GIFT OF 
 ENGINEERING LIBRARY 
 

ALTERNATING CURRENTS OF 
 ELECTRICITY : 
 
 THEIR 
 
 Generation, Measurement, Distribution, 
 and Application. 
 
 AUTHORIZED AMERICAN EDITION. 
 
 BY 
 
 GISBERT KAPP, C.E., 
 
 MEMBER OF THE INSTITUTION OF CIVIL ENGINEERS ; 
 MEMBER OF THE INSTITUTION OF ELECTRICAL ENGINEERS. 
 
 WITH AN INTRODUCTION 
 
 BY 
 
 WILLIAM STANLEY, JR. 
 
 NEW YORK: 
 
 THE W. J. JOHNSTON COMPANY, LTD., 
 
 41 PARK Row (TIMES BUILDING). 
 
 1893. 
 
Reprinted from Professional Papers of the Corps of Royal 
 Engineers, by permission of the Committee of the R. E. Insti- 
 tute, and with the consent of the author. 
 
 GIFT OF 
 
 LIBRARY 
 
INTRODUCTION. 
 
 THE writings of Mr. Kapp have always interested 
 American engineers. In fact, whenever a new 
 branch of our science develops into attractive im- 
 portance and requires "treatment," we expect that 
 Mr. Kapp will place the matter before us in simple 
 terms and illustrate the points of interest by exam- 
 ples possessing practical importance. The follow- 
 ing pages accord with the previous writings of Mr. 
 Kapp in this respect. 
 
 Starting with the assumption that the reader is 
 acquainted with the behavior of steady currents in 
 circuits whose constants are readily obtainable, he 
 proceeds to explain the growth of a periodic cur- 
 rent, and in so doing beguiles the student into 
 
 865686 
 
4 INTRODUCTION. 
 
 mastering a few simple mathematical methods, a 
 knowledge of which is fundamentally necessary. 
 
 As the volume advances its scope becomes appar- 
 ent, for it treats in a simple and yet effective man- 
 ner of periodic currents in general, of the phase 
 relations of impressed and induced E. M. F's pos- 
 sible in simple circuits, of Alternators (somewhat 
 in detail), of the requirements of Central Stations 
 (briefly), of Alternating Current Motors, and finally 
 of Multiphase Currents. One does not expect ex- 
 haustive treatment of any one of these subjects 
 within the compass of a small book. 
 
 From an educational standpoint Chapters I. and 
 II. are of especial importance. These forty 
 pages might well be increased fourfold, for al- 
 though they contain a summary of the elemental 
 knowledge necessary for a correct understanding of 
 the principles operating alternating currents in 
 simple circuits, possessing resistance and self- 
 induction, they do not treat of capacity effects and 
 the problems incident thereto. In Chapter IV. we 
 have some of the formulae for calculating induced 
 
INTRODUCTION. 5 
 
 E. M. F.s (whether occurring in alternators or in 
 transformers) with constants for particular cases of 
 armature coils. Chapter V. is devoted to Machine 
 Construction, and points out the dependence of 
 efficiency on core wastes, giving a curve of the 
 relation of watts per ton of core metal lost by 
 hysteresis, to the induction density. Chapter VI. 
 is devoted to transformers and briefly points out 
 the necessity for careful design in this, the simplest 
 of alternate current apparatus. The chapters on 
 Central Stations are of interest, as they not only 
 describe a few English plants, but also give us the 
 author's criticisms on various distribution methods. 
 The chapters on Alternate Current Motors and Mul- 
 tiphase Currents complete the little volume. 
 
 There are one or two opinions expressed by the 
 author to which exceptions may be taken, notably 
 the statement on page 143 that the resultant field 
 produced by quarter-phase currents varies 40$, and 
 that the Dobrowolski-Tesla arrangement of three 
 phased currents produces a shifting field of more 
 constant value than the quarter-phased or two- 
 
6 INTRODUCTION. 
 
 phased arrangement. For a discussion of these 
 points the reader may consult The Electrical World, 
 vol. xix., p. 249, Kelly; vol. xx., p. 4, Dolivo- 
 Dobrowolski; p. 36, Kelly, Steinmetz; p. 114, C. 
 E. L. Brown. 
 
 In general, however, Mr. Kapp's statements are 
 clear, true, and convincing, and are of interest and 
 value to every American engineer. 
 
 WM. STANLEY, JR. 
 
CONTENTS. 
 
 CHAPTER 
 
 I. INTRODUCTORY, . . . 9 
 
 II. MEASUREMENT OF PRESSURE, CURRENT, AND POWER, . 37 
 
 APPENDICES, . . ,. ' ~^ 44 
 
 III. CONDITION OF MAXIMUM POWER, . . . . -49 
 
 APPENDIX, . * ^.." , . . 5& 
 
 IV. ALTERNATING CURRENT MACHINES, . . 5& 
 
 V. MECHANICAL CONSTRUCTION OF ALTERNATORS, . 73 
 
 VI. DESCRIPTION OF SOME ALTERNATORS, . . . . 82 
 
 VII. TRANSFORMERS, . . 
 
 VIII. CENTRAL STATIONS AND DISTRIBUTION OF ALTERNATING 
 
 CURRENTS, '. - ' I0 5 
 
 IX. EXAMPLES OF CENTRAL STATIONS, . , . XI 7 
 
 X. PARALLEL COUPLING OF ALTERNATORS, . . - .123 
 
 XI. ALTERNATING CURRENT MOTORS, I26 
 
 XII. SELF-STARTING MOTORS, I36 
 
 XIII. MULTIPHASE CURRENTS, . . I4 
 
Alternating Currents of Electricity: 
 
 THEIR 
 
 GENERATION, MEASUREMENT, DISTRIBUTION, 
 AND APPLICATION. 
 
 CHAPTER I. 
 
 INTRODUCTORY. 
 
 WHEN we think or speak of electric currents we 
 are accustomed to regard them in the light of ma- 
 terial currents, of something which flows along a 
 path formed by the conductor, and has, therefore, 
 a direction. We say that electricity flows along 
 the conductor or through the conductor from the 
 place of higher to that of lower potential; in the 
 same way that water will flow from , the higher to 
 the lower level through a pipe. Such a view is, of 
 course, purely conventional. As a matter of fact 
 we do not know whether it is the positive electric- 
 
 9 
 
10 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 ity that flows ip. t a : given direction, or the negative 
 electricity that^febws in the opposite direction, or 
 , l <ynbth^r ^bot& electricities flow simultaneously in 
 opposite directions, or whether there is any trans- 
 fer of electricity through the wire at all. Indeed, 
 according to modern views, there is merely transfer 
 of energy,. but not through the wire, the transfer 
 taking place throughout the space surrounding the 
 wire. To talk about an electric current flowing 
 through a wire may therefore be an unscientific 
 way of expressing our meaning, but it is a very 
 convenient way, and, therefore, generally adopted. 
 Now in adopting this conception of the flow of a 
 certain thing called electricity along a predescribed 
 path, we have also adopted the idea that this flow 
 takes place in a direction which is perfectly well 
 defined in each given case. We have no sense by 
 which we can directly perceive an electric current 
 or note its direction. It is true that if we get a 
 shock we are made aware that a current has passed 
 through us, but no number of shocks will help a 
 man in the slightest degree to an understanding of 
 the real nature of electric currents, nor enable him 
 to determine their direction. We must be content 
 
INTRODUCTORY. II 
 
 to study, not the currents themselves, but their 
 chemical, thermic, magnetic, and mechanical ef- 
 fects. Amongst other things we must also deter- 
 mine the direction of current by one or other of 
 these effects. For instance, we know that a wire 
 stretched north-south over a compass needle, and 
 carrying a current, will deflect the needle. If the 
 north-seeking end is deflected to the left or west- 
 ward, we know by Ampere's rule that the current 
 flows from south to north. Conversely, if the de- 
 flection is in the opposite sense, we conclude that 
 the current is from north to south. If the current 
 is obtained from a battery without the intervention 
 of any piece of moving apparatus, such as a revers- 
 ing key, we notice that the needle once deflected 
 remains in that position as long as the current 
 flows, and we naturally conclude that the current 
 flows continuously in the same direction, that it 
 is, in fact, a " continuous " current. Now suppose 
 you were to notice that the needle, after remaining 
 deflected to the left for a certain time, were to 
 swing over to the right and to remain deflected in 
 that position an equal time, then again swing to 
 the left, and so take alternately these two opposite 
 
12 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 positions, you would immediately conclude that 
 someone had put a reversing key into your circuit, 
 and was amusing himself by working it at regular 
 intervals. The behaviour of the needle would, in 
 fact, have shown you that you have no longer to 
 do with a continuous current, but that your current 
 has become an alternating current, that is, a cur- 
 rent which changes its direction periodically. You 
 will notice that I have assumed that the needle has 
 time to follow each impulse of the current, in other 
 words, that the periodic time of the current is large 
 in comparison with the time of oscillation of the 
 needle. Suppose, however, that I were to work the 
 reversing key so fast that the needle cannot fol- 
 low the different impulses ; in this case it will, of 
 course, remain in its north-south position, and will 
 have become useless as an instrument for the de- 
 tection of an alternating current. We require an 
 apparatus which will respond far more readily than 
 a sluggish compass needle to the different current 
 impulses which follow each other with great rapid- 
 ity. To get such an apparatus, let us take an iron 
 diaphragm, and hold near the centre of it a coil of 
 insulated wire forming part of the circuit, or bet- 
 
INTRODUCTORY. 13 
 
 ter still, an electromagnet with a laminated core; 
 why the core should be laminated I shall explain 
 later on. For the present it interests us to note 
 that the poles must be in such a position that at 
 least one of them may act on the diaphragm. 
 Thus a ring-shaped magnet which has no free 
 poles would not serve our purpose ; a straight bar 
 magnet, however, will do well. Now observe what 
 happens if an alternating current is sent through 
 the coil of this magnet. At the moment of press- 
 ing down the key to complete the circuit the bat- 
 tery begins to send a continuous current through 
 the coil and the core begins to get magnetized. 
 The magnetization grows from zero to a maximum, 
 and retains that value until the key is lifted again, 
 when it falls to zero. Now reverse the current and 
 go through the same process. It is obvious that at 
 each reversal of the current the magnetization must 
 pass through zero, and the end of the core which 
 is presented to the diaphragm will alternately be- 
 come a north and south pole. The diaphragm will, 
 therefore, be alternately attracted and released, or, 
 in other words, it will vibrate, and if the period of 
 vibration is quick enough, that is, if I manipu- 
 
14 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 late the reversing key very rapidly, a musical note 
 may be produced. Conversely, if I approach an 
 electromagnet to a diaphragm and find that the 
 latter is not permanently attracted, but is set in 
 vibration and emits a musical note, then I conclude 
 that the current which flows through the coil of the 
 electromagnet is an alternating current, and the 
 rapidity of the alternations, or, as it is called, 
 the "frequency" of the current, can be judged 
 from the pitch of the note. In explaining this 
 experiment I have, for the sake of simplicity, as- 
 sumed that the current is furnished by a battery, 
 and that its alternating character is produced by 
 means of a reversing key. This mechanism is, 
 however, not an essential part of the experiment or 
 of its explanation. The essential part is that the 
 current shall grow from zero to a maximum, and 
 diminish again to zero, then change its direction 
 and grow to a negative maximum, diminish to 
 zero, then become positive again, and so on. Such 
 a current is produced by a certain class of electric 
 machines called "alternators," which will occupy 
 us a good deal during this lecture. But before en- 
 tering into this subject I wish to show you experi- 
 
INTRODUCTORY. 15 
 
 mentally the fact that an alternating current can 
 produce these oscillating or wave-like magnetic 
 effects which I described a moment ago. The ap- 
 paratus I shall use in my illustrations is extremely 
 simple. I have here a small electromagnet of the 
 kind used in connecting arc lamps to alternating 
 current circuits, and which is technically termed a 
 " choking coil." For a diaphragm I use the bottom 
 of an ordinary biscuit tin, and you will observe that 
 when I approach one end of the choking coil to the 
 biscuit tin there is emitted a sound which can be 
 heard all over the room. The sound is not exactly 
 a clear musical note, because, as might have been 
 expected in a rough-and-ready apparatus of this 
 kind, the elasticity of the diaphragm is by no 
 means perfect. But such as the sound is, it serves 
 quite well to show that the diaphragm is set vibrat- 
 ing by the current, and, in fact, every telephone 
 receiver exemplifies the same action. 
 
 The study of alternating currents is greatly facil- 
 itated by a rational and simple manner of repre- 
 senting them graphically. There are various ways 
 in which we can so represent not only alternating 
 currents, but any quantity which varies periodi- 
 
10 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 cally. The most obvious way of representing an 
 alternating current is by drawing a curve, the two 
 co-ordinates of which represent time and the in- 
 stantaneous current strength. In Fig. i the time 
 
 FIG. i. 
 
 is measured on the horizontal, and the current 
 strength on the vertical. We thus obtain a wavy 
 line which cuts at regular intervals through the 
 axis of abscissae. These are the points of reversal 
 when the current strength is maximum, positive 
 where the line lies above, and negative where it 
 lies below the axis. The exact shape of the curve 
 depends on the construction of the machine which 
 produces the alternating current; but I may at 
 once say that in nearly all the theoretical investi- 
 gations of alternating currents it is assumed that 
 the curve follows, or rather represents, a sine func- 
 
INTRODUCTORY. 1 7 
 
 tion, and that this assumption is sufficiently near 
 the truth for all practical purposes. All of you 
 know, of course, what a sinusoidal curve is, and I 
 need, therefore, not explain it at length. As, how- 
 ever, the way of plotting a sinusoidal curve brings 
 me to a second method of representing an alternat- 
 ing current graphically, I must say a few words 
 about it. Imagine yourself standing some distance 
 in front of a steam engine in a line with the axis of 
 the cylinder, and looking at the crank pin. The 
 latter will then appear to be moving up and down, 
 making equal excursions to both sides of the cen- 
 tre of the crank shaft. You will, in fact, see the 
 projection of the crank on a vertical, and the length 
 of this projection at any instant is equal to the 
 length of the crank multiplied with the sine of the 
 angle which the crank makes at that instant with 
 the horizontal. The angle is, of course, the pro- 
 duct of the angular velocity and the time; and 
 since the angular velocity is constant, you will also 
 obtain a sine curve by plotting the time on the hori- 
 zontal and the projection of the crank on the verti- 
 cal. The curve I in Fig. i has been so obtained. 
 We may, however, save ourselves the trouble of 
 
i8 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 plotting this curve, for we can represent the alter- 
 nating current more directly by the projection on 
 the vertical of a line OI (Fig. 2) revolving with a 
 constant angular speed round the fixed centre O. 
 
 The length of OI represents to any convenient 
 scale the maximum value of the current, or the 
 crest of the current wave, and its projection repre- 
 sents its instantaneous value. You see that for 
 
 FIG. 2. 
 
 half a revolution this value is positive, and for the 
 other half of the revolution it is negative. 
 
 In this diagram, which is called a "clock dia- 
 gram," we must therefore make a projection in 
 order to find the instantaneous value of the current. 
 This is less laborious than the plotting of a sine 
 curve, but it is possible to represent the current in 
 
INTRODUCTORY. . 19 
 
 a still more simple way. Those of you who are 
 familiar with Zeuner's valve diagram will immedi- 
 ately see how this can be done. Instead of draw- 
 ing the circle round O as centre, we draw it passing 
 through O. The diameter of this circle (Fig. 3) 
 
 O 
 
 FIG. 3. 
 
 represents to any convenient scale the maximum 
 value of the current. Then the instantaneous cur- 
 rent is given directly by the length of the revolv- 
 ing line between O and the circle. To obtain the 
 negative values of the current, we reproduce the 
 circle on the opposite side; this in the figure is 
 shown dotted. 
 
