four-pole drum, we need therefore only copy the connections which would be required in the two-pole drum. Thus, beginning the winding in the latter at wire 2, Fig. 44, we wind down 2, then across the back and up 9, then across the front and down 4, and so on. Precisely the same sequence of winding has to be used in the four-pole drum, Fig. 43, but since here the angular distance AND TEANSFOEMEES. 181 between adjacent conductors is half of the corres- ponding value in the two-pole armature, the cross- connections span only about one quarter instead of one half the circumference. It should also be noted that the front and back cross-connections are not equal in length. Thus the connection 2-9 spans seven wires,, whilst that 9-4 spans only five wires. The mean length between the two would be a connection spanning six wires that is, exactly one-quarter the circumference. If we continue in Fig. 43 the sequence of winding here indicated, we arrive again at the starting point, and so obtain a closed winding. This is technically known under the term " lap winding,'* from the fact that successive turns, like 2 B 9 F r 4 B 11 F, etc., overlap each other. The following is the winding table for the armature shown in Fig. 43 : P. B. F. B. F. B. F. B. F. B. . 24 2 1 9 2 4 3 11 3 6 3 13 3 8 J 15 1 10 17 12 19 14 1 21 2 16 3 23 3 18 3 1 3 20 8 3 1 22 5 0_ 24 7 2 1 9 2 4 3 11 The letters D and U are omitted because superfluous, as it is immaterial whether we start at any given wire by winding downwards or upwards. The result must be in either case the same. The letters F and B represent, as before, cross-connections, and the smaller numbers in the F columns represent the absolute potential in that part of the winding given in any convenient unit. To determine the potential at any 182 DYNAMOS, ALTEENATOES, point of the winding we have only to start at the negative brush (assumed to be a zero potential) and follow the winding, adding for each active conductor the number of volts it produces. The direction of electromotive force is shown, in Fig. 43, in the usual way by dots and crosses, and this corresponds to a disposition of field where the magnets are set at an angle of 45 deg., as shown. We thus have No electromotive force in wires 23, 24, 1 ; 5, 6, 7 ; 11, 12, 13 ; 17, 18, 19. Downwards electromotive force in wires 2, 3, 4 ; 14, 15, 16. Upwards electromotive force in wires 8, 9, 10 ; 20, 21, 22. Assuming, for the sake of easy calculation, that each wire adds 1 volt, and that the negative brush is touch- ing the commutator bar corresponding to the front connection 24-5, then we shall have 1 volt in con- nection 22-3, and 3 volts in connections 20-1 and 18-23. The next connection is at the back 23-16. and in it the potential will still be 3 volts, but if we pass through wire 16 to the front we lose 1 volt, as the electromotive force in this wire is downwards. The potential of the front connection 16-21 is therefore only 2 volts. As our object is to tap the armature at the point where the potential is highest, it follows that we must place the positive brush at a point which is beyond wire 20 (which is the last wire adding electromotive force), and before wire 16 is reached. As the point must be on a front connection, its locality is restricted AND TBANSFOKMEKS. 183 to either 20-1 or 18-23. Let us select the latter position, as that will place the brushes -B and + B, Fig. 43, exactly 90 deg. apart. We have seen that the current entering at - B and passing down wire 5, up 22, and so on, finds its way quickly out at brush +B. How about the other branch of the current, which passes down 24? If we follow this in the winding table, we find that it has to pass 18 wires before reaching the positive brush, 23-18 that is, three times as many wires as the former current. More- over, the potential will rise to 3 volts when we reach 11-6, then fall to zero when we reach 12-17, and then rise again to 3 volts when we reach 18-23. Clearly, it is advantageous to let the current out as soon as it has reached the 3 volts for the first time, and for this reason we must place a brush on the commutator section corresponding to the front con- nection 11-6, indicated in the diagram by + B'. Similarly, we must place a negative brush, -B', on the commutator bar corresponding with the front connection 12-17. In the winding table the posi- tion of the brushes is indicated by underlining the figures giving the voltage in the columns F, single underlining being used to denote the negative, and double underlining the positive brush. In wind- ing an armature in this manner we lay on succes- sive laps, with an advance of two between each lap and the following lap, and continue till we have gone -once round the armature. The only conditions which must be fulfilled in order that the winding may close on itself is that there be an even number of bars if counted all round the armature, and that the distance 184 \ DYNAMOS, ALTEENATOES, between the two bars forming one lap should be repre- sented by an odd number. Thus, starting with the last bar, which must have an even number, we wind down this and cross the back in a forward direction till we get to, say, the twenty-first bar. Here we wind up and cross the face in a backward direction to bar 2. We might thus say that the winding is laid on with a forward "pitch" of 21 and a backward "pitch" of 19. Or we might have a forward pitch of 17 and a backward pitch of 15, or any other combination in which the forward and backward pitch are odd numbers differing by 2. The pitch must, of course, be such as to embrace a little more than the angular width of the pole-piece, in order to fully utilise the field. If the pitch be chosen larger than necessary, the winding can still be used, but there is waste of copper in the extra length of cross-connections, and an increased armature resistance. An excessively large pitch, which would bring the two bars of one lap simultaneously under the influence of two equal poles, would not only reduce the voltage, but also increase the sparking difficulty. It is characteristic for this type of drum winding that precisely the same armature may be used in fields having different numbers of poles, the only alteration required being in the number of brushes, just the same as with a ring armature. Thus a drum with 24 con- ductors having a forward pitch of 7 and a backward pitch of 5 will work perfectly well in a four-pole field, provided the angular width of the pole-pieces does not exceed the space occupied by three bars. Precisely the same armature can be used in a two-pole field with AND TBANSFOBMEBS. 185 pole-pieces of the same dimensions. The electro- motive force would be the same in both cases, but the WINDING AND POTENTIAL TABLE FOE, SIX-POLE PARALLEL DRUM, 120 CONDUCTORS. F B. F. B. F. \\. F. B. F; B. F. 9 120 8 21 7 2 6 23 5 4 4 25 3 6 '' 27 1 8 29 o 10 31 Q 12 33 1 14 35 S 16 4 37 5 18 6 39 7 7 20 8 41 B 22 10 43 11 24 2j 45 1,1 26 14 47 15 28 16 49 10 to 30 10 51 10 32 16 53 15 34 14 55 13 36 12 57 11 38 10 59 9 40 8 61 7 42 63 s 44 4 65 s 46 * 67 1 48 69 50 71 52 U 73 1 54 s 75 s 56 4 77 5 58 6 79 7 7 60 8 81 9 62 to 83 11 64 is 85 Li 66 14 87 U 68 w 89 10 16 70 16 91 10^ 72 16 93 16 74 U 95 13 76 IS 97 11 78 10 99 9 g 80 8 101 7 82 6 103 6 84 4 105 3 86 2 107 1 88 109 ^0 90 111 2 92 113 1 94 8 115 3 96 4 117 6 98 c 119 7 7 100 8 1 9 102 1C 3 11 104 U 5 13 106 14 7 16 108 10 9 10 = 10 mm 110 W 11 U s 112 16 13 16 114 14 15 13 116 1.' 17 11 118 10 19 i 33 _ 48 f 29 32 E.M.F. upwards in ...\ 73 88 49 52 yg - J *-H 89 - s E.M.F. down wards in -! 5368 109 112 1 93 - 1C8 1 9 - 12 current with a two-pole field would be half that obtain- able with a four-pole field. To make this point clear, a winding table is here given for a six-pole parallel 186 DYNAMOS, ALTERNATORS, drum, having 120 bars, pitch forward 21 and backward 19. The position of the six brushes is indicated by underlining the corresponding numbers in the voltage WINDING AND POTENTIAL TABLE FOR FOUR-POLE PARALLEL DRUM, 120 CONDUCTORS. F. B, F. B. F. r, F. B. F. B. F. 4 120 4 21 S 2 s 23 2 4 * 25 1 6 1 27 8 29 ^ 10 31 12 33 14 i 35 1 16 * 37 18 3 39 3 3 20 4 41 4 22 5 43 6 24 7 45 8 26 9 47 10 28 11 49 j > l,> 30 12 51 & 32 13 53 14 34 14 55 15 36 16 57 16 38 16 59 16 16 40 16 61 - 42 16 63 16 44 15 65 15 46 14 67 14 48 13 69 7; 13 50 1,: 71 ^ 52 11 73 10 54 75 8 56 7 77 6 58 6 79 4 4 60 4 81 5 62 a 83 2 64 ,.' 85 1 66 1 87 68 n 89 70 91 72 93 74 i 95 1 76 97 2 78 3 99 3 3 80 4 101 4 82 103 6 84 7 105 8 86 B 107 in 88 11 109 12 12 90 12 111 13 92 13 113 14 94 U 115 15 96 15 117 16 98 16 119 J6 16 100 16 1 16 102 16 3 16 304 U 5 15 106 U 7 U 108 13 9 13 110 12 11 1 112 11 13 10 114 :> 15 s 116 7 17 6118 5- 19 4 \ E.M.F. upwards , E.M.F. downwards ...{ ^ 58 118 Idle wires .. {119 12 29 42 59 72 89 - 102 columns. It will also be seen by reference to these columns that the full difference of potential exists between adjacent bars, just as in the ordinary two-pole AND TEANSFOEMEES. 187 drum, but as the multipolar parallel winding is generally used for large currents and moderate volt- ages, the difficulties of insulation are not serious. In the winding table it is assumed that each of the six brushes touches two commutator segments, the negative brushes being at 0, and the positive brushes at 16. If we now take the same armature and place it in a four-pole field we obtain a perfectly feasible combina- tion, the angular width of the pole-pieces being, of course, the same as before. The winding table for this arrangement is given on opposite page. By reducing the number of poles from six to four, we have gained nothing in electromotive force, but we have lost one-third of the current, there being now only four circuits through the armature instead of six, as before. To employ a four-pole field to advantage we should have to increase the angular width of the poles and the total flux from each, and we should also have to make the pitch greater, say, 29 forward and 27 backward. Multipolar Series Winding. When discussing the multipolar parallel winding, we selected a ring armature as the starting point of our investigation, for the reason that its explanation is rather more simple than that of a parallel- wound drum. With series winding the case is reversed, the drum winding being more easily explained than the ring winding, and for this reason we shall begin the investi- gations with the former, taking as our first example a four-pole drum. The characteristic feature of all drum -armatures is that no wires of any kind pass through N2 188 DYNAMOS, ALTEBNATOKS, the interior : hence to get from one bar to the other we cannot admit any other kind of connections but those that lie entirely on the back or front face of the arma- ture core. The necessary consequence of this condition is that when we join two bars we can only join the back end of one bar to the back end of the other, or the front end of the one to the front end of the other, but in no case the back end of one bar to the front end of the other. Since the direction of electromotive force changes with the sign of the magnet pole, and since our object is to so couple up the bars that their electro- motive forces shall add up, it follows that the length of front and back connections must correspond to the angular distance between the poles, or, in other words, that the pitch, y, must be about equal to the total number of bars divided by the number of poles, p. We say advisably " about " equal, because, as will be shown presently, the total number of bars can never be an exact multiple of the pitch. A four-pole series arma- ture may be considered to result from the combination of two two-pole armatures in such a way that the elec- tromotive forces are added. Let us then suppose the two-pole armatures cut open and stretched into semi- cylinders, which we place together so as to form an armature of double the original diameter. The suc- cessive bars, which in the two-pole armatures were opposite (or 180 deg. apart), will now be only 90 deg. apart, so that in passing through four bars in their order of connection we shall go once round the armature. The pitch, in other words, will now not be forward and backward as in the parallel method of winding,, but always forward. It is also clear that the pitch AND TEANSFOEMEES. 189 must be an odd number, because if it were an even number we should never get any bars at all into the places distinguished by odd numbers. The distance between two successive bars wound downwards is, therefore, an even number, being twice the pitch, and in following the winding once round the armature we find that the bars coming under north poles have, say, even numbers, and the bars coming under south poles have odd numbers. Starting, then, with an even- numbered bar under one of the north poles, we arrive, after going once round, at a bar under the same pole, and this must also have an even number, though not, of course, the same number as the bar with which we started, as that would at once close the winding. By analogy with the two-pole drum we conclude that in going once round we must arrive at a bar either two in front or two behind that from which we started. The relation between the number of poles, p, total number of bars, r, and pitch, y, is therefore given by the formula T = p y 2, y being an odd number. Thus in a four-pole drum, with a pitch of 7, the number of bars may either be 30 or 26, but not 28, which would be the exact multiple of the pitch. With a pitch of 5 the number of bars would similarly be 18 or 22. We have in the foregoing assumed that the length of the connectors in front is the same as that of the con- nectors at the back, but this is not absolutely necessary. By having the same pitch at both ends we obtain a 190 DYNAMOS, ALTEENATOES, perfectly symmetrical winding, and the designer would y for this reason, naturally adopt such a winding where possible. It is, however, not an absolute necessity to have the same pitch back and front, and it might , under certain circumstances, even be advantageous to abandon the perfectly symmetrical winding for one that is slightly unsymmetrical. Suppose, for instance, we made in the four- pole machine the back connec- tors with a pitch of 7, and the front connectors with a pitch of 5, then we could employ 26 bars, the winding being 26-7-12-19-24-5-10, etc. Or we could make the back connectors with a pitch of 9, and the front con- nectors with a pitch of 7, when we could wind a 30-bar armature as follows : 30-9-16-25-2-11-18, etc. Electrically, either of these armatures is equivalent to the corresponding armatures (r = 26 and T = 30), which we obtained by making the pitch of the front and back connectors both 7. To include cases where the pitch, front and back, differs by 2, we must write our formula for the number of bars as follows : y being the smaller of the two pitches and an odd number. We could thus wind a six-pole 50-bar arma- ture with a pitch of 9 at the back and 7 in front. 6 50 ="2 (2 x 7 + 2) + 2. AND TEANSFOEMEES. 191 It is not necessary to give the whole winding table for such an armature, as a few figures suffice to show the sequence thus : 50-9-16-25-32-41 48-7-14-23, etc. If we assume the electromotive force to be down- wards in bars 6 to 10, 23 to 27, 40 to 44, and upwards in bars 48 to 2, 14 to 18, 31 to 35, we find that the negative brush must touch the commutator segments connected to the front ends of bars 5, 21, or 37, and the positive brush the segments connected with the front ends of bars 47, 13, or 29, the distance between the two brushes being either 60 deg. or 180 deg. The advantage of using unequal pitch for the front and back connectors is that we are not so restricted in the choice of the number of bars. Thus in a six-pole armature with an equal pitch of 7, front and back, we could not get more than 44 bars, whereas with an equal pitch of 9, front and back, we could not get less than 52 bars. Supposing, now, that when designing the machine we found that 44 bars would not give enough electro- motive force, and that with 52 bars the electromotive force would be too great, then we can help ourselves by making the first connectors with a pitch of 7 and the back connectors with a pitch of 9. The number of bars will then be either 46 or 50. The adoption of unequal pitch gives us, therefore, greater choice in the number of bars which can be adopted. This will be seen more closely from the following table, which refers to six-pole machines. 192 DYNAMOS, ALTERNATOKS, Pitch. Possible number of bars. Pitch. Possible number of bars. Front. Back. Front. Back. 7 7 40 and 44 19 21 118 and 122 7 9 46 50 21 21 124 128 9 9 52 56 21 23 130 134 9 11 58 62 23 23 136 140 11 11 64 68 23 25 142 146 11 13 70 74 25 25 148 152 13 13 76 80 25 27 154 158 13 15 82 86 27 27 160 164 15 15 R8 92 27 29 166 170 15 17 94 98 29 29 172 176 17 17 100 104 29 31 178 182 17 19 106 110 31 31 184 188 19 19 112 116 31 33 190 194 Similarly, the possible numbers of bars for eight-pole machines is given in the following table. Pitch. Possible number of bars. Pitch. Possible number of bars. Front. Back. Front. Back. 11 11 86 and 90 23 25 190 ani 194 11 13 94 98 25 25 198 202 13 13 102 106 25 27 206 210 13 15 110 114 27 27 214 218 15 15 118 122 27 29 222 226 15 17 126 130 29 29 230 234 17 17 134 138 29 31 238 242 17 19 142 156 31 31 246 250 19 19 150 154 31 33 254 258 19 21 158 162 33 33 262 266 21 21 166 170 33 35 270 274 21 23 174 178 35 35 278 282 23 23 182 186 35 37 286 290 To summarise : If the pitch at front and back are equal, the number of bars is given by AND TRANSFORMERS. 193 If there is a difference of 2 between the front and back pitch, the formula becomes ij being the smaller pitch, and in either case an odd number. FIG. 45. Having now settled the question concerning the possible number of bars, we return to our example of a four-pole machine. The diagram, Fig. 45, shows the winding for a four- pole drum having 18 conductors. The current enters at the negative brush, -B, and issues at the positive brush, + B, the branch passing down 18 receiving electromotive force from the wires 15, 2, 7, 12, and the 194 DYNAMOS, ALTERNATORS, branch passing down 13 receiving electromotive force from the wires 3, 16, 11, 6. This kind of winding is, of course, applicable to any number of poles. The following table gives the winding for an eight-pole drum having 202 conductor and a pitch of 25, front and back. Each active wire is supposed to produce 1 volt, and the numbers inserted into the columns F and B denote, as before, the absolute potential of the connections, assuming the negative brush to be at zero potential. To find the wires in which the electromotive force acts downwards or upwards, we require a drawing of the field showing the angular width of the poles. Let us assume that the latter is- such as to cover 21 wires, leaving a little over four wires in each neutral space. It is not necessary to draw the armature, as the position of the centre of the field poles may be simply marked out on a circle. Thus, supposing the centre of one pole to coincide with wire 202, then the centre of the next pole will be at 25J, and the others at 50J, 75f, 101, 126J, 151J, and 176f . Adding our 10 wires on either side, and round- ing off the fractions, we arrive at the following result : {192 10 f 11 14 40 60 36 39 gi jjj \ 61 65 1/11 1A1 ' P7 QO r ic -re Idle wires \ ,, 11t - j 1O OO : \.\.Ct - HO E.M.F. upwards in... -j^j? ~ JJ? \}*& ~ * 191 By reference to these figures, it is now an easy matter to insert the potential in the columns F and B r which has been done in the winding table here given. AND TBANSFOEMEES. 195 WINDING AND POTENTIAL TABLE FOR EIGHT-POLE SERIES-WOUND- DRUM. 202 CONDUCTORS ; PITCH 25. F. 13. F. B. F. 13. F. 13. 41 202 & 25 43 50 44 75 # 100 46 125 47 150 48 175 & 2CO 50 23 51 48 52 73 5S 98 54 123 55 148 56 173 57 198 5S 21 59 46 60 71 61 96 62 121 63 146 64 171 65 196 66 19 67 44 68 69 60 94 70 119 71 144 72 169 7S 194 ?4 17 75 42 76 67 77 92 78 117 70 142 SO 167 81 192 82 15 83 40 84 65 84 90 *t 115 B4 140 84 165 84 190 84 13 84 38 84 63 84 88 84 113 84 138 84 163 84 188 84 11 84 36 84 61 % 86 83 111 82 136 81 161 80 186 79 9 78 34 77 59 76 84 75 109 74 134 73 159 78 184 71 7 70 32 60 57 68 82 67 107 66 132 65 157 64 182 63 5 68 50 61 55 60 80 69 105 58 130 57 155 66 18C 55 3 54 28 53 53 52 78 61 103 50 128 49 153 48 178 47 1 46 26 45 51 44 76 43 101 42 126 41 151 40 176 39 201 38 24 37 49 36 74 35 99 34 124 ss 149 m 174 31 199 30 22 89 47 88 72 Vt 97 26 122 25 147 84 172 23 197 23 20 21 45 80 70 10 95 18 120 17 145 w 170 15 195 u 18 13 43 18 68 11 93 10 118 9 143 s 168 7 193 6 16 5 41 4 66 s 91 8 116 1 141 166 191 14 39 64 89 114 139 164 189 12 37 62 87 112 137 162 187 1 10 8 35 3 60 4 85 6 110 6 135 7 160 8 185 8 10 33 11 58 18 83 IS 108 14 133 15 158 16 183 111 6 18 31 19 56 80 81 21 106 22 131 23 156 24 181 25 4 26 29 87 54 88 79 29 104 30 129 31 154 32 179 33 2 34 27 35 52 36 77 37 102 38 127 39 152 40 177 41\ 202 42 196 DYNAMOS, ALTEENATOES, It will be noticed that there are no less than nine front connections which are at potential zero, and nine front connections which are all at the same potential of 84 volts. We might place the negative brush on any of the former and the positive brush on any of the latter. Selecting, however, in each case the connection equally distant on both sides from active wires, we find the position for the negative brush on that commutator segment which is joined with the connection 139-164, and the positive brush on the segment corresponding to connection 63-88. The two brushes will then be 135 deg. apart. It would, however, be equally correct to place, say, the positive brush on 115-140, when its distance from the negative brush would be 45 deg. In fact, if the angular width of the poles is sufficiently small so as to leave a large number of wires idle, eight brushes may be used spaced 45 deg. apart, of which four would be positive and four negative. This arrangement may be advantageous when it becomes important to reduce the length of the commutator without cutting down the brush surface. The number of commutator bars required is 101, or half the number of conductors. The displacement of the commutator sections relatively to the brushes may be represented in the winding table by drawing a pencil down the first and third F column. Thus, taking the positive brush, we may assume that at the moment to which the table refers the positive brush has just left the segment corresponding to connection 65-90, and is now only touching the segment corresponding to 63-88, as shown by the double underlining. A moment later it will also touch the segment corresponding to 61-86, and finally AND TEANSFOEMEES. 197 leave 63-88. To truly represent the action going on in the armature, all the numbers in the winding table must be considered to move downwards, so that the effect will be the same as if the numbers stood still and the brush oscillated up and down over the distance of two lines. It will be seen that the current must be reversed simultaneously in eight wires, but there are also eight magnet poles to produce the reversal. With this type of winding the difficulty of insulating adjacent conductors from each other is magnified. From what has been already said on the subject of parallel winding, it will be clear that had this armature been wound parallel the greatest difference of potential between adjacent conductors would have been 21 volts. It is now 84 volts, or four times as great. The insulation between adjacent bars must be strong enough to resist the full voltage of the machine, and for this reason the winding here described is only used for moderate pressures. For ordinary central station work on the three-wire system, where a pres- sure of 250 is about the maximum required, this winding is perfectly safe, and it has also been used successfully in power transmission, and for arc lighting up to 600 volts, but beyond this pressure the series ring winding is preferable. When discussing the multipolar parallel winding we found that an inequality in the strength of the fields must cause wasteful internal currents. This defect is entirely absent in the multipolar series winding. On reference to the winding table it will be seen that if there exists such an inequality, it must affect both branches of the current within the armature to the 198 DYNAMOS, ALTEENATOKS, same extent, so that the balance between them is not disturbed, and no wasteful currents can be generated. This is an important advantage, not only of this par- ticular winding, but of all methods of series winding. We shall now proceed to investigate the multipolar series ring winding. The transition from the drum to the ring is most easily made if we replace each bar by a coil wound over the ring in the usual Gramme fashion. In order, however, to leave the connectors where they were we must reverse the direction in which each alternate coil is wound. Thus in the four- pole armature, Fig. 45, we would wind the coil corre- sponding to bar 18, say, down on the outside and up through the inside of the ring, and the same with coils :2, 4, 6, etc. On the other hand, coils 1, 3, 5, etc., would be wound up on the outside and down through the inside of the ring. Such a winding is shown in Fig. 46, but to avoid overlapping and keep the illustra- tion clear, the number of coils is assumed to be 22, instead of 18. Beginning the winding at coil 22, we wind this down on the outside and finish at the out- side on the back. Coil 5 we wind up on the outside, down on the inside, and finish at the outside in front. The object of winding the coils alternately up and down is merely to get the connectors of the same length ; where that is not of importance the coils may all be wound the same way, the beginning and finish being both left on outside wires. We now connect the back of 22 with the back of 5, the front of 5 with the front of 10, the back of 10 with the back of 15, and so on, exactly the same as in a drum .armature. This winding has also the same fault, AND TEANSFOEMEES. 199 inasmuch as the difference of potential between adjacent coils is equal to the full pressure generated, and, as far as the author is aware, it has never been used in practice. The fault here mentioned can, how- ever, easily be removed, and on removing it we arrive at a winding which (originally invented by Ayrton and FIG. 46. 200 DYNAMOS, ALTEBNATOES, any pressure for which the ordinary two-pole ring winding is safe. Now if we wish to omit coil 5 we can do so, provided we supply a connection between 22 and 10. We would therefore have to join the back outside end of coil 22 with the front outside end of coil 10. The connection would then pass from back to front through the interior of the armature, at the same time crossing over to the opposite point of the diameter. FIG. 47. Such an arrangement would, however, be incon- venient. To avoid it, we need only increase coil 22 by half a turn by bringing the wire once more for- ward on the inside. This finishes the coil with an inside end [in front. The connector lies now entirely on the front face of the armature, as shown in Fig. 47. In the same way we may put half a turn on the inside to the coil numbered 10, and thus finish it also in front. AND TBANSFOKMEBS. 201 The connector 10-20 will therefore likewise lie in front, and treating all the even-numbered coils in the same way, we find that all the connectors come to the front f and the winding becomes perfectly symmetrical. The winding includes, however, only the even-numbered coils and misses the coils of odd numbers. Thus,. instead of a drum containing 22 bars, we have obtained a ring with only 11 coils; but if we give two turns to each coil we shall still have 22 external conductors, and therefore the same electromotive force as before. Counting, however, coils and not conductors, and giving the coils consecutive numbers, we can describe the winding by saying that the inside end of No. 11 is joined to the outside end of No. 5, the inside of the latter to the outside of 10, the inside of 10 to the outside of 4, and so on. The pitch in this case is 5, or half the sum of a front and back pitch of the equivalent drum winding. In the case described the two were equal, but they might also have differed by 2, and then the pitch of the ring winding, instead of being an odd number, would have become an even number. Calling yi and yt respectively the front and back pitch in a drum armature, the total number of bars is given by a The equivalent ring armature has half the number of coils, and calling y the pitch for the ring, we have 2 and the number of coils in the ring r = ^ y 1. o 202 DYNAMOS, ALTEENATOES, We have seen that in a drum armature the pitch must always be an odd number. In a ring armature, on the other hand, it may be either an odd or an even number. It will be an odd number if the front and back pitch of the equivalent drum (from which we may consider the ring to have been evolved) are equal, and it will be an even number if the front pitch is either greater or smaller by 2. It is convenient to tabulate the formulae for armatures wound for different numbers of poles ; we thus obtain the following table : The number coils must equal to of be Machine has 4 poles 8 y *I 6 poles 3 yl 8 poles 42/l 10 poles 5yl 12 poles 6 yl 14 poles ?7/l The pitch, y, being any even or odd number. It will be seen that whether the pitch is even or odd, the number of coils in machines having 4, 8, or 12 poles must always be an odd number. It must also be an odd number in machines having 6, 10, and 14 poles if the pitch is even, but if the pitch is odd the number of coils in machines having 6, 10, and 14 poles must be even. We have now found the law which governs the number of coils that can be used in series-wound multipolar ring armatures, and must now find a way to represent the winding by means of a table analo- gous to that we have adopted with drum armatures. For this purpose we must agree on some method of distinguishing in the table between the outside and inside ends of the coils. We might, for instance, AND TBANSFOKMEES. 203 agree that the outside wire of a coil is on the left and the inside wire on the right of the number repre- senting the coil in the winding table. Thus, if we write 31-62-30 it shall mean that the outside of 30 is connected to the inside of 62 and the outside of 62 to the inside of 31. This convention may be represented diagrammatically thus : Outside J AT i f n -1} Inside Wire { Number of Coil | Wire The following is the winding table for a four-pole ring armature having 63 coils (63 = 2 x 31 + 1). WINDING AND POTENTIAL TABLE FOR FOUR-POLE SERIES RING, 63 COILS. -2 Ei 4 El | # j5 42 .2 a 6 o t> 6 o > 3 o > 3 1 a p" O 6 t> 3 > o > 63 31 62 30 61 29 5 60 1028 15 59 20 27 25 25 58 30 26 35 57 40 25 45 56 50 24 55 55 60 23 65 54 70 22 75 75 53 80 21 85 52 90 20 95 51 100 19 105 50 105 18 105 49 105 17 105 105 48 105 16 105 47 105 15 105 46 105 14 105 45 105\IZ 100 44 95 12 90 w m 1 90 43 85 11 80 42 75 10 70 41 65 9 60 40 55 8 50 39 46 7 40 40 38 35 6 30 37 25 5 20 36 15 4 10 35 5 3 34 2 35 1 32 E.M.F. is directed E.M.F. is directed No. E.M.F. in coils /downward inside \ 3 13 \ upward outside J 35 44 /down ward outside \ 19 29 \ upward inside J 51 60 W'61 2 14 18 30 34 45 50 o2 204 DYNAMOS, ALTERNATORS, We suppose each wire on the outer circumference of the armature to produce 1 volt, and each coil to have five turns, so that the electromotive force of each coil will be 5 volts. It is evident that each connector must be joined to one segment of the commutator, and as there are as many connectors as there are coils, we must have as many segments in the commutator as there are coils- on the armature core. We may thus number the segments in the same way as we number the coils. The segments so numbered must, however, be con- nected either all to the inside wires or all to the outside wires of the coils, but not some segments to inside and some to outside wires. It will be seen from this table that there is in no part of the winding a greater difference of potential than 5 volts between two adjacent coils. The negative brush may be placed on any commutator segment between 30 and 33 on one side, and between 62 and 2 on the opposite side. The positive brush may be placed either on any segment between 14 and 17 on one side,, or on any segment between 46 and 49 on the opposite side. Two brushes only are necessary, placed 90 deg. apart ; but four may be employed to get increased brush surface if required. In this respect the series ring resembles the series drum, though in the ring the possibility of placing additional brushes is not of so much advantage, since the ring winding would naturally only be employed in cases where the voltage is high and the current low or moderate, so that the brush surface need not be very large. The question as to the angular distance between the positive and negative brushes is of consider- AND TEANSFOEMEES. 205 able practical importance. If accessibility, ease of supervision, and compactness of design were the only considerations involved, we would naturally place the brushes as near together as the character of the winding permits, but from an electrical point of view this is not a good arrangement. In the first place there is the danger that both brushes may at the same time be accidentally touched, and in the second place there is greater probability of flashing over from one brush to the other if the distance between the brushes is small. For these reasons it is safer to put the brushes as far apart as the character of the winding will permit. The law which regulates the relative position of the brushes is very simple. We have seen that there are half as many equidistant positions for the negative brush as there are poles, and the same number of intermediate positions for the positive brush. Supposing now that we place brushes all round occupying these positions, and then see which of these brushes we can omit. Let us, for example, retain two neighbouring brushes and take away all the others. This will give us the minimum distance between the positive and negative brush, and this must obviously be equal to the angular distance between neighbouring poles. Thus, in a four-pole machine the distance would be 90 deg., in a six-pole machine 60 deg., in an eight-pole machine 45 deg., and so on. If we wish to increase this distance we can advance one of the brushes by an amount corresponding to twice the polar angle, or four times or six times the polar angle. To advance the brush by one, three, or five times the polar angle would obviously not do, as we should then occupy 206 DYNAMOS, ALTERNATORS, positions of the same potential as that of the brush which has not been moved. The advance of one brush would, of course, only be adopted if it resulted in an increase of distance between the two brushes. Thus, in a four-pole machine, the advance through f say, twice the polar angle would be useless, as that would bring the brush again within a distance of 90 deg. from the fixed brush, only on the other side of it. Similarly, in a six-pole machine we should advance through twice, but not through four times the polar angle, and so on. The angular distance between the two brushes must therefore be an odd multiple of the polar angle. For convenience of reference the following table is given : Number of Poles. Angular Distance between Brushes. 2 180 4 90 6 60 180 8 45 135 10 108 180 12 90 150 14 77 128 180 16 112 158 18 100 140 180 20 90 126 162 Multipolar Series and Parallel Winding 1 . It is possible to combine the series and parallel method of winding in the same armature. For instance, we could wind a 12-pole drum with three independent circuits, starting at points 60 deg. or 120 deg. apart, each representing a four -pole series AND TEANSFOEMEES. 207 winding. We could then add a set of internal con- nectors, joining the bars of equal potential. The disadvantages of such an arrangement are that the front and back connectors become thrice as long as with the ordinary 12-pole series winding (spanning 90 deg. instead of 30 deg.), and that the internal cross- connections have to be added if we wish to avoid the use of 12 brushes. A better way is to wind the independent circuits side by side, each in the usual 12-pole series manner. The front and back connectors remain short, and no additional internal connectors are required, provided we make the two brushes wide enough to cover each at least as many segments as there are independent circuits. This method also leaves us free to choose as many independent circuits as may be convenient. The object of employing a combined series and parallel winding is to obtain bars of convenient sectional area. Suppose, for instance, we have to design a six-pole machine for 1,000 amperes. If we wind the armature series, each bar would have to be large enough to carry 500 amperes, and the connec- tions of large bars are difficult to make. There is, moreover, the difficulty of having to commutate the large current of 500 amperes. On the other hand, if we wind the armature parallel, we have to employ three times as many bars (each one-third the former section), and to make three times the number of joints. The space occupied by insulating material becomes larger, and the armature more expensive. There is the further danger of internal currents and waste of power, as previously explained. Neither 208 DYNAMOS, ALTEKNATOKS, method of winding employed alone is in this case quite satisfactory, but if we combine both we can obtain a perfectly satisfactory winding. Say, that to get the required electromotive force we want about 150 bars on the armature. We would naturally employ 1 52 bars, being 6 x 25 + 2, but as 500 amperes in each bar is too large we double the number of bars, and thus reduce the current to be commutated to 250 amperes. We would thus have 304 bars, and put these on in two series windings ; one series running : 304-50-100-150-200-250-300-46-96, etc. and the other 1-51-101-151-201-251-301-47-97, etc. The brushes must in this case be wide enough to cover each at least two segments of the commutator. CHAPTEK IX. Open-Coil Armatures The Brush Armature The Thomson-Houston Armature. Open-Coil Armatures. The simplest example of an open-coil armature is the so-called shuttle-wound armature represented in Fig. 48. It consists of a cylindrical iron core, in which two grooves are planed out for the reception of a coil, the ends of which are attached to the two semicircular segments of a commutator. In the figure the wires are shown passing behind the commutator, though in armatures as actually made they must, of course, be grouped to the right and left of it to make room for the hub of the commutator and the spindle of the armature. In the position shown, when the maximum number of lines of force passes through the coil, the electromotive force is zero, and the brushes short-circuit the two sections of the com- mutator. As the armature revolves, the flux through the coil diminishes until it is zero, when the armature occupies a position at right angles to that shown, and the electromotive force has attained its maximum value, and then the flux increases again to a maxi- mum, whilst the electromotive force decreases 210 DYNAMOS, ALTEENATOES, to zero. Owing to the action of the commutator, the connection between the external circuit and the coil is reversed each time that the electromotive force in the latter is reversed, so that the direction of electro- motive force in the external circuit remains the same, though the electromotive force changes or pulsates between zero and a maximum. If we represent the electromotive force as a function of the time, or the FIG. 48. angular position of the armature, we obtain a curve, as shown in Fig. 49 by the full line. Had the armature been provided with two contact rings, instead of a two-part commutator, the electromotive force at the brushes, which are the terminals of the external circuit, and, therefore, the current in the latter, would have been alternating, as shown by the full and dotted curve in Fig. 49. The part of this curve above the horizontal is the same as before, but every alternate impulse is now negative. By using a commutator we AND TEANSFOEMEES. 211 obtain impulses which are all in the same direction, and this holds good, not only for the shuttle-wound armature shown in Fig. 48, but for other types. We could, for instance, wind the coil over a portion of a ring-shaped core, as shown in Fig. 50, but in this arrangement only one side of the ring is active, and it would obviously be an improvement to place a coil FIG. 49. also on the opposite side of the ring, as shown in Fig. 51, The two coils must, of course, be coupled in series by having their inner ends joined across and their outer ends each to one section of the commu- tator. This armature is electrically equivalent to that shown in Fig. 48, though mechanically it is an im- provement over the shuttle type, because the winding support and insulation of the coils are easier and the 212 DYNAMOS, ALTEENATOES, armature is ventilated. The current will, however, be equally pulsating as that from the shuttle-type arma- ture. A current fluctuating as much as shown in Fig. 49 would be useless for lighting purposes, and would also, by virtue of the self-induction in the various portions of the circuit, cause severe strains on the insulation. The question therefore is, how can we prevent the electromotive force from fluctuating between FIG. 50. such wide limits ? Starting from the position shown in Fig. 51, and calling it in the diagram Fig. 52, we find that when the armature has turned through 90 deg., we get the first maximum of electromotive force, we get zero again at 180 deg., the second maximum at 270 deg., and so on. Thus, the best action will be within the limits of about 45 deg. and 135 deg., and 225 deg. and 315 deg. respectively, corre- sponding to the parts of the curve shown by thicker AND TEANSFOEMEES. 213 lines. If, then, we wish to avoid too great a fluctua- tion in the electromotive force, we would have to utilise only that part of the electromotive force curve in Fig. 52 which lies above the line y y. This can be done by reducing the length of the segments on the commutator from 180 deg. to 90 deg., but now a new difficulty crops up. It is true that during the time that the brushes make contact with the segments of the commutator the electromotive force does not vary FIG. 51. as much as before, but the contact is totally interrupted twice in each revolution, so that as regards continuity of current we are now really worse off than before. The remedy is, however, simple. We need only put another pair of coils on the ring at right angles to the first pair, and another commutator side by side with the first. Then, if we make the brushes wide enough to cover both commutators, the current can never be interrupted, because as the segment of one comrnu- 214 DYNAMOS, ALTEENATOES, tator leaves the brush the corresponding segment of the other commutator begins to make contact. The FIG. 53. second pair of coils serves to bridge over the break between/ and a and c and d, Fig. 52. The winding is AND TEANSFOEMEES. 215 shown in Fig. 53, but for clearness of illustration the segments of the two commutators are shown as con- centric circles. The electromotive force curve of the pair of coils marked 1 1 is shown in Fig. 52 by the full line, that of the other pair of coils, marked 2 2, by the dotted line. The resultant electromotive force is therefore represented by the curve e' a b c b' d ef. FIG. 54. There is yet another slight improvement possible. We have assumed that each segment of the commutator is only 90 deg., or a little more than 90 deg., long to ensure continuity of contact. The brushes would therefore have to rub alternately over insulating material and over metal. This would cause unequal wear and jumping of brushes. To avoid this defect, we can provide each segment with an extension projecting into the space between the two neighbouring segments, 216 DYNAMOS, ALTEENATOES, and thus reduce the width of the insulation so much that the brushes rub only on metal, as is shown diagrammatically in Fig. 54. The Brush Armature. The construction of armature at which we have here arrived is that of the well-known Brush dynamo. It FIG. 55. is, of course, possible to double or treble the number of coils and commutators, thus making an eight-coil or twelve-coil armature. The different sets of four coils are in this case coupled in series by the brush connections, and thus a greater degree of uniformity of electromotive force is obtained. Fig. 55 shows diagrammatically the winding and coupling up of an eight-coil Brush armature. The two sets of coils are marked 1 1', 3 3', and 2 2', 4 4', respectively, but the cross-connections are omitted AND TEANSFOEMEES. 217 to avoid complication of drawing. The commutators are shown, as before, arranged in concentric circles, though in reality they are placed side by side. If the current in the armature coils had no magnetic effect on the armature core the diameter of commutation would be vertical, and the flux through 1 and 1' would in the position shown be a maximum. But the current in the armature produces a flux of its own, which is superimposed upon the flux emanating from the field magnets, and by following the direction of the currents it is easy to see that the resultant flux within the core becomes a maximum at some place to the left of coil 1 and to the right of coil 1'. The true diameter of commutation will therefore not be vertical, but inclined in the sense of rotation. Consequently the electromotive force in coils 4 4' will be either zero or very feeble, whilst it will be a maximum in coils 2 2'. In the other coils the electromotive force will have an intermediate value. The current enters at the brush marked- B 1? which at the moment touches only the central portion of the segment belonging to coil 2'. There is thus only one path open to the current namely, through 2', then across to coil 2,and out by the brush + B 2 . From here the current flows by an external wire to brush B 3 , which touches simultaneously two commutator segments namely, those belonging to coils 3 and 1'. The current splits between these coils, and the two branches, after passing through 3' and 1, finally unite again and leave the armature at the brush B 4 . From here the current is led round the field magnets as shown, and to the external circuit by the terminal, + T. By this arrangement the coils of weakest P 218 DYNAMOS, ALTERNATORS, action are entirely cut out, those of medium action are coupled in parallel series, and those of strongest action in single series, each coil entering and leaving the circuit twice per revolution, thus : 2'-2 - 4 and 4 ' out - <4 "4, >3 -3' 1 and 1' out. 4 -4' .. 2 and 2' out. o o 1 - 1 ' 3 and 3 ' out - Ct t 2 -2'< i ~i'> .. ..4 and 4' out. o o For clearness of illustration, the magnet poles have been shown with cylindrical faces, but, in reality, as the armature is a short flat ring, the magnets are set with their axes parallel to the spindle on either side of the armature. The Thomson-Houston Armature. Fig. 56 shows another type of open-coil armature. It is that employed by Profs. Thomson and Houston in the arc-light machine which bears their name. As actually made, the armature belongs to the drum type, though spherical in shape, but for clearness of illus- tration the armature is shown as a ring in the diagram. We have here only three coils, the inner ends of which are connected together at 0, whilst the outer ends are connected each to the corresponding segment of a three-part commutator. In the position shown, coil D has the maximum of electromotive force generated in it, coil C has less, and coil A has very little or none at AND TRANSFORMERS. 219 all. If the current were allowed to pass through the iatter coil when it occupies the position as shown, the coil would add nothing to the electromotive force, but absorb some electromotive force by reason of its resist- ance. The brushes are, therefore, so set that the coil of weakest action is always cut out of circuit, the current passing through the other two coils in series. The diagram shows the armature in the position when the FIG. 56. positive brush has just left the segment a. A moment before, coils A and C were in parallel. Now, A will remain out of circuit during a sixth part of a revolution and then it will come into parallel with D, but only for an instant namely, whilst the negative brush bridges the sections a and d. Then D will be cut out and A will advance into the position of maximum action, while C will begin to recede from that position on the other side, and so on. During one revolution 220 DYNAMOS, ALTERNATORS, each coil is twice in circuit for a third of a revolution, and twice out of circuit for a sixth of a revolution. If the thickness of the brushes is only sufficient to bridge the gap between two commutator sections the parallel grouping of any two coils is only momentary, and this would obviously be inadmissible. The current would in this case have to change instantly, and heavy spark- ing would result. To avoid sparking, it is essential that each coil should, so to speak, be gradually pre- pared for its withdrawal from the circuit by being left for an appreciable time in parallel with another, and, for the time, stronger coil. Thus coil A must, before reaching the position indicated, remain for some time in parallel with coil C. The electromotive force in A is then directed towards the section a, but is growing weaker ; the electromotive force in C is directed towards c (in parallel with a), but is growing stronger ; so that A will eventually overpower C, and stop its current at about the moment when a passes from under the brush, and there will be but little sparking. In order^ however, to obtain this action it is necessary to pro- long the time of parallel grouping, and that is done by employing two brushes on each side, connected to- gether, but set one with a certain angular advance upon the other. By increasing the angle (shifting the leading brush forward and the trailing brush back- ward), the time during which a weak coil is in parallel with a strong coil can be increased, with the result of decreasing the joint electromotive force of these coils. The electromotive force of the machine may thus be regulated within wide limits by a suitable displacement of the brushes. CHAPTEE X. Field Magnets Two-Pole Fields Multipolar Fields Weight of Fields Determination of Exciting Power Predetermination of Characteristics. Field Magnets. The magnetic field within which the armature revolves may be produced either by the use of permanent steel magnets or electromagnets. The former are not so effective as the latter, and are only used in exceptional cases, notably in the older forms of machines for lighthouses and in very small dynamos, where simplicity of construction is of more importance than small weight such as mine exploders, medical machines, signalling apparatus, and machines for laboratory work. There is, besides simplicity, a further reason for using permanent steel magnets in preference to electromagnets for very small machines, and this is that the energy required for exciting the magnets becomes inordinately great when the size of the machine is reduced beyond a certain limit, as will be -shown later on. Machines with permanent steel magnets are known under the name of " magneto machines," whilst the term " dynamos " is more par- ticularly applied to machines in which the field is 222 DYNAMOS, ALTEENATORS, produced by electromagnets. Since magneto machines have only a very limited sphere of application, we pass at once to the consideration of the field magnets of dynamos. The number of types of field magnets which have been used or proposed for dynamos is exceedingly great, but the difference between many of these is more apparent than real. It will therefore be best not to attempt to give a complete list of all the various designs of magnets, but rather select a few represen- tative types for purposes of comparison. In any elec- tromagnet we have to distinguish between two circuits, the electric and the magnetic circuit. These two must be interlinked, so that the current through the electric circuit may produce a flux of lines of force through the magnetic circuit, and the difference in type of dynamo field magnets is due to the more or less suitable arrange- ment of these two circuits. Two-Pole Fields. The most simple arrangement is that shown in Fig. 23, Chapter V. Here we have a coil of wire, W,. interlaced with a ring of iron, B, cut open at G. If the gap G be made of cylindrical or tunnel-like shape, it may receive a cylindrical armature, and thus Fig. 23- may be considered as representing the field magnet of a dynamo machine, but on the whole not a good arrangement. In the first place, the length of wire in the coil is unnecessarily large, and this can be reduced by lapping the wire more closely round the iron ring, and spreading it over a greater portion of it. In the next place, the curved form of magnet is bad from a practical point of view partly because a forging of this. AND TBANSFOBMEBS. 223 kind is difficult to produce and to fix in the frame of the machine, and partly because it cannot be wound in the lathe. It has been shown in Chapter V. that neither the shape of the core nor the disposition of the exciting wire have a direct influence on the magnetic flux produced by a given exciting power, and we are therefore free to alter the shape and arrangement of the magnetic and electric circuit in such manner as may be convenient. Instead of a hank of wire we may thus use a cylindrical coil wound on a former in a lathe, and instead of the curved iron core we may use a core consisting of straight pieces, which are more easily forged, machined, and put together. We may also make the pole-pieces detachable from the magnet core proper if by doing so we obtain some advantage as regards manufacture, but in this case we must take care to fit the different parts of the magnetic circuit properly together so as not to impede the flow of lines when it passes from one part to the next. In this way we arrive at something like the design shown in Fig. 57a M is a straight cylindrical magnet core of wrought iron shouldered into the cast-iron pole-pieces, PP, and C is the exciting coil. It will be seen at a glance that this arrangement is electrically and magnetically equivalent to that shown in Fig. 23, but mechanically it is a great improvement. The design is simple and substantial, all the machin- ing can be done on a lathe or boring machine, and the coil may be wound on a separate frame and slipped on when the machine is put together. This winding of magnet coils separately is important, not only because of facility for repairs, but chiefly because 224 DYNAMOS, ALTEENATOES, FIG. 57 AND TEANSFOEMEES. 225 it is possible to keep the electrical and the mechanical part of the work in distinct departments. If the coil is wound directly upon the magnet core a much greater weight has to be handled, and there is a risk of the -insulation being injured by metal chips or filings, which are necessarily present in a shop where machine tools are at work and fitting is going on. For this reason it is best to do the winding and other electrical work in a separate shop. The design of magnet shown in Fig. 57a, although, as was already said, perfectly practical, is still capable of improvement in two ways. In the first place, the magnet being on one side of the armature, the field is slightly unsymmetrical, and in the next place the arrangement is very heavy. Both of these defects can be remedied by duplicating the magnetic circuit, as shown in Fig. 57b. We require now two exciting oils and more wire, but we obtain, on the whole, a lighter machine, and one in which the field is perfectly symmetrical. The field magnet, Fig. 57a, has another defect, inasmuch as the coil is short, and has therefore only a small external surface through which the heat generated by the passage of the current can escape. Practical experience has shown that for every watt absorbed by the resistance of the coil there must be provided a certain area of cooling surface, if the temperature of the coil is to be kept down at a safe limit. Authorities differ as to the exact number of square inches of cooling surface required per watt of energy dissipated, and it is obviously im- possible to lay down a hard and fast rule, as the . 226 DYNAMOS, ALTEENATOES, * ' disposition of the machine, with regard to the fanning action of the armature and the locality where the machine is used, must necessarily influence the rate at which the coil can dissipate heat, but, generally speaking, the cooling surface should not be less than 1 square inch and need not be more than 4 square inches per watt. To prevent the coil, in Fig. 57a, from becoming too hot, we must, therefore, either increase its external surface by making it longer and shallower, or we must put more copper into it. The first expedient is of doubtful value, as it leads to a much heavier field, and the second is expensive. We can, however, alter the design altogether so as to obtain enough cooling surface without increasing the weight of the field. We need only treat the part marked M as the yoke and put coils on the two limbs marked P P in Fig. 57a. In this way we obtain the design shown in Fig. 57c, which is a very favourite type. By putting two exciting coils on the magnet limbs, M M, we have not only increased the cooling surface, but have also materially decreased the whole weight of the machine. This design is known as the "overtype" field. By reversing it that is, putting the armature below and the yoke, Y, at the top we get the " undertype " field, which is also much in use, and is specially adapted for direct-driven machines, where it is important to get the spindle low down to correspond with the position of the engine shaft. In this case the machine is sup- ported from its pole-pieces by brackets or packing pieces of non-magnetic material. In the overtype these pieces are not required, and the yoke may be AND TEANSFOEMEES. 227 either bolted direct to the bed-plate or may be cast in one piece with it. This type of field, although lighter than the pre- viously described types, is still rather heavy if the diameter of the armature is large in comparison with its length. If such an armature must be employed, and if it is important to save weight, we may duplicate the field, and thus we obtain the type shown in Fig. 57d. This contains less iron than the overtype field, but more copper, and, although, on the whole, it is consider- ably lighter, it is also more expensive. Figs. 57e and 57f show fields of the " iron-clad " type. Their characteristic feature is that the yokes surround the magnets completely. There is conse- quently no stray magnetic field. Fig. 57e is very heavy, but requires little wire, whilst Fig. 57f is not quite so heavy, but requires more wire. To give at a glance an approximate idea of the amount of copper required in each type of field, the space occupied by the coils is shown in black. The fields are all designed to take the same size of arma- ture namely, a drum 12in. diameter by 15in. long. Multipolar Fields. An example of a multipolar field has already been given in Fig. 2, Chapter I. This is the double four- pole magnet used by the Brush Company in their " Victoria " dynamo. The armature is a ring of large diameter as compared to its length, and the poles are presented to the end faces from either side. We require thus eight magnet cores with their axes parallel to the spindle, four on either side. The outer 228 DYNAMOS, ALTEKNATOKS, ends of the cores are joined by two massive cast-iron yokes. Fields of this type are frequently used in alternators. FIG. 58. In machines with cylindrical armatures (whether dynamos or alternators) the pole-pieces are necessarily FIG. 59. parts of a cylindrical surface, and the axes of the magnet cores are generally at right angles to the AND TRANSFOEMEES. 229 spindle. Any multipolar field may be considered as a combination of bi-polar fields. Thus, by taking two fields of the type 57c, we can produce a four-pole field of the type 58. In a similar way Fig. 59 may be considered to result from Fig. 57e if we increase the curvature of the yoke so as to get room for another pair of magnets. The coupling up of the coils must FIG. 60. in this case be reversed, so that diametrically opposed poles have the same, and neighbouring poles the opposite, sign. By duplicating Fig. 57f, we obtain the field shown in Fig. 60. In this design fourj-poles are produced by the use of only two exciting coils. Fig. 61 may be considered to result from the com- bination of four fields of the type shown in Fig. 57a. 230 DYNAMOS, ALTEBNATOBS, If a field of more than four poles be required, we may produce it by combining three or more fields of the 57c type ; but this presents considerable mechanical difficulties iu supporting the magnets, and is also, for other reasons, less advantageous than an expansion of the arrangement, Fig. 59, which is shown in Fig. 62 .as applied to a 10-pole machine. Fig. 61 may also be FIG. 61. expanded into a field of six, eight, or more poles, and is with continental makers a favourite type. Another type exclusively used on the Continent is the reverse of Fig. 59, the poles being placed inside the armature, which must in this case be overhung, the active con- ductors being on the inside. Fig. 63 shows a 10-pole field of this kind. To give an idea of the relative weight of armature in Figs. 62 and 63, the outlines of the armature core have been inserted in the diagrams, AND TRANSFORMERS. 231 which represent machines of equal output and equal speed. The field of Fig. 63 is about half the weight of Fig. 62, but this advantage is bought at the cost of a more difficult mechanical construction, both as regards the support of the armature core and the positive driving of the armature conductors. FIG. 62. There is no hard-and-fast rule by which we can judge the merit or otherwise of any of these types of field. The voltage, size, and speed of the machine, the greater or lesser importance of small weight, the possibility of obtaining soft steel castings, the relative 232 DYNAMOS, ALTEENATOES, cost of copper and iron, the energy permitted for exci- tation, the temperature rise allowed, and. last, but not least, the skill of the designer, are all items on which the value of any type depends ; but, as a general guide, a few facts may here be usefully stated. If pole-plates are used with Fig. 58, whereby it is possible to make the section of magnets not too much different from a. FIG. 63. square, or if the armature is fairly short, whereby the magnets' section naturally approaches a square, the amount of exciting wire required is not excessive, and the total weight of field is very moderate. As far as iron and copper are concerned, this type of field is fairly cheap, but the mechanical support of the magnets is somewhat expensive because it must be formed AND TBANSFOEMEES. 233 entirely of gunmetal brackets or chairs. Another drawback is that there is little ventilation for the armature and less for the inside of the field coils, so that .the heating will be greater than in machines of less compact design. Fig. 59 requires the same amount of magnet wire or possibly a little less than Fig. 58, but the whole field is much heavier if the yoke be made of cast iron. If the yoke be made of soft cast steel it need only be from one-half to one-third the section of the cast-iron yoke, and then Fig. 59 becomes lighter than Fig. 58. There is the further advantage that no gunmetal supports are required, the field being of the iron-clad type. The whole design is more open than Fig. 58, and the ventilation of armature and magnet coils is better. Fig. 60 is a very simple design and requires about the same amount of copper as Figs. 58 and 59 ; it is, however, very heavy if cast iron be used for the yoke. With cast steel the weight may be brought down to less than either of the previous designs, especially in small machines. The fact of the armature and field coils being protected by the surrounding yoke renders this design suitable for machines which are exposed to rough usage, such as tramway motors. Machines of this type have also been used for shiplighting, where an iron-clad field has the advantage of not disturbing the compasses. The field shown in Fig. 61 is heavy and expensive. It requires gunmetal supports and rather more wire than Fig. 58, but the cooling surface of the coils is large and the ventilation very good. This type is used for 10 and more poles in the newest design of Edison central-station machines, and an E 234 DYNAMOS, ALTEKNATOKS, example is also furnished by the new generator of 300 kilowatts (2,400 amperes at 125 volts) used for the distribution of electrical energy for motive power throughout a small-arms factory near Liege.* In this machine, which is more remarkable for its dimensions than its output, the armature is 15ft. 9in. diameter, and the field has 20 poles. The magnet cores and poles are of soft cast steel and weigh 10 tons, whilst two tons of exciting wire are used. The speed of the machine (which is direct driven by a Van der Kerchove engine) is ] 60 revolutions per minute, giving the arma- ture the remarkably high peripheral speed of over 8,000ft. per minute. At this speed the weight of field is about 901b. per kilowatt output. In machines of the type, Fig. 58, the weight of field is under lOOlb. per kilowatt for a peripheral speed of armature of 2,000ft. per minute. This is three and a half times better than the condition of the Liege machine, the field of which is of the type shown in Fig. 61, but expanded to 20 poles. Weight of Fields. A rough comparison of the different types of field as regards their weight has been made above, but in order to bring this important matter more clearly into view, it appeared to me desirable to give the reader some examples actually worked out so that he could compare figures rather than mere general state- ments. The figures given refer, of course, only to the particular cases selected, and their relative value would come out differently if we made the designs for a larger or smaller output, or a different speed or * L'EUctriden, vol. iv., No. 39, p. 177, September 10, 1892. AND TRANSFOEMEKS. 235 different armatures. In order to get representative figures it was, therefore, necessary to select fairly representative cases, and I have chosen for two-pole machines an output of 25 kilowatts, at 550 revolutions, as being about midway in the range of output and speed for which two-pole machines would usually be adopted. The armatures are 12in. diameter by 15in. long, and have, therefore, a peripheral speed of 1,730ft. In two cases the armatures are 15in. by 15in., and have a peri- pheral speed of 2,150ft. For the fields having four poles I have chosen an output of 80 kilowatts, at a speed of 380 revolutions, as being fair average conditions for which four-pole machines would be employed. The armatures are in all cases 24in. diameter by 20in. long, and have a peripheral speed of 2,380ft. Before giving the results of this investigation it is necessary to say a few words on the methods employed in designing the fields. The laws which govern the amount of exciting power or ampere-turns for any given configuration of magnets, will be found below in this and the next chapter. For the present it is only necessary to state that these laws have been followed in determining the amount of field wire required, and that due regard has been paid to armature reaction (see Chapter XI.), heating limit, and percentage of exciting energy. Where advis- able, pole-horns or pole-plates have been added to reduce exciting power or length of wire ; and in two cases (Figs. 64 and 65) the poles have been cut so as to reduce armature reaction and permit the use of a lighter field. The armature in these two cases has been increased to 15in., and is, of course, heavier R2 236 DYNAMOS, ALTEENATOES, and more expensive than the 12in. armature, which is used throughout the other two-pole fields. In all FIG. 64. the two-pole machines the armature is designed for a copper loss of 3| per cent. Precisely the same armature (24in. diameter by 20in. long) is u^ed in FIG. 65. all the four-pole fields, and it has been designed for a copper loas of 2J per cent. AND TRANSFORMERS. 237 As regards the copper loss in the fields this has been limited to 3J per cent, in the two-pole and to 2 per cent, in the four-pole fields, except in those cases where the heating limit made it desirable to work with a smaller expenditure of power in the field. The temperature rise has been determined in -every case, and will be found in the table below. The weights given are simply for the iron in the magnetic circuit and for the copper wire, but do not include the weight of any formers, terminals, AND TEANSFOEMEES. 