 To illustrate the use of any of these graphic 
 methods of representing alternating currents, let 
 us suppose that we have to solve the following 
 problem : We have an iron core wound with two 
 independent coils, each carrying an alternating 
 
20 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 current. The two currents shall have the same 
 frequency, that is to say, the time which elapses 
 between two succeeding positive maxima or nega- 
 tive maxima shall be the same for both currents, 
 but the maxima in the two currents shall not occur 
 at the same moment. In other words, the phase 
 of one current shall lag behind that of the other, 
 just as in a two-cylinder steam engine one crank 
 lags behind the other. Now the problem we have 
 to solve is : what will be the magnetization of the 
 core at any instant? To find this we must of 
 course know the instantaneous value of the excit- 
 ing power, or the ampere turns resulting from the 
 action of both currents combined ; we must, in fact, 
 find what resultant current acting alone will have 
 the same effect as the two given currents acting 
 together. Let, in Fig. i, the curves I and II rep- 
 resent the two currents, or better still the ampere 
 turns of these currents, then the ampere turns of 
 the resultant current are found by plotting the 
 algebraical sum of the ordinates. Thus we obtain 
 curve III. It is self-evident, and needs, therefore, 
 no elaborate proof, that this curve can also be 
 obtained from Fig. 2 if in that figure we draw a 
 
INTRODUCTORY. 
 
 21 
 
 parallelogram of currents (precisely in the same 
 way as in mechanics we draw a parallelogram of 
 forces), and use the resultant O III to plot the sine 
 curve. You see that we can combine currents in the 
 same way as mechanical forces. I have proved this 
 for the case that the currents flow in two independ- 
 ent coils, but a glance at Fig. 4 will show you that it 
 
 D 
 
 FIG. 4. 
 
 also holds good if the two currents are sent through 
 the same coil. Here we have two machines, Ai 
 and A2, mechanically coupled, and therefore pro- 
 ducing currents of the same frequency. These 
 currents, I and II, flow into one circuit containing 
 a coil C. It is evident that in the circuit BCD 
 there flows only one current, which is the algebraic 
 sum of I and II. 
 
 Now let us change the arrangement to that 
 
22 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 shown in Fig. 5. Here we have to do with only a 
 single current, for both machines and coil C are 
 coupled in series ; but we have to do with two elec- 
 
 FIG. 5. 
 
 tromotive forces, namely, those of the machines. 
 I assume that the coil C in itself has no electromo- 
 tive force. In this case also it is self-evident that 
 the current which will be forced through C is due 
 to the algebraic sum of the two electromotive 
 forces, and that all I have said about the determi- 
 nation of the resultant current is directly applicable 
 to that of the resultant electromotive force. In 
 other words, we may use any of the three graphic 
 methods of representing currents also for represent- 
 ing electromotive forces. 
 
 These graphic methods of investigation, and es- 
 pecially those based on the clock diagram, are so 
 
INTRODUCTORY. 23 
 
 useful and so simple that I shall employ them fre- 
 quently in the course of these lectures in preference 
 to analytical methods, and it is therefore expedient 
 to familiarize you at the outset with the clock dia- 
 gram. For this purpose I select, by way of exam- 
 ple, a case which is very frequently met with, and 
 which is represented by Fig. 6. Lest you should 
 
 FIG. 6. 
 
 think that this case has merely theoretical impor- 
 tance, I may at once say that a certain deduction 
 which flows naturally from its consideration is of 
 great practical importance in motors driven by 
 multiphase currents, since on it depends the start- 
 ing torque of such motors. If you compare Figs. 
 5 and 6 you will find that they only differ in this : 
 that an electromagnet S has been substituted for the 
 machine A2. The circuit represented in Fig. 6 
 
24 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 consists of a machine A, giving an alternating elec- 
 tromotive force, a resistance B, consisting of a 
 bank of glow lamps, and an electromagnet S. This 
 electromagnet has a property which is technically 
 called "self-induction/' and, before going further, 
 I must briefly explain to you what is meant by 
 self-induction. You know that an electromotive 
 force is set up in a wire whenever the wire cuts 
 across magnetic lines of force. Since the wire 
 must necessarily form part of a closed circuit (for 
 if the circuit were not closed there could be no cur- 
 rent), the cutting of lines must be accompanied by 
 an increase or decrease in the number of lines or 
 total induction threading through the circuit, and 
 we may therefore also say that whenever the total 
 induction through a circuit changes, there is an 
 electromotive force set up in the circuit which is 
 the greater the more rapid the change. In fact, 
 the rate of change, that is, number of lines added 
 or withdrawn per second, multiplied with the num- 
 ber of turns of wire, gives the electromotive force 
 set up in the coil. Going back to Fig. i, we have 
 seen that the curve I represents the current as a 
 function of the time. Suppose there is no other 
 
INTRODUCTORY. 25 
 
 coil wound over the core, then the ordinates of the 
 curve represent to a suitable scale also the exciting 
 power on the core, and it is obvious that the mag- 
 netization of the core, or, to speak correctly, the 
 total induction passing through it, will change 
 more or less in accordance with the curve I. If 
 the permeability were constant, the induction would 
 be strictly proportional to the exciting power, and 
 by the selection of a suitable scale the curve repre- 
 senting induction could be made to coincide with 
 the current curve I. Now for low values of the 
 induction, say between zero and 3,000 or 4,000 
 lines per square centimetre, we may regard the 
 permeability of soft, well-annealed wrought-iron as 
 approximately constant, and if we do not press the 
 induction beyond this point, we may without any 
 great error assume that the current curve I also 
 represents the total induction through the core. 
 For the points where the current passes through 
 zero, and which momentarily interest us the most, 
 the assumption is, of course, quite correct. But if 
 the curve I represents the total induction, then the 
 geometrical tangent to it at any point represents 
 the change of induction in unit time, or, as I said 
 
26 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 just now, the rate of change of induction at the par- 
 ticular moment represented by the point on the 
 curve. Thus, reading off the time on the horizon- 
 tal axis, we can, by drawing the tangent to the 
 current curve at the corresponding points, find the 
 rate at which the total induction changes at each 
 moment. I said just now that the rate of change, 
 multiplied with the number of turns in the coil, 
 gives the electromotive force generated at any in- 
 stant in the coil, and it will now be clear to you 
 that this electromotive force, which we call the 
 "electromotive force of self-induction," must be 
 proportional to the geometrical tangent to the cur- 
 rent curve. The steeper this line, the greater is 
 the electromotive force. Thus you see that when 
 the current is either a positive or negative maxi- 
 mum, the tangent is horizontal, and therefore at 
 those moments the electromotive force of self- 
 induction is zero. On either side of maximum cur- 
 rent it has a definite value, but this value is posi- 
 tive on one side and negative on the other side of 
 maximum current, since the slope of the tangent 
 changes from upward to downward when passing 
 this point. Where the current curve intersects the 
 
INTRODUCTORY. 27 
 
 horizontal axis, the slope of the tangent is evi- 
 dently greatest, and we therefore see that the elec- 
 tromotive force of self-induction is a maximum 
 when the current passes through zero, and it is 
 itself zero when the current is a maximum. This 
 then is, in general terms, the relation between the 
 current curve and the curve giving the electromo- 
 tive force of self-induction. It remains yet to de- 
 termine the exact nature of the latter. We have 
 seen that the ordinates of the electromotive force 
 curve are proportional to the geometric tangent 
 drawn to the current curve. Now how do we draw 
 the tangent to the point A for instance ? We draw 
 a straight line through this point, and one very 
 near it, on the current curve. To speak correctly, 
 I should say infinitely near it. At this infinitely 
 near point the current will have increased from i to 
 i -f di, and the time from t to t -f- dt. The ratio of 
 di to dt is therefore equal to the geometrical tangent 
 at A. But this ratio is the differential quotient of 
 the current in respect to time, and we thus find 
 that the curve giving the electromotive force of 
 self-induction is the first differential of the current 
 curve. 
 
28 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 I have up to the present entirely avoided the use 
 of mathematics, but now it becomes necessary to 
 introduce a few simple formulae. Going back to 
 Fig. 2, suppose that the radius OI, the projection 
 of which gives the instantaneous value of the cur- 
 rent, makes n complete revolutions per second. Its 
 angular speed is then o> = 2itn, and its angular 
 position at the time t is a = W, counting the time 
 from the moment that the radius is horizontal. 
 Let I be the length of the radius, which also repre- 
 sents the maximum of the current strength, or crest 
 of the wave, then the instantaneous value of the 
 current at the time / is 
 
 / = I sin tot (i), 
 
 and the electromotive force of self-induction at that 
 moment is 
 
 e a Lwl cos wt (2), 
 
 L being a coefficient which depends on the perme- 
 ability of the core, the magnetic reluctance of the 
 whole magnetic circuit, and the number of turns in 
 the coil. At the time when the current passes 
 through zero we get the maximum value of the 
 electromotive force, which is 
 
 E. = LI (3), 
 
INTRODUCTORY. 29 
 
 and we can also write the equation for the instan- 
 taneous value of the electromotive force of self- 
 induction in the form 
 
 e a = E 8 cos w/, 
 or 
 
 e a = - E 8 sin ( ut - - ) (4), 
 
 from which you will see that this value may also be 
 graphically represented by a sine curve, but lag- 
 ging behind the current curve by 90 degrees. To 
 obtain the electromotive force curve, which is 
 shown dotted in Fig. 7, we must therefore imagine 
 
 a crank OE 8 rigidly attached to the crank OI (Fig. 
 8) at an angle of 90 degrees, and we must plot the 
 projections of this second crank on the vertical as 
 ordinates in Fig. 7. A study of this diagram (Fig. 
 7) will help you materially to an understanding of 
 
30 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 the phenomena of self-induction. As time pro- 
 gresses, from left to right you see that at first the 
 current is positive and increases. But self-induc- 
 tion opposes the increase, and its electromotive 
 force is therefore negative. The dotted curve is 
 below the axis. This opposition becomes fainter 
 as the current approaches its maximum value, since 
 the rate of change of the induction becomes less 
 and less. When the current has reached its posi- 
 tive maximum, the rate of change has become zero, 
 and the opposition of self-induction has vanished. 
 The dotted curve passes through the axis. A 
 moment later, the current is still positive, but is 
 now decreasing. Again self-induction opposes the 
 change ; its tendency is to keep the current up at 
 its maximum strength. The electromotive force 
 of self-induction tries to push on the current ; it is 
 positive, and the dotted curve rises above the 
 horizontal. This tendency to push on the current 
 increases until the current has become zero, and 
 begins to flow in the reverse direction. The nega- 
 tive current is now opposed by the positive electro- 
 motive force of self-induction, but the opposition 
 grows fainter as the current grows stronger, and so 
 
INTRODUCTORY. 3! 
 
 the see-saw of pushing on and checking back the 
 current is kept up. 
 
 The point which interests us most is what must 
 be the electromotive force given by the machine A, 
 in Fig. 6, to produce the current shown by the 
 curve in Fig. 7. To simplify our investigation we 
 shall assume that the ohmic resistance of the coil 
 S and machine A is negligible in comparison with 
 the ohmic resistance of the bank of lamps B, or 
 that it is included therein ; also that the only part 
 of the circuit having self-induction is the coil S. 
 Then it is immediately obvious that a voltmeter 
 placed across the terminals of this coil will indicate 
 the electromotive force of self-induction, and a 
 voltmeter placed across the lamps will indicate the 
 electromotive force corresponding to the product of 
 current and the resistance of the bank of lamps. 
 But it is not immediately obvious that the sum of 
 these two readings will give us the electromotive 
 force as measured by a voltmeter across the ter- 
 minals of the machine, and I will show you pres- 
 ently, by theory and by experiment, that this is 
 not the case. Assuming the resistance of the bank 
 of lamps to be a fixed quantity r, it is clear that the 
 
32 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 instantaneous lamp volts equal the product r X /, 
 and that they can be represented by a sine curve e r 
 of the same phase as the current curve. In Fig. 8 
 
 FIG. 8. 
 
 the radius of maximum lamp volts OE r must there- 
 fore coincide with the radius of maximum current 
 OI. The radius of maximum volts of self-induc- 
 tion is OE 8 , and this, as I have already shown, lags 
 behind the current radius by 90 degrees. To find 
 the machine volts at any instant, we must combine 
 the curves e r and e s , but remember to take the lat- 
 ter with the opposite sign, for the self-induction 
 opposes the current. This gives us the curve e in 
 Fig. 7. To find the machine volts from Fig. 8 we 
 have to draw a radius of such length and position 
 that it may be regarded as the resultant of the lamp 
 
INTRODUCTORY, 33 
 
 volts E r , and an electromotive force diametrically 
 opposed to that of self-induction. We prolong, 
 therefore, the line E 8 O beyond O, and make OE/ = 
 OE 8 . Completing the parallelogram, we thus find 
 the resultant OE, which gives us the maximum 
 machine volts, or "impressed electromotive force." 
 The diagram (Fig. 8) is very instructive. In the 
 first place, it enables us at once to find an expres- 
 sion for the angle of lag <f>. You see that the tan- 
 gent of this angle is given by the ratio of the elec- 
 tromotive force of self-induction to that usefully 
 expended over the lamps. I must here remark 
 that when I speak of electromotive force and cur- 
 rent I mean, for the present, always their maxi- 
 mum values. Retaining the notation previously 
 employed, we have, therefore 
 
 tan <p = 
 
 rl ' 
 tan ? = -~ (5). 
 
 
 Next we can find an expression for the current as 
 a function of the impressed electromotive force and 
 the constants of the circuit. Since the triangle 
 OE.E is rectangular, we have 
 3 
 
34 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 E 3 = E r a + E 8 a , 
 
 or, with our previous notation 
 E 2 = r 2 P + L 2 /T, 
 
 E 
 
 (s-). 
 
 If we had to do with a continuous current, its equa- 
 
 p* 
 tion would be I = Since the term under the 
 
 r 
 
 square root must, under all circumstances, be larger 
 than unity, the current produced by an alternating 
 electromotive force must always be smaller than the 
 current which an equal but continuous electromo- 
 tive force would produce in the same circuit. 
 
 The term ^/r" -\- L/V is called the " impedance " 
 of the circuit, and Lw its "inductance." As an aid 
 to memory, I reproduce in Fig. 9 Dr. Fleming's 
 diagram, in which these terms are recorded. You 
 have seen that Ohm's law is not applicable to alter- 
 nate current circuits, but if we substitute the im- 
 pedance for the ohmic resistance, this law becomes 
 applicable. 
 
INTRODUCTORY. 35 
 
 I have yet to explain the meaning of the quantity 
 which we called L, and which we introduced in 
 order to take account of the number of turns in the 
 coil, and other properties of the circuit. Of course, 
 most of you will long ago have recognized in this 
 L the usual coefficient of self-induction, but, for 
 
 the sake of completeness, I must prove this. There 
 are various definitions for the coefficient of self- 
 induction, but the following will serve my pur- 
 pose : " The coefficient of self-induction is the ratio 
 between the counter electromotive force in any cir- 
 cuit and the time rate of variation of the current 
 producing it." * In symbols 
 
 Sumpner, The Variation of Coefficients of Induction. Phil. 
 ..June, 1887, p. 453. 
 