239 Or, in English measure, X= ZE . ... . (34) where E = 21,880-- (25) In this expression the length of the circuit, L, must be inserted in inches and the area, A, in square inches ; /x, being merely a numeric, remains the same in both systems of measurement. In the special case that the part of the magnetic circuit under consideration contains only air or other non-magnetic substance /m. becomes 1, and we have K = '8^ E = 1,880 5?, A A since E = |i A and Z = B A, we find the ampere-turns required to produce the flux, F, in air by X = |i A x '8 A. X= -S^L . . . . (35) and similarly for English measure X - 1,880 B L . . . / (36) It is generally convenient to determine the exciting power separately for each part of the magnetic circuit, because the flux is not the same in all its parts. In a dynamo machine we have to distinguish between the flux through the armature, that through the air space (assumed to be the same), and that through the pole- pieces, joints, magnet cores and yokes, which is always larger than the armature flux, because a certain pro- portion of the lines generated within the magnet coils never passes through the armature, but produce what 240 DYNAMOS, ALTEENATOES, is termed a leakage field through the air surrounding the exciting coils. Since leakage is simply a magnetic flux through air, and must follow the general law V F =^p~, it will be seen that the amount of leakage must depend on the extent of the surfaces which are under different magnetic potentials, their distance apart, and on the difference of magnetic potential or magnetomotive force. Generally speaking, the leakage will be the greater, the greater the exciting power the larger the external surface of pole-pieces, and the less the distance between poles of opposite sign or between poles and yokes. The magnetic resistance of joints is generally neglected, and in well-made machines, where the joints are properly faced and strongly pressed together mechanically, their resistance is quite insignificant com- pared to that of other parts of the circuit. Professor Ewing* has experimentally investigated the magnetic resistance of joints by observing the decrease of induc- tion with the same magnetising power in a bar which had been successively cut into two, four, and eight pieces. He found that by applying mechanical pressure to the joints their resistance was diminished, and since in a well-made machine the joints are either strongly bolted up or are a good driving fit, we may take it that the necessary mechanical pressure for a good magnetic fit is obtained. Ewing gives the resistance of the joint in comparison with an equivalent layer of air between the surfaces. For H = 30, and |i varying from 14,550 to 9,800, the equivalent layer of air is *002 centimetre *Phil. Mag., Sept., 1888. AND TEANSFOEMEES. '241 thick. For H = 50, and ^ varying from 15,950 to 13,300, it is '0013 centimetre thick, and for H = 70, and |S varying from 16,820 to 15,200, it is '0009 centimetre thick. If we calculate from Swing's figures what exciting power is required to overcome in each case the resistance of the joint, we come to the remarkable result that with an increasing induction the exciting power actually diminishes. We find for D E > D 2 E 2 . This is again a matter which must be left to the judgment of the calculator. In const ant- voltage machines where it is for commercial reasons advisable to work over a region fairly high up on the charac- teristic, the two curves come so near together that an error in estimating the variation in the length D E has little influence on the final result, Moreover, it should be remembered that the formula (41) gives us the greatest possible amount of armature back ampere- turns if we insert the gap distance measured on the drawing, so that if we neglect the correction altogether the voltage of the machine may come out slightly too high, but never too low. A fault of this kind can of course be very easily compensated in the finished machine. 278 DYNAMOS, ALTERNATORS, Fig. 73 shows the static curve of Fig. 70 with the -dynamic added, the latter being drawn from the lowest point at which sparkless collection is just possible, and when the diameter of commutation coincides with the polar edges to the highest point when half this lead is assumed to be necessary for sparkless collection. FIG. 73. External Characteristic. An interesting case is that of a series machine. In such a machine the armature current traverses the field winding, and the exciting power is, therefore, strictly proportional to the current. The total field strength, and, therefore, also the strength of the fringe producing commutation, increases with the armature back turns ; and by properly designing the machine, it is possible to keep the lead constant over a fairly large range of out- put. In this case the exciting power is proportional to AND TEANSFOBMEBS. 279 280 DYNAMOS, ALTEENATOES, the main current, and we may draw the characteristic so as to represent the relation between current and field strength, or if the speed be constant between current and armature electromotive force. In plotting the dynamic characteristic we must, therefore, make the length, D E, Fig. 72, not a constant, but proportional to B, and it follows that the dynamic characteristic now passes through the origin, .0, of the co-ordinates. Fig. 74 shows this characterisation for the machine to which the magnetisation curve, Fig. 70, refers. S is the static electromotive force curve for con- stant speed which we would obtain by exciting the magnets separately and measuring the brush volts ; O D is the dynamic characteristic. The terminal pressure of the machine is the difference between the dynamic electromotive force and the loss of volts through the ohmic resistance of armature and magnet coils. The pressure thus lost is, of course, proportional to the current, and may be represented to the same voltage scale as the electromotive force curves by the straight line, OR. The length of ordinates between OB and OD gives, therefore, terminal volts, and by plotting these values over the horizontal as a base we obtain the curve T, giving the pressure at the terminals as a function of the current. This curve is called the "external characteristic," to distinguish it from the curve D, which is sometimes called the "internal characteristic." It will be noticed that the external characteristic has a tendency to droop as the current increases, and does, indeed, droop considerably when the current has be- come so large that the balance between armature AND TBANSFOBMEES. 281 reaction and the strength of the fringe of the field producing commutation is no longer maintained, and it becomes necessary to advance the brushes (dotted part of the curves) in order to get sparkless collection. This drooping of the terminal electromotive force curve is especially noticeable in machines of older construc- tion, in which both the resistance and armature reactions are large. In modern machines having comparatively strong fields and small armatures, the armature reaction is slight, and there is but little loss of electromotive force through resistance. With such machines, unless considerably overloaded, there is no droop in the characteristic. An exception to this rule is, however, formed by the various types of open- coil armatures used for arc lighting. In these machines the armature reaction is enormous, producing a very decided droop in the characteristic, which is, how- ever, a positive advantage, as it protects the machine from excessive strains when overloaded or short- circuited. Armature Cross Ampere-Turns. We have now to consider the part played in the working of a machine by the cross turns on the arma- ture namely, the wires a to c and b to d (Fig. 71). Each group is obviously equivalent to a sheet of current flowing between two parallel iron surfaces of breadth A. and the distance S apart, the total strength of current being r c , whilst the current density per TT a inch or centimetre is ^ - = y. u 282 DYNAMOS, ALTERNATORS, To determine the effect of the sheet of current on the induction between the two surfaces, we suppose the latter to be straightened out into a plane, Fig. 75, when A A represents the surface of the armature, PP that of the pole, and C C the sheet of current. Select- ing any point p on the pole face at a distance a from the centre, we find that the induction within the air //F/A/; A\ N N ^\^^ B FIG. 75. space at p is due to the action of all the current elements to the right and left of that point, the inte- gration being extended to the edges of the polar face. A current element, ydy, at the distance y from p pro- ^ duces a magnetising force H = 2 o and this inte- grated over all the elements to the right of p gives the AND TRANSFORMERS. 283 induction through p due to that part of the current sheet which lies to the right of p. Neglecting the comparatively very small magnetic resistance of the iron part of the path of lines, this induction is -^Ljf 1 7_ _ a j. In a similar manner we find the induc- 2 3 \ 2 / tion due to that part of the current sheet which lies to the left of p, or 7I y ( - + a ) . This is obviously of 2 o \ 2 / the opposite sign, and the resultant induction is the algebraical sum of these two values namely : For a = that is, for the centre of the pole-piece the induction is zero, and for a = - that is, for the edges 2 of the pole-piece it is a maximum, being positive for one and negative for the other edge, as shown by the sloping line, B B. Its value is - = T c -- 2 o 2 o TT a This is the induction due to the armature cross turns only, but in addition there is the induction due to the exciting coils on the field magnets, and to find the true induction within the air space we must add these two values. In Fig. 76 is reproduced the line B 1? B 2 , but with the ends joined to the axis of abscissae by sloping lines, B B 1 and B 3 B 2 , as it is obvious that the induc- tion cannot abruptly change from nothing to a maxi- mum at the polar edges. There must be a kind of fringe also to the field of induction produced by the -armature current, as there is a fringe to the field of u2 284 DYNAMOS, ALTERNATORS, induction produced by the exciting coils. The field! induction is, of course, constant over the whole of the polar face, and is represented in Fig. 76 by the horizontal line, P x P 2 , whilst the fringes are repre- sented by the sloping lines, P P! and P 3 P 2 . The FIG. 76. true induction is found by combining the two diagrams r which gives us the line P D x D 2 P 3 . This curve can also be obtained experimentally.* Let r in Fig. 77, C represent the commutator and A a piece of fibre or other insulating material through which two * First suggested by Prof. S. P. Thompson, a voltmeter being used instead of condenser key and galvanometer. AND TEANSFOEMEES. 285 laoles have been drilled for the reception of two pointed wires, bent down on to the commutator. Care must be taken to make the distance between the points equal to the pitch of the sections, and to keep the points fairly sharp, so that the surface of contact of each shall be less than the width of the insulation between the sections. Otherwise there would be flashing over FIG. 77. from one section to the next. The back ends of the two wires are connected with a delicate voltmeter, or, better still, with a condenser, B, discharging key, K, and ballistic galvanometer, G. The fibre piece, A, is mounted on a pin, which can be set in any desired position round a graduated circle (not shown in the diagram) so as to bring the points of contact succes- sively into various positions with regard to the polar face. Whilst the key remains in the position shown, 286 DYNAMOS, ALTERNATOR S, the condenser receives a charge which is proportional to the induction (ordinate of the line Dj D 2 ) in that part of the field to which the then position of the piece A corresponds. On pressing down the key, we dis- charge the condenser through the galvanometer and obtain a deflection, which is, of course, also proportional to the induction. By plotting the angular position of A, which we read off on the graduated circle, on the horizontal and the throw of the galvanometer on the vertical, we obtain to an arbitrary scale the curve N FIG. 78. We may also use the same instrument to determine the variation of electromotive force round the commu- tator* by using only one contact wire for instance, that connected directly to the condenser; and connect- ing the back contact of the key to one of the brushes. In this case we obtain a curve of electromotive force of the general shape represented in Fig. 78. If there * First done by Mr. W. Mordey. AND TRANSFORMERS. 287 were no armature reaction that is, if the readings were taken when no current is permitted to flow through the armature the curve would be of the general character shown by the dotted line. An armature giving a diagram of the general character shown in Fig. 76 will run without sparking. The brush would have to be placed somewhere in the region between P and D , the exact spot depending on FIG. 79. the amount of induction required to balance the self- induction of the armature wires ; but there is, at any rate, a sufficiently strong field to produce commutation. In other words, the armature cross-induction is small as compared with the forward induction produced by the field winding. Now let us enquire how the matter stands if the armature cross-induction is comparatively large. Let us, for instance, assume that DoBj is larger than DO PI- In this case tne point D 1? Fig. 79, falls 288 DYNAMOS, ALTEENATOES, below the axis, and the field under the influence of which commutation takes place becomes negative. There may or may not be the small hump near P . This depends on the shape of the polar edges. It may be just possible to obtain sparkless collection by placing the brush into the position E, but this would be merely a chance success upon which no prudent designer should rely. I only mention this as affording a possible explanation of the few cases in which sparkless collection has been obtained with machines in which the armature cross-induction exceeded the field induction. As a general rule, we may, however, take it that under such circumstances sparkless collec- tion is impossible. In order to get sparkless collection it is obvious that the point D 1 must remain above the axis, and that, therefore, D B x must be smaller than D P r This condition will be obtained if the ampere- turns on the field magnets required to overcome the resistance of the air space exceed the cross ampere- turns of the armature. Calling the latter Xx we have Xa > XX, where X a = '8x2^ X a =l,880x2 1 that is to say, if we enlarge the dimensions of the normal machine the second term becomes smaller and the critical resistance larger. This is quite natural. The larger machine is more powerful, and can, therefore, force current through an external circuit of increased resistance. If, however, q < 1 that is to say, if we reduce the linear dimensions of the normal machine so as to get a small model the second term on the right becomes larger and the critical resistance smaller. It is then only a question of how much we must reduce the dimensions to get a model which will only work on an external circuit of no resistance, and if we go a fraction below this size, the model will not even excite itself. This limit will obviously be reached if K n = AND TEANSFOEMEES. 299 To show the application of this formula, let us take as an example the machine to which the external oharacteristic, Fig. 74, refers, and assume it to be the normal machine. The total internal resistance of such a machine would be about 2J ohms, and the critical resistance of the external circuit about 40 ohms. This gives ~Kn = 42*5. Let us now make a model to one- fifth size. The largest resistance through which this model would just be able to send a current would then 9%5 be 42'5 - '- = 30 ohms. The normal machine had ()'n an armature 18in. diameter, running at 500 revolutions per minute. The model would therefore have an armature 3'6in. diameter, and this would run at 2,500 revolutions. If we now still further reduce the size of the model, and run proportionately faster, we arrive finally at a model which will not work at all. This limit will be reached'if 2-5 that is, if the model is made to a scale of T Vth. The diameter of the armature would be a little over lin., and the speed 8,500 revolutions. This is, however, merely the theoretical limit, and could not possibly be reached in practice. The wire would be so fine that it could scarcely be handled and the insulating cover- ing would only be half a mil thick. Moreover, the clearance would have to be reduced to something like T |oth of an inch, and this at the high speed of 8,500 revolutions would not be mechanically safe. To obtain 300 DYNAMOS, ALTERNATORS, a model that will work, we should therefore have to* make it to a scale considerably larger than T Vth. As regards motors, there is no such limit to their size. The power being supplied to the field and arma- ture electrically from an outside source, we can always make the model work if we expend enough power on it. From what has been said above on the question ot reducing the size of dynamos, it will be obvious that* the design and manufacture of very small machines to work as generators presents considerable practical difficulties, and this is the reason why such machines are, as a rule, not made self-exciting at all, but are pro- vided with field magnets of hardened steel, as was already stated in Chapter X. Large Dynamos. A far more important question, however, is that of an increase in the linear dimensions of any given type of machine. The modern tendency, especially in con- nection with central station work, electric traction, and power transmission, is in the direction of larger and still larger machines, and the question arises whether the demand for such machines can be satisfied by simply increasing the linear dimensions of any type which has proved successful when built for a small or moderate output, or whether it becomes expedient to change the type when the output exceeds a certain limit. To find an answer to this question let us first investigate how the output increases with an increase of linear dimensions in a two-pole dynamo this being the type which is generally employed for machines of AND TBANSFOEMEKS. 301 moderate size. Leaving aside for a moment the part played by the field magnets, the output of such a machine is limited by three conditions. Limits of Output. 1. The efficiency of the armature that is, the ratio of watts generated to watts available at the brushes. . 2. The heating limit that is, the ratio of watts wasted in the armature to total cooling surface, due account being taken of the provision for ingress and egress of air. 3. The sparking limit as given by the minimum in- duction in the air space under the leading polar edge. In order to put the large machine mechanically into the same condition as the small machine, we assume that its armature has the same peripheral speed. The rotary speed must therefore be reduced in the same proportion as the linear dimensions are increased. It will be shown presently that the limits of output imposed by these three conditions are different, and we shall for this reason take them separately. First, as to efficiency. If the large machine has q times the linear dimensions of the small machine, the resistance of the armature will be times that of q the small machine, or a little less, because there is proportionately less space occupied by insulation and more by copper. Suppose we work both armatures -at the same induction, then the useful field will be increased in the ratio of q 2 , and the electromotive force in the ratio of q. E ' = E q, 302 DYNAMOS, ALTEENATORS, while the armature resistance will be Rfl' = By, , g or a little less. The waste of power per cubic inch of iron in the armature core due to hysteresis will be reduced in the ratio of , the frequency of reversal being reduced in q this proportion, but as there are q 3 as many cubic inches, the hysteresis loss will be increased in the ratio of q 2 . In addition to this loss, we have to con- sider the loss of power by eddy currents in the iron and copper. As regards eddy currents in the iron, the loss per cubic inch of core will be the same if we employ the same thickness of plates (generally 20 to 25 mils), and the total loss will therefore be increased in the ratio of w, C-E a = - Since q > 1 it is obvious that only the upper sign is possible, and we find, therefore, that by inserting for C', q 2 C (in 42) we make the right-hand term too small. Now to obtain equality that is to say, to comply with the condition of equal efficiency of the two armatures we must so alter AND TEANSFOEMEES. 305 We have next to enquire how the output is limited by heating. The cooling surface varies as the square of the linear dimensions, and to get the same tempe- rature rise (the peripheral speed and, therefore, the efficiency of ventilation being equal) the waste of power in the large armature may be q 2 times that in the small armature, or in symbols (W* + W, +C 2 E a ) (f = (f W h + (f W f + C' 2 ^ a 2 (W/ + C 2 K a y = q* W, + C' 2 ^L . .' (43) 2 As regards limit of output by heating, hysteresis has no influence. This is quite natural, since both the hysteresis loss and the cooling surface are proportional to the square of the linear dimensions, but as regards Poucault losses this proportionality does no longer exist. The latter increase as the cube of the linear dimensions, and become therefore relatively of more importance as the dimensions are increased. If it were permissible to neglect them altogether, the current would be C' = C q *. ' as to make the right-hand term larger. This will be the case if we assume C' ^- q 2 C. Equation (42) may also be written thus : . W* Wfc .q is obviously smaller than q iL_, and this is again smaller than jfO _ _, so that the first term on the right is smaller than the first term on C the left. Similarly, the second term on the right is obviously smaller than the second term on the left If equality is to be preserved, the third term on the right must, therefore, be larger than the third term on the left that is, C' must be larger thau q 2 C. 306 DYNAMOS, ALTEENATOKS, Let us now see whether the pressure of eddy currents raises or lowers the limit of output. Equation (43) may also be written thus : W, (q' 2 - q 2 W. This will best be seen by an example. Taking the design of the machine, Fig. 57c, as the small machine, and doubling all its dimensions, let us see what output we may expect from the enlarged machine. The arma- ture of the small machine is 12in. diameter by 15in. long. At 550 revolutions per minute the output is :25 kilowatts, with a total armature loss of 1,200 watts. The large machine would have an armature 24in. -diameter by 30in. long, and having four times the cooling surface we may work it with a total loss of 4,800 watts. It is not necessary to give the calcula- tion in detail, but the result may be thus stated, the first figure referring to the small and the second to the large machine. Armature resistance, "015 and 006 ; exciting power, 23,000 and 60,000 ; weight of iron plates in armature, SOOlb. and 2,6001b. ; weight of iron in field, 2,6001b. and 21,5001b. ; power required for excitation, 3J per cent, and 1'95 per cent. ; speed, 550 and 275 revolutions ; output, 250 amperes at 100 volts and 700 amperes at 230 volts. The heating and sparking limits are the same in both machines. If the relation W = g 2 W held good in practice, the -output of the large machine would only be 4 x 25 = 100 kilowatts. In reality it is 7QQ ^ 3Q = 161 kilowatts, but this result has been obtained by slightly departing AND TEANSFOEMEES. 309* from the strict proportionality in the dimensions between the two machines, with the result that the- large machine is rather heavy in comparison with its- size. It is also heavy in comparison with its output.. From the figures given above, it will be seen that the iron weight in the small machine is 2,9001b., and in the large machine 24,1001b. a ratio of 1 : 8'3 ; whereas the ratio in output is 25 : 161, or 1 : 6*45. To put it in another way, the small machine weighs 1161b. per kilowatt, and the large machine weighs 1501b. per kilo- watt. As regards weight and cost, the large machine is therefore not as good as the small machine, and this shows that the same type of machine is not equally suitable for all sizes. It may be useful to recapitulate here the results obtained above as to the limits of output depending on the three conditions of efficiency, heating, and sparking : Output of large machine for same 1 -, = ^ 3 efficiency as small machine J Output of large machine for same ) W >=== Wo^ heating as small machine J Output of large machine for same \ W' ~ W o 2 sparking as small machine j The limit of output as determined by the condition of equal efficiency is, as a rule, not reached. We naturally expect the large machine to have a higher efficiency than the small machine, and since the limit of output refers to equal efficiency it cannot be reached in cases where we demand a higher efficiency. More- 310 DYNAMOS, ALTEENATOES, over, the limit of output dependent on the efficiency condition is far higher than that due to the other two conditions, so that in any case we could not take full advantage of it without incurring the risk of heating and sparking. The output of the large machine will 5 therefore lie between W q 2 and W (f, whereas its weight will, of course, be q 3 times that of the small machine. It would appear from this investigation that the larger the machine the heavier and more expensive does it become relatively to its output, but it should be remembered that this conclusion only holds good under the circumstances to which our investigation was applied, and which are : (1) That the small machine is already working right up to the limit of output imposed by the condi- tion of heating and sparking ; (2) that precisely the same limits are observed in the large machine ; and (3) that it is in every detail a faithful but enlarged copy of the small machine. In practice, however, the output of machines which may be called small (say, under 15 kilowatts) is generally not so much limited by heating or sparking as by the efficiency condition, and we may therefore venture to raise the sparking and heating limits in the large machine so that its output will be rather larger than given by the above expressions. The case is different if the small machine from which we start is already itself of a sufficient size to make its output dependent more on the sparking and heating limit than on the efficiency limit. In this case we have no margin to work upon, and a still larger machine, although designed precisely on the same lines as the successful machine of moderate size, may AND TRANSFOEMEES. . 311 and probably will turn out to be an unsuccessful design. Thus there is no difficulty in producing very good designs of two-pole machines for 50 or even 100 kilo- watts output, but if we attempt to apply the same designs to machines of 300 or 600 kilowatts output, we shall find that these larger machines are more than six times as heavy and expensive than their smaller proto- types. We conclude from this that the two-pole type is not suitable for large machines. Advantage of Multipolar Dynamos. Large machines must, however, be made, and the ques- tion now arises, how should they be made in order to be at least not worse, and, if possible, better, than small and moderate size two-pole machines in point of weight and cost? Practical experience has answered this question in favour of multipolar machines. Whereas for small and moderate size machines the bi-polar type is undoubtedly the best, there is a limit of output beyond which a four-pole machine is preferable. If we still further increase the output, we find that a point is eventually reached where a six-pole machine is better than a four-pole, and so on, the number of poles increasing with the output. The precise points ut which a change from two to four or from four to six poles, and so on, becomes expedient, depends on a variety of circumstances, and no hard-and-fast rule can be given, but that the value of a design depends on the appropriate choice of type the reader can easily find out for himself by making comparative designs for various sizes of machine. Without, however, going so far as to prepare a whole series of designs, we may 312 DYNAMOS, ALTERNATORS, show the effect of increasing the number of poles by an example, and for this purpose we take the 25-kilowatt machine (250 amperes, 100 volts, 550 revolutions) design, Fig. 57c, particulars of which were given in the table on page 66. The weight of the iron plates in the armature is 3001b., that of the iron in the field is 2,6001b. The diameter of the armature is 12in., and its length 15in. Let us now make a four-pole machine having an armature of double the diameter, but the same radial depth of iron (in this case 3fin.) and the same length. Assuming that we employ the type of field shown in Fig. 58, page 228, its weight will be very nearly double that of Fig. 57c, provided we work with the same total induction. The number of turns on the armature and its resistance will be doubled, and if we work at half the speed, the electro- motive force will be doubled, but the current will remain the same. The four-pole machine, with an armature of 24in. by 15in., and running at 275 revolu- tions, will have the same efficiency and the same spark- ing limit as the two-pole machine with an armature of 12in. by 15in., and running at 550 revolutions. The output will, however, be doubled. Let us now see by how much we would have to increase the linear dimen- sions of the two-pole machine to get double the output. Without going into complicated calculation, we may assume that W' = W , and the result will be a current running up in the right-hand part of the conductor, and down in the left-hand part. When the conductor has passed the edge of the pole-piece (as shown by the rectangle a b on the right), and provided the field under the pole-piece is uniform, there will be no eddy currents, because the induction in a will then be the same as that in b. The field can, however, only be uniform if the machine is working on open circuit. The induction for the whole length of the pole-piece is then represented by the horizontal line PI P 2 , Fig. 76, page 284, and eddy currents occur only under the leading and trailing polar edges, but not under the pole-pieces themselves. If the machine works on a closed circuit, the line representing induction is distorted, as shown 322 DYNAMOS, ALTEKNATOES, by D 1 D 2 , and there are eddy currents, not only in those conductors which at any given time are under the polar edges, but in all the intermediate conductors as well. Moreover, the eddy currents at the trailing edge are increased by reason of the larger induction. We conclude from this that the loss of power by eddy currents in a machine working on closed circuit will be greater than in the same machine working on open circuit. In order to reduce this loss of power various means may be adopted. The most obvious remedy is, of course, to laminate the conductor. This may be done by building it up of narrow strips, insulated from each other, but in contact at the ends. In this case the edge of the pole-piece must be of such a shape as not to coincide with the edge of the conductor, so that only a small portion of the latter can at any time be in a field of different strength from that acting on the rest of the conductor. Another way of laminating is by building the conductor up of cable with insulated strands pressed into the desired shape. We may also chamfer the polar edges, as shown by the dotted line in Fig. 83, to make the transition from the neutral space to the strong field more gradual ; or we may place the conductors in grooves, which cause the lines of induction to snap across so suddenly as to give no time for the generation of eddy currents. Other things being equal, or proportionate, it will be clear that the electromotive force causing eddy currents i& directly proportional to the average induction ; the eddy currents themselves are proportional to the electromotive force generating them, and the waste ' AND TEANSFOEMEES. 323: of power is therefore proportional to the square of the induction. Eddy Currents in the Armature Core. The eddy currents in the armature core itself follow very much the same law as those in the external con- ductors. When the core is turned up in a lathe there is danger of the tool burring over the edges of the plates, and bringing them into contact, notwithstand- ing the paper insulation ; and if this happens, the armature core becomes coated with a thin film of more or less continuous metal in which eddy currents can circulate. In addition to these there are also eddy currents in the body of each plate, but with thin plates these are exceedingly small. With careful workman- ship it is also possible to almost completely avoid contact between the external edges of the plates, so that, as a rule, the loss of power by eddy currents in the armature core may be reduced to a negligible quantity. Eddy Currents in the Interior of Ring Armatures. In addition to the losses detailed above, there is in- ring armatures another loss caused by eddy currents in the internal conductors and metal parts within the armature core. If the sectional area of the core be sufficient, there is, of course, no internal field in a machine working on open circuit. But as soon as a current flows an internal field is produced (see Fig. 70) r and since the lines of this field are stationary in space they must be cut by the internal conductors, the shaft, hub, and supporting arms of the armature core, -324 DYNAMOS, ALTEENATOES, as will be seen by Fig. 84. The internal field due to the armature current is shown by dotted lines, and a few of the internal conductors, C, are also shown. It the hub, with the arms, were made of iron, the internal field would become much stronger and the losses greater. To minimise this loss, the best modern ring machines are made with a hub and arms of gun- FIG. 84. metal. This is, however, only a palliative. The loss cannot be entirely avoided, and it is important to note that it increases with the output. This kind of loss does, of course, not occur in a drum armature, since there are no internal conductors, and it follows that, other things being equal, the drum machine must have a slightly higher efficiency than the ring machine. AND TEANSFOEMEES. 325- Experimental Determination of Losses. The determination of the total losses in a dynamo, when working on open circuit, can be made very accurately by running the machine as a motor and observing the power supplied. Care must, of course, be taken to so adjust the supply of power that the machine runs at its normal speed and with the normal brush voltage. If this be the case, the strength of field and the field excitation will be approximately the same as- when the machine works as a dynamo. They cannot,, of course, be exactly the same because of armature reaction and resistance, but as the effect of these dis- turbing influences is approximately known, it is easy to so alter the excitation as to fairly represent the actual working conditions. The measurement of electric power supplied to the armature can be made with very great accuracy, and the power supplied for field excitation is also easily found. All we require for the experiment is a speed counter, a voltmeter, and an ampere-meter. The result of such an experiment is, however, not sufficient for practical work. It is no doubt of some value to know exactly how much power is wasted in the field and how much is wasted in the armature, but as regards the latter we want something more. In addition to knowing the total waste, we want to know how this total is made up. We wish, in other words, to separate the total loss into its component parts, so that we may see in what direction improvements may be possible, or what the effect of any alteration in design has been. Take, as an example, the question of how far the conductors 326 DYNAMOS, ALTEENATOES, should be stranded or otherwise subdivided. The greater the amount of subdivision, the more space is wasted in insulation and the more expensive becomes the machine. On the other hand, the more we sub- divide, the smaller becomes the eddy-current loss. The design of machine actually adopted is therefore a com- promise between that which is theoretically perfect and that which is commercially feasible, and in order that the designer may be able to strike the balance between these conflicting conditions properly, he must know up to what point subdivision of conductors is of import- ance. This point he can only determine if he is able to measure the loss occasioned by imperfect sub- division in any type of conductor ; in other words, if he can separate eddy-current losses from the total loss. For the same strength of field the hysteresis loss is obviously proportional to the speed, and the same holds good for the frictional losses, provided the speed be not reduced too much. The eddy-current losses being pro- portional to the square of the electromotive forces which produce them, must, for the same strength of field, be proportional to the square of the speed. Taking advan- tage of the fact that the two kinds of losses follow different laws, we can separate them as follows : We excite the machine under test from an independent source, and keep the excitation constant. We also send a current through the armature, whereby the latter is set revolving, and we vary the voltage applied so as to get a variation in speed. The current required to run an armature light is so small that we may neglect arma- ture reaction and resistance, and consider the measured AND TEANSFOEMEES. 327 brush voltage to be equal to the armature electromotive force. We now take three readings namely, speed (ri), current (c), and voltage (e). If we increase the voltage, we increase all the readings ; and by suitable arrange- ments for the purpose we can very rapidly take a large FIG. 85. number of readings. If we plot the current as a func- tion of the speed, we obtain a sensibly straight line, Fig. 85, and the point A, where this line cuts the ver- tical, corresponds to the current at which the armature would just start, provided the frictional resistance were not increased at a very slow speed or at rest. Since the coefficient of friction does, however, increase, it would 328 DYNAMOS, ALTERNATORS, be incorrect to determine the point A by measuring the current at starting, but we can find it by measuring the current for a moderate speed and projecting the line backwards. The length A = c represents, then, the initial current at no speed, and the length B F = c represents the maximum current at the normal speed, n = B. Since the resistance due to hysteresis and friction is independent of the speed we may consider the maximum current, c, made up of two parts,. namely, c = B H required to produce the torque which just balances the resistance due to friction and hysteresis and c-c = H F, required to produce the torque which balances the resistance of eddy currents. Calling Wfc the loss due to hysteresis and friction, and W/ that due to eddy currents, we have the total measured loss W = e c ; W/, = e c ; W/ =e (c-c ). We are thus able by means of a very simple experi- ment to determine the eddy-current loss, but it should be remembered that this determination is only valid for the machine working on open circuit. When the machine is working on closed circuit, the eddy-current loss is increased for the reasons above stated. It is, however, possible to adapt the method here described for the measurement of eddy-current losses under full load. We require for this purpose two machines of equal size and type, and a third machine of AND TEANSFOEMEES. 329 smaller power, but giving the same current. The two machines to be tested are rigidly coupled, and their armatures are placed in series with each other and with the small machine. The | fields are so arranged that one machine is working as a generator and the other as a motor, the power to keep the combination at work being supplied by the small machine. By suitably adjusting the field excitation of the two machines and the electro- motive force of the small machine, we can keep the current fairly constant over large variations of speed, and thus obtain a series of readings which enable us to separately determine the various losses. CHAPTER XIV. Examples of Dynamos Ronald Scott's Dynamo- Johnson and Phillips's Dynamo Oerlikon Dynamo- Other Dynamos. Examples of Dynamos. To give an even approximately complete collection of drawings and descriptions of the various types of dynamos now in the market would extend this book far beyond its proper limits. As it will, how- ever, be useful to show at least in a few cases how the general principles of dynamo design set forth in the preceding chapters are carried out in practice, I give in Figs. 86, 87, and 88, illustrations of dynamos belonging to three distinct and represen- tative types. Fig. 86 shows a bi-polar undertype machine suitable for belt or direct driving. Fig. 87 shows an overtype machine for belt-driving, and Fig. 88 a multipolar machine for large output and slow speed, arranged for direct driving by a turbine. The descrip- tions of these machines are here given, each under the name of its maker, to whom I am indebted for the particulars of construction. Ronald Seott's Dynamo. This machine, Fig. 86, is designed for an output of 200 amperes at 80 volts when driven at 600 revolutions AND TEANSFOEMEES. 331 Y2 332 DYNAMOS, ALTERNATORS, per minute. The armature core (10 Jin. diameter by 13in. long) is built up, as usual, of soft-iron washers, and contains in cross-sections 66 square inches of iron. It is drum wound with 136 bars and special end con- FIG. 86. Ronald Scott's Dynamo. End View. nections, the latter consisting of flat copper strips split in the centre and bent spirally in opposite directions, as shown in the detail view. The split does not extend the whole length of the plate, so that a small part of the plate at one end is left the full width. This part AND TRANSFORMERS. 333 Section A A. Section through Armature. . 86. Details of Ronald Scott's Dynamo. OF THE T \TT.T3 GTW 334 DYNAMOS, ALTEENATORS, is provided with two V-shaped cuts (see longitudinal section of armature) for holding together by insulating cheeks. The free ends are soldered to the ends of the bars, each of which latter is composed of three copper strips 64 mils thick by 312 mils high. The total area of one bar is thus 3 x -064 x '312 = "06 square inch, giving a current density of 1,720 amperes per square inch. The resistance of the armature from brush to brush is "014 ohm. The field magnets are rectangular iron slabs, 13in. x 7in. in section, having an area of 91 square inches. They are compound wound with 2,040 turns of shunt wire and 14 turns of copper tape for main coils. Kesistance of shunt 13*5 ohms, and of main 00213 ohm. From these data we find the shunt current to be 5*9 amperes, and the loss of pressure in main coils to be *42 volts. The electromotive force required for an output of 200 amperes at 80 volts can now be calcu- lated thus : Brush volts = terminal volts + loss in main coils. = 80 + '42 = 80'42. Loss of pressure in armature = 205'9 x '014 = 2'88 E = 80-42 + 2-88 = 83'3. The total useful induction is found by formula (33) y page 42. E = Z r n 10~ 6 ; 83'3 = Z . 136 . 600 . 10~ 6 ; 83'3 = Z -0816 ; AND TEANSFOBMEES. 335 Z = 1,022 in English measure ; or F = 6,132,000 in C.G.S. measure. The average density of induction in the armature 1,022 . core is B a = > B a = 15*5 in English measure ; or S = 14,500 in C.G.S. measure ; and if we assume a leakage of 33 per cent., the induc- tion through magnets is B m = 14' 7 in English measure, or = 13,700 in C.G.S. measure. The total exciting power is made up of that given by the shunt coils (5*9 x 2,400) and that given by the main coils (200 x 14), or in all X = 16,960. The electrical efficiency of this machine is given by the maker as 92 '5 per cent. Johnson and Phillips's Dynamo. The machine illustrated in Fig. 87 represents a type which is with English makers a favourite one for small and medium-sized dynamos. Each maker has, of course, his own special design as regards proportions and construction of details, but the general type of field is that shown in Fig. 57c. The reason why this type is so much used will be clear on inspection of Fig. 57, page 224, and the table on page 237. The construction is mechanically strong and simple, the 336 DYNAMOS, ALTEENATOBS, amount of exciting copper is very moderate, and the commutator and bearings are at a convenient height. AND TBANSFOEMEES. 337 'The fact that the bed-plate of the machine may be utilised as yoke, and that no gunmetal supports are required for the field, is an additional advantage, because tending to reduce cost. FIG. 87. Johnson and Phillips's Dynamo. The particular machine illustrated is designed for an output of 15 kilowatts when driven at 870 revolutions per minute. Terminal pressure 140 volts. The arma- ture core is made up in the usual way of soft iron 338 DYNAMOS, ALTEENATOKS, washers, insulated from each other, and supported on the three wings of a central hub. The washers are pressed together by end checks, also provided with wings and hub, so that the spaces between the wings remain open from end to end, and air can pass freely through the armature between the hub and the core, the flow of air being pro- moted by the fanning action of the connecting strips between the commutator and the armature bars. In armatures which are completely closed at the ends the heat generated in the iron core can obviously only be dissipated by passing through the external surface that is, through the copper con- ductors and their insulation ; but if proper provision is made for end ventilation, a considerable portion of the heat due to hysteresis and eddy currents in the core is carried off by the air direct, and to that extent the winding is kept cooler. In addition to this end- to-end ventilation, provision is made for a moderate amount of radial ventilation by the insertion between the thin iron washers of pairs of stouter iron washers, kept a definite distance apart by fibre distance-pieces, so that air channels are left. These stout washers are provided with external projections, or teeth, penetrating through the winding, but insulated from it by fibre and mica. Thus a series of holes is left, through which air can escape radially, and this also helps to some slight extent to keep the armature cool. The chief reason for the employment of these stout washers with projecting teeth is, however, a mechanical one namely, to transmit the driving power from the spindle to the external con- ductors in a positive and reliable manner. It has been AND TKANSFOBMEBS. 339> shown, in Chapter IV., p. 81, how the force can be calcu- lated that is required to move a conductor carrying a given current through a magnetic field of given intensity. It was there shown that with a current of 100 amperes flowing through the wire, each foot of wire is subjected, in a field of 5,000 C.G.S. units, to a drag of about 3^1b. In a stronger field the force would be greater, and in a weaker field smaller, but, for a rough calculation, we may take a force of 3Jlb. per 100 ampere-feet, or *0351b. per ampere-foot of conductor as a fair average value. Thus in a two-pole machine, with an armature 12in. long, each of the conductors under the pole-pieces (or about 75 per cent, of all the conductors) would be subjected to a drag of 3Jlb. when the total armature current is 200 amperes, or Iflb. when the total arma- ture current is 100 amperes. This, taken for one conductor alone, is not a very large force ; but if it be remembered that the number of conductors is counted by hundreds, It will be seen that the aggregate effect is one of considerable magnitude. It is also necessary to bear in mind that a dynamo machine may at some time or other be subjected to rough usage, such as an accidental short-circuit, when the current, and consequently the mechanical strain on the conductors, will be much greater than during regular work, and for this reason it is very important to make ample provision for positive driving. In the machine illustrated there are two sets of stout washers, or driving discs, each having four driving horns. The total force required for pushing the conductors through the field is therefore divided between eight driving horns. What is the force which -340 DYNAMOS, ALTEENATOES, each horn must exert in regular work ? Assuming for the purpose of this calculation, which need obviously only be an approximation, that the machine has an efficiency of 85 per cent., we find that the total power put into the spindle at 870 revolutions per minute will be 15/0 85 = 17-6 kilowatts, or about 23'6 h.p. A small portion of this power is absorbed in losses occurring in the bearings and armature core, and does, therefore, not reach the armature conductors, but it would be pushing scientific accuracy beyond the limit of practical work, if we were to make a deduction on that account, especially as there may be initial stresses in the driving horns, due to imperfect workmanship in laying the conductors on, which are quite beyond the reach of calculation. We have, therefore, to do 23'6 h.p. by means of eight horns, or very nearly 3 h.p. per horn. The core is lOin. diameter by 12in. long, the discs being 2in. wide. The speed at which the driving energy is transmitted is therefore ?^ x 870 = 2,270ft. 12 i ,, , . -o 33,000 x 3 per minute, and the force is P = * , or in .2, .270 round figures P = 431b. The net cross-sectional area in the armature core is A a = 39 '5 square inches, and there are 216 armature bars, the end connections being in the shape of semi- circular copper plates, with tags at each end. These plates are separately insulated and placed spirally side by side into the insulated channel of a cast-iron carrier. As will be seen from the longitudinal section of the machine, the tags are bent at right angles to the surface of the plates, and thus form at each end of the AND TRANSFORMERS. 341 carrier a row of connecting-pieces, to which the ends of the corresponding bars are soldered. The resistance of the armature, warm, is '0507 ohm, and that of the shunt coils (1,452 turns on each limb) is 26*05 ohms. The magnets are formed by wrought- iron slabs lljin. wide by 5Jin. thick, and their area is A m = 62 square inches. At 140 volts the armature current is 107 amperes for the external circuit, and 140/26'05 = 5'37 amperes- for excitation, or a total of 112 '37 amperes, causing a loss of 5*7 volts in the armature. The total useful field is therefore found from the formula 145-7 = Z x 216 x 870 x 10~ 6 , Z * 773. The electrical efficiency of the machine is the ratio of the output to the electrical energy generated in the armature conductors, or 140 x 107 17 145-7 x 112-37 ' = 14,980 . ~ 16,372' tj = 91 '5 per cent. In the two examples of dynamos here quoted, the electrical efficiency has been given to show the method of calculating it, but from a practical point of view it is not the electrical, but the mechanical efficiency (sometimes also called the commercial efficiency) which is of importance, and it will, therefore, be useful to cite the example of a dynamo, also made by Messrs. Johnson and Phillips, for which the mechanical 342 DYNAMOS, ALTEBNATORS, efficiency has been determined by the method described in the last chapter. The machine is of the same type as shown in Fig. 87, but larger. Armature core, 14in. diameter by 19in. long. Radial depth of core, Sin. Output, 42 kilowatts (600 amperes by 70 volts) at 470 revolutions per minute. Field, compound wound for constant terminal pressure. Shunt exciting power, 20,000 ampere-turns ; main exciting power, 10,000 ampere-turns. Loss of pressure over main coils, 1 volt ; loss of current in shunt coils, 13*62 amperes. The armature contains 84 subdivided bars, and the cross-sections of connectors exceeds that of the bars by 70 per cent. Total armature resistance from brush to brush, '0036 ohm when warm. From these data we find Loss of energy in shunt coils 970 watts. Loss of energy in main coils 600 watts . Loss of energy due to armature resist- ance 1,358 watts. Total ................................. 2,928 watts. The electrical efficiency of this machine is therefore The mechanical efficiency is, of course, lower, because, in addition to the 2,928 watts absorbed by resistance in the field and armature, we must provide sufficient energy to cover the losses due to magnetic and mechanical friction and eddy currents. These losses were determined in the manner detailed in the last chapter. The field of the machine was separately excited, and AND TRANSFORMERS. 343 a current sent through the armature so as to run the machine light as a motor. By plotting the current as a function of the speed we obtain a straight line, which cuts the axis of ordinates at the point corres- ponding to 9'2 amperes. This, therefore, is the current required at that particular excitation for overcoming all frictional resistances. When the pressure was raised to 73 volts the speed was 464 revolutions per minute, and the current was 17 amperes. We have therefore Total losses W = 17 x 73 - 1,241 watts. Frictional losses W h = 9'2 x 73 = 671'6 watts. Eddy-current losses W/ = 7'8 x 73 = 569'4 watts. These losses refer, of course, only to the speed of 464 revolutions per minute, and for a different speed other values would be found. It is, however, not necessary to repeat the experiment for different speeds, since the law of these losses is known. It was shown in the last chapter that the frictional losses vary as the speed and the eddy-current losses as the square of the speed. It is, therefore, possible to represent each group of losses by a simple expression thus : Wfc = h. n, W = /n 2 , where n is the speed in revolutions per minute, and h and / are coefficients for frictional and eddy-current losses respectively. 1 o avoid large numbers it is con- venient to insert, not the speed, but the speed divided by 100 thus: W h = h ~%- 00 344 DYNAMOS, ALTERNATORS, We can now determine the coefficients h and / from the observed values for W& and W/ , and find h = 144-2 /=26-5. The losses at 470 revolutions per minute are then found to be W h = 144-2 . 4-70 = 680, W, =26-5 . (4-70) 2 = 583; or a total of 1,263 watts for the machine running light at 470 revolutions per minute. If we allow an increase of 30 per cent, in the eddy-current losses when running at full load, we find that 1,439 watts are wasted over and above the 2,928 watts absorbed by resistance in the field and armature, bringing the total loss up to 4,367 watts. The mechanical efficiency of the machine when working at full load is therefore ^42,000 ~ 46,367' per cent. Oerlikon Dynamo. The machine shown in Fig. 88 is a very interesting illustration of the best modern practice in large slow- speed machines for high voltage. It is the generator for a power transmission plant at Innsbruck, designed and built by the Oerlikon Engineering Works, Switzer- land. The machine is of the 10-pole type, with vertical spindle, arranged for direct coupling to the shaft of the turbine, and its output is 240 kilowatts at 1,550 volts, the speed being 230 revolutions per minute. The draw- ing is to one-twenty-fourth of full size, or in. to the AND TEANSFOEMEES. 345 FEG. 88. Oerlikon Dynamo. Sectional Elevation. Z 346 DYNAMOS, ALTEENATOES, FIG. 88. Oerlikon Dynamo. Plan. AND TEANSFOEMEES. 347 foot, and the dimensions can thus be taken by scale, but for the convenience of the reader a few of the principal dimensions may be here mentioned. The yoke ring and magnets are in two castings, no pole- shoes being used. External diameter of yoke ring 8ft. 5in., width 24in., thickness 6|in. Magnets pro- jecting inwards 13|in. ; of rectangular cross-section 21in. x 13fin. External diameter of armature core, 59in. by 21in. long, and 5Jin. radial depth. This gives a circumferential velocity of 3,550ft. per minute. The air-space is *79in., and the clearance between outside of binding wire and poles is only about Jin. It is obvious that with so large a diameter and so small a clearance, the workmanship must be extremely good, and that special care must be given to this point in the design. How this has been done will be seen in the vertical section. The armature is series ring-wound, and the end connections are placed immediately above the arma- ture, the commutator, which is 36in. in diameter by lOin. long, being again placed above the end connec- tions. There is no bearing outside the commutator, and the brushes are carried on a ring supported by four brackets from the yoke. Other Dynamos. Mr. R. W. Weekes, in his articles on " The Direct- Current Dynamos at the Crystal Palace Exhibition of 1892," published in the Electrical Engineer, April, 1892, gave a series of tables containing particulars of the various machines exhibited. The information compiled by Mr. Weekes should prove very useful z2 348 DYNAMOS, ALTERNATORS, for reference, and for this reason it is reproduced; here. It should be remembered that the figures in these tables are based upon statements obtained from the makers themselves, and as different makers adopt different limits as regards temperature rise and sparking in fixing the output, it follows that the comparison between the different machines can only be an approximation. It is, however, sufficiently near the truth to give a correct idea of the relative merits of the different designs. In comparing machines of different type it is, of course, essential to take account of the circumferential velocity of the armature, and this has been done in the first table by adding a column, in which the output is given on the supposition that the circumferential speed of the armature in all machines is 2,000ft. per minute, the output being considered directly proportional to the speed. The figures in this column have been used to determine the output per ton weight and per square foot of floor space in the second table. The type of each machine is indicated in the first table by reference to the illustrations in the previous chapters. The second and third tables con- tain particulars of armature, commutator, and field magnets, and also columns giving total field strength and induction. The latter is given as useful induc- tion through armature and field magnets, as it was impossible to obtain correct information regarding magnetic leakage in each case. The true induction through the field magnets is therefore in all cases greater than shown in the table for the useful induction. AND TKANSFOEMEES. 349 sapd jo jgqumjs ' Jl -Si --! s s s "gs "~(5 ' " sait ""as "'a "s ets, ust of field ference sg i js o o Ji-al C<1 C<) U3 U3 I i-^eooo rooioeo^o l 1 1 OWrH 1 QrH (MJ^I OOOOOOO(MOO (MOOOO rHOOCslOlOiOlO^l^ 1 ^^iO'7-lO 's 350 DYNAMOS, ALTERNATORS, 51 I Iff I ! I I I I l|| i i ctL ! | | | | | I I I I .aS-Sh ! I |g I x | | i i | l l ! | | o2 & SS3 ~ * ^ I I I 00 O O I ^ * I II- * *i i ISM, I-I.I-H.I-IOO rjieo.ocoeoiM Jini-iooio.Oi-iirioocC ? i v i85sce i-^oo-r^^ooc^ I ? CO ? . QJ J '//////////////, s 1 ^ *, B FIG. 95. 2. The If p represents the number of poles on one side, and D the mean diameter of the armature, then 2 p d = TrD, and the linear speed is TrD 60 electromotive force in volts can then also be written thus : -m rk n AND TEANSFOEMEES. 367 If instead of one loop only we had 2p loops all joined in series, we would have 4p = r active wires, and the electromotive force would be It is instructive to compare this expression with formula (32), giving the electromotive force of a con- tinuous-current two-pole dynamo. It has been pointed out that with a series-wound multipolar armature the electromotive force is increased in the same ratio as the number of pairs of poles is increased. Thus, in a four-pole machine we have two pairs of poles and double the electromotive force ; in a six-pole machine, we have three pairs of poles and three times the electro- motive force, and so on. To get the total electro- motive force of such an armature, we have therefore to multiply the electromotive force, as given in formula (32), by the number of poles of equal sign employed. If the machine has p north poles and^> south poles, we thus find the total electromotive force to be or precisely the same expression as above. We thus find that our alternator, having an armature with 2 p single loops, or r = 4^> active wires, and a field con- taining a total flux of p F lines, produces the same effective electromotive force as a continuous- current dynamo in which T, p, and F are the same. There is, however, this difference, that whereas in the dynamo there are two parallel circuits through the armature, ihere is only one such circuit in the alternator ; and if 368 DYNAMOS, ALTERNATORS, we allow the same current in each conductor in both cases, the output of the alternator will only be half that of the dynamo. This result has been obtained on the supposition that the adjacent wires of two neighbouring coils occupy no appreciable space, a condition which cannot be fulfilled in practice. We may approximate to it by employing a toothed armature once, but then only imperfectly. Let us now see how the case stands if we cover an appreciable space on the armature with coils, as would naturally be done in order to increase r and the electromotive force. The electromotive force line would then assume a shape somewhat as shown in Fig. 94. To determine the effective electromotive force we must assume a certain proportion between the width of poles, d, and the internal or blank space of the coils. The external width of the coil would naturally be made equal to the width of poles, so that no winding space shall be wasted. Assume, then, that the band of conductors on each side of the coil occupies a space equal to one quarter the polar width. This will leave a blank space inside the coil equal to half the polar width, and the maximum electromotive force, represented by the sections C D and F G of the line B r will be kept up during half the time of each cycle, the changes occupying the other half, as shown by the sloping lines. We can now find by integration the square root of the mean square of the electromotive force line, an operation which is so simple that it need not be given at length. The result is 'TM- (47). AND TBANSFOBMEBS. 369*' The electromotive force of this alternator is only 81*7 per cent, of the electromotive force of a dynamo with the same number of conductors on the armature and the same field. Let us next investigate the case where poles of alternate sign follow each other on the same side of the armature, such as in the field of the Siemens and ^ *i SL a /; .,*uJ l^*,,, ^///'y '///?////// A t\x*0\\v FIG. 96. Ferranti alternators, and let us assume that the distance between the poles is equal to their width, d. The pitch from pole to pole will now be 2 d, or twice as great as in the former example, and the outside width of the coil will naturally be made equal to the pitch so that no winding space between adjacent coils- shall be wasted. As regards the width of the blank. -370 DYNAMOS, ALTERNATORS, space within the coil, designs vary, but we may assume as a fair average that it is about equal to half the polar width. In Fig. 96 the coil is shown in the position of maxi- mum electromotive force, which occurs only at one instant, and the electromotive force line B assumes the zigzag shape E E as shown. If each side of the coil contains w active conductors, the electro- motive force is due to 2 w conductors, and its value is in absolute measure As there are 2 p coils, the number of active conductors is r = 4p w, and the maximum electromotive force of the whole armature is in volts E = 4pFr-? 10- 8 . . . ' (48) 60 The instantaneous electromotive force at the moment when the centre of the coil is at the distance x from the centre of the magnet is obviously taken between the limits of x = and x = d ; and to find the area of the curve giving the squares of the instantaneous volts we must integrate e 2 d x between ft TT"2 these limits. The result is : area= -; and as the > base of this area is d, we find the mean ordinate = , 3 and the effective electromotive force = E. AND TRANSFORMERS. 371 To get the effective voltage we must therefore divide the expression (48) by the square root of 3 : e = 2-31 .pFTr-^ 10- s . . . (49) 60 The electromotive force of this alternator is there- fore 2*31 times that of a dynamo having the same number of conductors on the armature and a field of equal strength. It is obviously not necessary to have poles on both sides of the armature. We could, for instance, as shown in the lower figure, replace the poles on one side by the smooth iron core of an armature. In this case it would only be necessary to double the exciting power on the remaining set of magnets to get the same total field strength as before, and the alternator becomes thus directly comparable to an ordinary multipolar drum-wound dynamo. Some types of alternators are indeed so constructed, notably the Westinghouse machine, and that built by the Electric Construction Corporation. The coefficient 2'31 is of course only applicable to machines in which the width of coil, width of pole, and pitch are in the ratio indicated. Had we assumed different proportions, the coefficient would also have been different. To show the effect of a variation in these proportions we may take the case of a ring- wound alternator in which the pitch is 8in., width of coil 4in., and width of pole 5in. The advantage of widening the pole is that the maximum electromotive force, instead of being only momentary, as in the previous case, is maintained for an appreciable time, and thus the effective electromotive force is raised without 372 DYNAMOS, ALTERNATORS, increase of maximum electromotive force. A high maximum electromotive force, although it may only be momentary, throws, nevertheless, a great strain upon the insulation, and to avoid this it is advisable to make the width of the active part of the coil either larger or smaller than the width of the pole, so as to avoid the sharp peak in the electromotive force line. In the construction shown in Fig. 97 this has N $ fc S t\ o\NXs.\\v.\v:-NxN\\\\sl Ys///////////////////,/A S FIG. 97. been done by making the coil lin. narrower than the pole, and the maximum electromotive force is thus kept up during the time that the armature travels lin. The maximum electromotive force is now only or by 25 per cent, smaller than in the previous case,. whereas the effective electromotive force is 64'6 per cent, of the maximum, instead of only 57'8 per cent. 1 / as before. The coefficient now works out to x '646^ o = 2-06. e = 2-06 pF T 10-* . . . (50) 60 AND TRANSFORMERS. 373 Thus, while we have lowered the electromotive force by only 11 per cent., we have lowered the strain on the insulation by 25 per cent. With an effective pressure of 2,000 volts the insulation of the machine would be subjected to a strain of -i - = 3,100 volts, 0'646 whereas in the previous machine the strain would be 3,400 volts. It would, of course, be possible to shape the contour of the polar faces so that the electromotive force line becomes a true sine curve, in which case the strain on the insulation would be reduced to 2,000 V2 - 2,828 volts. From the examples above given, it will be seen that it is possible in every case to determine the effective electromotive force beforehand, provided the configu- ration of poles and coils is known. For every type of alternator we thus find a certain coefficient giving the ratio of the effective electromotive force of the alter- nator to the electromotive force of a continuous-current dynamo having the same field and the same number of conductors on the armature. The electromotive force of the alternator is thus given by the formula . . . (51) or in English measure e = KpZ T >ilQ- 6 . . . (52) the coefficient K depending on the particular type of .alternator under consideration. 374 DYNAMOS, ALTEENATOES, In the following table are given the values of K for different cases, including those referred to at some length above. The width of poles and space occupied by the armature winding are expressed as a fraction of the pitch, the pitch being the distance between two poles of opposite sign on the same side of the arma- ture. Thus, in the Siemens, Ferranti, or Westinghouse machines, the pitch is simply the distance between the centres of two neighbouring polar faces. In the Mordey machine the pitch is half that distance. Reference Number. Pitch Ratio of K. Poles. Winding. 1 2 3 4 5 6 7 8 1 1 1 62 50 50 33 o-oo 1-00 50 50 1-00 50 33 1-000 580 817 * 2-060 1-635 f 2-310 V 2830 VA 2-220 I Sine Function. In comparing different designs it should be remem- bered that the coefficient K is the ratio of electro- motive force between the alternator and the equivalent continuous-current dynamo. Thus, the equivalent to a Mordey nine-pole machine for which K may assume either of the values given under 1,2, or 3, is an 18-pole drum dynamo, and it is the electromotive force of such a dynamo which must be multiplied with K to get the effective electromotive force of the alternator. In the machines to which cases 4, 5, 6, and 7 refer, poles of AND TEANSFOEMEES. 375' opposite sign succeed each other on the same side 01 the armature, and their number, which must, of course, be even, is the same as that of the equivalent dynamo. The cases given under 4 and 6 approach most nearly to designs as actually found in practice, and it will be seen that either does not materially differ from the value of K which was obtained on the supposition that the electromotive force line is a true sine curve. It should further be remembered that the values for K were obtained on the assumption that the field is sharply defined, but this is in reality not the case. There must at the polar edges be fringes where the induction shades off to zero, and thus all the sharp corners in the line of electromotive force B (Figs. 92, 94,95, 96, and 97), become rounded off, and the two last-mentioned lines will therefore more or less approach to sine curves. In consideration of these cir- cumstances we shall not introduce any appreciable error if we assume that any ordinary commercial alternator has an electromotive force line of sinui- soidal form; and as this assumption considerably facilitates calculations in connection with alternators and transformers, it will in the following be made where convenient. Self-Induetion in Armatures of Alternators. Any electric circuit of such shape that an electro- motive force can be generated in it by electromagnetic induction, must also have electromagnetic inertia or self-induction. That this cannot be otherwise can easily be seen by the following consideration. In order that an electromotive force may be generated, the 376 DYNAMOS/ ALTEENATOES, circuit must be threaded by a varying number of lines of force, and in order that threading may be possible the circuit must necessarily be in the form of one or more loops. But if we send a current through a loop of wire there is produced a magnetic whirl all round the wire, Fig. 12, the lines of which pass in the same sense through the loop. In other words, the current becomes interlinked with the lines of force produced by itself, and any change in the current strength is accompanied by a corresponding change in the total induction produced by the current. The change in the induction produces in its turn an electromotive force in the conductor commonly called the electromotive force of self-induction. It will thus be seen that it is a physical impossibility to construct an alternator which shall have no self-induction. The electromotive force of self-induction is obviously proportional to three quantities : (a) the induction, (6) the number of loops, and (c) the rate at which the induction changes, or the number of reversals in unit time. The induction, again, is propor- tional to the current, provided the permeability of the medium surrounding the coil may be assumed to be constant, so that the electro- motive force of self-induction is proportional to the current. Let / be the field produced by unit current (10 amperes) and per turn of the coil, then with a current of I and T turns in the coil the field will be I T/. Let the current be reversed 2 n times per second, giving a frequency of n complete cycles per second, then the maximum electromotive force of self- induction at the moment when the current passes AND TEANSFOEMEES. 