36 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 and substituting i from equation (i), we have 
 e 8 = Latl cos iot (2), 
 
 which is identical with equation (2) , and shows that 
 the L we then introduced is indeed the coefficient 
 of self-induction. 
 
CHAPTER II. 
 
 MEASUREMENT OF PRESSURE, CURRENT, AND 
 POWER. 
 
 When showing you the last experiment, I had 
 occasion to use a voltmeter, and the question we 
 have now to consider is what is the relation be- 
 tween the reading of the instrument and the maxi- 
 mum electromotive force in the circuit. That the 
 reading must be less than the true maximum is 
 obvious, but less by how much? 
 
 To answer this question we may use the analyti- 
 cal or the geometric method. I give the former in 
 Appendix I. of this chapter and the latter, which is 
 due to Mr. Blakesley, in Fig. 10. A Cardew volt- 
 meter measures not directly volts, but simply the 
 amount of heat developed in its wire per unit of time. 
 The rate at which heat is developed at any instant 
 is the product of the instantaneous current and the 
 instantaneous volts; but as the current passing 
 
 37 
 
38 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 through the wire is proportional to the volts, the 
 rate at which heat is developed is proportional to 
 the square of the instantaneous volts, that is, to O e 
 squared in Fig. 10, if by OE we represent the max- 
 imum volts. Now, to find the general effect of a 
 large number of succeeding instantaneous voltages 
 on the voltmeter, we have to draw the projections 
 O e of OE for a large number of positions. Let us 
 take these positions in pairs, such as OE and OE', 
 with an angular interval of 90 degrees between 
 
 FIG. 10. 
 
 them. It is evident that for such pair the sum of 
 the squares of the projections is equal to the square 
 of the maximum voltage, and that the mean vol- 
 tage is y 2 E a . This is independent of the actual 
 position of each pair, and is, therefore, the mean 
 value of all the possible pairs. The volts read on 
 
MEASUREMENT OF PRESSURE, CURRENT, AND POWER. 39 
 
 the Cardew (or any other instrument, the action of 
 which depends on the square of the voltage) must 
 therefore be multiplied by the square root of 2 in 
 order to get the maximum volts ; or in symbols, if 
 by e we represent the volts shown by the instru- 
 ment, and by E the maximum volts 
 
 E 
 * = ~r .................... (7)< 
 
 A/2 
 
 At the Paris Congress, in 1889, it has been decided 
 to call e the " effective " volts. 
 
 The same reasoning which I have here applied 
 to the measurement of pressure can also be applied 
 to the measurement of current, provided that the 
 measuring instrument is of a kind in which the 
 movable part is subjected to a force varying as 
 the square of the current. Thus a Siemens' dyna- 
 mometer, a Thomson ampere-balance, and similar 
 instruments, will indicate the " effective current " 
 
 '=4= ................... () 
 
 A/2 
 
 It is important to osberve that this is not the same 
 thing as the mean or average current. To under- 
 stand the distinction, let us first settle what quan- 
 
40 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 tity we call the mean current. Imagine an alter- 
 nating current commutated each time it passes 
 through zero, and let the unidirected but pulsating 
 current thus obtained pass through an electrolytic 
 apparatus, say, for instance, a copper voltmeter. 
 The weight of copper thrown down in unit time is 
 a measure of the " mean strength " of our pulsating 
 current. The mean current strength thus defined 
 is about 90 per cent, of the effective current 
 strength, so that to get the true mean current we 
 must multiply the reading of the Siemens' dyna- 
 mometer by f 90. The proof for this is given in Ap- 
 pendix II. of this chapter. 
 
 We have seen that the measurement of pressure 
 and current is a very simple matter ; but the meas- 
 urement of power, to which I must next draw your 
 attention, is not quite so simple as with continuous 
 currents. You know that if we wish to determine 
 the power given to a circuit by a continuous cur- 
 rent we have merely to observe the amperes and 
 the volts, and multiply them to get the watts. If 
 we divide the watts by 746, we get the result in 
 horse-power. With alternating currents this is not 
 quite so simple, and if we were to compute the 
 
MEASUREMENT OF PRESSURE, CURRENT, AND POWER. 41 
 
 power in this manner, our results would be gen- 
 erally too large, and never too small. The reason, 
 of course, is that the instant of maximum amperes 
 does generally not coincide with the instant of 
 maximum volts. To get the true power we must 
 integrate the product of the instantaneous volts 
 and amperes over a complete cycle, and divide by 
 the time required to perform the complete cycle. 
 The matter is treated analytically in Appendix III. 
 of this chapter, while here I treat it graphically, 
 
 FIG. ii. 
 
 using again Mr. Blakesley's method. In Fig. 1 1 
 OE and OI represent electromotive force and cur- 
 rent at any given moment, OE' and OI' their 
 position a quarter period later. The current lags 
 behind the electromotive force by the angle <?. 
 
42 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 Using small letters for the projections of E and I 
 on the vertical, the mean value of the power for 
 the two positions is obviously ei -\- e'i' -f- 2. 
 
 From the diagram, the following equations are 
 obvious : 
 
 ei = EI sin a sin /?. 
 e'i' = EI cos a cos /?. 
 
 Combining these we find the mean power 
 
 py 
 w = -'- (cos a cos /9 -j- sin a sin ). 
 
 EI 
 
 W = COS (a - /3). 
 
 EI 
 a/ = cos <p (9), 
 
 and this is the same for every pair the position of 
 which differs by 90 degrees. It is, therefore, the 
 true equivalent power. 
 
 p T 
 
 Since e = and / = , we have also 
 
 V2 V2 
 
 w = ei cos <p (10), 
 
 where e and i are the volt and ampere readings, as 
 obtained by our usual instruments. 
 
 You see we have first to determine the " appar- 
 
MEASUREMENT OF PRESSURE, CURRENT, AND POWER. 43 
 
 ent " watts as if we had to do with a continuous 
 current, and then to get the true watts we must 
 multiply by the cosine of the angle of lag. It is, 
 however, not always easy to determine the angle of 
 lag, and to avoid the labour and possible errors of 
 such a determination, various instruments have 
 been invented for the direct measurement of power, 
 which are called wattmeters. The best-known 
 form of wattmeter is constructed similarly to a Sie- 
 mens' dynamometer. The fixed coil, containing a 
 few turns of thick wire, is connected in series with 
 the main circuit, and the movable or suspended 
 coil, containing many turns of fine wire, is con- 
 nected as a shunt to the main circuit. A non- 
 inductive resistance is put in circuit with the mov- 
 able coil to reduce the self-induction of the shunt 
 circuit. (For theory of wattmeter, and corrections 
 to be applied, see Appendix IV., following.) 
 
44 ALTERNATING CURRENTS OF ELECTRICITY, 
 
 APPENDIX I. 
 
 Voltmeter absorbs in time T the energy 
 
 /"V 
 -dt. 
 r 
 
 
 sin 2 (a>t) d ( 
 r Q \ / \. 
 
 i?! 
 
 a) r 
 
 2 r 
 
 And since 
 
 w = 
 r 
 
 E 
 = 
 
MEASUREMENT OF PRESSURE, CURRENT, AND POWER. 45 
 
 APPENDIX II. 
 
 Mean current, as determined by electrolysis, is cou- 
 lombs divided by time 
 
 T 
 
 Ut =. 7T. 
 
 2 
 
 Mean current 
 
 C = 7^- / * i. 
 
 t = I sin (/) A 
 
 2 
 
 The effective current is 
 
 I 
 
46 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 therefore 
 
 or very nearly 
 
 c = 0*9 /. 
 
 APPENDIX III. 
 
 Work done by current during one cycle is wT, and 
 per second it is 
 
 i /T 
 
 = = I etdt. 
 1 /o 
 
 IE / 27 r , 
 w = ;7p / Sin a sin (a 4- y) da. 
 
 W ~~ ~27tJo 27r OS ^ S ^ n ' "^ + S ^ n ^ S ^ n a COS a ^ a - 
 
 lEr / i x /T 
 
 = ilT L COS ^ vl ~ ~ sm a cos a j-f sin ^ I -^ sin 8 a 
 
 IE r -i IE 
 
 w == r I cos ^ or w = cos > or / = /V cos <P 
 
 27T |_ 2 
 
MEASUREMENT OF PRESSURE, CURRENT, AND POWER. 47 
 
 APPENDIX IV. 
 
 Let <f> be the angle of lag in the circuit, the power 
 given to which is to be measured, and let d be the angle 
 of lag in the fine wire coil of the wattmeter, due to its 
 self-induction. Let I be the current through the thick 
 wire coil, and / the current through the fine wire coil, 
 then the power indicated by the wattmeter, if the cur- 
 rents were steady, would be Kri I where K is the co- 
 efficient of the instrument, and r the resistance of the 
 fine wire coil. The true watts of the alternating cur- 
 rent of E volts are 
 
 W = IE cos <p. 
 The indicated watts are 
 
 W = K (Reading). 
 
 W = K>/ cos (<p - d) I = KE cos d cos (<f>- 3) I. 
 
 Therefore, to get true watts, we must multiply the 
 watts indicated by 
 
 cos <f> 
 
 cos d cos > - 8 
 
48 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 which expression can also be written in the form 
 
 i + tanM 
 i + tan 3 tan <p ' 
 
 If the wattmeter has no self-induction, d = o, and no 
 correction is required. Again, if the self-induction of 
 the wattmeter is equal to that of the circuit to be 
 measured 
 
 , i + tan 8 d 
 
 tan d =: tan 0, and ; ' = i. 
 
 i -f tan d tan <p 
 
 In this case also no correction is required. In all 
 other cases the corrections given in this formula must 
 be applied. 
 
CHAPTER III. 
 
 CONDITION OF MAXIMUM POWER. 
 
 It is important to investigate the conditions 
 under which we can obtain a maximum of power 
 in a given circuit. This is the deduction of which 
 I have spoken a little while ago as flowing natu- 
 rally from the investigation of the case represented 
 by Fig. 6. Here we have an alternating current 
 machine, a self-induction, and a bank of lamps. 
 The self-induction we cannot diminish, and the 
 machine volts we cannot increase. How must we 
 manage our lamps to get a maximum of power into 
 them, and therefore to get a maximum of light out 
 of them? Without entering into any lengthy 
 mathematical investigation, you can see at once 
 that the ohmic resistance of the bank of lamps will 
 have a great deal to do with the amount of power 
 usefully expended. If the resistance is very high, 
 the lamps will get very nearly the whole of the 
 4 49 
 
50 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 machine volts, but then the current will be small. 
 If, on the other hand, we lower the resistance too 
 much in our desire to get a large current, we shall 
 have to sacrifice nearly the whole of the pressure, 
 since the self-induction, which now is fed by a 
 large current, will choke back most of the available 
 voltage. You see that either too little or too much" 
 resistance is bad, and we have to find that resist- 
 ance which will give us the best effect. This will 
 be the case when the volts over the lamps equal 
 the volts over the self-induction, either being about 
 70 per cent, of the machine volts. I give the ana- 
 lytical proof in an appendix to this chapter and the 
 geometric proof by means of the clock diagram 
 (Fig. 12). Let, in this figure, the circle represent 
 the given machine volts, and let OE 8 be the volts 
 of self-induction corresponding to the current OI. 
 Then the tangent of the angle at I is obviously equal 
 to Lw (by equation (3)). The power given to the 
 lamps is (by equation (9)) w = J^ IE cos ?, that is, 
 the projection of the volt radius on the current 
 radius, multiplied by the current, and divided by 2. 
 But the projection of the machine volts OE gives 
 us the lamp volts OE r and the current is proper- 
 
CONDITION OF MAXIMUM POWER. 51 
 
 tional to the volts of self-induction (see triangle 
 OIE S ), so that we can also say the power is propor- 
 tional to the product of lamp volts and self-induc- 
 tion volts (that is, to the shaded area in Fig. 12), 
 
 FIG. 12. 
 
 and our problem can also be stated in these terms : 
 Find that position of OE for which the shaded 
 area becomes a maximum. Obviously this will be 
 the case when the line OE forms an angle of 45 de- 
 grees with the horizontal; in other words, when 
 the current lags by one-eighth of a period behind 
 the impressed electromotive force, and when the 
 volts measured over the self-induction equal the 
 lamp volts. This condition will be fulfilled when 
 the resistance of the bank of lamps is 
 
 r = 
 
52 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 In order to simplify the explanation, I have as- 
 sumed that in Fig. 6 the resistance, the self-induc- 
 tion, and the seat or source of electromotive force, 
 are different and distinct parts of the circuit. This 
 was, however, not essential. We could, for in- 
 stance, assume the self-induction to be part and 
 parcel of the machine, or even of the bank of 
 lamps, and yet our result would have been the 
 same. Nay, more. Suppose we take away the 
 lamps and put in their place a series wound dynamo 
 with well-laminated field magnets. Whichever way 
 the current is sent through the machine it will al- 
 ways revolve in the same direction, and the alter- 
 nating current must, therefore, set it in motion. 
 Now, imagine the period of the current very long, 
 in fact, so long that the electromotive force of self- 
 induction of the magnet coils and armature may be 
 neglected. Then the only force opposing the cur- 
 rent in its flow through the armature is the counter 
 electromotive force developed by the latter, which, 
 at constant speed of rotation, is proportional to the 
 field strength. Now, if we do not excite the mag- 
 nets strongly (and on account of hysteresis and 
 other losses it is advisable to work with a low in- 
 
CONDITION OF MAXIMUM POWER. 53 
 
 duction) , we may consider the field strength to be 
 proportional to the current, so that the only force 
 which opposes the current will in this case be at all 
 times proportional to the current strength. It will, 
 in fact, be the same kind of opposition as is pro- 
 duced by ohmic resistance, but with this difference, 
 that, instead of converting the electric power into 
 heat in the lamps, we convert it into mechanical 
 power, which may be taken off the spindle of the 
 motor. So far the motor, although supplied with 
 an alternating current of very long period, will 
 work exactly as if it were joined to a continuous 
 current circuit. But now let us increase the fre- 
 quency of a current, that is to say, let us shorten 
 the period and have more and more current waves 
 per second. This will add to the counter electro- 
 motive force of the motor (which is useful, because 
 accompanied by the giving out of mechanical 
 power) another electromotive force which is en- 
 tirely useless, namely, the electromotive force of 
 self-induction. This must considerably decrease 
 the power obtainable from the motor, first, because 
 the current strength has been decreased by its 
 action ; and, secondly, because with the electromo- 
 
54 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 live force of self-induction now having become a 
 large quantity, a considerable lag of the current 
 behind the machine volts must take place. A few 
 years ago I experimented with a motor of this 
 kind, and found that the power obtainable from the 
 machine when coupled to an alternating current 
 circuit was only about one-sixth its normal power 
 on a continuous current circuit. In this motor the 
 self-induction was far too large as compared with 
 its counter electromotive force. By our rule, the 
 electromotive force of self-induction should have 
 been equal to the counter electromotive force. 
 In this case the motor would give about 70 per 
 cent, of the power it could develop with a contin- 
 uous current. If it were possible to make motors 
 which fulfill the condition I have explained, it 
 would be a very easy and practical solution of the 
 problem how to make the existing lighting stations 
 which supply alternating current available for the 
 distribution of power; but I doubt very much the 
 possibility . of this solution of the problem. The 
 self-induction of such a motor must always be enor- 
 mously high, but a way in which we can at least 
 approach the best condition of working is by lower- 
 
CONDITION OF MAXIMUM POWER: 55 
 
 ing the frequency and increasing the rotary speed 
 of the motor. I have devoted some time to this 
 method of working alternate current motors, be- 
 cause it has already acquired practical importance, 
 not indeed in the regular working of these ma- 
 chines, but in the starting of them. The Ganz 
 motor is started without a load, as if it were an 
 ordinary continuous current machine, and after it 
 has acquired a certain speed it suddenly begins to 
 work as an alternating current machine. When in 
 this condition the load can be thrown on, and the 
 machine will eVen stand a certain amount of ex- 
 cess load. 
 
56 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 APPENDIX. 
 
 The power is w = ^ IE cos y, or substituting for cos 
 the value and for I the value 
 
 V s <* a L a Vr* 
 
 we have also 
 
 w = w 
 
 ^ i" 
 
 r 
 
 The variable is r, and to find for which value of r 
 the power w becomes a maximum, we resolve the 
 
 equation = o, and find r = wL, and the maximum 
 power 
 
 i E ' 
 
 w = \ 
 
 fc r 
 
 or, if by e we represent the effective voltage, such as 
 would be indicated on a Cardew voltmeter, we have 
 
 also r 
 
 e* 
 
 w = 
 
CONDITION OF MAXIMUM POWER. 57 
 
 The analogy with the well-known rule for maxi- 
 mum power from a source of continuous current is re- 
 markable. According to this rule, maximum power 
 will be developed in the external circuit, if its resist- 
 ance is equal to the resistance of the battery or machine 
 which gives the current. If E is the electromotive 
 force of the battery, and r its internal resistance, the 
 maximum power which is obtainable in an external 
 circuit of equal resistance is 
 
 iE 2 
 
 w = > 
 
 4 r 
 
 precisely the same expression as obtained above for al- 
 ternating currents. 
 
CHAPTER IV. 
 
 ALTERNATING CURRENT MACHINES. 
 
 When discussing the electromotive force of self- 
 induction, we have seen that this is produced by the 
 change in the total induction passing through the 
 electric circuit, or, which comes to the same thing, 
 by the cutting of wires across magnetic lines of 
 force. In a choking coil the magnetization changes, 
 and we thus obtain an electromotive force without 
 the necessity of moving the wire; but when the 
 strength of the field is a constant, and its position 
 in space remains the same, then we must move the 
 wire in order to get an electromotive force, and 
 this is precisely what we do in our alternating cur- 
 rent machines or "alternators." The most simple 
 conceivable form of alternator is shown in Fig. 13. 
 Here we make use of the vertical component of the 
 earth's magnetic field, and the electromotive force 
 
 is a maximum when the wire is either at its high- 
 
 58 
 
ALTERNATING CURRENT MACHINES. 
 
 59 
 
 est or lowest position (crank vertical), and when 
 the wire is in the extreme right or left position 
 (crank horizontal) the electromotive force is zero. 
 The apparatus shown in Fig. 13 is, in fact, simply 
 
 t > FIG. 13. 
 
 a mechanical model of the clock diagram. In this 
 figure the bearings and standards supporting them 
 are represented as forming the terminals ; and wires 
 attached to them as shown, and led to a solenoidal 
 electromagnet, will energize the latter. Provided 
 the strength of the field were sufficiently great, we 
 could, when the crank is rapidly rotated by a cord 
 and pulley, produce with the electromagnet the 
 effects I have shown you when the coil was con- 
 nected to a transformer. But the strength of the 
 field provided by the earth is not nearly sufficient. 
 
60 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 We must resort to an artificial field produced by 
 electromagnets, such, for instance, as is shown 
 in Fig. 14, where NS are the polar surfaces of two 
 electromagnets, between which a coil C is rotated. 
 If the polar surfaces extend some distance beyond 
 the diameter D of the coil, we may assume that the 
 field within the space swept by the coil is uniform, 
 and then the number of lines or total induction 
 
 s 
 FIG. 14. 
 
 passing through the coil at any instant will be pro- 
 portional to the sine of the angle the coil forms 
 with the vertical. The electromotive force will 
 then be proportional to the sine of the angle the 
 coil forms with the horizontal. Calling H the field 
 intensity, / the length of the coil, v the velocity, 
 and r the number of wires counted on both sides, 
 
ALTERNATING CURRENT MACHINES. 6l 
 
 the maximum electromotive force in C.G.S. meas- 
 ure, when the coil is vertical, will be 
 
 Hztfr. 
 
 It is convenient to introduce instead of H, the 
 number of lines per square centimetre, the total 
 induction F passing through the coil ; and instead 
 of the linear velocity, the number of revolutions 
 per second, which, in this case, where we have to 
 do with a two-pole machine, is equal to the fre- 
 quency n. A simple algebraical operation, which 
 need not be reproduced, here gives us the following 
 formula for the maximum electromotive force : 
 
 E = 27tnF -. 
 
 2 
 
 The effective electromotive force is obtained by 
 dividing this expression by the square root of two, 
 and if we wish to get the electromotive force in 
 volts we multiply by 10 to the power of minus 8, 
 or in symbols 
 
 e = 2 -22, Fr# io" 8 ................ (n). 
 
 Now suppose we remove the armature shown in 
 Fig. 14, and replace it by one wound to give a 
 
62 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 continuous current. We use the same total length 
 of wire, but spread the turns evenly all round the 
 circle and put on a commutator. As you know, the 
 electromotive force of this machine will now be 
 
 e Yrn io" 8 . 
 
 The current flows through the armature in two 
 parallel circuits, and if we allow the same current 
 density in the armature wires, we shall obtain a 
 continuous current of twice the strength of the 
 alternating current. On the other hand, the alter- 
 nating current will have 2*22 times the voltage, so 
 that the output of the alternator will be 1 1 per 
 cent, greater than that of the continuous current 
 machine. In the alternator we save the commuta- 
 tor, and you see, therefore, that for equal output 
 the alternator is a cheaper and lighter machine 
 than the continuous current dynamo. 
 
 The alternator shown in Fig. 14 is, however, not 
 the kind of machine used in practice. I have only 
 chosen it as a simple example to show the relation 
 between continuous and alternate current machines. 
 In practice the latter are made with a number of 
 poles in order to bring down the speed to reasona- 
 
ALTERNATING CURRENT MACHINES. 63 
 
 ble limits, and the wire is not bunched together, 
 but is spread more or less over the surface of the 
 armature. There is also this difference : that the 
 poles of the field surround the armature more 
 closely, and consequently the transition from a 
 north to a south field is more abrupt, than in Fig. 
 14. Notwithstanding these differences, the elec-, 
 tromotive force of alternators as practically made 
 is very nearly that given in Formula (i i), and the 
 comparison of weight and cost which we found 
 just now holds good for the machines as actually 
 built. 
 
 You will see from the diagram on the wall that 
 alternators are all characterized by two main fea- 
 tures a corona or ring of magnet poles and a ring 
 of armature coils, either one or the other being 
 movable. The particular shape of the poles, their 
 arrangement mechanically, the method of winding 
 the armature coils, and many other details, may be 
 changed in many ways, but the main features re- 
 main the same. 
 
 For purposes of study it is convenient to imagine 
 the pole ring and the armature ring cut open and 
 spread into straight lines. We need then only 
 
64 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 consider one coil and two or three poles, as shown 
 in Fig. 15. The electromotive force at any mo- 
 ment is obviously proportional to the number of 
 wires which happen at that moment to be covered 
 by one or both poles, care being taken to count, in 
 
 LnJ 
 
 FIG. 15. 
 
 the latter case, the difference in the number of 
 wires, since the poles act differentially. We can 
 thus plot a curve giving the resultant electromotive 
 force as a function of the position of the coil in 
 front of the poles, and since at constant speed this 
 position changes proportionately with the time, the 
 curve also gives us the electromotive force as a 
 function of the time. Now you will easily see that 
 the shape of this curve depends on the width of 
 the poles and length of coil. It also depends on 
 their relative shape. But not to complicate our 
 investigation too much, I assume that both poles 
 and coils are rectangular, which in machines of the 
 
ALTERNATING CURRENT MACHINES. 65 
 
 Westinghouse and Lowrie Hall type is strictly, and 
 in most other machines is approximately, true. As 
 an extreme case regarding the width of poles, we 
 may take a machine in which the north and south 
 poles are placed so close as almost to touch each 
 other. In this case the width of poles is equal to 
 their distance or pitch. Machines with alternate 
 poles set so closely are not made ; but the Mordey, 
 in which poles of the same sign, separated by equal 
 intervals of blank or neutral spaces, is a practical 
 illustration of the same principle. Suppose now 
 that we put into such a field an armature, the whole 
 surface of which is covered by coils, then the length 
 of each coil must also equal the pitch, and there 
 will then be only one position, namely, that in 
 which the centre of the coil coincides with the 
 centre of the pole, when all the wires in the coil 
 are producing electromotive force in the same di- 
 rection. In every other position the electromotive 
 force in one part of the coil is opposed to that in 
 the other part. In such a machine the wire is not 
 used to the greatest advantage, and the electromo- 
 tive force curve becomes a zigzag line as shown in 
 Fig. 1 6. The question which interests us most is 
 5 
 
66 ALTERNATING CURRENTS OP ELECTRICITY. 
 
 that of the effective electromotive force represented 
 by this curve. Experimentally we can, of course, 
 easily determine it. We need only connect a Car- 
 dew voltmeter to the terminals of the coil and take 
 a reading ; but it is important to know beforehand, 
 that is, before the machine is built, what volts we 
 may expect to get. Consider for a moment what 
 it really is that the voltmeter measures. It is the 
 
 
 NORTH 
 
 SOUTH OR ) 
 NEUTRAL 
 
 NORTH 
 
 1 
 
 
 IHttlllllli 
 
 ARMATURE 
 
 
 
 
 X 
 
 FIG. 16. 
 
 amount of heat developed per second in its wire. 
 With the quick alternations produced by the ma- 
 chine there is no time for the wire to change its 
 temperature, and its resistance is therefore con- 
 stant. The amount of heat dissipated per second 
 is then the square of the effective volts divided by 
 the resistance, and this is also equal to the integral 
 of the square of the instantaneous volts multiplied 
 
ALTERNATING CURRENT MACHINES. 67 
 
 by the differential of the time, the integration 
 being extended over one second; or we may ex- 
 tend the integration only over the time occupied 
 by one half period and divide the result by that 
 time; this will also give us the heat per second. 
 But as we want to know the volts and not the heat 
 generated per second, we need not concern our- 
 selves about the resistance of the voltmeter wire at 
 all, and simply take the square root of the integral 
 dt; this gives the effective volts. To do this 
 graphically, as shown in Fig. 16, scale theordinates 
 of the zigzag line, square the readings, and plot to 
 an arbitrary scale the result. Thus we obtain the 
 tent-like figure shown in the diagram, the area of 
 which is the integral, or, to speak quite correctly, 
 is proportional to the integral of square of instan- 
 taneous volts and time. The height of a rectangle, 
 of equal base and area, is the square of the effective 
 volts. It is thus possible to determine beforehand, 
 for any given arrangement of field poles and arma- 
 ture coils, what the effective volts will be, and, 
 roughly speaking, the larger the shaded area, the 
 higher will be the voltage of the machine. For 
 instance, in Fig. 17, I have assumed that the field 
 
68 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 of Fig. 1 6 has been retained, but that the armature 
 coils have been made only half the length for the 
 same number of turns. Only half the surface of 
 
 \ 
 
 FIG. 17. 
 
 the armature is now covered by wire, and the max- 
 imum electromotive force is maintained for a quar- 
 ter period instead of being momentary as before. 
 This gives a trapezoidal line for the electromotive 
 force curve, and the shaded area is now considera- 
 
 FIG. 18. 
 
 \ 
 
 bly larger than before. Let us now go back to the 
 first armature, and run it in a field the poles of 
 which are only half the width, the total induction 
 being, however, the same. Here again we get a 
 
ALTERNATING CURRENT MACHINES. 69 
 
 trapezoidal electromotive force curve (Fig. 18), and 
 the same voltage as in Fig. 17. If we now shorten 
 the coils, we come back to the zigzag lines, but the 
 peaks are higher (Fig. 19), and the voltage, as 
 shown by the shaded area, is again increased. The 
 arrangement shown in Fig. 19 is that usually met 
 with in modern alternators, but owing to the fringe 
 of lines at the corners of the pole pieces, the elec- 
 
 \ 
 
 FIG. 19. 
 
 tromotive force curve is not quite as sharp as here 
 shown. The peak is rounded off and the sides are 
 more wavy, the curve approaching, in fact, very 
 nearly to a true sine curve. Leaving, however, 
 such refinements aside, it is easy to work out an 
 expression for the effective volts in each given 
 case either graphically by the use of such diagrams 
 as Figs. 1 6 to 19, or analytically. The operation 
 
7<D ALTERNATING CURRENTS OF ELECTRICITY. 
 
 is somewhat laborious, but in no sense difficult, 
 and it would be useless to burden this lecture with 
 it. I will merely state the results. If you will 
 refer back to Formula ( 1 1 ) you will see that the 
 effective electromotive force of a simple coil, re- 
 volving in a uniform field, is given by the product 
 of a constant (in this case 2*22), the total induction 
 or number of lines emanating from one field pole, 
 the number of wires counted on both sides of the 
 coil, and the frequency. If, instead of a machine 
 with two poles and one coil, we had made a ma- 
 chine with 10 poles and five coils, coupled in series, 
 the electromotive force of each coil w.ould have 
 been five times as great; if the machine at 20 poles 
 and 10 coils it would have been 10 times as great, 
 and so on. You see, therefore, that the electro- 
 motive force is simply proportional to the total 
 number of wires coupled in series, and to the num- 
 ber of pairs of poles, and Formula (i i) is right for 
 a machine with any number of poles. The same 
 kind of formula is also correct for any arrangement 
 of poles and coils, but the coefficient is different in 
 each case. This coefficient is really the ratio of 
 the electromotive force of the alternator to that of 
 
ALTERNATING CURRENT MACHINES. 7 1 
 
 a continuous current dynamo of equal weight and 
 arrangement of field and armature. If the machine 
 has r pairs of poles, and runs at a speed of N revo- 
 lutions per minute, its electromotive force of a con- 
 tinuous current machine is 
 
 (12), 
 
 or if by Z we denote field strength in English 
 measure 
 
 e = /ZrNio- ................. (13). 
 
 Let K be the coefficient which depends on the 
 shape of poles and armature coils, then the elec- 
 tromotive force of our alternator is 
 
 N 
 e = K/Fr io~ 8 ................ (14). 
 
 ............. .....(15). 
 
 e =KFrio- 8 ................... (16). 
 
 To find the electromotive force we must therefore 
 determine the coefficient K for each case, and, as 
 I have already said, this is not a difficult mathe- 
 matical problem. The result for the cases I have 
 brought before you is as follows : 
 
72 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 (i). If machine gives a strictly sinu- 
 soidal electromotive force, . ^=2-22 
 (2). Width of poles equal to pitch, and 
 
 length of coils equal to pitch, . = 1*160 
 (3). Width of poles equal to pitch, and 
 length of coils equal to half the 
 pitch, ;; ." r; . a _ . =1-635 
 (4). Width of poles equal to half the 
 pitch, and length of coils equal 
 to pitch, . . . . = 1-635 
 
 (5). Width of poles equal to half the 
 pitch, and length of coils equal 
 to half the pitch, . . . =2-300 
 If you compare the first and last line of this 
 table, you will find that there is only 3*^ per cent, 
 difference between the two coefficients. The last 
 line refers to machines as actually built, and the 
 first line to ideal machines having a true sinusoidal 
 electromotive force curve. You see that, as far as 
 the effective electromotive force is concerned, the 
 assumption that ordinary commercial alternators 
 follow the sine law is practically correct. 
 