377 through zero will be 2 TT n I rf for each loop or turn, and E s = 27rftT 2 /I for the whole coil of r turns. The product r 2 / is called the coefficient of self-induc- tion, and is usually designated by the letter L. Since the self-induced field depends on the permeability of the medium, and since the useful field, F, produced by the magnets depends also on this quantity, it is obvious that we cannot afford to make /small. On the contrary, we must aim at making the permeability large by reducing the air-space and widening the polar surfaces as much as possible, so as to produce a high effective electromotive force with a moderate exciting power. It follows that if we wish to reduce the electromotive force of self- induction we must decrease T, and increase the strength of the magnet field. This means that we must employ very strong field magnets and few turns of wire on the armature. A machine with very small self-induction must therefore be large, heavy, and expensive in comparison to its output. There is, how- ever, no advantage gained by reducing the self-induc- tion beyond a certain limit, and we find, therefore, that all commercial alternators have an appreciable self- induction. It is an easy matter to test an alternator for its self- induction. We need only, while the machine is at rest, send a measured current of the normal frequency through the armature and measure the electromotive force at its terminals. A certain correction must, of course, be made to eliminate the effect of armature resistance, but this correction is so obvious and easily applied as to need no further description. The coefficient of self-induction for one armature coil is B B 378 DYNAMOS, ALTERNATORS, T 2 f, and as there are 2 p coils in series, the coefficient of self-induction for the whole armature is L - 2p r 2 /. The electromotive force required to drive the current through the armature is therefore E, = 27r?iLI, all quantities being taken in absolute measure. The current in the above formula is the maximum or crest of the current wave, but since the current measure- ment by any instrument such as a Siemens dynamometer, Kelvin balance, or any alternate-current ampere-meter, gives the effective and not the maximum current, we must multiply the current reading, i, in amperes by to get the value of I in absolute units. To get the electromotive force in volts, we must multiply by 10~ 8 ; and if we wish to express the coefficient of self-induction in quadrants instead of centimetres we must multiply by 10, so that the above formula in practical units becomes : E s = 2 TT n L 10 x 1-41 i KH x 10-*, or maximum volts of self-induction E, = 2 irn L 1'41 i. If we call the effective electromotive force of self- induction e g) then E* = 1/41 e ti and the above formula may also be written thus : e s = 2 TT n L i . . . . (53) Since the frequency n is known, and i and e s can be measured, we can find the coefficient of self-induc- tion ; or we may measure directly the coefficient of self-induction by means of a secohmmeter, and from it find the value of e s or E s corresponding to any armature AND TEANSFOEMEES. 379 current i. It should be noted that L is not constant, but varies according to the position which the arma- ture occupies in the field, as will be seen from Fig. 98, which represents a Mordey armature in two positions, the upper diagram A showing position of maximum electromotive force, and the lower, B, of zero electro- motive force. When the armature is in the position of maximum electromotive force, one half of each of the coils a, 6, c is active, and the field^magnets form somewhat imperfect cores to all the armature coils. A B FIG. 98. In the position of zero electromotive force the field magnets form perfect cores to the coils a and c, but the intermediate coil, 6, has no core at all. The permeability of the medium surrounding these inter- mediate coils (mostly air) will therefore be a minimum, but to make up for this the permeability of the medium surrounding the other coils (mostly iron) will be a maximum, whereas in the other position the perme- ability has an intermediate value, and is the same for all the coils. It is impossible to say at a glance whether the self-induction in position A or in position B will be the greater. Tests made by Prof. Ayrton on a Mordey machine showed that the difference is not BB 2 380 DYNAMOS, ALTEENATOES, very great,* the coefficient of self-induction being "038 quadrant for position A, and *036 quadrant for posi- tion B. He also found that both values decreased by about 14 per cent, when the magnets were full} 7 ex- cited, which is quite natural, since the permeability of the magnet cores must decrease when there is an initial induction passing through them. Clock Diagram. It has already been pointed out that the electro- motive force of self-induction is proportional to the rate at which the self-induced field changes, and since this rate is greatest at the time when the field passes through zero, it follows that the electromotive force of self-induction must be a maximum at the moment when the current passes through zero, and must itself be zero when the current is a maximum. This inter- dependence between these two quantities can easily be represented by an algebraical formula, and is indeed so represented in all the text-books on alternating currents, but for practical work a graphic representation is pre- ferable, because the variations in the different quantities can be more easily followed and comprehended. One of the first to employ graphic methods in connection with alternating-current problems was Mr. Thomas Blakesley,t and the diagrams which will in future be used, although different from his diagrams, are an application of the method of treatment originally indicated by him. * Discussion on Mordey's paper on " Alternate- Current Working " at the Institution of Electrical Engineers, May 30, 1889. t " Alternating Currents of Electricity," Electrician, 1885. AND TBANSFOBMEKS. 381 Let us now see how we can represent an alternating current graphically. If we suppose the line I, Fig. 99, to revolve round as a centre n times per second we shall, when looking at it from a distance, in the direction X 0, see its projection on the vertical, Y, continually expanding and shrinking alternately above and below the horizontal. The length of the projection at any instant is I sin a, and this expres- sion is of the same character as that which we found in the beginning of this chapter for the instantaneous value of the electromotive force in the coil of our elementary alternator, Fig. 89. It was then shown that the instantaneous electromotive force is e = E sin a, 382 DYNAMOS, ALTEKNATOES, and if we suppose that no other electromotive force acts in the circuit, then the maximum current by TP Ohm's law would be I = , and the instantaneous r current would be i = , or i = I sin . If we suppose the line O I to represent to any arbitrary scale the strength of the maximum current, then the projec- tion of I on the vertical at any instant will to the same scale represent the strength of the current at that instant. It is clear that an electromotive force may be represented in the same way. Thus, if O E r represents to any arbitrary scale the maxi- mum electromotive force which is required to force the maximum current, I, through the resistance, r, of the circuit, then the projection of E r on the vertical will give the instantaneous value of the electro- motive force. The electromotive force of self-induction may be represented in the same way. It has been shown that when i = that is, when I in the diagram is horizontal the electromotive force of self-induction is a maximum. At that instant then the radius repre- senting the maximum electromotive force of self- induction must stand vertically that is, at right angles to the current radius. The only question to be considered is whether the radius of self-inductive electromotive force will point upwards or downwards. Suppose that the current radius revolves clockwise (hence the term clock diagram), and that I is to the left of O. At that moment the current passes through zero and begins to increase. By Lenz's law the self- induction must tend to prevent the increase of cur- AND TRANSFORMERS. 383 Tent that is to say, the radius of self-induction must point downwards. Let OE S represent the maximum value of electromotive force of self-induction drawn to the same scale as O E r , then the projection of E s on the vertical will give us the instantaneous value of the electromotive force of self-induction. The lines 1 and ES revolve round together, always preserving their mutual right angular positions. In determining the position of I and E r it has been assumed that no other electromotive force but E r acts in the circuit. This assumption we now see was incorrect, since, in addition to the electromotive force E r which is required to overcome the resistance of the circuit, there is also active the electromotive force of self-induction, E g . If, then, we wish to preserve the current at its assumed strength, we must introduce a new electromotive force to counteract the electromotive force of self-induction. This must obviously be opposed to it and of the same magnitude, as shown by the dotted line E l . The alternator must, therefore, not only give the electromotive force E r , but also the electromotive force E s 1 , or, in other words, it must give the resultant electromotive force, E. It will be seen that E must under all circumstances be larger than E, r . Now imagine the field magnets of the alternator excited and the external circuit open. The pressure measured at the terminals of the armature -p will be = . If we close the external circuit so as to v/2 obtain the current I, we find that the electromotive force producing this current has now fallen to the value E/. , the difference being due to self-induction. It will 384 DYNAMOS, ALTERNATORS, be seen from the diagram that E 2 = E r 2 + E g 2 , and formula gives us a new way of determining the average self-induction of an alternator. We need only determine for the same speed and excitation the terminal voltage at full current and when running on open circuit. In the latter case we get what may be termed the static voltage, E, and in the former the dynamic voltage less the small per- centage wasted in armature resistance. If E be the resistance of the armature, and Ee the terminal voltage,, then E r = E + E I. The two measurements give us therefore at once E. = VE 2 - E y 2 . . . . (54) and from this we find by formula (53) the coefficient of self-induction, L. An example will make this matter clear. A 30-kilo- watt alternator of the author's design, when running at a frequency of 70 cycles per second was excited to give 2,100 volts at the terminals with a current of 15 amperes. I in this case is therefore 21 '1 and E = 2,960. The armature resistance is 7 ohms, causing a loss of 148 volts. The dynamic electromo- tive force, E r> is therefore 2,960 + 148 = 3,108 volts. When the external circuit was interrupted the ter- minal pressure rose to 2,295 volts, corresponding to E = 3,230. The electromotive force of self-induction, is therefore E s = V3,230 2 - 3,108 2 , or E s = 908. By formula (53), if substituting maximum for effective values, we have 908 = 2 TT 70 L 21'1 ; L = '0977 quadrant. AND TEANSFOEMEES. 385 A correction is, however, here necessary. It will be shown in the following chapter that a lagging current tends to weaken the field, and consequently to reduce the value of E r below the value due to self-induction only. The coefficient of self-induction obtained above is therefore greater than its true value, such as can be measured with a secohmmeter, or determined by the previously-described method. Power in Alternating-Current Circuit. The rate at which work is being done by any current, or, as it is also called, the activity or power of the current, is the integral of the product of pressure and current into time, divided by the total time over which the integration extends. When the current is con- tinuous and constant, the integration is a very simple operation, and the power is found by multiplying current and electromotive force. The same holds good with an alternating current, provided current and elec- tromotive force are in the same phase, but if this is not the case then there are periods when the current is positive and the electromotive force negative, or vice versa, and the activity during these periods is a nega- tive quantity, meaning that the circuit, instead of absorbing power, gives out part of the power previously absorbed, and the power actually absorbed during a complete cycle is less than would be the case if the current and electromotive force phases coincided. Let the electromotive force and current occupy the positions shown, in Fig. 100, by the lines E and I, then the activity at that instant would be given by the product of the lines o e and o i. OF THE TT Ttf I V F. "R .Q T T -V 386 DYNAMOS, ALTERNATORS, After a quarter period, E will have advanced into the position E 1 , and I into the position I 1 . Let us now determine the power corresponding to each posi- tion and take the mean : e i = E I cos a cos ft e ifi = E I sin a sin ft. FIG. 100. Mean power = ei + e l i l E I (cos a cos 8 + sin sin WL 2 COS (ft - a). Now, the difference between ft and a is, as will be seen from the diagram, simply the angular distance between the electromotive force radius and the current AND TRANSFORMERS. 387 radius, or the angle by which the current lags behind the electromotive force. The mean power between the two positions is therefore given in watts by half the product of maximum volts and maximum amperes into the cosine of the angle of lag : W = 1H cos . . . . . (55) 2 Had we chosen any other pair of conjugate positions the result would have been the same, and we thus find that the mean power for any two positions, and there- fore for the whole cycle, is given by the formula (55) . Since E = e *J% and I = i ^/2, we have also : "W = e i cos (56) To get the power put by an alternator into any circuit we must therefore measure the effective volts and effec- tive amperes, and multiply the product by the cosine of the angle of lag The diagram Fig. 100 has been drawn on the supposition that the radii O E and O I represent the maximum of electromotive force and current respectively ; but it is obvious that we may draw the diagram to represent effective volts and amperes, when the projection of the ampere line on the volt line, multiplied by the length of the volt line, will represent true watts. Conditions for Maximum Power. The immediate result of self-induction in the arma- ture of an alternator, or anywhere else in the circuit, is a reduction in the output. The machine induces a greater electromotive force than can reach the part of the 388 DYNAMOS, ALTERNATORS, circuit where the power is required, and consequently we require a larger machine than would suffice if current and electromotive force were in the same phase. The pro- duct of effective pressure and effective current is some- times called the apparent power, and the ratio between the apparent and the true power gives, in a rough-and- ready way, an indication as to the extent to which the material used in the construction of the machine is use- fully employed. This ratio has received the name "plant efficiency." Now, a large amount of self-induction in an alternator reduces its plant efficiency, and increases its weight and cost per kilowatt output, though it need not necessarily decrease the mechanical efficiency of the machine. On the other hand, a certain amount of self-induction is necessary in machines intended to be worked in parallel, and for power transmission, as will be shown in Chapter XVI. The question which interests us for the moment is, however, as to the conditions under which a given electromotive force will produce a maximum of power in a given circuit containing a certain amount of self-induction either in the armature or elsewhere. Let A in Fig. 101 be an alternator, L a part of the circuit having self-induction, and E. an inductionless resistance in which it is desired to take up the maximum possible amount of power, with a given induced electromotive force in the arma- ture of the alternator. What value must we give to the resistance, B, in order to absorb in it the largest possible number of watts. Not to complicate the problem needlessly, we assume that neither the arma- ture nor any other part of the circuit except E ha& resistance. AND TRANSFORMERS. 389 If we had to do with a continuous current we should get the more power the more we reduced the resistance B, but with an alternating current this is obviously not the case. For as the current increases, so does also increase the electromotive force of self-induction in the coil L, and less electromotive force remains available for supplying power to B. On the other hand, if we increase B, the current will be reduced, and less of its electromotive force will be choked back by L, so that more electromotive force remains available for B, but then the current is also smaller, and the power taken up FIG. 101. may be again reduced. It is evident that there must exist one definite value for the resistance of B at which the power taken up is a maximum. This value can easily be determined. Let, in Fig. 101, o e s represent the electromotive force of self-induction corresponding to the current o i, and let o e represent the electro- motive force of the machine. The electromotive force available for B is then o e r , and the problem is to make the product of i with e r a maximum. Now i is proportional to e s , and hence the problem may also be stated in these terms : Find that value of B for which 390 DYNAMOS, ALTEENATOES, the product of electromotive force used up in E and electromotive force required for L becomes a maximum. The product e s x e r is given by the area of the shaded rectangle, and it is at once obvious that the area will be greatest when the rectangle becomes a square, that is when e r = e K , and when the angle of lag is 45 deg. The actual resistance of K is now found by applying formula (53). The plant efficiency in this case is I/ ^2 = 71 per cent. Application to Motors. Assume that, instead of a resistance, we had placed at R a series-wound dynamo with laminated field magnets. This machine will offer a threefold opposi- tion to the passage of the current. First, by virtue of its ohmic resistance ; secondly, on account of its self- induction ; and thirdly, because when running it will produce a counter electromotive force in the same way as with a continuous current. Suppose the field magnets to be worked at a low degree of magnetisa- tion (few series turns) then the counter electromotive force will be very nearly proportional to the current, and will be of the same order as the electromotive force required to overcome an inductionless resistance that is to say, it will be correctly represented by the product of a constant into the current, and the above investigation becomes at once applicable to this case. AND TRANSFORMERS. 391 Neglecting the ohmic resistance of the motor, we thus find that the power it can develop will be a maximum if the volts required to overcome its self-induction equal the volts required to overcome its counter electromotive force. As with high frequencies the electromotive force of self-induction of such a motor is very much greater than any counter electromotive force that could be developed at a reasonable speed, it will be seen that a low frequency is essential if the condition of maximum power is to be fulfilled or even approached. The above investigation is of importance in some forms of self-starting single-phase alternate- current motors. CHAPTEE XVI. Working: Conditions Effect of Self-induction- Effect of Capacity Two Alternators working on same Circuit Armature Reaction Condition of Stability General Conclusions. Working Conditions. When we have to do with a continuous-current dynamo, the question whether its electromotive force is used up to overcome an ohmic resistance merely, or also a counter electromotive force, is of no importance, and so long as the external circuit is adjusted in such way as to take the same current at the same voltage the working of the machine is not altered, whether work is done on arc lamps, incandescent lamps, batteries, or electromotors. We may, without alter- ing the working condition, substitute one apparatus for the other requiring the same current and voltage. With an alternator this is not so. The condition under which the machine works depends not only on the terminal voltage and current, but very largely also on the kind of work the current is doing. Thus, when lighting incandescent lamps the self-induction in the external circuit will be very small, and the lag of current behind terminal electromotive force will be AND TRANSFORMERS. 393 -very nearly zero, while the lag of current behind in- duced electromotive force will be limited to the small amount resulting from the self-induction of the arma- ture. On the other hand, when lighting an arc lamp the solenoid in the lamp increases the total self-induc- tion in the circuit considerably, and we shall now have, not only a lag of current behind the induced electro- motive force, but also behind the terminal electromotive force. Although apparently the current and terminal voltage may be the same, the machine in these two cases works under very different conditions. These conditions will again be altered if we introduce a con- denser (such, for instance, as a few miles of concentric cable) into the circuit, or if there is a second source of alternating electromotive force working on the same circuit. It is necessary to consider these various cases somewhat in detail. .. Effect of Self-induction. One effect of self-induction namely, that of retarding the current and lowering the plant efficiency and power put into the circuit has already been explained in the previous chapter, and need not be repeated here. There is, however, another effect produced which must be taken into consideration, and this is the reac- tion of the armature current on the field. Let, in Fig. 102, W represent one loop of an armature coil moving from left to right between the field poles, N S. When this loop is in the position shown at A, the electromo- tive force is a maximum, and is induced downwards in the left and upwards in the right wire. If there were .no self-induction, the current would at that moment c c 394 DYNAMOS, ALTERNATORS, also be a maximum, and would, owing to the symme- trical position of the wires, neither strengthen nor weaken the field. But, on account of the retarding influence of self-induction, the current will only become a maximum when the loop has moved some distance to the right, as shown at B, and the result is that it will weaken the field. What is true for a single loop is more or less true for the whole armature, so that, generally speaking, the effect of self-induction is not only to reduce the power which can be put into the circuit under a given voltage, but also to reduce the induced voltage itself. The drop in terminal pressure from open circuit to full load is, therefore, slightly greater than can be accounted for by self-induction only. Effect of Capacity. Imagine an alternator supplying a bank of incandes- cent lamps at the end of a concentric main several miles long. The main will act as a condenser placed in parallel with the bank of lamps. Not to complicate the problem needlessly, we will assume that the ohmic resistance and self-induction of the main and of the AND TEANSFOEMERS. 395 alternator are negligible. The induced electromotive force will then be the same as the terminal electro- motive force, and the two will be in the same phase. Let, in Fig. 103, E represent this electromotive force, and O I the current which flows when the bank of lamps has a certain resistance. In addition to this working current, there will also be a current flowing in FIG. 103. and out of the condenser. If K be the capacity of the condenser, and e the instantaneous potential difference between the two surfaces (in our case equal to the instantaneous value of the machine electromotive force), d e then i k = K is the instantaneous value of the d t d e current, and since - = 2 d t n E cos a, we find the c c 2 396 DYNAMOS, ALTERNATORS, maximum value of the condensei; current to be I* = 2-TrrcE K, and . ik = I c cos a, in C.G.S. units, or, in practical units, I k = 2 TT n E K 10-8. . . . (56) where Ik is the maximum value of the condenser current in amperes, E is the maximum value of the condenser electromotive force in volts, and K is the capacity of the condenser in microfarads. It is obvious that the same formula holds good when the effective values of current and electromotive force are inserted i k = 2 TT n e K 10~ 6 . . . (57) The condenser current must, of course, be in advance of the electromotive force by a quarter period. We have, therefore, to draw the line repre- senting this current upwards from O in Fig. 103. The length of this line we find from formula (56), and the angle, y , at E is such that y = 2 TT n K 10~ 6 . Thus if E were altered we should find the corre- sponding points, I k , by drawing lines parallel to the dotted line E I* . The machine has to give the current O*I to the lamps, and also the current O Ik to the condenser ; in other words, it has to give the resultant current, 1. This, as will be seen from the diagram, is in advance of the electro- motive force. Instead of a lag we have now a lead, 0, and the position of the loop of wire, W, in which the current becomes a maximum will be reached before the loop has advanced into the position of maximum AND TEANSFOEMEES. 397 electromotive force shown in Fig. 102A. The arma- ture current will therefore strengthen the field. Mr. Swinburne has proposed to make use of this property of condensers to produce a leading current,, in order to obviate the necessity of applying any exciting circuit to the field magnets of an alternator. He suggested to simply place a condenser across the terminals of the armature. The residual magnetism of the field magnets would suffice to induce a weak electromotive force which would cause a condenser current to flow. This, in its turn, would strengthen the field, and raise the electromotive force, pro- ducing more condenser current, and so on until the full voltage had been attained, the action being the analogue of that on which depends the self-excitation in dynamos. It would thus be possible to obtain a self-exciting alter- nator. Although a machine of this kind could doubt- less be made and worked, the advantage of doing without an exciter would, however, hardly compensate for the increased cost. It must be ^remembered that the omission of exciting coils in such a machine would only be apparent. In reality it would have exciting coils, but they would be part and parcel of the arma- ture. This means that we would have to apply our exciting coils in a part of the machine where room is very limited, instead of on the magnets, where any required room can easily be obtained. The increased number of armature conductors would also augment self-induction, and thus partly neutralise the effect of the condenser. Two Alternators working- on the same Circuit. The question of the behaviour of alternators when 398 DYNAMOS, ALTERNATORS, two or more are working on the same circuit is one of great importance not only in central-station work, but also in transmission of power. First, as regards central stations. There can be no doubt that, for economical working, it is necessary to reduce or increase the amount of plant in action at any time so as to correspond as nearly as possible to the demand for current at that time. If the station contained only two large alternators each capable of bearing the maximum load, we should not only have a needlessly large percentage of spare plant, but we should be working the machinery at a very low average output, and consequently at low efficiency. To avoid these defects we must instal a reasonable number of smaller machines, and in order to avoid complication in the switch gear, it is desirable that these machines should be capable of working together on the same external circuit. As regards transmission of power, it is of course essential that the two alternators namely, the generator and the motor should be coupled to the same circuit. To facilitate the investigation, we start with the assumption that one of the two coupled machines is so large, and has so little self-induction and resistance, that its working condition shall not be altered what- ever changes may take place in the circuit, or however much the working condition of the other machine may change. This condition of things would very nearly obtain in a central station where a large number of machines is working on to the same pair of omnibus bars, and one small machine has to be added or with- drawn. In this case the change will scarcely affect the group of machines, and we may assume that the AND TRANSFORMERS. 399 voltage on the omnibus bars remains the same what- ever may be the current given to or taken from them by the small machine. In making this assumption we limit the investigation to the small machine, and avoid the complications which arise in considering the behaviour of two machines simultaneously. We have then to consider the following combination : A large machine without resistance and without self- induction supplying a large amount of power to an ex- ternal circuit, and also coupled to a small machine having resistance and self-induction, both machines running with the same frequency, and having the same terminal pressure. Various problems present themselves in practical work with machines so coupled, and amongst these one of the most important is the following : Let the machine be supplied with mechanical power by its own engine, and determine the working conditions under which it will give a definite electric output with the highest possible plant efficiency. This problem may also be stated in another way namely, how must a number of alternators in a central station be worked in order that, when coupled to the omnibus bars, each may give, not only the same current, but also the same power. Since the losses in the machine can only be com- paratively small, any variation in the working condition cannot alter the total efficiency very much, and conse- quently the conditions of equal output between the different machines will approximately be attained if we take care to have the brake power of the engines as near as possible alike. If the engines are fitted with sensitive governors of the usual type namely, arranged 400 DYNAMOS, ALTERNATOR S, to keep the speed constant this condition would not be fulfilled, because the speed is already controlled by the frequency, and must be the same for all the engines. Suppose, however, that the governor is so adjusted that it shall not come into action at the normal speed, but merely in the event of the engine racing, then the power supplied by the engine per revolution will only depend on the steam pressure and the cut-off, and may be considered to be constant. As the speed is fixed, the total power put into the alternator will therefore be constant, and its electric output will be approxi- mately constant. The condition of constant output can thus be very nearly attained by running the engine without a governor and with a fixed cut-off. Should it be necessary to vary the power this may be done by a governor regulating the pressure in the main steam-pipe, the regulation affecting all the engines simultaneously. After this digression into the engine part of the problem let us go back to the electrical part, as stated above. We have there an alternator whose armature is impelled by a constant torque, and the problem is to find the relations between the output, current, lag, and exciting power. A convenient way of stating the exci- tation is to state the voltage which the machine would give on open circuit. Thus, if we say the machine is excited to 2,100 volts we do not mean that its terminal pressure when a current is flowing is 2,100 volts, but that the field is excited to such a degree that when the machine is running on open circuit the pressure at the terminals is 2,100 volts. We may therefore substitute for the term strength of field the term armature voltage, and AND TRANSFORMERS. 