CHAPTER V. 
 
 
 
 MECHANICAL CONSTRUCTION OF ALTERNATORS. 
 
 Speaking generally, we may say that the con- 
 structive requirements and the points to which par- 
 ticular attention must be paid in designing alterna- 
 tors are very much the same as obtain in dynamos, 
 but there may be certain differences. In the first 
 place, the armature of a dynamo is, on account of 
 its commutator and brushes, necessarily more com- 
 plicated than that of an alternator. On the other 
 hand, the field is simpler. The majority of dyna- 
 mos are made for low or moderate voltage, whilst 
 alternators are generally made for high voltage. 
 This requires greater care in the insulation, and 
 compels us to avoid certain methods of winding, 
 which for a loo-volt dynamo are quite admissible. 
 In the design of both kinds of machine we must 
 pay attention to eddy currents and hysteresis, but 
 in alternators these disturbing and injurious effects 
 
 73 
 
74 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 are far more serious than in dynamos. The reason 
 is that both the wire and the iron, if the armature 
 has an iron core, are subjected to a more rapid 
 reversal of induction. Special precautions must 
 therefore be adopted. The core must be well lam- 
 inated, and the conductor should not exceed a cer- 
 tain section. What that maximum section should 
 be depends, of course, on the general design of the 
 alternator, but we may take it roughly that, where 
 round wire is used, its diameter should not exceed 
 140 mils., and where strip is used its thickness 
 should not be more than 100 mils. Another and 
 very effectual cure for eddy currents is to embed 
 the conductor entirely in iron, an arrangement 
 which has been first proposed by Wenstrom, and 
 has been largely used by Brown, the latest example 
 being his large three-phase current alternator at 
 Lauffen. The conductor is a solid copper rod of 
 about 1^2 inches in diameter, threaded through 
 holes in the armature core. A conductor of that 
 size, if placed on the surface of an armature where 
 it is subjected to some 80 field reversals per second, 
 would get hot in a few minutes, yet, arranged as it 
 is in Mr. Brown's " three-phaser, " it keeps perfectly 
 
MECHANICAL CONSTRUCTION OF ALTERNATORS. 75 
 
 cool. It is the fact that the conductor is sur- 
 rounded on all sides by iron which produces this 
 result. A still more striking illustration of the 
 effect of iron in preventing eddy currents is Thom- 
 son's welding machine. Here we have a solid 
 conductor of many square inches in area, in which 
 the welding current is generated. But this con- 
 ductor is the secondary circuit of a transformer, 
 and is surrounded by the iron of the transformer. 
 Professor Thomson's explanation of the fact that 
 in all such cases eddy currents are avoided is that 
 the speed at which the wire cuts through the lines 
 of force is much greater than its speed of motion, 
 that, in fact, the lines at first yield and, so to say, 
 stretch, but finally, when the tension becomes too 
 great, snap suddenly past the wire. Thus all parts 
 of the wire are cut at almost the same instant by 
 the lines of force, and this leaves no time during 
 which the differences of electromotive force, and, 
 therefore, eddy currents, could be developed in the 
 wire. I, personally, do not feel competent to either 
 confirm or refute this explanation, but coming from 
 so high an authority as Professor Elihu Thomson, 
 am satisfied to accept it. That wires embedded in 
 
76 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 iron, or surrounded on all sides by iron, are nearly 
 free from eddy currents is, however, an undoubted 
 fact. 
 
 From what I have here said you will see that in 
 one way or another we can avoid, or at least greatly 
 reduce, the loss of power by eddy currents in alter- 
 nators. Now let us see whether this is also the 
 case with the other source of loss, namely, " hyste- 
 resis. " Under this term we comprise a certain phe- 
 nomenon, first investigated by Ewing, and which 
 maybe popularly described as "magnetic friction." 
 The lines of force in being forcibly dragged through 
 the iron core of the armature continually change 
 its magnetization, and the core, even if most care- 
 fully laminated, so as to avoid eddy currents, still 
 becomes hot if revolved in an excited field. It is 
 at once obvious that the power thus wasted will be 
 the greater the more rapid the reversal of magneti- 
 zation, and the greater its amount. This loss takes 
 place in dynamos as well as in alternators, but to a 
 different extent. In a dynamo the reversal is com- 
 paratively slow. Take, for instance, a two-pole 
 machine, running at 600 revolutions per minute, or 
 10 revolutions per second. The whole mass of the 
 
MECHANICAL CONSTRUCTION OF ALTERNATORS. 77 
 
 armature core undergoes, therefore, in every second 
 ten complete cycles of magnetic change. But in 
 modern alternators the change is about ten times 
 as rapid, the frequency being 100. If we allowed 
 the same induction, that is, number of lines per 
 square centimetre of core section, the alternator 
 would waste ten times the power, and this would, 
 of course, be inadmissible. There is only one 
 way in which we can reduce the waste of power, 
 and that is by adopting a lower induction. Thus, 
 whilst in dynamos the induction ranges from 14,000 
 to 20,000 lines per square centimetre, it is only 
 
 fc. 
 
 8000 4000 6000 8000 10000 12000 14000 10000 18000 20000 
 INDUCTION 
 
 FIG. 20. 
 
 about 5,000 in alternators. The exact induction at 
 which it is best to work varies, of course, with the 
 
78 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 type and size of machine, and as every design is a 
 compromise, you must not consider the 5,000 as a 
 hard-and-fast rule. To enable you, however, to 
 deal with each given case on its own merits, I give 
 in Fig. 20 a curve showing the loss of power by 
 hysteresis per ton of iron when the frequency is 
 100. The induction is measured on the horizontal, 
 and the power (in kilowatts) on the vertical. This 
 curve has been compiled from the experimental 
 results of Professor Ewing. I may incidentally 
 mention that this curve is approximately repre- 
 sented by the equation * 
 
 (B \ l ' s>s> 
 1 .(17), 
 1 0007 
 
 or if the induction B is given in English lines per 
 square inch 
 
 Power = -160 B 1 - 65 (18). 
 
 The power is given in kilowatts per ton of iron 
 when the frequency is 100 complete cycles per sec- 
 ond. For a different frequency the power is pro- 
 portionally altered. 
 
 * Steinmetz in his classical researches on hysteresis gives the 
 exponent as 1.6. 
 
MECHANICAL CONSTRUCTION OF ALTERNATORS. 79 
 
 There being necessarily always some waste of 
 power, if the armature has an iron core it was nat- 
 ural that inventors should turn their attention to 
 the construction of an alternator with a coreless 
 armature. In fact, the Meritens machine, which 
 was one of the first commercial alternators, and is 
 used to this day in lighthouse work, has no iron in 
 the armature. Then there comes the Siemens, also 
 without iron, the Ferranti, and the Mordey. In all 
 these machines the loss by hysteresis is avoided, 
 and if this were the only consideration, they would 
 undoubtedly be better than their rivals with iron- 
 cored armatures. But as I have said before, every 
 design is a compromise, and it is quite possible 
 that the machine with iron in its armature is as 
 good a compromise as one without iron. The fact 
 that the majority of American machines, all the 
 German machines, including those now made by 
 Messrs. Siemens and Halske, and a good half of 
 the English machines have iron-cored armatures, 
 is in itself sufficient proof that the hysteresis loss 
 is not an insurmountable obstacle. There are es- 
 pecially two points in favour of using iron. The 
 first is that we are thereby enabled to give the 
 
8o ALTERNATING CURRENTS OF ELECTRICITY. 
 
 armature greater mechanical strength than can be 
 done in machines where the armature coils are at- 
 tached singly and held by insulating material. The 
 second is that the presence of iron tends to dimin- 
 ish the magnetic resistance of the air-gap, and thus 
 saves exciting energy. In Mr. Brown's three- 
 phaser, for instance, the total exciting energy does 
 not amount to more than y 2 per cent, of the total 
 power. 
 
 I have, a moment ago, spoken of the differences 
 between alternators and dynamos from an electrical 
 and mechanical point of view. There remains yet 
 to notice an important point of difference, namely, 
 the absence in alternators of a commutator and 
 brushes. You all know that these are the most 
 delicate parts of a dynamo, and although in modern 
 machines of moderate voltage these parts are per- 
 fectly reliable and easily handled, the case is dif- 
 ferent when we attempt to build dynamos for 1,000 
 or 2,000 or more volts. We encounter then diffi- 
 culties which are absent from alternators, and it is 
 mainly on this account that engineers who have to 
 design power transmission schemes over long dis- 
 tances are beginning to turn their attention to some 
 
MECHANICAL CONSTRUCTION OF ALTERNATORS. 8 1 
 
 forms of alternator as the most certain means of 
 solving such problems. I shall have something 
 more to say on this subject in the third lecture. 
 For the present I must limit my remarks to the 
 machines as required for lighting. 
 6 
 
CHAPTER VI. 
 
 DESCRIPTION OF SOME ALTERNATORS. 
 
 In the limited time at my disposal it would be 
 impossible for me to give you anything like an 
 exhaustive account of the various machines now in 
 use. I shall therefore only describe a few of them 
 as being representative examples. 
 
 i. The Ferranti Alternator. The field magnets 
 are wrought-iron bars of trapezoidal section (Fig. 
 
 FERRANTI. 
 
 FlG. 21. 
 
 21), cast into massive yoke rings, which can be 
 drawn apart at right angles to the shaft, so as to 
 expose the armature for examination and repair. 
 
 82 
 
DESCRIPTION OP SOME ALTERNATORS. 83 
 
 The latter is of disc pattern, and the coils are in- 
 serted in pairs. The conductor is a corrugated 
 copper strip wound with a strip of vulcanized fibre 
 of equal width upon a laminated brass core. The 
 conductor is thus insulated from the core, and the 
 latter is insulated from the supporting" ring. This 
 double insulation is an important feature of the 
 machine. The core is held in gun-metal cheeks, 
 which are provided with side wings for ventilation. 
 The attachment of each pair of cheeks to the sup- 
 porting ring is by means of a shank passing through 
 insulating washers into a cavity in the ring, and 
 secured by a nut. The cavity is cast out with sul- 
 phur. To avoid too great a loss by eddy currents 
 the conductor is made very thin; the winding is 
 split up into two, four, or more parallel circuits. I 
 may here incidentally mention that where an arma- 
 ture winding is thus split up, great care must be 
 taken to have all the magnets of equal strength, as 
 otherwise there would be created with the arma- 
 ture differential currents, which would waste far 
 more power than the eddy currents, which the ar- 
 rangement was intended to avoid. The Ferranti 
 machines now working at Deptford are giving an 
 
8 4 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 electromotive force of 10,000 volts, and to prevent 
 flashing over to the magnets the latter are provided 
 with double caps of ebonite. 
 
 2. The Mordey Alternator. This is also a coreless 
 machine of the disc pattern, but the armature is 
 fixed whilst the magnets revolve. The armature 
 coils (Fig. 22) are wedge-shaped, and the conductor 
 
 1 
 
 FIG. 22. 
 
 is a thin copper strip wound on a slate core, the 
 layers being separated, as in the Ferranti coils, by 
 a thin strip of insulating material. The attach- 
 ment is made at the outer and wider end of the coil 
 to a gun-metal supporting ring. The magnets are 
 of cast-iron, and so shaped as to require only one 
 coil C of exciting wire. This is wound on a cen- 
 
DESCRIPTION OF SOME ALTERNATORS. 85 
 
 tral cylindrical partjj/, to both sides of which are 
 pole pieces of peculiar star-like form. Thus 
 the poles on one side of the armature are all of the 
 same sign, and those on the other side are of the 
 opposite sign, the lines of force passing from N to 
 S at right angles through the surface of the arma- 
 ture, and all in the same direction. There is thus, 
 properly speaking, no reversal of magnetization, 
 but merely a change from full induction when a 
 wire is between opposite poles, to no induction 
 when it is between neighbouring poles, and the 
 general effect is the same as if we had half the field 
 strength alternating. To apply our formulae for 
 the electromotive force of this machine we must, 
 therefore, introduce not the whole field strength F 
 or Z, but half its real value. 
 
 3. The Westinghouse Alternator. As a good ex- 
 ample of an alternator, the armature of which con- 
 tains iron, we may take the Westinghouse machine, 
 which, in its important details, is very .similar to 
 the Thomson-Houston. The armature is cylindri- 
 cal (Fig. 23), and is covered by link-shaped coils, 
 with the wires parallel to the shaft, the rounded 
 ends of the coils C being bent inwards, and secured 
 
86 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 to the end faces of the armature core. In the 
 Thorn son- Houston machines the coil ends are not 
 
 turned inwards. The field magnets NS are set 
 radially outside the armature, and their outer ends 
 are connected by a yoke ring Y. According to our 
 theory, the best arrangement as regards width of. 
 coil is half the pitch, which means that the central 
 space of the coil should have the same width as the 
 magnet, but Professor Thomson, when experiment ~ 
 ing with various coils, found that a coil having a 
 slightly smaller internal space gave a higher elec- 
 tromotive force when the machine was working 
 under full load. His explanation is that the cur- 
 rent in the armature wires alters the original mag- 
 netization of the field, tending to concentrate the 
 lines towards the leaving edge of the pole piece, 
 and thus produces a more intense but narrower 
 
DESCRIPTION OF SOME ALTERNATORS. 87 
 
 field. The inner space of the coils, which is free 
 from winding, should therefore also be made nar- 
 rower. 
 
 4. The Kapp Alternator. In this machine (Fig. 
 24) the armature is of the disc pattern, and con- 
 
 tains an iron core A made by coiling a strip of thin 
 charcoal-iron with a strip of paper upon a support- 
 ing ring. The coils are wound transversely round 
 the core. The field magnets in the larger ma- 
 chines are of wrought iron, with expanded pole 
 shoes, and are set parallel to the shaft on both sides 
 of the armature core, presenting the same poles 
 NN SS on opposite sides. The outer ends of the 
 magnets are joined by cast-iron yokes YY. Owing 
 to the angular position of the pole shoes, each wire 
 does not enter the field simultaneously over its 
 
88 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 whole length, but the entry is a little more gradual, 
 whereby the sharp peaks in the line of electromo- 
 tive force (Fig. 19) are toned down, and the curve 
 is made to approach a sinusoidal form. The cur- 
 rent is collected by rubbing contacts from insulated 
 rings, which are set on opposite sides of the arma- 
 ture, that is, so far apart that it is impossible for 
 a man to touch both simultaneously. The coeffi- 
 cient K for this machine varies between 2-3 and 
 2 /, according to the particular design chosen. 
 
 5. The Kingdon Alternator. In all the machines 
 described up to here, the wire, either on the field 
 or on the armature, is in motion, but in the King- 
 don machine all the wires are at rest, the only re- 
 volving part being an armature containing no wire. 
 The machine consists of a laminated iron cylinder, 
 with radial teeth projecting inwards, and the arma- 
 ture and field coils are wound over alternate teeth. 
 The revolving part is a wheel provided with half 
 as many laminated iron keepers as there are teeth 
 in the stationary part, and these keepers are so 
 arranged as to bridge magnetically neighbouring 
 teeth. Thus the- teeth over which the armature 
 coils are wound become alternately parts of a posi- 
 
DESCRIPTION OF SOME ALTERNATORS. 
 
 live and negative magnetic circuit, and an alternat- 
 ing current is produced. 
 
 6. The Kennedy Alternator. Mr. Kennedy has 
 further developed this idea, mainly by reducing the 
 number of armature and field coils, and avoiding 
 the generation of an alternating current in the lat- 
 
 
 
 FIG. 25. 
 
 ter. The machine (Fig. 25). has two armature and 
 two field coils wound in pairs, and placed into re- 
 cesses in a skeleton frame of soft iron laminated 
 bars. There are two keeper wheels on the spindle, 
 but stepped in relation to each other by half a 
 period, so that when the keepers of one wheel have 
 
90 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 completely closed the magnetic circuits around one 
 pair of field and armature coils, the keepers of the 
 other wheel are midway between the fixed bars, 
 and the magnetic circuits around the second pair of 
 armature and field coils are interrupted. The elec- 
 tromotive force in those coils is at that moment 
 zero, and it is also zero in the other coils, through 
 which the induction is a maximum. Half a period 
 later the induction becomes a maximum in the sec- 
 ond, and zero in the first pair of coils, and this 
 change of induction produces an alternating elec- 
 tromotive force in all the coils. Now it is obvi- 
 ously possible to couple the two field coils in series, 
 and in such way that the electromotive force 
 created in one is opposed to that in the other, and 
 thus to neutralize the reaction of the keeper on the 
 exciting circuit. The exciting dynamo has then 
 merely to overcome the ohmic resistance of the 
 two coils, as in any other machine. The two arma- 
 ture coils may be coupled in series or parallel. 
 
CHAPTER VII. 
 
 TRANSFORMERS. 
 
 I have already drawn your attention to the fact 
 that alternators are generally designed for high 
 voltage. The reason is obvious. If we wish to 
 carry the current, be it for lighting or power, to 
 any distance, we must use a high voltage, in order 
 to bring the section of our conducting wires or 
 mains down to a size which makes the whole enter- 
 prise commercially possible. But to give our cus- 
 tomers a current of some thousands of volts would 
 be dangerous and inconvenient, for glow lamps re- 
 quire a current of about 100 volts when arranged 
 in parallel, that is, in the way in which they are 
 of most use to private consumers. The question 
 therefore arises what to* do with our high-pressure 
 current when we have brought it to the place where 
 its energy is required for lighting lamps. Obvi- 
 ously we must transform it ; we must lower its volt- 
 
 91 
 
p2 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 age and increase its strength. Now there are two 
 ways in which this may be done. We may use 
 the current to work a motor, and use the power 
 given out by the motor to drive a dynamo of 100 or 
 200 volts. The direct current can then be distrib- 
 uted to the lamps in the usual way, and we may 
 even supplement the installation by secondary bat- 
 teries, so as to be able to shut down our machinery 
 during the hours of minimum demand. As far as 
 I know, this system of transformation has only, up 
 to now, been used in one installation, namely, at 
 Cassel, in Germany. At the first glance it may 
 seem complicated and costly, but it has many ad- 
 vantages, which will probably lead to its adoption 
 in other towns. 
 
 The other system which is at present in general 
 use is that of direct transformation by means of 
 induction coils. Here we need no moving machin- 
 ery, but simply a stationary apparatus consisting of 
 a laminated iron core and two coils (Fig. 26). One 
 of these consists of many turns of fine wire, and is 
 technically termed the primary coil P, and the 
 other of fewer turns of stouter wire called the 
 secondary coil S. The high-pressure current is 
 
TRANSFORMERS. 
 
 brought by the mains w, and the low-pressure cur- 
 rent is supplied to the lamp L by the secondary 
 mains W. You will observe that there is abso- 
 lutely no connection between the two sets of mains, 
 and this is a great guarantee for the safety of the 
 system. The action of this apparatus, which is 
 technically known under the name of "trans- 
 
 w 
 
 w 
 
 \Vv\j 
 
 w 
 
 PIG. 26. 
 
 former," will be clear to you from what I have said 
 in the first lecture about the generation of an alter- 
 nating electromotive force. The primary coil mag- 
 netizes the iron core in alternate directions, and at 
 each reversal the lines of force cut through the 
 wires of the secondary coil. The latter must there- 
 fore become the seat of an alternating electromotive 
 force. If we denote by F the total induction, and 
 
94 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 call n the frequency, the maximum electromotive 
 force generated in each turn of wire is 
 
 and the effective electromotive force is this value 
 divided by the square root of 2. If the coil con- 
 tains T U turns, the total effective electromotive force 
 in the large circuit will be 
 
 e^ 4-45 7/FT a io" 8 volts ............ (19). 
 
 The changing induction affects, however, not 
 only the secondary, but also the primary coil, and 
 in the latter there will be developed an electromo- 
 tive force which we compute by the same formula, 
 only substituting for r a the number of primary 
 turns T,. You see, therefore, that the transforming 
 ratio is given by the ratio of the turns of wire in 
 each coil ; but this is only approximate, since not 
 the whole electromotive force generated in the sec- 
 ondary reaches its terminals. We must deduct the 
 electromotive force used up in overcoming the 
 ohmic resistance of the secondary coil. In like 
 manner the electromotive force which opposes the 
 current in the primary coil is a little smaller than 
 the terminal electromotive force, because the ohmic 
 
TRANSFORMERS. $5 
 
 resistance also opposes the primary current. The 
 transforming ratio therefore varies with the load, 
 but I may at once say that in good transformers 
 the variation as determined by ohmic resistance is 
 exceedingly small, generally about 2 per cent. 
 There is, however, another cause of variation, 
 namely, magnetic leakage, and a transformer made 
 as shown in Fig. 26 would exhibit this phenom- 
 enon in a most objectionable degree. You see that 
 the two coils meet in the middle of the core. Now 
 the primary wants to magnetize the core in one 
 direction and the secondary wants to magnetize it 
 in the opposite direction. The result is that the 
 two streams of induction come, so to speak, into 
 collision about the middle of the core, and some of 
 the lines which the primary coil tries to shoot 
 through the secondary are squeezed out sidewise, 
 and contribute nothing to the secondary electro- 
 motive force. You might perhaps think that this 
 is of no moment, for we can make up for the loss 
 of these lines by putting a few more turns of wire 
 on the secondary. But if we did that we should 
 get too much electromotive force at light loads. 
 To see this clearly let us begin with no load on the 
 
g ALTERNATING CURRENTS OP ELECTRICITY. 
 
 secondary. Then there is no current in S and no 
 collision. The lines created by the primary pass 
 without opposition through the secondary, and F in 
 Formula (19) has its full value. Now switch on 
 some lamps and a secondary current will flow. We 
 shall have some collision of lines, and F in the for- 
 mula, and therefore the electromotive force, will 
 become smaller. The more lamps you switch on, 
 the more current flows through both coils, and the 
 more violent becomes the collision, and therefore 
 the number of lines lost. In a word, we generate 
 more lines than we can utilize. The obvious rem- 
 edy for this defect is to place the coils relatively to 
 each other into such a position that the lines gen- 
 erated by the primary cannot evade passing through 
 the secondary. For instance, we can wind one coil 
 over the other, or we can split up the coils into 
 short sections and place them alternately over the 
 core. Even with these precautions there is some 
 magnetic leakage, but this does not as a rule lower 
 the voltage by more than i or 2 per cent. Thus in 
 a good transformer we may expect to get, with con- 
 stant primary voltage, a terminal pressure varying 
 between 102 and 99 or 98 volts, when the load is 
 
TRANSFORMERS. 97 
 
 increased from zero to full out-put. These figures 
 refer to small transformers of 50 or 100 lamps. 
 With large transformers it is quite possible to limit 
 the total voltage drop to something under 2 per 
 cent. The transformer shown in Fig. 26 is defec- 
 tive in other ways besides its great voltage drop. 
 The lines passing through the core have to come 
 back through air, and the great magnetic resistance 
 of their path through air requires a strong magne- 
 tizing current, or, in other words, the primary cur- 
 rent will be considerably greater than in a trans- 
 former, in which the return path is made more 
 easy. One way of doing this is to increase the 
 surface of the core ends, and this Mr. Swinburne 
 has done in his " Hedgehog " transformer. The 
 core consists of iron wires which at the ends are 
 curved outwards. Thus part of the return path is 
 through iron. Another method, and this is gen- 
 erally used, is to make the whole return path of 
 iron. We may, for instance, employ a closed iron 
 frame (J, Fig. 27), and wind the primary and sec- 
 ondary coils C over each other on two opposite sides 
 of this frame. The iron frame or core is composed 
 of thin plates, more or less insulated from each 
 7 
 
9 8 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 other to avoid eddy currents. This type of trans- 
 former is called a "core transformer." Or we may 
 employ only one coil and surround it by a double 
 
 FIG. 27. 
 
 frame, as in Fig. 28, a kind of iron shell, and this 
 construction is called a "shell transformer." Both 
 figures have been drawn to represent transformers 
 of equal out-put. The depth of the core is sup- 
 posed to be equal, and its width in Fig. 28 is twice 
 as great as in Fig. 27, to make up for their being 
 only one coil. At the first glance it is difficult to 
 say which is the better transformer, though prac- 
 tically the balance of advantages seems to lie with, 
 the shell type, which is most in favour with the 
 makers of this kind of apparatus. If we enquire 
 what it is we must aim at in the design of a good 
 
TRANSFORMERS. 
 
 99 
 
 transformer, we find that the length of wire should 
 be small in order to reduce ohmic resistance and 
 cost, that there should be as little iron as possible, 
 and that the magnetic circuit should be short. Now 
 these are contradictory conditions. To reduce the 
 length of wire we must work with a high total in- 
 duction, so that a small number of turns should 
 give us the required electromotive force. But a 
 large induction means either a great loss by hys- 
 teresis or a stout core, and a stout core means that 
 the length of each turn of wire is great. It further 
 means a longer magnetic circuit and a greater 
 
 FIG. 28. 
 
 weight of iron, which again increases the loss by 
 hysteresis. You see here again the successful de- 
 sign must be a compromise, but a compromise in 
 
100 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 which a preponderance of weight is given to hys- 
 teresis. We must remember that a transformer is 
 continuously at work whether we take current from 
 it or not, and hence the hysteresis loss goes on day 
 and night. Even an extra loss of y 2 per cent, by 
 hysteresis will therefore be felt in the all-day effi- 
 ciency of the apparatus, and is, therefore, more 
 serious from an economical point of view than a 
 loss of several per cent, by copper resistance, be- 
 cause transformers, when used for lighting, only 
 work a very short time daily under full load. On 
 the other hand, we must not allow an excessive 
 copper loss, as this would disqualify the transformer 
 on account of too great a voltage drop. We are 
 thus hemmed in on all sides by conflicting condi- 
 tions, and the design of a good transformer is by 
 no means so easy a task as might appear at the first 
 glance. As a starting point, we may take it that 
 the magnetic and the electric circuit should be as 
 short as possible, and this condition will be best 
 fulfilled by a circular or square shape, or as near 
 an approach to such a shape as possible. In fact, 
 if you examine the successful transformers in the 
 market, you will find that this condition is fulfilled 
 
TRANSFORMERS. IOI 
 
 in either one or the other circuit, but not in both. 
 I have not succeeded in estabHs-hi^g; ^nd I "can 
 therefore not give you any, h^fd-and-fasfc rules j for 
 the construction of transformers, b\lt 'hi "ordei* ^a 
 enable you to see what enormous influence slight 
 alterations in the proportions have on the weight 
 and cost of the apparatus, I have prepared for your 
 proceedings some 27 different designs, all for a 
 loo-light transformer. Four of these designs are 
 given full size in Plates I. and II., pages 156-7. 
 In all these the copper loss is 2 per cent. The 
 hysteresis loss is given in each case. You can see 
 at a glance what a great difference there is in the 
 amount of copper required, and how by a skilful 
 choice of the proportions the cost of the apparatus 
 can be reduced without lowering its efficiency. 
 
 Before concluding this part of my subject, I wish 
 to draw your attention to the relation existing be- 
 tween the linear dimensions of a transformer and 
 its out-put and hysteresis loss. Imagine that after 
 designing a score or so of transformers you have at 
 last arrived at a type with which you feel satisfied ; 
 but suppose it is not the size you want. How will 
 you alter its linear dimensions? Let us try what 
 
102 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 we shall get if we make everything twice as big, 
 ' including; tti^' size of the wire. We retain the in- 
 di;et.ion per square "centimetre at the 4,000 or 5,000, 
 k wliich'we found" will give us a loss of say \y 2 per 
 cent, by hysteresis. We also retain the number of 
 turns in both coils. The total induction is then 
 four times as great, and the electromotive force 
 also four times as great. The resistance of the 
 coils has been reduced to one-half its former value 
 (area of wire four times as great, and length twice 
 as great). If we are satisfied to have the same 
 copper loss, we can allow a current which will give 
 us four times the previous voltage loss, but as the 
 resistance has been halved the current will be eight 
 times its former value. Thus the current is eight 
 times and the volts are four times as great as be- 
 fore; the out-put will, therefore, be 32 times as 
 great. But 32 is two to the fifth power, and hence 
 we see that the out-put of a transformer varies 
 as the fifth power of its linear dimensions. The 
 weight, cost, and hysteresis loss, on the other hand, 
 all vary as the cube of the linear dimensions, and 
 the weight per kilowatt of out-put varies inversely 
 as the square of the linear dimensions. Or, in fig- 
 
TRANSFORMERS. 103 
 
 ures, if 40 Ibs. of copper and iron were required for 
 each kilowatt produced by the small transformer, 
 only 10 Ibs. per kilowatt will be required in the 
 larger ; and if the small transformer wasted 2 per 
 cent, of its power in hysteresis, the large trans- 
 former will only waste ^ per cent. Let the large 
 transformer have x times the out-put of the small 
 one, then linear dimensions must be proportional 
 to x\. Weight and cost per kilowatt and percen- 
 tage loss by hysteresis will be proportional to x$. 
 This calculation neglects, however, the working 
 temperature which, for obvious reasons, must not 
 exceed a certain limit. In practice it is found that 
 for every watt lost by hysteresis, eddy currents, and 
 ohmic resistance a cooling surface of from five to 
 ten square inches must be provided. As the larger 
 transformer has, relatively to its out-put, a smaller 
 external surface than the smaller transformer, it is 
 not possible to take full advantage of the law be- 
 tween linear dimensions and out-put here given. 
 In part, owing to the difficulty of heating, we very 
 soon arrive at a limit of out-put when a further 
 increase of dimension varies the out-put scarcely 
 faster than the weight and cost. Thus in practice 
 
104 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 it is found that although a transformer of 12 
 kilowatts does not weigh nearly as much as four 
 transformers of 3 kilowatts, a transformer of 60 
 kilowatts weighs and costs very nearly twice as 
 much as a transformer for 30 kilowatts. 
 
CHAPTER VIII. 
 
 CENTRAL STATIONS AND DISTRIBUTION OF ALTER- 
 NATING CURRENTS. 
 