401 the problem may now be stated in these terms : Given a definite driving power and omnibus or terminal voltage, how does the current and lag depend on the armature voltage? Not to complicate the problem too much, we neglect at first armature reaction. It will be shown later on to what extent the armature current FIG. 104. adds or detracts from the field-exciting current, and it is thus an easy matter to correct the excitation corre- sponding to the assumed armature voltage when current and lag are known. Let, in the clock diagram, Fig. 104, the inner circle represent the terminal or omnibus voltage, and 402 DYNAMOS, ALTEENATOES, outer circle the armature voltage, and let the current line be drawn to the left from 0. The loss by ohmic resistance for any given current can be calculated and marked off on the current line. We thus get point A. The electromotive force of self-induction acts down- wards, and must be balanced by an electromotive force acting upwards. Let this be C. To drive the cur- rent through the armature we must therefore have the electromotive force OB, which is the resultant of A and C. It should be noted that whatever may be the current, the resultant electromotive force must lie along the line B, the direction of which depends only on self-induction and resistance, but not on any other quantity. It is also important to note that the length of the lines OA, OB, and OC are proportional to the strength of the current, and that we may there- fore take any of these lines say, for instance, O C to represent the current to a suitable scale. To get the current C through the armature we must have the resultant electromotive force, O B ; and this may also be considered the resultant of the omnibus and armature electromotive forces. We have now simply to find the position of a parallelogram of forces of which B is the resultant. Two such parallelograms are possible, and only two. In one of these the armature electromotive force lies to the right of the vertical, which means that the arma- ture current flows in opposition to the armature elec- tromotive force, and must therefore give power to the machine. With this parallelogram, which corresponds to the machine when working as a motor, we shall not -deal at present. The other possible parallelogram AND TEANSFOEMEES. 403 shows the action of the machine when working as a generator, and is drawn in the diagram. The arma- ture electromotive force is represented by the line O E a , and the omnibus electromotive force by the line O Ej , which is, of course, equal and opposite to the electromotive force at the armature terminals. The angle of lag is <, and the power put into the machine (including loss by resistance, but irrespec- tive of frictional, hysteresis and eddy-current losses) is found by multiplying the current with the armature electromotive force, and with the cosine of <. In other words, we must project E a on to the current line, which gives the point F, and multiply F with the current. It is, of course, supposed that the effective values, and not the maximum values, of current and electromotive force are plotted. The multiplication may be done graphically. It was shown above that C may to a suitable scale represent the current, consequently the area of the rectangle O C D F represents the power put into the machine. In the same way the area of the rectangle O C H G represents the power obtained from the machine, and the area of the rectangle O C B A represents the power wasted in armature resistance. Since the power put in is a constant, the product of D C and D F must be constant, and the point D must lie on a rectangular hyperbola as shown. It is now easy to draw the diagram for other working conditions. Say, for instance, we wish to have a larger armature current. The point B will then be shifted higher up on the line of resultant electromotive force. In Fig. 105 this 404 DYNAMOS, ALTERNATORS, line and the hyperbola are reproduced from Fig. 104, The problem is to find what armature electromotive force will be required in order to increase the armature current to the desired extent. Say C represents the current selected. Draw a horizontal till it meets the line of resultant electromotive force at B and the hyperbola at D. The end of the radius, representing FIG. 105. armature electromotive force, must be somewhere on the vertical through D, the point F being its projec- tion on the horizontal, as before. To find the point E a , intersect the line D F with an arc drawn from B as a centre with a radius equal to the terminal electromotive force. The armature electromotive force is now E a , and is much smaller than before. AND TRANSFORMERS. 405 The mechanical power absorbed by the machine is of course the same as before, but the power delivered is much smaller, whilst that wasted in armature resist- ance is much larger. To reduce the waste power to a minimum it is, of FIG. 106. course, necessary to excite the machine to such a degree that with the same amount of power absorbed the armature current shall be a minimum. That is to say, the point D should come down on the hyperbola, and B on the line of resultant electromotive force as far as possible. 406 DYNAMOS, ALTERNATORS Now the lowest possible position of B will be reached when B E a becomes horizontal. If we chose B still lower, the radius of terminal electromotive force will not reach the vertical through D, and this shows that the machine cannot possibly absorb the power when giving so small a current. In Fig. 106 the point B is found by drawing from K a line parallel to the line of resultant electromotive force. This gives the arma- ture electromotive force E a , the points E a and D, of course, coinciding. The terminal electromotive force is now in phase with the current, and the machine works with the highest possible efficiency that is to say, the output is a maximum. The machine also works now with the highest possible plant efficiency. The diagrams here explained at some length are not drawn strictly to scale. Modern machines have far less resistance and generally, also, less self-induction than shown in these diagrams. It was, however, necessary to assume comparatively large values for the electromotive force of self-induction and that lost in resistance, in order to make the geometrical construc- tion more easily understood. In Fig. 107 is given a diagram drawn to scale, which refers to a 60-kilowatt alternator as actually built. The following are the particulars of this machine : Terminal electromotive force... 2,000 volts. Current 30 amperes. Frequency 60 cycles per second. Armature resistance 1- 94 ohms when warm. L = '069. e s = 26 i. To make the diagram clear the lines of construction AND TEANSFOEMEES. 40T are omitted, and the points giving the position of the radius of armature electromotive force are joined by a curve. These points are marked 1, 2, 3, etc., and the corresponding points on the circle of omnibus electro- motive force, which is, of course, diametrically opposed to the terminal electromotive force, are similarly marked. This diagram shows at a glance the current corresponding to any armature electromotive force, and the lag of current with regard to armature and terminal electromotive force. The resultant electromotive force is measured on the sloping line next to the axis of ordinates. The current line is always horizontal and to the left of the centre. The lines representing arma- ture volts are partly above the current line (points 1 to 5), and partly below (points 6 to 9). In the former case the current lags and in the latter the current leads. It will be noticed that the armature voltage may vary within very wide limits (this variation being produced by varying the exciting current), and yet the powder absorbed by the machine remains constant in. this case 60 kilowatts. The only difference is that with either too strong a field or too weak a field the current becomes excessive, and the efficiency and out- put drop, because of the greater amount of power wasted in overcoming the ohmic resistance of the armature. The best working point is at 5, when the armature current is in phase with the omnibus voltage and the machine is excited to give, on open circuit, 2,200 volts. Although diagram Fig. 107 gives us all the infor- mation required, it is not in such a form as to show at a glance the interdependence between field strength, or 408 DYNAMOS, ALTEKNATOES, armature voltage and current. In this respect the diagram devised by Mr. R. W. Weekes, and shown in FIG. 107. Fig. 108, is preferable. It is constructed from Fig. 107 by plotting armature voltage on the horizontal and current (which can be read off in Fig. 107 on the line AND TBANSFOEMEES. 409 of resultant electromotive force) on the vertical. Thus we obtain a volt-ampere curve which shows at a glance what current will be given by the machine when the excitation is varied, but the driving power kept constant at 60 kilowatts. We can thus construct a series of volt-ampere curves, each curve corresponding to a definite driving power. In the diagram two only are shown namely, for 60 and for 10 kilowatts. These curves, shown in thin lines, have been obtained by the FIG. 108. construction explained above with reference to Fig. 107, and no correction has been made for armature reaction. The curve shown by a thick line includes the effect of armature reaction, as will be explained presently. The point of importance to be noted is that to each driving power (or load on the machine) there corresponds one particular excitation at which the current is a minimum and the efficiency a maximum. If we excite more the current will be increased, and if we excite less the current will also be increased, the efficiency in both DD 410 DYNAMOS, ALTERNATOES, cases being diminished. It follows that the output cannot be controlled by adjusting the excitation, but must be controlled by adjusting the driving power. The best excitation for 60 kilowatts is, however, not very different from the best excitation for 10 kilowatts, the two curves having the lowest point near each other. Armature Reaction. It has already been pointed out that in all cases where the armature current leads or lags, it produces a magnetising or demagnetising effect on the field, and it now becomes necessary to make an investigation as to the magnitude of this effect. The question is of a somewhat complex nature, and before attempting a solution it will be well to state in general terms some of the conditions which influence the magnetising or demagnetising effect of the armature current. In the first place, it will be clear that this effect must be directly proportional to the current. It will also be clear that an increase of lag must increase the demagnetising effect of the armature on the field, but it is not at first sight possible to say whether this effect will be simply proportional to the lag. The shape of the coils and pole-pieces and the shape of the current curve must naturally affect this relation. It will also be obvious that the effect cannot be a constant one, but must be a periodic function of the time. Since, however, the pole-pieces and magnet cores are gene- rally solid, and since the exciting circuit has necessarily a large self-induction, the resultant field cannot vary within very wide limits, and may, in fact, without committing any great error, be considered con- AND TRANSFORMERS. 411 stant. The demagnetising effect, or armature back ampere-turns (to adopt the term used in connection with dynamos) , can therefore be arrived at by integrat- ing the momentary effect over the time of a complete period. Let X represent the back ampere-turns at any instant, then the exciting power which must be added to the field in order to compensate for the back ing power of the armature will be IX dt ampere-turns. J In attempting a solution of this integral, it must be remembered that X is the product of instantaneous current multiplied, not necessarily with the total number of turns in the armature coil, but only with the number of turns occupying at that instant such a position that the current can exercise a demagnetising effect. The solution is therefore somewhat compli- cated, and, in certain cases, impossible. But in the simple case when the width of poles and coils is equal to half the pitch, which corresponds more or less with the majority of machines as actually built, an approxi- mate solution is possible. Calling the angle of lag, and w the total number of active wires in one coil, we have w x= and by substituting for sin a an exponential series, we arrive at the approximate solution that the average or effective back exciting power of one armature coil, and, therefore, of the whole armature, is X, = w i V2 ^ (-58) 7T the effective value of the current being taken. DD 2 412 DYNAMOS, ALTERNATORS, This formula is only an approximation, and gives- the back ampere-turns slightly too large, but the error is so small that in practical work it may be neglected. If we wish to express the lag, 0, in degrees, the formula may also be written thus : X 6 = '0156 w i . . . . 59) To take an example, let us suppose that in a 100-kilowatt machine each armature coil contains 80 active conductors and carries 50 amperes. Then w i would be 4,000. Let the lag as found from the working diagram be 20 deg., then the total back ampere- turns will be '0156 x 4,000 x 20 = 1,248. In order that the machine may work under the conditions corresponding to the working diagram, we would, therefore, have to apply to the field magnets 1,248 ampere-turns of exciting power over and above the exciting power corresponding to the armature voltage shown on the diagram. This correction has been made in Fig. 308, where the volt-ampere curves, shown in fine lines, represent the working conditions for 60 and 10 kilowatts respectively when armature reaction is neglected, and the full-line curve for 60 kilowatts when armature reaction is taken into account. In making the correction, it is of course necessary to know the characteristic of the machine when working on open circuit, or, as we have called it in connection with dynamos, the static characteristic. This is found in the same way. The machine is run light at about its normal speed, and the exciting current is varied. Readings are taken of speed, exciting current, and terminal voltage. This gives us the armature voltage AND TRANSFOEMEES. 413 at the normal speed as a function of the exciting current, Fig. 109, and the curve representing this relation is the static characteristic of the machine. The working diagram, Fig. 107, gives us the current and angle of lead or lag corresponding to any armature voltage. The corresponding exciting power is then found from the static characteristic. We next calcu- late from (59) the armature reaction, which in the case 7oU "V FIG. 109. of a leading current must be deducted, and in the case of a lagging current must be added to the field ampere- turns found from the characteristic. This gives us the exciting power which must actually be applied to the field, and the corresponding armature voltage which would result if the machine were running on open circuit. It is this value which has been taken for the abscissse of the volt-ampere curves, shown in the heavy line in Fig. 108. It need hardly be said that this 414 DYNAMOS, ALTEKNATOKS, diagram could also be drawn by plotting as abscissae >. not the armature voltage, but the exciting current. It will be noticed that the divergence between the two volt-ampere curves corresponding to an output of 60 kilowatts is not very great. This is due to the fact that the diagram was constructed for a machine having a reasonable amount of self-induction. The result, as will be seen from Fig. 107, is that even within wide limits of armature voltage the angle of lag or lead remains moderate, and the amount of armature reac- tion, as given by formula (59), is comparatively small. The practical conclusion is that in the neighbourhood of the best working point small variations in the exciting current have no very great effect on the armature current produced by the machine. A great increase or a great decrease in armature voltage has. however, the result of appreciably increasing the arma- ture current, and if the excitation, and with it the armature voltage, is reduced beyond a certain limit, the corresponding ordinate misses the volt-ampere curve altogether (where the latter is dotted), and this shows that the machine cannot any more hold the engine in step and racing must ensue. When working with a normal field the combined steam-alternator is, however, perfectly stable, thanks to the appreciable amount of self-induction. The case would, however, be entirely different had we assumed the machine to possess extremely little self-induction say, for in- stance, so little that the electromotive force of self- induction would be equal to the electromotive force lost in resistance. Although it is, on account of excessive cost, quite im- AND TRANSFORMERS. 415 practicable to build a machine in which this condition is fulfilled, the consideration of such a case is interest- ing, and the reader should construct for himself the respective working diagram and volt-ampere curves. He will find that the smaller the self-induction the greater is the variation in the angle of lag or lead produced even with very small changes of exciting current, and the more pointed becomes the volt- ampere curve when armature reaction is neglected. FIG. 110. If it is taken into account the tendency is to slightly widen the two limbs of the curve, but not materially, because the condition on which the design of the machine is based preclude the possibility of a strong armature reaction. The machine is to have extremely small self-induction. This means that we must pro- vide an extremely strong field and an armature with very few conductors. The magnetising or demagnetis- ing power of such an armature is necessarily very feeble, and it will be the less felt as it has to be exerted upon a field which itself is initially very strong. The result will be that the volt-ampere curve, even when 416 DYNAMOS, ALTERNATORS, armature reaction is taken into account, will present the shape of a very narrow and pointed V, as shown in Fig. 110. This is, roughly, the curve for a machine in which the electromotive force of self-induction at full load only amounts to a few per cent, of the arma- ture electromotive force. It has already been pointed out that such a machine must have a very strong field, and would be very expensive to build. Apart, however, from the question whether it would be commercially practicable, we have to consider the question whether such a machine would be desirable for central-station work. Let us go back for a moment to the case (described a few pages previously) when several machines, each absorbing the same power, deliver current to a pair of omnibus bars at a central station. It is, of course, desirable to have all the machines working under the same conditions that is, giving the same current and the same output in power. To attain this object the machines must be so excited as to give the same armature volts. But how are we to know when the excitation is right ? The ampere-gauge in the exciting current only tells us what exciting power we apply, but as there may be slight differences in the air-space and other constructive details, equality of exciting current does not neces- sarily mean equality of armature volts. There is, further, the difficulty of getting all the ampere- gauges to give absolutely reliable readings and of adjusting the field rheostats with great nicety. On paper it is easy enough to assume the condition that all the machines shall be excited to such a degree as AND TEANSFOEMEES. 417 to give absolutely the same armature volts, but in practice this is not possible. We must expect to have certain variations in voltage. Now, let us see what such a variation means in the two cases of (a) machines with a reasonable amount of self-induction and (b) with machines of extremely little self-induction. In the former case, to which Fig. 108 refers, a considerable variation in armature volts means a very small variation in armature current, as the volt-ampere curve has the shape of a very wide and rounded V. If, then, we adjust the exciting currents of the various machines to be only approximately equal, we can be certain that the machines, if pro- vided with equal driving power, will give not only equal output, but also equal current. Conversely, we shall be able to adjust the driving power by the ampere- gauge in the armature circuit of each machine. This is not possible in the latter case. An inspec- tion of Fig. 110 will show that with constant driving power a very small variation in field strength pro- duces a very large variation in armature current. The ampere-gauge in the armature circuit is therefore 110 guide whatever as to the output of the machine, and the driving power cannot be adjusted thereby. In other words, it is extremely difficult to get the load equally divided between the various machines. The difficulty increases as the self-induction of the machine is diminished, and if it were possible to abolish self- induction altogether, it would be impossible to work the machine on any circuit in which there is another electromotive force active. In this case the volt- ampere curve would shrink to a point, and to work at 418 DYNAMOS, ALTERNATORS, that precise point it would be necessary to adjust the field with mathematical accuracy, which is, of course, utterly impossible in practical work. Self-induction, so far from being an objectionable feature in alter- nators, is, in reality, a very valuable property, and it is only by virtue of this property that machines can be worked in parallel and used for the transmission of power. Condition of Stability. We have up to the present dealt with machines working on the same circuit without specially con- sidering the question whether they would work in parallel or in series. Parallel working is, of course, implied in all the working diagrams hitherto given, because in all cases the lines of armature electromotive force and omnibus electromotive force included an angle of more than 90 deg.; but as this question is one of considerable practical importance it is worth while to investigate it further. The problem may be stated thus : Given a certain omnibus electromotive force and armature electromotive force, how does the output of the machine vary with the angle of lag between the two electromotive forces ? To explain the practical bear- ing of this problem, let us assume that the armature voltage leads over the omnibus voltage, and that the machine works steadily, the engine supplying a certain amount of power. Now, suppose that from some cause the power of the engine increases. The immediate effect will be to push on the machine so as to increase its lead. If this increase of lead is accompanied by a sufficiently large increase of output, the steam-engine and its alternator will settle down into a new working con- AND TEANSFOKMEBS. 419 dition which will be stable. If, however, the increase of lead should result in a decrease of output, then the working will be unstable, and the engine will begin to race. To simplify the explanation, we shall assume that the omnibus voltage is produced by a very large machine, the self-induction and resistance of which may be neglected. Let the large and small machine be mechanically coupled, and let the coupling be adjustable, so that the two armatures may be set relatively to each other at various angles. In one position of the coupling the maximum electromotive force occurs in both machines simultaneously ; with other settings the maximum electromotive force shall occur in the small machine sooner than in the large one, when the small machine may be said to lead, or later, when it may be said to lag. In drawing the clock diagram for each case, it is necessary that we should be quite clear as to the direction in which each electromotive force acts. Take the case of the large and small machines being coupled in parallel, and assume that in the clock diagram of the large machine the electromotive force would, at a given moment, be shown by a line running from the centre vertically downwards. Since this electromotive force must be opposed to that of the small machine, it would have to be represented in the clock diagram of the latter by a line running from the centre vertically upwards. In the clock diagram of the small machine the omnibus electromotive force must be diametrically opposed to the terminal electromotive force and of equal magnitude, the resistance of the connecting 420 DYNAMOS, ALTERNATORS, cables between the two machines being considered negligible. When the two machines are coupled in series, the electromotive force line in the clock diagram of the large machine retains, of course, its direction when transferred to the clock diagram of the small machine. FIG. 111. Parallel coupling is shown diagrammatically in Fig. Ill, where m is the small and M the large machine with the lamps coupled across their common leads. The clock diagram above is so simple that a few words of explanation will suffice. At the moment to which the AND TBANSFOEMEES. 421 diagram refers the large machine produces through its "armature a downward electromotive force, which, transferred to the small machine, becomes an upward electromotive force, as shown in the clock diagram. This is opposed to the downward electromotive force produced at the terminals of the small machine at that moment. Suppose we have coupled up the two arma- tures mechanically in such a position that the small machine leads by the amount shown in the diagram. The omnibus electromotive force and armature electromotive force (which in the case illustrated is the smaller of the two) combine to produce the resultant electromotive force, OB. This is, then,, the electromotive force which drives the current through the small machine, and has to overcome, first, the armature resistance, OF, and, secondly, the elec- tromotive force of self-induction, B F. Whatever may be the resultant electromotive force, the ratio between its two components is the same. In other words, since BF is vertical to OF the angle BO. constant, and will the more approach a right angle the less electromotive force is lost in armature resistance. In modern machines the resistance of the armature is very small, and the angle at B is therefore very acute, and that at O very nearly a right angle diagram it has, however, been shown sensibly smaller than a right angle in order to make the construct clear. , . The mechanical power given to the small machine is found by multiplying the current with the projection of the armature electromotive force on the current line Since the electromotive force is proportional to. 422 DYNAMOS, ALTEENATOKS, the current, we caii also represent the power by the area of a rectangle the base of which is the projection of armature electromotive force on the current line, and the height of which is the electromotive force of self-induction. This gives the figure O D G H. The rectangle F D G B represents the power supplied to the omnibus bars, and F B H that wasted in the armature. Now let us change the coupling so as to work with a different lead, and repeat the geometrical construction above explained. We shall thus get another value for the power, and we may in this way determine the power for any given lead. If the results be plotted in polar co-ordinates, we obtain a curve of the shape shown in Fig. 112 on the left, and marked "Generator." This curve for modern alternators having small arma- ture resistance is nearly a circle, and if armature resistance may be neglected, it becomes a true circle. The power given by the engine to the machine is represented by the length, O P, cut off on the radius, O K, drawn to represent the lead of the small machine over the large machine. It will be seen that if the lead be zero, or very small, the power is also very small, but increases rapidly as the lead increases. We have up to the present always supposed the small machine to be rigidly coupled with the large machine. Let us now imagine the coupling bolts to be suddenly slipped out, and see what happens. Let, at the moment of uncoupling, the lead and power be represented by the line P, and suppose that from some cause the power of the engine is diminished. The engine will slightly hang back, and the lead will be diminished. This will AND TEANSFOEMEES. 423 cause the point P to run back on the power curve nearer to that is to say, the engine will be required to give less power than before. On the other hand, if by increasing the steam pressure or altering the ^cut-off we let the engine do more power, it will push FIG. 112 on, and thus increase the lead, bringing the point, P, farther away from O on the power curve, and increasing the power required by the alternator. It will thus be seen that the working is perfectly stable. Any tendency of the engine to push on too far is im- mediately checked by the greater output, and any OF THE 424 DYNAMOS, ALTERNATORS, tendency to lagging on the part of the engine is counteracted by the decrease of output. There is, however, a limit to this automatic adjustment of load and power in either direction. If the engine pushes on until the radius O K coincides with O A, the power which can possibly be taken up by the machine has reached its utmost limit. A slight increase of lead beyond this point results in a decrease of output, and thus the engine will overpower the machine. In other words, it will begin to race and get out of step with the large machine. The part of the power curve where this will happen is shown by the dotted line. If we wish to work on any point of the dotted power curve, we must retain the mechanical coupling between the two machines. Now let us en- quire what working on the dotted part of the power curve really means. It means that the small machine must lead by more than 90 deg. that is to say, its elec- tromotive force must be on the whole not opposed to, but in the same direction as that of the big machine. In other words, the two machines must be coupled in series. We see, therefore, that only by employing a rigid coupling is it possible to work the two machines in series. If not mechanically coupled, they can only work in parallel. The diagram contains also a power curve on the right marked " Motor/' This refers to the working of the small machine as a motor, when its armature must la^ behind that of the big machine. The more we load the motor the more the lag increases, and an increase of lag will at first produce a very rapid increase in the power given out. As the lag approaches the line B AND TRANSFORMERS. 425 the increase of power becomes less rapid, and if we load the motor so much as to produce this lag the working will be unstable that is to say, the slightest further increase of load will throw the machine out of step. Within the range of the power curve shown in full, the working of the motor will, therefore, be stable; and to provide for the possibility of any sudden and accidental increase of load it is best to work normally with a small lag, which is only another way of saying that the motor should be worked well within its power. The range within which the machine may safely be worked either as a generator or as a motor is shown in the diagram by the angle marked " Normal working." This is an angle of about 45 deg. between the two extreme positions of the armature when the machine changes from being a generator giving full normal output to a motor producing full normal power. Taking the machine as a generator only, the danger of being at any time supplied with too much power is, of course, not nearly so great as that of being over- loaded when working as a motor, and we may there- fore work with a greater lead than shown in the diagram. Say that we work with a lead of 40 deg., which gives a power margin of 60 or 70 per cent. In this case the range from full output to zero is comprised within an angle of from 40 deg. to zero. This refers, ot course, to a two-pole machine. For a 20-pole machine the range measured on the crank-pin circle of the engine is only 4 deg. to zero. Say we have two steam-alter- nators working in parallel. If the crank-pin of one engine is by 4 deg. in advance of that of the other engine, the former will at that moment give the whole E E 426 DYNAMOS, ALTERNATORS, output. If the advance is more than 4 deg., it will give not only the full output but also some power for driving the other machine. This would cause a surg- ing of power between the two machines, which may make parallel working impossible. It must be remem- bered that, although the engine of the leading machine cannot permanently supply the power required for the whole of the output, it may do so for an instant by virtue of the energy stored in its flywheel, and the momentary overload may be sufficient to throw the machine out of step. The remedy for this trouble is, of course, to ensure that no engine shall have a ten- dency to lead or lag behind the other at any time, and for this reason high-speed direct-coupled engines are preferable to low-speed belted engines. If the latter must be used, it is well to make arrangements by which it is possible to time the switching-on of machines so that it shall take place when the engine is in the same part of the stroke as the other engines already working. We must, in other words, synchronise, not only the alternators, but also the engines. The method of coupling two machines shown in Fig. Ill, although it allows a current to run through the two machines in series, is not the one usually under- stood by the term series coupling. In Fig. Ill there may be a current circulating between the two machines, but, in addition, there must be a current flowing through the lamps. Now, in true series work- ing, the lamp current must flow in series through the two machines, and there is no other current possible. In Fig. Ill the series current through the two machines is, so to speak, a mere accidental effect which may or AND TRANSFORMERS. B 427 FIG. 113. may not take place, and, as was shown, it cannot take place when the machines are running free of mechanical control. The machines in this case simply put them- BE 2 428 DYNAMOS, ALTERNATORS, selves into parallel. Now let us see what will happen when the connections are designedly arranged for series working, as shown in Fig. 113. Here the lamps cannot be lighted unless a current is flowing in series through the two machines. The electromotive forces of the two machines produce together the resultant electro- motive force, O B, and this has to do two things. It has to drive the current through the resistance of the whole circuit, consisting of lamps, leads, and the two armatures, and it has to overcome the electromotive force of self-induction of both armatures. Since resist- ance and self-induction are constants, the ratio between the two electromotive forces is always the same whatever may be the value of the angle of lag, $, y of the armature electromotive force of the small machine behind that of the large machine. The angle B F remains therefore constant, although it shifts bodily round to the left as the lag is increased by suitable alteration in the mechanical coupling between the two machines. The power ab- sorbed by the large machine is proportional to the area of a rectangle having F G for its base and F B for its height. Similarly the power absorbed by the small machine is proportional to the area of a rectangle having G for its base and F B for its height. If we now alter the coupling so as to set the small machine to work with a greater lag and repeat the construction, we find the power corresponding to the new angle of lag. By plotting the result in polar co-ordinates we obtain power curves as before, but these are of an entirely different character. In Fig. 114 the power curves are shown for two AND TKANSFOEMERS. 