 The principal reason for the use of alternating 
 currents in connection with the supply of light from 
 a central station to private customers is that in con- 
 sequence of the high pressure which can safely be 
 used we are able to take on customers, whether 
 near or far, and thus carry on the business of light 
 purveyors on a larger scale, and presumably with 
 a greater profit, than if we were restricted to those 
 customers only who live near the station. In a 
 general sense this argument is perfectly sound, but 
 it would be a mistake to apply it indiscriminately 
 and say that in all cases the supply by means of 
 alternating currents is preferable to that by con- 
 tinuous currents. Whether an engineer has to de- 
 sign works himself, or merely to inspect and approve 
 works carried out by others, it will always be his 
 
106 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 first concern to see that the works shall be a com- 
 mercial success. We cannot build central stations 
 or any other works without the aid of the financier, 
 and the financier cares very little for any technical 
 perfection ; all he cares for is that the work should 
 pay, and unless the engineer can give him that as- 
 surance he will not co-operate. Hence it is the 
 business of the engineer not only to design his 
 works so as to be technically a success, but also 
 commercially. 
 
 In considering the relative merits of the two sys- 
 tems, we must take into account a variety of local 
 circumstances, some of which not only are beyond 
 the reach of mathematical representation, that is, 
 representation by concrete figures which we can use 
 in our calculation, but may even be but vaguely 
 known at the time the station is being designed. 
 For instance, the number of lamps which will be 
 required in any given district, the daily lighting 
 time of each lamp, and the distribution of lamps 
 between the different classes of houses in the dis- 
 trict, are matters which we cannot foretell with ab- 
 solute certainty. We can but make a guess based 
 on previous experience. Another matter of some 
 
CENTRAL STATIONS AND ALTERNATING CURRENTS. 107 
 
 importance, but about which it is extremely diffi- 
 cult to form an estimate beforehand, is the danger 
 of being served with an injunction for noise or 
 vibration by some of the kind neighbours, who are 
 always on the look-out how to make a little money 
 out of the difficulty of others. This danger is evi- 
 dently greater in the direct current system, because 
 with it we have not a very wide choice as to the 
 position of our station, but must place it fairly near 
 to and preferably in the centre of the district to 
 be lighted. With the alternating current system 
 we can afford to go farther afield with our station, 
 into a neighbourhood the inhabitants of which are 
 not so particular as to noise and vibration. Then 
 there is the question of the total extent of the dis- 
 trict to be lighted, the possibility of working by 
 water power, or if not, the cost of coal and water, 
 the quality of the latter, the possibility of obtaining 
 condensing water, and many other points which 
 have to be considered. 
 
 If we have to do with a compact and densely 
 lighted district, where most of the lamps can be 
 placed within a few hundred yards of the station 
 (or at any rate within a radius of about 1,000 
 
108 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 yards), then the direct current system is generally 
 the best. One of its greatest advantages lies in the 
 fact that we can supplement the dynamos by storage 
 batteries, and use the latter during the hours of 
 minimum demand. For economical reasons we 
 are obliged to use compound engines, but, as you 
 know, a compound engine, except when condens- 
 ing, does not work with economy when lightly 
 loaded, and it is therefore advantageous to shut 
 down the engines altogether in the early hours of 
 the morning and during the daytime, putting the 
 batteries on for the supply of the few lamps re- 
 quired. In this respect the direct current has a 
 distinct advantage, but this advantage becomes less 
 and less felt as the total power of the station is in- 
 creased, because in a large station the number of 
 lamps, even in the daytime, will be large enough 
 to fairly load a small engine, and if we can obtain 
 condensing water the engine, even if only partly 
 loaded, will work with fair economy. 
 
 A point at present in favour of direct currents is 
 the ease with which they can be used for motive 
 power, but there is every prospect that ere long 
 alternate current motors will become a practical 
 
CENTRAL STATIONS AND ALTERNATING CURRENTS. IOQ 
 
 success. At any rate, the use of motors on town 
 circuits has with us not yet become so popular that 
 we need attach any great weight to this point. The 
 principal advantage of the alternating current sys- 
 tem is that we can use small mains, and yet keep 
 the pressure throughout the district very nearly 
 constant. With continuous currents not only do 
 we require more copper in the mains and feeders, 
 but where the feeders are long, the loss of pressure 
 in them amounts sometimes to as much as 20 per 
 cent, of the total or station voltage, and in such 
 cases some complicated arrangements are required 
 for the regulation of the voltage, so as to keep the 
 pressure at the feeding centres at least approxi- 
 mately constant. 
 
 There are two ways in which we can use trans- 
 formers. We can bring the high-pressure mains 
 right into the house of each customer and give him 
 his own little transformer, or we can place large 
 transformers at certain sub-stations, and lay through 
 the streets a second system of low-pressure mains, 
 with house connections, in the same way as if the 
 supply were by direct currents, only that in this 
 case the low-pressure mains need not be so large, 
 
110 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 since we can put down as many sub-stations as we 
 please, and thus reduce the distance to the lamps 
 to any desired limit. The system of a separate 
 transformer for each customer has hitherto been 
 most used, but it is not the best. It is true that by 
 it we save the cost of the secondary mains and the 
 cost of the sub-stations, items which a company in 
 its early pioneering days, when customers were few 
 and far between, could not easily afford. On the 
 other hand, the objections to the use of separate 
 transformers are great, and as time goes on, that 
 is to say, as the use of the electric light extends, 
 these objections acquire additional weight. In the 
 first place, there is some danger in having a high- 
 pressure apparatus in one's house. You may put 
 your transformer into the cellar in a fireproof case 
 and lock it up, but when you have thousands of 
 transformers in as many houses, the chances are 
 that in one or two cases the locking up may be for- 
 gotten, and some inquisitive person may touch a 
 terminal. A further objection lies in this : that a 
 number of small transformers cost more money and 
 waste more energy than one large transformer. 
 Let us take for example twenty houses, each wired 
 
CENTRAL STATIONS AND ALTERNATING CURRENTS. Ill 
 
 for fifty lamps. Each house must get its so-light 
 transformer. The whole of the fifty lamps will 
 not be lighted simultaneously every day. Probably 
 not more than half-a-dozen times in the year will 
 each transformer be worked at its full out-put, and 
 there is the hysteresis loss going on in it day and 
 night. This loss means waste of power and devel- 
 opment of heat ; indeed, I have heard of one case 
 in which the heat given out by a transformer 
 placed in a wine cellar was sufficient to keep the 
 cellar at a nice even temperature all the year round. 
 General experience tells us that scarcely more than 
 J^, or at most 60 per cent., of the lamps wired in 
 a district are ever alight simultaneously. The 
 maximum joint demand for current of our twenty 
 houses will therefore never exceed 600 lamps, and 
 we can substitute for the twenty separate trans- 
 formers of fifty lights each, one single transformer 
 of 600 lights. From what I have said before about 
 the influence of size on the cost of transformers, 
 you will see that the single large transformer will 
 cost scarcely more than a third the money required 
 for the twenty small ones, and that even if we put 
 down two large transformers so as to keep one in 
 
112 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 reserve, we shall do it for little more than half the 
 money. Similarly, the loss of power by hysteresis 
 will be reduced to one quarter, and this is a very 
 important consideration. Take for instance a sta- 
 tion designed for 20,000 lamps, of which 12,000 
 will be alight simultaneously during the two or 
 three hours of maximum demand. The average 
 lighting time of each lamp fixed is in London about 
 500 hours per annum. If we allow with small 
 transformers a loss of 2 per cent, by hysteresis, the 
 power continuously absorbed by all the transform- 
 ers connected to the central station will be equiva- 
 lent to that required by 400 lamps. We are wast- 
 ing, therefore, day and night current which could 
 feed 400 lamps. In a year we waste not less than 
 3,500,000 lamp hours, whereas our total income 
 from the 20,000 lamps is only 10,000,000 lamp 
 hours. This means that even if there were no 
 other sources of loss we would have to send out 
 energy from our station representing 13,500,000 
 lamp hours, but we could only get paid for 10,000,- 
 ooo lamp hours. This is only 74 per cent, effi- 
 ciency. Now suppose we use sub-stations and 
 large transformers, the hysteresis loss will fall to 
 
CENTRAL STATIONS AND ALTERNATING CURRENTS. 113 
 
 i per cent. , and the efficiency will rise to over 90 
 per cent. We can further improve the efficiency 
 by putting down at the sub-station not one trans- 
 former only, but two or more of different size, and 
 make arrangements for the insertion or withdrawal 
 of transformers from the two circuits (the high and 
 low-pressure circuits), in accordance with the de- 
 mand for current, so that during the hours of light 
 load the hysteresis loss will only take place in the 
 smallest transformer of the group. Mr. Ferranti, 
 Mr. Gordon and myself have, independently of 
 each other, devised an apparatus which switches in 
 and takes out the transformers automatically. 
 
 The employment of large transformers at sub- 
 stations has this further advantage: that the total 
 length of high-pressure mains is thereby consider- 
 ably reduced, and that there are no branch connec- 
 tions on these mains. We are thus able to get 
 higher insulation. You know that an insulation of 
 many hundreds of megohms per mile can be easily 
 attained in a continuous cable, but after the cable 
 has been laid, and branch connections have been 
 made, the insulation is much lower, the reason 
 
 being that at every joint the insulation has first to 
 8 
 
114 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 be stripped, and then made good again. Now it is 
 one thing to put on the insulation in the factory, 
 where every precaution can easily be taken to en- 
 sure perfect work, and it is quite another thing to 
 do the same kind of work at the bottom of a trench 
 or pit in the street. No matter how careful we are, 
 the insulation put on under these circumstances can 
 never be so good as that put on by the covering 
 machines in the cable factory. For this reason a 
 system of simple mains radiating from the central 
 stations to the sub-stations must show a higher in- 
 sulation than a complicated network of mains cov- 
 ering the whole district. 
 
 I have given you here the main reasons for the 
 adoption of transforming sub-stations in connection 
 with alternate current distribution, but, in applying 
 them to each given case, you must not forget to 
 take into account the commercial element. A sys- 
 tem of working may be scientifically the best, and 
 yet not the best financially. Thus the system gen- 
 erally applied at the present time in London in 
 alternating current stations is that of a separate 
 transformer for every customer, not because it is 
 theoretically the best, but simply because it is com- 
 
CENTRAL STATIONS AND ALTERNATING CURRENTS. 115 
 
 mercially the only feasible system. I have, how- 
 ever, no doubt that as the use of the light becomes 
 more general, the various companies will find it 
 advantageous to change to the system of sub-sta- 
 tions. I have hitherto not said anything as to the 
 comparative cost of continuous and alternate cur- 
 rent stations, and it is indeed very difficult to state 
 it in any definite way. The cost of boilers, en- 
 gines, and accessory apparatus will be about the 
 same in both systems. The alternators will be a 
 little cheaper than the dynamos, and there will 
 also be the cost of the battery against the continu- 
 ous current system. On the other hand, we have 
 to remember that the whole engine power may be 
 slightly less, since during the hours of heavy light- 
 ing the battery assists the engines. Taking, then, 
 one thing with another, there will not be any very 
 great difference in the cost of the plant at the cen- 
 tral station on the two systems. The difference is 
 mostly outside. If the district is large, the extra 
 cost of the heavy feeders and mains will, with con- 
 tinuous currents, be much greater than that of the 
 high-pressure feeders and low-pressure mains if 
 alternating currents are used, and the margin left 
 
Il6 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 will be more than sufficient to pay for the trans- 
 formers at the sub-stations. If the district be 
 small, and the lighting compact, then the balance 
 will be the other way. The cost of mains will be 
 about the same in the two systems, but we shall 
 not be able to save enough on the cost of the feed- 
 ers to pay for the cost of the transformers. Each 
 case must, in fact, be judged on its own merits, 
 and what I have said here about comparative cost 
 is merely intended as a guide in forming such a 
 judgment. 
 
CHAPTER IX. 
 
 EXAMPLES OF CENTRAL STATIONS. 
 
 As examples to illustrate this lecture, I choose 
 three types of central stations, distinguished from 
 each other mainly by the character of the motive 
 power employed. In the first type the motive 
 power is steam, in the second it is water power, 
 and in the third it is electricity. 
 
 I . The Sardinia Street Station of the Metropolitan 
 Electric Supply Company. The boilers are of the 
 Babcock Wilcox type, and placed on the ground- 
 floor. The battery of boilers is parallel to the two 
 rows of engines in the adjoining room, also on the 
 ground-floor, but at a slightly higher level. This 
 arrangement of boilers and engines has the great 
 advantage of reducing the length of steam-piping, 
 and minimizing the inconvenience resulting from 
 a failure of any particular length of steam-pipe. 
 
 The steam-pipe forms what is technically termed 
 
 117 
 
Il8 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 a ring main, and valves are inserted at suitable 
 points, so that any length can be cut out without 
 disturbing the supply of steam through the rest of 
 the piping. Adjoining the boiler-room, and con- 
 nected with it by a tram line, is a vast underground 
 coal store; a very admirable arrangement, espe- 
 cially in a station situated, as is that of Sardinia 
 Street, in a district where coals can only be deliv- 
 ered by cart, and where, consequently, the delivery 
 may, in times of heavy frost or fog, be interrupted 
 for some days or weeks. The engines are of the 
 compound high speed Westinghouse type, and 
 drive by belt Westinghouse alternators placed on 
 an upper floor. Alongside one wall of the machine- 
 room is placed the switchboard, by means of which 
 any desired combination between the alternators 
 and external circuits can be quickly made. During 
 the hours of light load all the circuits are put on to 
 one or two machines, but as the load increases 
 other machines are started, and some of the cir- 
 cuits are transferred to them. The machines are 
 not worked in parallel. As regards the mains, I 
 must mention an ingenious arrangement due to 
 Mr. Bailey, the engineer to the company. In 
 
EXAMPLES OF CENTRAL STATIONS. 1 19 
 
 order to avoid trie difficulties connected with the 
 insulation of joints, when these are made in the 
 streets Mr. Bailey makes, as far as possible, all 
 connections of the high-pressure mains by terminal 
 blocks on the customer's premises. Under this 
 arrangement the insulation is only stripped at the 
 ends which enter the terminals, and which them- 
 selves can be perfectly insulated. It is true that 
 under this arrangement the total length of cable 
 required is slightly increased, namely, by the length 
 of the bight taken into each house ; but this is only 
 a small percentage of the straight run of main. 
 Further, we have the advantage that each house 
 is, so to speak, served by duplicate mains, namely, 
 one on either side, and that, therefore, the house 
 need not be cut off even if one length of main in 
 the street should for any reason have to be discon- 
 nected. We have here, in fact, the electrical equiv- 
 alent of the ring main between the engines and 
 boilers. 
 
 2. The Lynton Station. This is worked by water 
 power from the River Lyn on a fall of 96 feet, the 
 water being supplied to the turbine through a 30- 
 inch pipe. Owing to the high fall the speed is 
 
120 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 sufficient for driving the alternators, which are 
 Mordey machines directly coupled one on either 
 side of the turbine. Each alternator is capable of 
 developing 37*5 kilowatts. The speed is regulated 
 by a slide valve in the main water supply pipe worked 
 by a hand-wheel. The mains are lead-covered Cal- 
 lender bitumen cables laid underground. 
 
 3. The Keswick Station. This is also worked by 
 water power obtained from the River Greta, but 
 since the fall is only 20 feet, the alternators are 
 driven by belt from the turbine shaft. The plant 
 comprises two 3O-kilowatt Kapp alternators, the 
 necessary exciting machine, switchboards and in- 
 struments, and a boiler and Westinghouse engine 
 to serve as an auxiliary source of power in case of 
 drought or frost. The mains are insulated cables 
 placed overhead on oil insulators, but for a certain 
 distance they had to be taken underground, and 
 then a Brookes' pipe line is used. 
 