429 machines of equal electromotive force, called A and B. The machines will work with maximum power if they are so coupled up mechanically that the lag of A behind B is zero that is to say, that the maximum electro- motive force occurs in both simultaneously. This con- dition of working corresponds in the diagram to the radius line E. If we now set the machine A back to O E a , it will absorb the power O A, and the machine B will absorb the power B, and so on for any other setting of the coupling. 430 DYNAMOS, ALTEENATOES, When dealing with machines coupled parallel, we have seen that even after slipping the coupling bolts the machines would run on in a perfectly stable condition. This is not so in the present case. For imagine that after the coupling bolts are slipped, the engine of B, which is leading, gives a little more driving power. The immediate result will be that A will be left a little further behind that is to say, the radius O K x will shift a little further to the left. This will decrease O B, the power absorbed by the leading machine, with the necessary result that the leading machine will go still further ahead. The working is therefore unstable, and the machines cannot work in series. If the engines are governed to constant speed, the machine A will set itself to a lag of 180 deg. that is to say, it will go into parallel with B (the radius of the power curves will then occupy the position B ) and no work will be done on the lamp circuit. The small loops near the centre refer to the working of the machines as motors. From what has here been explained, it will be clear that alternators when run- ning free cannot be coupled in series, but will work perfectly in parallel, provided the driving power is applied evenly throughout the cycle. In other words, the success of parallel running depends simply on the engines, and the way they are governed. When dealing with the working of one alternator on to a pair of omnibus bars, we have assumed that the voltage on the bars is kept constant by a large machine or a number of small machines, so that the terminal voltage of the machine under consideration is fixed beforehand. It remains to investigate the case of two- AND TRANSFOEMEES. 431 machines working in parallel, neither of them so much more powerful than the other as to completely control the terminal voltage. Let us take two machines, A and B, driven by engines of equal power, and let us see what will happen if the armature voltage is not the same in both machines. In the first place, it will be obvious that the terminal voltage must be the same in both machines, and must be in phase with the resul- FIG. 115. tant current if the latter is doing work on an induction- less resistance. In the next place, it will be seen that the current through each machine may be larger, but cannot be smaller, than half the resultant current, Since the driving power on both machines is the same, the output must be the same, and therefore the current must be the same. Let us first excite both machines to the same degree, so that their armature electromotive forces shall be exactly equal, and let this be E, giving a terminal 432 DYNAMOS, ALTERNATORS, electromotive force, O E , Fig. 115. The machines will now each give a minimum current, i , or together, 2i , and work with maximum efficiency. The line E Ee represents the electromotive force required to overcome self-induction and armature resistance, and corresponds to line B K in Fig. 106. Let us now see how we must alter the armature electromotive forces in order that the machine A may give the current represented by the line (H A in magnitude and direction, and the machine B the current i B . To get the current ZA through the armature we must provide, in addition to the terminal electromotive force E, an electromo- tive force, E E A , to overcome armature resistance and self-induction. In other words, we must excite the machine to such a degree that on open circuit it will give the electromotive force represented by the line O E A . A similar construction applied to machine B shows that its electromotive force must be E B . It is thus perfectly safe to couple two machines together of widely different voltage, each driven by an engine exerting the same driving power. A similar con- struction to Fig. 115 can be applied in the case that the two engines do not exert the same driving power, the only difference being that the two currents will then be unequal, and the points i^ i B will not be on the same vertical. We might thus have, say, 2,500 volts in B and 1,500 volts in A before coupling up, and after the machines are coupled up they would both settle down to about 2,000 volts terminal pressure. General Conclusions. It will be useful to recapitulate briefly some of the AND TEANSFOEMEES. 433 Conclusions of the above investigations regarding the working conditions of alternators. All commercial alternators have an appreciable amount of self-induction. Alternators with very small self-induction must necessarily be very large, heavy, and expensive, and could not safely be used on any circuit to which there is connected another source of alternating electromotive force. The primary effect of self-induction is to produce a lagging current and lower the terminal voltage. Its secondary effect is to place the armature current into such a phase that it produces a certain demagnetising action on the field. Thus both self-induction and armature reaction tend to lower the terminal voltage. The effect of capacity is to produce a leading current and raise the terminal voltage, and this effect is enhanced by armature reaction. It is impossible to couple free-running alternators in series. It is possible to couple free-running alternators in parallel. Armature resistance does not assist in parallel working, the lower the armature resistance the better. A certain amount of self-induction is indispensable for parallel working. If there is too much self-induc- tion, parallel working is still possible, but the plant efficiency is needlessly lowered. If there is too little self-induction, it becomes very difficult to adjust the excitation so as to obtain the same output from all the machines. For safe working the excitation should be pushed beyond the lowest point of the volt-ampere curve, so 434 DYNAMOS, ALTERNATORS, that an increase of excitation will produce an increase of armature current. Two alternators of different voltage may be safely coupled in parallel, and will then give an intermediate terminal voltage. CHAPTER XVII. Elementary Transformer Shell and Core Type- Effect of Leakage Open-Circuit Current Working Diagrams. Elementary Transformer. The electromotive force generated in the armature coil of an alternator is due to the change in the magnetic flux passing through the coil, the change being produced by relative movement between field and armature. If it were possible to produce a changing flux in any other way the result would, of course, be the same. We might, for instance, place a second coil close to the first in such a position that the whole or a part of the self-induced flux of one coil passes through the other, and induces, therefore, in it an electromotive force. Such an apparatus is known under the name of transformer, the coil through which we send the alternating current being called the primary or driving coil, and the other coil from which we obtain electromotive force and current being called the secondary or driven coil. The object of using a transformer is to obtain the secondary current of any desired voltage, and if the construction of the apparatus is such that the same flux must under all circumstances pass 436 DYNAMOS, ALTERNATORS, through both coils, it will be at once obvious that the electromotive forces induced must be directly propor- tional to the number of turns of wire contained in each. If we call F the total flux in C.G.S. measure, n the frequency, and T the number of turns, the maximum electromotive force occurring at the moment when the flux passes through zero is E = 2 TT n F T . . . . (60) as will be obvious from what was said on page 355. The effective electromotive force in volts is E = 27 T_rc F r 10- 8 . (61) v/2 E = 4-45 n F r 10~ 8 . . . (62) Conversely, if we impress an electromotive force of E volts on the coil, the current which will flow must be such as to produce a field of F = ^ 1QS lines of force . . (63) 4'45 n T In this formula we neglect, for the sake of simplicity, the ohmic resistance of the coil. An inspection of (62) and (63) will show that the larger F, the smaller may be T for a given voltage that is to say, the less copper is needed for the coil. In order to reduce the cost and size of the coil to withstand a given voltage, we must, therefore, so design it that a moderate current may produce a strong self-induced field ; in other words, we must provide the coil with an iron core. Shell and Core Type. We arrive thus at the apparatus shown in Fig. 116, AND TRANSFORMERS. 437 where A is an alternator supplying current to the pri- mary coil, P, whilst a lamp, L, obtains current from the secondary coil, S, the magnetic connecting link between the two coils being formed by the iron core, C. Some of the flux induced by the driving coil in C passes through the driven coil, but not all. In the first place, there is necessarily some lateral leakage of lines all along the surface of such a core, even if one coil only is acting, and in the next place this leakage is very much in- creased by the action of the driven coil. The reason lies in this, that by Lenz's law the magnetising action FIG. 116. of the driven coil must necessarily be opposed to that of the driving coil, resulting in a tendency to the forma- tion of poles in the middle and at the two ends of the The immediate result of this leakage is that the core. electromotive force generated in S must be lower than would be the case if there were no leakage. There is the further defect that the magnetic circuit is only partially formed by iron, the rest being air, which offers great resistance to the flow of lines and necessi- tates the expenditure of a very large driving current. This defect is, of course, easily remedied. We need 438 DYNAMOS, ALTEBNATOKS, only provide a continuous iron path for the lines of force, or, in other words, provide the transformer with a closed magnetic circuit. This may be done in a variety of ways. One very obvious way is to use a core of the kind customary in Gramme armatures, and to wind the primary and secondary coils on it in Gramme fashion, or we might reverse the position of iron and copper, forming the coils of two hanks of wire and winding iron wire at right angles to and over the copper coils so as to envelope them in a kind of iron shell. The former are called core transformers and the latter shell trans- formers. When the iron part of the transformer is made up of plates, a construction adopted in all modern designs, this distinction between the core and shell type is not always equally clear, as anything like a complete iron envelope or shell to the coils is impos- sible with plates. We may, however, define a shell transformer as having a double or multiple magnetic circuit, and a core transformer as having a single magnetic circuit. AND TRANSFORMERS. 439 In Fig. 117 are shown three typical designs, A and B being of the core type and C of the shell type. The primary and secondary coils are shown side by side, and the area of the iron core is the same in all cases. The sectional area of the coils is also the same throughout, so that, roughly speaking, the currents and voltages of all three transformers may be taken as the same. Our aim in designing a transformer must, of course, be to obtain maximum output and efficiency with a minimum weight and cost of materials. The quantity of iron in A is the same as in B, but in C it is less. Again, the amount of copper in A and C is the same, but in B it is less. We find thus that A has no advantage over either of the two other types. Of these the core type contains less copper than the shell type, but to make up for this the shell type con- tains less iron ; and it is not possible to say offhand which is the best. To answer this question it is neces- sary to work out the designs for each type in detail with due regard to the magnetic properties of the iron to be used in the transformer. Effect of Leakage. It has already been pointed out that the driving and driven coil tend to magnetise the core in opposite directions. These magnetising forces are of course proportional to the ampere-turns in the two coils, whilst the resultant magnetisation or the flux actually passing through both coils is due to the combined action of the two coils. We have therefore to distin- guish between three fields the main field, F, com- prising all the lines of force which pass through both 440 DYNAMOS, ALTERNATORS, coils, the leakage field, F x , which passes only through the primary, and the leakage field, F 2 , which passes only through the secondary coil. Strictly speaking, the leakage field is not the same for all the turns of a coil, as some leakage lines ooze out of the core before they reach the end of the coil ; but the general effect may nevertheless be represented by a well- defined leakage field affecting the whole of the coil. To explain the effect of leakage, let us assume that it FIG. 118. were possible to find some medium of zero perme- ability in which the transformer can be placed, and that a leakage path for each coil is specially provided by a closed iron circuit of such dimensions as to produce the same leakage effect as takes place if the transformer is placed in air. In Fig. 118 the main field, F, passes through both coils, the leakage field Fj through the primary only, and the leakage field F 2 through the secondary only. The electromotive force due to the main field is in the primary, E! = 4-45 n F TI 10~ 8 , AND TEANSFOEMERS. 441 and in the secondary E 2 - 4-45 n F 10 8 TI and r 2 being respectively the number of turns in the two coils. In addition, there is in the primary coil an electromotive force due to the leakage field of e l = 4-45 n F x TI 10~ 8 volts, and in the secondary an electromotive force of e 2 = 4'45 n F 2 r 2 10~ 8 volts. The effect of leakage will evidently be the same as if coils having self-induction were inserted outside the transformer in the primary and secondary circuits. FIG. 119. Diagrarnmatically, this is represented in Fig. 119, where T represents a transformer having no leakage, and L! and L 2 choking coils of such self-induction as to be equivalent to the apparatus shown in Fig. 118. The terminals a, b and c, d are the terminals of the transformer, and the electromotive force measured between each set of terminals is now influenced by the action of the choking coils in the same manner as in a real transformer it is influenced by magnetic leakage. It will be shown presently that under certain conditions the effect of leakage is to lower the F F 442 DYNAMOS, ALTERNATORS, voltage on the secondary terminals as the output of the transformers is increased. If the primary terminals are joined to mains in which the pressure is kept con- stant, we get a certain electromotive force on the secon- dary terminals when the secondary circuit is open. If we now close the secondary circuit by the insertion of lamps we find a drop in voltage. This is partly due to the ohmic resistance of the driving and driven coil, and partly to magnetic leakage. The more lamps we put on, the more is the pressure lowered, and it becomes U FIG. 120. important to so design the transformer that this "voltage drop " shall remain within reasonable limits. In other words, we must reduce the resistance of the windings as far as possible, and so group the coils as to have as small a leakage field as possible. In the design shown in Fig. 117c, the leakage field will be considerable, but if we group the coils as shown in Fig. 120, it will be very much reduced, because the magnetic resistance of the leakage path is increased. In the same way is it possible to reduce the leakage of Fig. 117B by placing the coils, not side by side, but one within the other. AND TEANSFOEMERS. 443 Open-Circuit Current. A transformer working on open secondary circuit must take from the primary mains sufficient current to produce that field which will just balance the primary voltage. This current is called the open- circuit current, and it is, of course, desirable that it should be as small as possible. If the magnetic pro- perties of the iron are known, we can easily calculate the magnetising current. This current has to do two things : it must supply the power wasted in hysteresis and eddy currents, and it must produce the magneto- motive force required to drive the total flux round the magnetic circuit. Since flux and electromotive force are in quadrature, no power is spent in producing the flux, and the corresponding component of the mag- netising current is a wattless current, whilst the other component giving power must, of course, be in phase with the electromotive force, and is a watt current. Thus, if i is the total open-circuit current, and 4 and ifi its two right-angular components required respec- tively for the supply of power and magneto-motive force, we have The apparent watts supplied on open circuit are i Ej, and the true watts ih E 15 the ratio between the two being called the power factor* = * . This is a is coefficient which approaches the nearer to unity, the smaller ip is in comparison to ih, and is therefore a rough kind of measure for the greater or lesser conduc- * Fleming, Proceedings Institution of Electrical Engineers, vol. XXI. FF2 444 DYNAMOS, ALTERNATORS, tivity of the magnetic circuit. In modern transformers the power factor varies from 70 to 80 per cent. If the power factor is 71 per cent., it means that the number of ampere-turns required to produce the field is the same as the number required for supplying the waste power. If the power factor is larger than 71 per cent., it means that the power wasted requires more current than the production of the field. We can now proceed to calculate the open-circuit current. Let /x be the permeability of the iron (generally between 1,000 and 3,000), I the length of the magnetic circuit shown by the dotted lines in Fig. 120, and A the cross-sectional area of this circuit, then to produce the induction, B, a magnetic force, H = is required. Since H = ^ ^ TI , we have in /x I absolute measure This refers, of course, to the crest of the wave. If" we wish to obtain the effective current in amperes we must multiply by 10 and divide by V2, which gives ~r> 7 Magnetising current in amperes, i^ = *565 -- (64) M T! If w represents the loss in watts per cubic centimetre of iron per cycle at the induction, B, on account of hysteresis and eddy currents, then the total loss is : ih ~&i = w I A n. * Inserting E x from (62) we have w 10 s I Watt current in amperes 4 = '225 - . (65) B TI AND TRANSFORMERS. 445 The value of w can be found from the hysteresis curve, page 132, with a suitable addition for eddy currents, which has to be determined by experience for every type of transformer, but is generally very small, espe- cially if the thickness of plates does not exceed 10 mils. It is, of course, very important that the open-circuit ^current shall be small. When transformers are used in central-station work they must necessarily be connected to the mains for a much longer time than corresponds to their period of full or even moderate output. Indeed, in the majority of stations as at present arranged, the transformers are continuously under pressure, but are only used for some few hours -each day. During the rest of the time the transformer simply wastes primary current and power, and to reduce this waste to a minimum is one of the points aimed at by the makers of modern transformers. Formulas (64) and (65) show us how this may be done. We must work at a low induction, have a short magnetic circuit, and employ the very softest iron that is procurable. One method of reducing the induction is to increase the frequency, and we accordingly find in practice that the same transformer worked at a higher frequency has a smaller open-circuit current and a smaller loss. It must, however, be pointed out that the length of the magnetic circuit (the dotted lines- in Fig. 120) cannot be reduced without cramping the space avail- able for winding, whilst, on' the other hand, too great a reduction in B (by increasing the area of the core) lengthens both the perimeta of the coils and the magnetic circuit, so that the best design for any given 446 DYNAMOS, ALTERNATORS type of transformer must always be a sort of compromise- between a number of contradictory conditions. A low electric resistance is important on account of voltage drop and beating at full load ; a low magnetic resistance is of importance on account of open-circuit current and waste of power at no loads or ligbt loads. So botb tbe electric and tbe magnetic circuit sbould be as sbort as possible. Working Diagrams. We may use tbe clock diagram to explain tbe working of a transformer, and in order to begin witb a simple case we sball assume tbat tbe primary and secondary coils are so well interlaced tbat tbe re is left no space between tbem for tbe passage of leakage lines ; in fact, tbat there is no magnetic leakage. It will also be convenient to assume a transforming ratio of 1 : 1 in tbis and in tbe following cases. Tbere is no need to draw tbe diagram for any otber ratio, since we can always imagine one of tbe windings to be afterwards so cbanged as to produce any otber ratio. All pressure effects in tbe altered coil will tben cbange in tbe same ratio as tbe winding, and all current effects in tbe inverse ratio. Tbus if we double tbe number of turns we double tbe electromotive force and balve tbe current ; we quadruple tbe resistance and double tbe loss of pressure by resistance. Tbe total ampere-turns produced by tbe coil remain, bowever, tbe same. Not only can we imagine botb coils to bave an equal number of turns, but we may assume tbat tbis number is 1 namely, tbat tbe primary and secondary each consist of one turn of wire, having a sectional area AND TRANSFORMERS. 447 equal to the aggregate area of the wires in a coil of many turns. This assumption, as will be seen presently, is made so that we may use the same scale for amperes and ampere-turns in the clock diagram. We assume constant pressure at the primary termi- nals and a variable resistance in the secondary circuit this resistance to be non-inductive. Let, in Fig. 121, O I 2 = i 2 represent the effective current in the secondary circuit produced by the impressed electromotive force, O E 2 . Let the electromotive force required to over- come the resistance of the coil itself be represented by the length R 2 , then the terminal pressure avail- able for doing work in the external circuit is e 2 = R 2 E 2 . Let F represent the effective ampere-turns required 448 DYNAMOS, ALTERNATORS, to produce such a field as will give the impressed electromotive force e 2 . The line O F must be at right angles to E 2 , and to find the position of the primary current we must draw such a parallelogram as will give F as the resultant. Thus we find 01!=%, the primary current. The power wasted has to be supplied by the primary current, and we may represent it as the product of this current with a certain electromotive force. Let this be Kj, then the length of this line will represent not only the electromotive force lost in overcoming the resistance of the primary coil, but also that wasted on account of hysteresis and eddy currents. To drive the current through the primary coil, we must therefore supply to its terminals an electromotive force which must counterbalance the electromotive force induced by the field, and that lost in resistance, hysteresis, and eddy currents. We make Ej 1 = E 2 and Ej 1 E x = E lf which give us E x = e l as the position and magnitude of the primary terminal electromotive force. The power put into the transformer is e 1 ^ cos , and the power taken out is e% i lt giving the efficiency, e 1 ^ l cos All the quantities plotted in Fig. 121 are obtained from the formulae previously given ; F being the effective ampere-turns calculated from (64) . The trans- forming ratio is e z /e lt and if there were no losses this should be unity. It is, however, obvious from the diagram that e 1 > e. 2 , making the actual transforming ratio on full load less than unity. If we now increase AND TRANSFORMERS. 449 the external resistance in the secondary circuit and repeat the construction, we shall find that the line representing the primary current becomes shorter and less inclined, whilst e l becomes slightly reduced. Since, however, e l was to be kept constant, we must lengthen all the lines in the diagram proportionately to satisfy this condition. It is obvious that, partly for this reason and partly because of the reduction in K 2 , the pres- sure on the secondary terminals must increase that is to say, as we reduce the load on the transformer the secondary voltage rises. At the same time the lag, <, increases. The diagram has been drawn out of scale to make the construction clear. In reality, the line OF is very much shorter in comparison with O I 2 than shown. I 2 represents several thousand ampere- turns, and F only some hundreds, or even less than one hundred, so that the inclined lines all become much steeper. The voltage losses, R 2 and B lf are also smaller than shown, the result being that the total voltage drop becomes limited to a few per cent, of the terminal pressure. We have next to investigate the effect of magnetic leakage. As it has already been shown how resistance and other losses can be treated in the clock diagram, it will not be necessary to include these losses in the following investigation. To do so would needlessly complicate an already intricate problem. We shall, therefore, assume that we have to do with a trans- former which, except for leakage, is perfect that is to say, which has neither resistance nor hysteresis nor eddy-current losses. Those who have to do with transformers have long OF THE 450 DYNAMOS, ALTERNATORS, ago discovered that although a transformer when working on incandescent lamps may have an exceed- ingly small voltage drop, the same transformer when working on arc lamps or motors shows a very much greater drop. Again, a transformer when working on a condenser such as a water resistance, or, better still, a long line of concentric cable may show a negative drop that is to say, may actually give a voltage rise when loaded. In what follows no attempt will be made to give a quantitative solution of the problems connected with the working of transformers under various conditions. It will suffice to show in a general way the reasons why transformers show a drop or a rise under certain circumstances, and the reader will then be able to work out specific cases quantita- tively for himself. The first case that we take is one which occurs very frequently in practice namely, when the transformer works on an inductionless resistance, such as a bank of incandescent lamps. In Fig. 122, T is the trans- former, and B the inductionless resistance. In the working diagram above, the same letters as occur in Fig. 121 refer to the same quantities, and need na further explanation. Let E s2 be the electromotive force of self-induction produced by the leakage field F 2 , then O E 2 J must obviously be the induced electromo- tive force in the driven coil. The resultant ampere- turns producing the main field must be at right angles to it and a quarter period in advance. This gives the line O F, and we can now find the line of primary current O 1^ Now the primary current has its own leakage field, F 3 , producing an electromotive force of AND TEANSFOEMEES. 45 1 self-induction which must be counteracted by the electromotive force E s i, a quarter period ahead of O I r Ej 1 , the induced electromotive force in the primary, must be equal and opposite Eg 1 , and to find FIG. 122. the terminal electromotive force of the driving coil we combine Ei and Ej 1 , which gives us E x . An inspection of the diagram shows at a glance that the primary terminal electromotive force must be greater 452 DYNAMOS, ALTEKNATOES, than the secondary terminal electromotive force. It is obvious, also, that if we do not allow a secondary current to flow, the two terminal electromotive forces FIG. 123. are equal. We see, therefore, that the transformer, although giving 100 per cent, efficiency, has a voltage drop when working on incandescent lamps. AND TEANSFOEMEES. 453 We next take the case of there being in the external circuit a self-induction in series with the resistance, Fig. 123. Such a case arises if arc lamps or motors only are worked by the transformer. E S2 represents the voltage due to the leakage field in the driven coil as before, and the length E S2 , E s represents the voltage absorbed by the self-induction, L. The voltage absorbed by R is OE rj and the terminal voltage is O E 2 . Adding the voltage due to leakage on the left we find E 2 X , the induced voltage in the driven coil. That in the driving coil is E^, the rest of the FIG. 124. diagram being constructed as before. The voltage drop is now greater. (Transformers for series arc lighting are made pur- posely with a large leakage field so as to give a heavy voltage drop, and consequently an approximately constant current. The design is shown diagrammati- cally in Fig. 124.) It is sometimes necessary to work incandescent lamps and arc lamps or motors in parallel off the same transformer. This arrangement and working diagram are shown in Fig. 125. The inductive circuit must, of course, have some resistance, and will gene- 454 DYNAMOS, ALTERNATORS, rally also have some counter electromotive force in phase with the current. The latter must therefore lag FIG. 125. behind the terminal electromotive force of the trans- former by less than a quarter phase. The current AND TRANSFORMERS. 455 passing through E is O I R> and that passing through L is I L , giving the resultant current O I 2 . The rest of the diagram is constructed as before. It will be seen that the voltage drop is very considerable, and this conclusion is borne out in actual work. Central- station engineers know that if arc lamps or motors are FIG. 126. ridded to an incandescent light circuit fed by a trans- former the voltage drop is increased. The last case we take occurs when a transformer has to supply current through a long concentric main of considerable capacity. Here the current passing through the driven coil is the resultant of the watt current which is in step with the terminal electromo- 456 DYNAMOS, ALTERNATORS, tive force, and the capacity current which leads by a quarter period. In Fig. 126 the previous lettering has been retained, and I K represents the capacity current. The construction is so simple as to need no further explanation, and it will be seen that, instead of there being a drop, there is actually a rise of terminal voltage when the main is switched on. Various other combi- nations of resistance, self-induction, and capacity could be given, but the examples here explained will suffice to show the method of using the clock diagram for the solutions of all similar problems. CHAPTEK XVIII. Examples of Alternators The Siemens Alternator The Ferranti Alternator Johnson and Phillips's Alternator The Electric Construction Corporation's Alternator The Guleher Company's Alternator The Mordey Alternator The Kingdon Alternator. Examples of Alternators. The following is a slightly condensed reprint of a series of articles published by Mr. E. W. Weekes in the Electrical Engineer in July and August, 1892, descrip- tive of the alternators which were on view at the Crystal Palace Electrical Exhibition held in the beginning of that year. The information then collected is quite up to date now, and will be found useful for reference. The alternators made at present can be classified into two characteristic divisions : First, those in which the magnetic lines have a fixed path of constant resistance, and the electromotive force is produced by conductors intersecting this path ; and second, those in which the resistance and shape of the magnetic circuit is varied, and the electromotive force is produced by the change of induction caused by such variations. GG 458 DYNAMOS, ALTERNATORS, The first class includes all the older designs, and may again be subdivided into two divisions i.e., those alternators which have moving armatures and fixed magnets, and those in which the field magnets revolve and the armature is fixed. In all these machines collecting rings are needed either for the armature or the exciting circuit, but as no commutation is required the collectors can be easily designed to run cool and sparkless. In the second class of alternators the collectors can be dispensed with, and the manufacturers of these machines make this fact one of their claims for support. Another way in which alternators have been classified is as to whether they have iron in their armatures or not. The disadvantage of the use of iron is loss from hysteresis, but owing to the low induction used in the armature iron and to the small amount required, this loss can be reduced to about 1 per cent, of the output by careful design. On the other hand, the presence of an iron core makes the armature mechanically stronger. The following are the principal requirements which have to be considered in a good alternating-current dynamo to be worked at a high pressure : (a) Perfect mechanical design to ensure that the machine can be run continuously; (b) strength and stability in the armature ; (c) perfect insulation in the armature coils, and arrangements so that little difference of potential shall exist between two adjacent parts ; (d) ease of repair of a defective coil when needed ; (e) the collecting gear should give no trouble ; (/) efficiency. AND TRANSFORMERS. The Siemens Alternator. 459 The magnets are constructed with wrought-iron cores, fitting into the cast-iron frame, which is cast in -two halves and clamped together. The exciting coils are wound on brass bobbins, and so connected that the FIG. 127. adjacent poles round the frame have always opposite polarity, and also that any two magnets facing each other are of opposite polarity. Thus, the lines of force pass always through the armature at right angles to it. The details of the construction of the armature can be well seen in Fig. 127. The centres of the bobbins 460 DYNAMOS, ALTEENATOES, are made of hard wood and bound with brass. Then a layer of insulation, such as fibre or press- spahn, is cemented on, and the conductor is wound tightly round this. The connections are made by two wires, which are led through well-insulated holes in the supporting plates. These plates are made of German silver, and clamp both the wooden core and the conductors. There is a layer of insulation under each place, and the two bolts shown passing through the wood core both clamp the plates together and also take the strain due to the centrifugal force in the bobbin when revolving. The metal parts are exposed to some changes of induction due to the magnets, and hence German silver is used, as on account of its high specific resistance it reduces the eddy currents generated. The other ends of the plates are slipped on and bolted to the hub, which has a ring projecting of the same thick- ness as the armature conductor and insulation. When renewing a damaged coil the bolts are taken out, and the coil and German-silver plates, etc., are removed as a whole. To give stability to the outer circumference of the armature, where the conductor might tend to be displaced by mechanical stress, strips of brass are placed on each side and riveted together. The ends of these strips are linked together and thus form a chain completely round armature. To reduce noise the spaces between the polar faces are filled in with wood, so that the surface presented to the armature is continuous. The collectors are two copper rings, and a pair of ordinary copper- wire brushes are used to take the current off each. The following particulars refer to a low-pressure AND TEANSFOEMEES. 461 Alternator of this type : Output, 80 volts 500 amperes at 400 revolutions ; complete cycles, 66 per second ; number of poles, 20 ; weight complete, 2 tons ; floor space, 3ft. 6in. by 5ft. 6in. The Ferranti Alternator. This is in first principles like the Siemens machine described above, but the constructive details are diffe- rent, especially as regards the armature. The cores round which the conductor is wound are made of lamina- tions of brass and asbestos, Figs. 128 and 129. The radial brass strips have a longitudinal corrugation pressed in them, so that when placed together these form keys to prevent any individual strip being displaced. The thickness of the asbestos between the laminations is increased along the radius, so as to give the necessary angle to the core. When the core is built up to the correct shape, it is clamped firmly, and a brass connec- tion is burnt on to the thin end. This is done by running molten metal over the ends of the strip till they fuse together. The core is then machined at both ends to the proper shape, and the solid brass end is drilled for the bolt, which acts as an elec- trical and mechanical connection. The inside end of the copper conductor is brazed on to this solid end. This copper strip also has a corrugation in it to prevent side displacement, and is wound bare with a strip of fibre as insulation between the succeed- ing turns. A large strain is kept on the strip while being wound, and this forces the insulation well into the groove, which securely keys the turns together. In mounting the coils, one carrier is provided for each pair 462 DYNAMOS, ALTERNATORS, of coils, as shown in Fig. 128. There is a sheet of fibre insulation on each side of the coil when placed in the carrier, but the bolt which secures the coil in situ also connects the inner end of the conductor to the carrier. Hence the carrier connects the two inside ends of the coils it holds. The outside ends of the conductors are joined where the coils in adjacent carriers touch. This FIG. 128. is done by brazing the two outside ends together before the coils are fixed into position. With this system of connection, it is clear that the individual carriers must be well insulated both from the frame and from each other. The shank of the carrier is first insulated with porcelain where it passed into the hole in the driving ring. This ring is hollow inside, and a large rect- AND TRANSFORMERS. 463 angular nut is then keyecTon to the shank so that it leaves a small space all round. Sulphur compound is then run into this space, and both firmly clamps the nut by expansion and also insulates it. The porcelain insulation is used to give a greater surface insulation, and also for fear a spark should ignite the sulphur if it FIG. 129 was exposed. The two halves of the armature are connected in parallel so as to reduce the maximum voltage between any two coils. In a 245-kilowatt machine, when working at 2,400 volts, we get 200 volts produced in each bobbin, and hence a maximum difference of potential of 400 volts between the two adjacent bobbins in one carrier. At 464 DYNAMOS, ALTERNATORS, this place ebonite strips are introduced to tighten up the armature coils, and these strips thus give special insulation where it is needed. The lower ends of the coils are blocked up in the carrier by means of insu- lated metallic segments, shown in Fig. 129. This method of connecting the armature is exceedingly con- venient in case of repairs being needed. If one coil should be injured by any mishap, it and the one next it in the adjacent carrier are undamped and lifted out together, and the connection is completed to two new coils by the simple operation of bolting them into place. The connections from two diametrically oppo- site points on the armature are taken through the inside of the main shaft to two well-insulated copper rings. The collectors used are two half rings of brass, with blacklead introduced to give the necessary lubri- cation and conductivity at the same time. The field magnets of this machine consist of wrought- iron slabs cast into the frame of the machine. The frame is built up in segments, which, when bolted together, embrace the armature. The exciting coils are wound on formers and slipped on, being securely fastened in places. The oiling arrangements are ex- ceedingly well devised. The oil is forced up in the bearing at the underside of the shaft, and so tends to float it. The oil pumps at either end are worked by means of eccentrics fixed to the shaft. The efficiency of the machine should be high, but although the lamination of the core will reduce the Foucault currents in the brass strip, it is probable that this loss will still be higher than hysteresis loss in an iron-cored armature. The brass, however, gives AND TEANSFOEMEES. 465 exceptional stability to the armature. The power required to excite this machine is supplied by a current of 150 amperes at 30 volts, which is equal to 1*85 per cent, of the total output. The following are the details of the alternator: Volts, 2,400; amperes, 100; speed, 335; complete periods, 66 per second ; number of bobbins, 24 ; conductor, 40 mils by fin. wide ; number of turns per bobbin, 40; insulation, vulcanised fibre, 20 mils thick ; weight of armature conductor, 2501b. ; area of pole face, 126 square inches ; exciting coils wound with 522 turns of 160 mils wire ; weight of whole machine, 18 tons 7 cwt. ; floor space, 9ft. 9in. by 13ft. Sin. ; height, 9ft. Sin. Johnson and Phillips's Alternator. In this machine, which has been designed by the author, the arrangement of the field magnets is different from the two last described, as the opposite poles have in this case the same polarity. The magnetic lines of force pass from one magnet to the next on the same side of the machine through the iron core of the armature. So, though a set of poles is required on each side of the armature to give magnetic and mechanical balance, yet the magnetic lines generated by the set of poles on each side of the armature are distinct in their action. The magnet cores are made of wrought iron, with expanded polar faces, and inlet into cast-iron frames, as seen in Fig. 130. The pole face is made nearly rectangular, so that there shall be an equal number of lines of force entering the armature core at all distances 466 DYNAMOS, ALTERNATORS, from the centre. This is to prevent as much as possible the flow of lines from one lamination of the core to the next, which would produce eddy currents FIG. 130. in the iron. The cast-iron frame into which the cores are fastened is made in two halves, and bolted together to facilitate the removal of the armature when needed. AND TRANSFORMERS. 467" In the large machines, each ring of magnets is arranged to withdraw along the axis of the armature by means of a rack and pinion gear to enable the armature to be examined in situ. The armature core is built up by winding charcoal-iron strip with paper insulation of the full width of the core on to a cast-iron spider ring till the desired depth is obtained. The number of arms in the spider is half the number of poles in the machine, so that two coils are wound in each space between the arms. The outside of the core is then made up with hard wood to the desired contour where the coils have to be wound. The wood blocks all round are secured in position by bolts, and bound on by means of steel wire wound in the circumferential groove left for this purpose. The coils are direct driven by means of shoulders on the wood and the spider arms. The core is insulated with mica and two layers of vulcanised fibre where the con- ductor has to be wound, and the cast-iron spider is fitted with ebonite caps where needed for insulation. In the small machines all the armature coils are connected in series, but in the larger central-station alternators the two halves of the armature are con- nected in parallel to reduce the voltage between any two adjacent coils. The connections are made to bolts in the spider ring, which are well insulated from the spider itself. The current is collected by ordinary copper brushes, of which there are two to each collecting ring. This ring has its collecting surface vertical, and not horizontal, as is the case in the other alternators. This is done to enable the collector to- be placed well inside the magnet frame, so as to render 468 DYNAMOS, ALTERNATORS, the dangerous parts less exposed. The magnet poles are filled in to prevent noise, as already explained. The following particulars refer to the two machines given in the list. The 15-kilowatt alternator is designed to give 2,000 volts at 900 revolutions. The weight complete is 2 tons 5 cwt., and floor space 4ft. 9in. by 3ft. It has 10 poles, and hence gives 75 complete cycles per second. The 120-kilowatt machine gives 1,000 volts and 120 amperes at 600 revolutions. Weight complete 6 tons 3 cwt., and floor space 5ft. 9in. by 6ft. 9in., height 5ft. 6in. It has 20 poles and gives 100 complete periods per second. The power used to excite the field is 1'8 per cent, of the output. The weight of the machine is made up as follows : cwt. qr. Ib. Bed-plate 47 1 23 Armature 17 1 26 Two magnet rings 17 3 14 Forty magnet cores 17 2 20 Copper on magnets 13 3 Pulley 6 3 14 Other parts 2 18 Total 123 1 3 The Electric Construction Corporation's Alternator. The 30-kilowatt alternator made by this firm has its 'field magnets revolving inside a fixed armature. The construction of the field magnets is as follows : The 18 poles, which are made of wrought iron of 3in. by 6in. section, are inlet radially into a solid ring of wrought iron, which is shrunk on to a cast-iron hub or AND TRANSFORMERS. 469' spider. This hub is securely keyed on to the shaft^ and the ends are closed by thin iron plates to prevent loss of power due to the air current caused by the sup- porting arms. The exciting coils are wound on sheet- iron formers, which are securely fastened on to the radial magnets. This requires careful attention, as the centrifugal force at normal speed tending to throw a. FIG. 131. bobbin off the magnets, is nearly 150 times the weight of the bobbin. The coils are connected up in series, and the two ends are led to collecting rings fixed on the shaft. The exciting current is supplied to these two rings by means of two pairs of copper-gauze brushes. This enables one brush to be adjusted and bedded without affecting the working of the machine. The 470 DYNAMOS, ALTERNATOBS, iron core of the armature is in this case external to the conductors, and consists of a ring built up of thin charcoal-iron segments, the lamination being at right angles to the axis of the machine, Pigs. 131 and 132. These segments are clamped I FIG. 132. between the two halves of the frame, which are made of cast iron. Their internal diameter is larger than that of the wrought iron, and the spaces so left at the ends are filled in with wood, which forms the insulating support for the armature coils. These coils AND TRANSFORMERS. 471 are wound flat on wooden cores, and then laid on the inner surface of the wrought iron with a sheet of insu- lating material between. Another wooden ring at each end keeps the coils in position, and securely clamps both the wooden core and the conductors. This ring is made in segments, so that when it is necessary to take out a coil, one segment only need be displaced. The breadth of the wooden cores is about equal to twice the breadth of the winding. Thus on the armature surface the cores and the conductors occupy equal space alternately, as shown in Fig. 132. The connections between the armature coils are made in the channels cast in the frame. There are spaces left in casting for the conductors to come through, and the joints are well protected by the external lagging of wood. As the armature is fixed, the two ends, after all the coils are connected in series, are led to two terminals, which also are usually placed under the wood lagging. This ensures that no dangerous shock can be got from the machine, as the high-tension parts are inaccessible. The magnets for the machine given in the list are excited from a 100-volt circuit, and take 16 amperes ; thus 5*3 per cent, of the total power given out is required to excite the field. The details of this alternator are as follows : Output, 1,000 volts 30 amperes at 600 revolutions ; 60 complete periods per second ; weight complete, 2 tons 15 cwt. ; floor space, 4ft. 6in. by 4ft.; height, 4ft. 4in.; armature, 36in. diameter, 6in. active length ; conductors, '015 square inch section, wound in 12 coils of 34 turns each ; 12 poles of wrought iron, 3in. by 6in. 472 DYNAMOS, ALTERNATORS, The Guleher Company's Alternator. In this machine, designed by Mr. G. Fricker, the field-magnet details are somewhat similar in shape to- those of the alternator just described, but there the similarity ends. The magnets consist of a heavy star- shaped casting, having 12 radial arms, Figs. 133 and FIG. 133. 134. This casting is mounted on the spindle. The exciting coils are wound on bobbins made of sheet iron with brass flanges, and the depth of winding increases with the radius, so as to get as much wire on as possible. The bobbins are slipped on and held in position by two iron bolts which screw into the AND TRANSFOEMEES. 478 1mb, and are riveted into the upper flanges of the bobbin. These bolts take all the centrifugal strain, which tends to throw the bobbins off. The power required to excite this machine is 2 33 per cent, at three-quarter full load. This is lower than in the last- described machine having the same type of field FIG. 134. magnets, owing to the small air-gap used. The armature can best be considered as an improvement the Lontin pole type, the improvement con- on sisting in filling up the spaces between the poles with iron, to prevent the variations of magnetic flux. In this machine the armature is built up of charcoal- H H 474 DYNAMOS, ALTERNATOES, - iron plates *016in. thick, placed radially, and so shaped that, when completed, they form a complete ring with 24 slots in it, into which the armature coils can be placed. These plates are clamped together in a frame by bolts passing through the cast-iron end rings. The armature conductor used is copper strip *162in. by *08in., and 25 J turns of this are wound on edge on a former. The insulation used between the core and the con- ductor is shellaced asbestos and fibre or a thin layer of teak. When completed, the coils are com- pletely embedded in iron. The iron path in the armature offers nearly constant resistance wher- ever the poles may be, and hence there is little surging of magnetic lines. This does away with the need of laminated field magnets, such as are used in the ordinary Lontin type machine. Owing to the short air-gap, the magnetising force required is much reduced, and can be obtained more economically in spite of the limited space for winding and the use of cast iron. There are, however, corresponding dis- advantages. The amount of iron used in the armature is about double that required in the previously de- scribed machine, and the hysteresis loss will be increased almost in the same ratio that the magnetis- ing power is decreased. The other objection is, that in machines with embedded conductors, the armature reaction is much increased owing to the small air-gap. Thus, the exciting current has to be varied consider- ably to prevent alteration in the terminal pressure when the load is varied. Also with high voltages the insulation of the embedded coils would be a rather difficult matter. The coils can be removed individually AND TBANSFOBMEBS. 475 if one should become damaged, and to facilitate this the whole armature is placed on slides, and can in a short space of time be moved along parallel to the axis till clear of the armature field. A multiple threaded screw is used to obtain the necessary force, and at he same time a fairly rapid motion. The slots in the armature iron into which the coils are placed cause a slight variation of induction at the surface of the magnets. To prevent eddy currents in the iron, grooves about T Vin. broad are turned in it Jin. deep. The machine makes very little noise when working. The following are the details of the 30-unit alter- nator given in the list : Output, 100 volts 300 amperes at 700 revolutions ; 70 complete periods per second ; weight complete, 30cwt. ; floor space, 4ft. lOin. by 3ft.; height, 4ft. ; armature conductor, *08in. by *162in., wound in 12 coils of 25J turns each ; weight of con- ductor, 391b. 12oz. ; magnets of cast iron, of lOin. by 5 Jin. section. The Mordey Alternator. This machine differs in both principle and detail from any before described. In this alternator the direction of the lines of force through the armature coils is never reversed, as in all previously described machines, but the electromotive force is produced by a variation of the magnetic field through the coil from the maximum to practically zero. This is done by having twice as many coils as there are poles. Then when one coil is directly opposite a pole, and hence has the maximum field throughout it, the adjacent coils are midway between two poles, and have practically HH 2 476 DYNAMOS, ALTEENATORS, no magnetic flux passing through them. The field- magnet design for obtaining a number of consecutive poles of the same polarity is simple and easy to manu- facture. The magnetic circuit consists practically of a short bar of cast iron excited by one large coil, and with inverted claw pole-pieces fastened on either end to form the returning path of the magnetic lines. In the alternator, the centre core, of cast iron, is keyed to the shaft, and the star-shaped end castings having the number of poles required are bolted against each face of this. The exciting coil is wound on a strong bobbin, which slips on the core. In the centre of the coil there is a space left in the winding to clear the armature coils. The advantage of thus causing the armature to project into the coil is that the magnetic circuit can be then shortened radially. The exciting current required is taken by two brass rings connected to the 'exciting coils, but the method of connecting to the revolving ring is better than the ordinary brush arrangement. It is done by means of a flexible band of copper gauze so folded as to give a rectangular section. The one end of the strip is secured to the terminal and the other has a weight attached. Thus, when hanging over the brass collecting ring, the weight gives the tension required to ensure perfect contact. The armature coils are wound on cores of porcelain, which gives stiffness and good insulation without the disadvantages of the metallic core i.e., hysteresis or eddy currents. The conductor is a copper strip, which is wound bare with a strip of insulating material between each layer. The inside and outside ends re- spectively are connected by flexible conductors through AND TEANSFOEMEES. 477 FIG. 135. German- silver clamps, which hold the outer end of the coil. The bolts holding these plates of German silver on to the coil are all provided with spring 478 DYNAMOS, ALTEENATORS, washers, so that the grip on the porcelain is to a certain extent flexible. One side of the clamp is faced up in the lathe, so that when it is placed against the frame of the armature it ensures the coil being in a plane perpendicular to the axis. In the larger alternators the inside end of each armature coil has also a small brass clamp over the conductors to prevent any displacement of the individual strips taking place. The frame of the armature consists of a large ring usually cast in half and bolted together, Fig. 135. One radial face is machined in the lathe, and to this the coils are bolted. The bolt holes are elongated radially, so that the coils can be packed more tightly together after the working strain has compressed the various parts, and hence loosened them. The armature coils are connected half in series and the two halves in parallel to prevent a high potential difference between adjacent coils in all alternators having an output of 50 kilowatts and over. The mechanical details are well designed and carried out, the oiling arrangements being automatic. Two small oil-pumps are driven by belts off the magnetic spindle, and ensure a good circulation of oil all the time the machine is at work. The following are some particulars of the Mordey alternators given in the list. The 100-kilowatt alter- nator gives 2,000 volts and 50 amperes at 430 revolu- tions. The weight complete is 9 tons 1 cwt., and the floor space occupied is 8ft. 3Jin. by 6ft. 4fin. The armature ring is 5ft. lOin. diameter and has 28 bobbins. There are 14 poles to each magnet casting, thus giving 100 complete periods per second. The magnets are AND TEANSFOBMEES. 479 4ft. 8in. mean diameter, and the armature ring is 5ft. lOin. The details of the weight are : tons cwt. qr. Ib. Shaft 8 3 18 Bed-plate 2 10 2 Armature.. 10 1 12 Each magnet casting 1 16 2 The 50-kilowatt machine gives 2,000 volts and 25 amperes at a speed of 600 ; weight complete, 4 tons ; floor space, 6ft. 7 Jin. by 5ft. 6fin. ; the armature ring has 20 bobbins, and is 4ft. 6in. diameter. The magnets are 3ft. 4fin. diameter, and each pole has 10 pole- pieces. Details of weight : tons cwt. qr. Ib. Each pole 15 1 20 Magnet spool ,. 13 1 22 Armature ring complete 6 20 Shaft 2 3 15 Bed-plate and bearings 1530 The Kingdom Alternator. This machine belongs to the class of alternators in which the electromotive force is produced by changes an the magnetic path. These changes cause a fluctua- tion of lines of force in certain definite places where the armature coils are situated. The diagrammatic sketches, Figs. 136, 137, and 138, will help to show ihe principle of action. The iron parts are all built up of charcoal-iron plates. The outer ring, which has a number of pro- jections on the inside, forms the core for both the 480 DYNAMOS, ALTERNATORS, armature and exciting coils. The latter are placed' over the projections marked S N, and the armature coils are placed over the intermediate projections marked A. The revolving masses of iron which FIG. 136. complete the magnetic circuit are also laminated, and are clamped in position by bolts passing through two- steel discs. FIG. 137, In Fig. 136 the keeper bridges cross the armature- and the south pole of the field magnet, so that the lines of force pass as shown by arrows. Fig. 137 shows the condition of the magnetic circuits when the keeper AND TEANSFOEMEKS. 481 has passed on till it is exactly opposite the armature core. Then the actions of the north and south pole tend to produce equal and opposite magnetic flux in the armature core, and hence neutralise each other, so at that instant no lines of force pass through the armature core. In position Fig. 138 the keeper unites the north pole to the armature, so that the flux is again a maximum, and in the opposite direction to that in Fig. 136. The keeper has now been moved through one thirty-second of a revolution, as there are 16 poles,. FIG. 138. and the electromotive force induced will have passed through half a complete cycle. On comparing Figs. 136 and 137 with respect to the magnetic resistance of the iron circuits, it will be seen that in Fig. 137 the resistance offered to the magnetic flux is much greater than in Fig. 136, whilst the magneto-motive force is doubled. In an intermediate position the resistance will have increased without a corresponding increase of magneto-motive force. This will cause a variation of the flux in the magnets and tend to produce an alternating current in the 482 DYNAMOS, ALTERNATOKS, exciting coils. This effect, and the large masses of iron exposed to changes of induction, and hence causing a large hysteresis loss, are the objections to this class of machine, but they may be reduced con- siderably by careful design. The adjoining list of alternators has been compiled in the same way as that previously given for dynamos ; and the same general remarks apply to it. The mean circumferential speed of the armature or moving magnets is in each case much higher than that adopted in direct-current dynamos. The limiting safe speed is, of course, a function of the mechanical strength of the design. Messrs. Johnson and Phillips work at the highest speed, 8,000ft. per minute, and their con- struction of core is well able to stand this. The Brush Company's magnets have a circumferential speed of 6,300, and the other makers show an average of about 5,000ft. per minute. As regards the material used for the core, four of the seven makers use iron, and the others use respectively porcelain, laminated brass, and wood. AND TRANSFORMERS. 483 _ I Reference number. to to OS CO * " tO -^I >1 ... o -. 33 ~ Mean dia- meter. Circumfe^ r e n t i a 1 speed, feet per minute M H- i-" H-. M I Number of 4- V > ' KH**J o co oo X X OS 1 t>0 ob 1 6 co w 1 6 !|! Section. Per cent, ol output for exciting. Material for co I-" t tO tO t-i I-" H-i tO tO 0504^- OOtC bSOOO Number of coils. t2S o ^ P. ,500 Sg? 5 - fc! S I Number of 1 turns per coil. j? n OS tO tO CO H-M 10 Total num b e r of turns in series. Number of parallel circuits. Weight of conductors. The Co The E The Johns Johns Ferra Sieme Wood nti ns house an Reference number. Gu so so Brush any ctric Co lcher Co pany lips lips El H S 1 1 II t ^IOW 01 O Oi j>o J-'J* t-'jo to g?g Revs, per minute. Volts. Amperes. , 5 Kilowatts. > o I COW h^tOOl -^00 O O en en tn en O Cn XXX XXX Ci tn CO OS CO CO * Cn O5 f DOO 005*-? CD en CO co ocoo *-coo Complete pe- riods per second. Weight in tons. Length. Breadth. Height. _ J Eo a, o 5 E I Kilowatts per o co en -a co en H I ton. tO tO M Op M tp M -JOfflj j-loh- 1 o-^oo ooocn Kilowatts per square foot floor space. I 3ST ZD A. Activity, Unit of 41 Air-Space 55 Alternate- Current Circuit, Power in 385 Alternator Armature 362 Armature Self-Induction 375 Bi-polar 358 in Central Stations 398 Classification _ 457 Combination 399 Definition 10 Details of 483 in Earth's Magnetic Field 357 Electric Construction Corporation's 371 Electromotive Force of 364 Elementary 352 Examples of 457 Ferranti 461 Gulcher , 472 Interdependence of Field, Current, and Electromotive Force 407 Johnson and Phillips's 465 Kingdon , 479 Mordey 475 Pitch Ratio of 374 Requirements of Good 458 on Same Circuit .. 397 Siemens 459 Sixty-Kilowatt 406 Structure of 20 Test for Self-induction 377 for Transmission 398 Uses of 21 Voltage, Effective 356 Westinghouse .. ....... 371 11. INDEX. Aluminium Works 24 Ampere-Turns 88 Back 270 Cross 281 Ampere, Unit of Current 78 Ampere's Rule 69 Analogy, Electric, Magnetic Circuits ... 108 Armature 16 Attraction ... 57 Attractive Force of Magnet 45,53 Back Ampere-Turns 270, 411 Balanceof 66 Bars, Table of 192 Brush 216 Cross Ampere-Turns _. ... 281 Current and Field Strength 417 Drum, End Connections 168 of Electromagnet 89 Electromotive Force of 150 Electromotive Force in Two-Pole 146 Open-Coil 209 Potential Table for Drum 165 Reaction 410 Resistance 172 Thomson-Houston 218 Two Parallel Circuits in 367 Voltage 400 Voltage Function of Current 412 Windings > 158 Attractive Force in Dynes 63 B. Bars, Armature, Table of 192 Bi-polar Winding 159 British Heat Unit 43 Brushes..... 16 Angular Distance Between 206 Armature ... .. 216 C. Calorie 43 Capacity, Effect of . .. 394 C.G.S. System 38 Characteristics 253,274, 278 Choking Coils 441 INDEX. iii. Circuit, Closed Magnetic 5& Clock Diagram 380,401,420 Coercive Force 117 Collection, Sparkless 289 Commutation 261 Commutators 16,217 Conclusions, General 432 Condenser Current 396 Electromotive Force 396 Connections, Cross, in Victoria Dynamos 176 End, in Drum Armature 168 Conversion of Energy 11 Cooling Surface 225 Coupling in Parallel 420 Coupling Machines, Method of 426 Cowles Aluminium Works 24 Critical Conditions 297 Current Action on Magnet 68 Commutation 261 Condenser 396 Eddy 317, 318, 320, 323 Field Strength of 71 Fluctuation 212 Leading 397 and Load 409 and Magnets, Examples 81 Magnetic Field of 69 and Magnets, Forces Between . 78 Turns... 88 Unit of .. 77 D. Density of Magnetic Matter , 59 Dimensions, Influence of Linear, on Output 294 Dynamo Definition , 1O Efficiency M: 11 Electric Machine, Definition 9 Fawcus and Cowan's 362 Johnson and Phillips's 335 Large , 300 Main Parts 1& Multipolar, Advantages of 311 Oerlikon 344 Scott's 330 Small 295 Uses of 21 Various Tables of 349, 350, 351 IV. INDEX. Dynamo Victoria 17, IS, 19 Victoria, Winding 176 Dyne 41 E. Eddy Currents ... 317 Efficiency Dynamo 11 How Determined 11 Pumps 11 Steam-Engines 11 Turbines 11 Electric Construction Corporation's Alternator 371,468 Electrical, Energy Measuring 12 Electromagnet 87,89 Electromotive Force A Maximum 393 Alternator or Dynamo ... 369, 371 of Alternators 364, 373 of Armature 150 Condenser 396 Distribution in Armature Wires 161 Dynamic 262 Effective, of Transformer 436 Induced 136, 141 Instantaneous, Effective 355 Lowering of 262 Measurement of , 35H Resultant 428 of Self-induction 376,382 Static 261 in Two-Pole Armature 146 Energy absorbed by Glow Lamps 43 Conversion 11 Electrical, Measuring 12 of Magnetisation 126 Engines, High-Speed 426 English System of Measurement 83 Equipotential Surfaces 31 Erg _ 41 Ewing on Magnetisation 118 Exciting Power 244, 246, 251, 252, 257 Power and Induction 90 Exploring Pole 29, 31,32 F. Faraday's Discovery 22 Fawcus Dynamo 362 INDEX. V. Terranti's Alternators 23,461 Field of Current 69 Design of Two-Pole 224 Diagram 55 Magnetic 27 Magnets 16, 221 of Mathematical Pole ... . 46 Mechanical Representation 36 Multipolar Designs 228 Strength of 33 Strength of Current 71 Two-Pole 222 Weight of 234 Field Magnets Excitation 244, 251, 252, 257 for Four-Pole Machines 238 for Two-Pole Machines 237 Fleming's Rule 145 Flow, Magnetic 70, 110 Force 37 Attractive 45 of Gravity 37 Lines of 29 Lines of, Cutting or Threading 139 Magnetic 94 Magneto-motive 108 Unit: of 41 Fringe 244 G. General Conclusions 432 Glow Lamp, Energy Absorbed 43 Governing with Alternators 400 Gramme 22 Gravity, Force of 37 Gulcher Alternator . 472 H. Heat, Unit, British 43 Hopkinson Method of Investigation 130 on Magnetisation of Iron 116 Hysteresis 130 I. Induction 16 I I VI. INDEX. Induction Air-Gap 64 Exciting Power 90 Factor 62 Self, in Armature _ 375 Self, Electromotive Force of 376 Integral, Line, of Magnetic Force 95, 106 Intensity of Magnetisation 59 Iron Magnetic Properties of 113 Magnetisation of 116 Saturation . .114 J. Johnson and Phillips's Alternator ..... 465 Joints, Magnetic Resistance 240 Joule .. 42 K. Kingdon Alternator 479 Kriegstetten-Solothurn Transmission _ 23 L. Lag 410, 411 -and Lead 423 and Output 4l!S and Self-Induction 415 Lap Winding 181 Leading Current 397 Lead and Lag 423 Leakage 248 Magnetic 449 of Transformer 439 Lenz's Law 382 Lines of Force 29, 34 Load and Current 409 Losses , ., 302,314,325 M. Machines in Series 420 Magnet, Action of Current on 68 Magnetic Circuit 56, 108 Field 27, 100 Field of Current 69 INDEX. Vll. "Magnetic Fields, Measuring Weak 17 Flow 70 Flow of Magnetism in 110 Force ., 94, 95 Leakage 449 Mechanical Representation 36 Moment 45, 49 Permeability 92 Potential ^ 47 Resistance 108 Whirl 69 Magnetisation Energy of 126 Intensity of 59 Unit of 47 Magneto-motive Force 108 Magnets and Current, Examples 78, 81 Magnets, Field , 221 Interaction of 25 Measuring Weak Fields 51 Measurement Alternate-Current 13 Electrical Energy 12, 14 of Electromotive Force 306 English System S3 Glow-Lamp 13 Units 14 Mechanical Forces between Currents and Magnets 78 Moment, Magnetic 45, 49 Mordey Alternator 475 Motors 390 Definition 10 Field Magnets 227 Machines, Electromotive Force in 153 Multipolar Series Winding 187 Overloading 425 N. Normal Working ., ,... 425 0. Oerlikon Dynamo 344 Ohm's Law 108 Output, Influence of Dimensions upon 294 Limits of ., 301 Vlll. INDEX. P. Pacinotti 22 Parallel Coupling 4-20 Winding 173 Permeability, Magnetic 92, 117 Pitch Ratio of Alternator 374 Pixii 22 Pole Mathematical 44 Mathematical Field of 46 Physical 44 Potential, Magnetic 47 Table for Drum Armature 165 Table for Eight-Pole Series Drum 195 Table for Four-Pole Parallel Drum 186 Table for Four-Pole Series Ring 203 Table for Six-Pole Parallel Drum .. 185 Power Conditions of Maximum 387 in Alternate-Current Circuit 285 Curves 42S of Dynamos and Alternators 21 Factor 443 Unit of 41 Waste 405 Pull of Electromagnet 89 Pump Efficiency 11 R. Reaction, Armature 410 Resistance Armature 172 of Joints 240 Magnetic 108 Unit of, C.G.S 144 Retentiveness 117 Ring Winding, Multipolar 198 S. Saturation, Magnetic, of Iron 114 Schaffhausen 24 Self -Induction, Coefficient 384 Effect of 393 Series Winding 187, 195, 198 Siemens Alternator 459 Sine Law 360 Solenoid 90, 102 INDEX. IX. Sparking 165, 177, 179, 220, 265 Sparkless Collection 289 Stability, Condition of 418 Steam-Engine Efficiency 11 Strain, Prevention ,. 167 Strains 58 Stream Lines 37 Surface Cooling ... 225 Equipotential 31 Symmetry 57 System, C.G.S 38 T. Testing, Hopkinson's Method 121 Thomson-Houston Armature 318 Torque 50, 400 Total Field 62, 99, 100 Transformer with Arc and Incandescent Parallel 453- Capacity Used with 455 Designs 438 Elementary '435 on Incandescent or Arc Circuits 450 Inductionless Resistance 450 Leakage 439 Open-Circuit 443 Power put into 448 Self-Induction and Resistance 453 for Series Arc Lighting 453 Shell and Core Type 436 Type a Compromise 446 Waste 445 Working Diagrams 448 Transmission 23 Alternators for 398 Turbines, Efficiency 11 U. Units 14, 37 Unit Current 77 Force 41 Magnetism 47 Resistance, C.G.S 144 Work 43 Uses of Dynamos 21 X. INDEX. V. Victoria Machine 17, 18, 19, 176 Voltage, Terminal 430 W. Watt 42 Watt-Second 42 Weight of Field Magnets 234,237,238 W^estinghouse Alternator 371 Whirl, Magnetic 69 Winding Armature 158 Bi-polar 159, 169 Lap 181 Multipolar Machines 180 Multipolar Parallel 173 Multipolar Series Drum 187 Multipolar Series and Parallel 203, 206 Multipolar Series Ring 198 Table 171, 181, 185 Table, Drum Armature 161, 165, 195 Working Conditions 392 Work, Unit of 42 or THE ^^\ :VERSITT) OF J i *" YB 536 '776 THE UNIVERSITY OF CALIFORNIA LIBRARY