 4. The C asset Station. This is an example of a 
 central station where the motive power is electricity. 
 There are two stations in the town in which dyna- 
 mos are driven by Kapp alternators working as 
 motors. The alternating current is supplied from 
 
EXAMPLES OF CENTRAL STATIONS. 
 
 121 
 
 a water-power station four miles distant. Fig. 29 
 shows the arrangement diagrammatically. At the 
 power station a turbine drives two Kapp alterna- 
 tors, each designed to give 30 amperes at 2,200 
 
 Op 
 
 o 
 
 D 2 _J_ 
 
 
 D 3 | JD 4 
 J 
 
 999 
 
 FIG. 29. 
 
 volts. The machines are coupled in parallel, and 
 the current is taken by a concentric lead-covered 
 cable to Cassel, where the cable splits into two 
 branches each leading to a lighting station. At 
 each of these lighting stations there is a 6o-kilo- 
 watt alternator coupled direct to two 3O-kilowatt 
 
122 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 dynamos wound for 1 10 volts, one dynamo on each 
 side of the alternator. The dynamos are arranged 
 on the three-wire system, and work on to a three- 
 wire network common to both stations. At one 
 of the stations there is also a battery of storage 
 cells, from which the town is supplied during the 
 hours of minimum demand. Towards evening, 
 when it is necessary to supplement the batteries by 
 dynamo power, or when it is desired to re-charge 
 the batteries, the dynamos are switched on to the 
 network, and receive current from it. This sets 
 them in motion, and, working for the time being 
 as motors, they run up the alternators to synchro- 
 nizing speed. The alternating current is then 
 switched on, and the action between the machines 
 is reversed, the alternators acting as motors, and 
 driving now the dynamos. The two stations sup- 
 ply at present current for 2,600 i6-candle-power 
 lamps burning simultaneously, or 3,500 lamps 
 wired, but provision has been made to extend the 
 plant, so as to eventually supply 12,000 lamps 
 wired. 
 
CHAPTER X. 
 
 PARALLEL COUPLING OF ALTERNATORS. 
 
 I have already pointed out that for economical 
 reasons it is advisable to work the engines at a 
 station as nearly as possible at their full load, and 
 you will easily see that this condition can most 
 easily be fulfilled if the alternators can be worked 
 in parallel. For were it only possible to work each 
 machine quite independently of the other machines, 
 we should be obliged to keep a larger number of 
 machines working on small loads, and as the hours 
 of light load greatly exceed those of full load, the 
 engines would be used under very uneconomical 
 conditions. But if we can couple the alternators 
 parallel, then we can put on and take off machines 
 exactly in accordance with the demand for current, 
 and have our engines fairly well loaded at all times. 
 Some years ago it was believed that alternators had 
 
 to be designed specially for working in parallel, 
 
 123 
 
124 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 and certain makers claimed this quality of their 
 machines as something specially in their favour. 
 If parallel running succeeded it was put down to 
 the credit of the particular type of alternator ; if it 
 failed the design of the alternator was considered 
 faulty. It is only recently that we have come to 
 recognize that the real difficulty of parallel run- 
 ning is not in the alternator at all, but in the en- 
 gine. Any alternators when driven by turbines 
 which have an absolutely constant angular speed 
 will run in parallel perfectly, but if you drive the 
 machines from slow speed steam engines by means 
 of belts or ropes, any irregularity in the angular 
 speed of the engines is magnified by reason of the 
 multiplication of speed, and the machine becomes 
 alternately a generator and a motor, the transition 
 from one state to the other being accompanied 
 by heavy mechanical and electrical strains, which 
 render anything like smooth working impossible. 
 The condition of successful parallel working is, 
 therefore, a direct-coupled engine having a very 
 even angular speed. This is a point of great prac- 
 tical importance, and it is intimately connected 
 with the general question of alternators used as 
 
PARALLEL COUPLING OF ALTERNATORS. 125 
 
 motors, since when the engine fails to keep up its 
 even angular speed the alternator steps in and 
 compels it to do so ; it acts, in fact, for a moment, 
 as a motor, and controls the engine. 
 
CHAPTER XL 
 
 ALTERNATING CURRENT MOTORS. 
 
 When investigating the transmission of power 
 by alternating currents, we may consider the cir- 
 cuit as consisting of three parts : a line having a 
 definite resistance; an alternator working as gen- 
 erator at one end ; and another alternator working 
 as motor at the other end. Such a conception 
 would be the most obvious, but it is not the best, 
 because we are thereby compelled to investigate 
 simultaneously the behaviour of two machines. To 
 simplify the treatment I shall assume the following 
 case : Given a pair of terminals, between which by 
 some means we maintain a constant alternating 
 electromotive force at constant frequency, and the 
 source from which this electromotive force is sup- 
 plied shall be so abundant that we may take any 
 amount of energy from the terminals, or put any 
 
 amount of energy into them, without altering in 
 
 126 
 
ALTERNATING CURRENT MOTORS. 127 
 
 any way either the pressure or the frequency. 
 Such a pair of terminals would, for instance, be the 
 omnibus bars at a central station, if from them we 
 supply a small motor. Suppose the motor run up 
 to synchronizing speed, and then switched on to 
 the omnibus bars. We now want to know the re- 
 lation between the mechanical power obtained, the 
 current through the armature, and the strength of 
 field. This apparently complex problem can be 
 solved graphically by means of a clock diagram in 
 a very simple manner. 
 
 It is self-evident that we can only obtain power 
 from the motor if it runs at such a speed that the 
 frequency of the electromotive force developed in 
 its armature coils is exactly the same as that of the 
 current which drives it, and that the electromotive 
 force of the motor must be opposed to the current. 
 
 We must, therefore, at first employ some exter- 
 nal source of power to run the motor up to the 
 proper speed before switching on. But how are 
 we to know when the proper speed has been reached ? 
 No tachometer or speed counter can give us this in- 
 formation with sufficient accuracy, especially since 
 there may be slight variations in the frequency of 
 
128 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 the supply current. If we wish to put two alter- 
 nators in parallel, we also must know exactly when 
 their phase and frequency coincide, and for this 
 purpose we use an instrument called a " synchro- 
 nizer." It consists mainly of two small transform- 
 ers (Fig. 30) the primaries of which are connected 
 
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 FIG. 30. 
 
 to the terminals of the two alternators which are to 
 be coupled parallel. Two of these terminals may, 
 of course, be permanently connected, as shown in 
 the figure, but the other two must only be con- 
 nected by the switch S when the machines are in 
 step. The secondaries of the two transformers are 
 connected as shown, and into this circuit are placed 
 some incandescent lamps. By following out the 
 connections you will easily see that if the two ma- 
 
ALTERNATING CURRENT MOTORS. 129 
 
 chines are in opposite phase, that is, in a condition 
 when you must not couple them, there is no elec- 
 tromotive force on. the lamps, but that when the 
 machines are in the same phase, or, as we call it, 
 "instep," then the lamps get the full electromotive 
 force of the two transformers coupled in series. 
 We thus know that when the lamps are dark the 
 machines are out of step, and when they light up 
 the machines are in step. But complete darkness 
 or complete brightness can only occur when the 
 frequencies are absolutely the same. Generally, 
 the frequencies will be different, and the lamps 
 will flicker. Thus, suppose one machine is running 
 at its normal speed, and the other is being started 
 up, at first there will be very rapid flickering in the 
 lamps. As the speed of the second machine in- 
 creases, the flickering becomes less rapid, and by de- 
 grees, namely, as the speed approaches that which is 
 required for synchronism, there appear regular beats 
 in the light of the lamps, which get longer and 
 longer. You watch your opportunity, and throw 
 the switch on in the middle of a beat when the 
 lamps are alight. The machines are then so nearly 
 in the right step that the first rush of current pulls 
 9 
 
1 30 ALTERNATING CURRENTS OP ELECTRICITY. 
 
 them dead into step, and they remain, as it were, 
 interlocked in that condition. The electrical coup- 
 ling is, in fact, comparable to a kind of interlocking, 
 which is as secure as if the two armature spindles 
 were connected by spur gearing. To test the reli- 
 ability of this electrical interlocking, I have run a 
 60 and a lo-kilowatt alternator in parallel, supply- 
 ing the power from two independent sources. I 
 have then cut off the power from the small machine. 
 It ran on exactly as before. Next, I put a load on 
 the small machine, and increased it to 25 horse- 
 power; still the machine ran on. I left the load on 
 for some hours, and then suddenly withdrew and 
 again put on a large portion of the load, but the 
 machine kept in step. There is, of course, for 
 every machine a certain load at which it will be 
 torn out of step, just the same as there is for every 
 spur wheel a load which will strip its teeth. In 
 the machine with which I experimented it should 
 be possible to break down the synchronism with a 
 load of about 30 horse-power, that is, twice the 
 normal load, but I was not able to determine the 
 breaking off load experimentally because the belt 
 by which power was taken from the motor began 
 
ALTERNATING CURRENT MOTORS. 131 
 
 to slip at 25 horse-power. The machines with 
 which I experimented were of my own type, but, 
 as I have said before, there is no particular virtue 
 in the design, any modern alternator with a smooth 
 armature core, and having a fair efficiency, will be- 
 have in exactly the same manner. 
 
 Having now given you some practical results of 
 parallel running and transmission of power, I must 
 briefly explain the theory of it. Fig. 3 1 represents 
 the condition of a machine supplying current to a 
 non-inductive resistance. OB is the electromotive 
 force which it would at its then excitation give on 
 open circuit, AB is the electromotive force required 
 to overcome its self-induction with the current it 
 actually gives, AR is the electromotive force re- 
 quired to overcome the armature resistance, and 
 RO is the electromotive force available for the ex- 
 ternal circuit. If in a central station we have 
 already a number of machines running in parallel, 
 OR would be the electromotive force on the omni- 
 bus bars, and if we wish to switch in a new ma- 
 chine we would, in order to have it in the same 
 condition as the others, excite it to such a degree 
 that on open circuit it will give the electromotive 
 
13* 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 force OB. We run the machine up to the right 
 frequency and switch it on. For the sake of the 
 present investigation, I will assume the new ma- 
 chine can be mechanically geared with one of the 
 other machines in such a way that its electromotive 
 force shall lag or lead in comparison with the om- 
 nibus electromotive force by any desired angle. 
 Thus in Fig. 32 OR represents the omnibus electro- 
 
 FIG. 31. 
 
 motive force, and OB the machine electromotive 
 force, the angle between the two being ensured 
 constant by the mechanical gearing. By drawing 
 the parallelogram ORCB we find the resultant elec- 
 tromotive force in the new machine OC, and this 
 can be regarded also as the resultant of the electro- 
 motive force of self-induction CD, and that lost in 
 armature resistance OD. If we regard the coefficient 
 
ALTERNATING CURRENT MOTORS. 133 
 
 of self-induction constant, then the angle ?>, which 
 OD makes with OC, is the same as that which in 
 Fig. 31 RA makes with RB, and the direction of 
 the line OD in Fig. 32 is at once defined. The 
 
 FIG. 32. 
 
 point D is found by dropping a perpendicular from 
 C on this line. Since OD represents the electromo- 
 tive force used up in resistance, and since we know 
 the resistance, it is easy to calculate the current. 
 We know then the direction and magnitude of the 
 current as well as of the electromotive force, and 
 we can find the work done by the machine. For this 
 purpose we multiply the current with the electromo- 
 
134 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 tive force, and with the cosine of the angle enclosed 
 between the two lines. The work thus found, we 
 mark off on the line OB or its prolongation . Now let 
 us shift our mechanical gearing and find in the same 
 manner the current and work for a different angle 
 between the omnibus and machine electromotive 
 force, and repeating the construction for various 
 phase angles, we obtain the curves on Fig. 33, 
 which show current, and work as functions of the 
 phase angle. The outer curve on the left repre- 
 
 FIG. 33. 
 
 sents the work given out by the machine when its 
 phase angle lags from O to about 180, the inner 
 curve represents the work absorbed by the machine 
 (when working as motor) when its phase angle lags 
 from 1 80 to 360. The curves on the right repre- 
 sent similarly the work given to or taken from the 
 
ALTERNATING CURRENT MOTORS. 135 
 
 omnibus bars. You will notice that about half of 
 the curves are dotted. The dotted parts refer to 
 an unstable condition of working, and the diagram 
 shows at a glance why it is impossible to run two al- 
 ternators in series if they are independently driven, 
 that is, not mechanically geared together, as I have 
 assumed to be the case for the purpose of explaining 
 how this diagram is obtained. You will also see 
 that a moderate difference in the phase angle is 
 sufficient to transform the machine from a strong 
 generator into a strong motor. The difference of 
 position in the two cases is about 90, but you must 
 remember that the diagram represents a two-pole 
 machine. In reality the machines are made with 
 many more poles, and the angle is much smaller. 
 For instance, if there were eighteen poles the angle 
 would only be about 10, and this explains why it 
 is essential for parallel working, and also for power 
 transmission, to employ engines which will impart 
 to the machines an almost absolutely constant an- 
 gular velocity. 
 
CHAPTER XII. 
 
 SELF-STARTING MOTORS. 
 
 From what I have here said you will conclude 
 that there is no difficulty in transmitting power by 
 a single alternating current, but that the motor is 
 not self-starting. The system is thus encumbered 
 by the necessity of providing a separate machine 
 and some storage of power to set this in motion. 
 The most convenient way is to use the exciter for 
 this purpose, and drive it by a storage battery. 
 When the alternator is working as a motor it drives 
 its own exciter, and the latter may at the same 
 time be used to charge the battery up again ready 
 for the next start. The complication and cost of 
 this arrangement are not very serious objections 
 when we have to deal with large powers, but for 
 the distribution of small parcels of power the neces- 
 sity of providing a separate exciter and a storage 
 
 battery, in addition to the motor proper, is a fatal 
 
 136 
 
SELF-STARTING MOTORS. 137 
 
 objection, and various attempts have been made to 
 design a self-starting alternate current motor. One 
 of these, and I may at once say the most successful 
 one, is due to Mr. Zipernowsky, whose firm (Ganz 
 & Co., of Budapest) showed at the Frankfort Exhi- 
 bition several of these machines at work. In the 
 limited time at my disposal I cannot attempt to 
 give you a detailed description of these, nor enter 
 into the many refinements of construction which 
 have been found necessary in developing the ma- 
 chine practically. I must content myself to give 
 you the main principle of it. In Fig. 34 M is a 
 laminated magnet and A an armature wound with 
 a single coil, the ends of which are brought to 
 a two-part commutator. It is, in fact, the well- 
 known Siemens shuttle armature, also employed 
 in the small Griscom motor, and the apparatus, as 
 here shown, is nothing else than a very simple form 
 of continuous current motor, which is self-starting 
 from almost any position. The only position when 
 the motor will not start is when the armature is 
 placed so that the brush on each side touches both 
 commutator segments at once. To start the motor 
 from this position, it is of course necessary to 
 
138 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 slightly shift the brushes to one side or the other 
 of the dead centre. From what I have said in 
 Chapter I., you will easily see that this kind of 
 
 FIG. 34. 
 
 motor will also start and work with an alternating 
 current, but its power will at first be very slight. 
 Observe now what happens when the alternating 
 current is switched on whilst there is no load on 
 the motor. It will start and gather speed as all 
 series wound motors do. If the current were con- 
 tinuous, the motor would very soon begin to race, 
 but with an alternating current this cannot happen, 
 because in trying to get up a racing pace the arma- 
 ture must pass through that speed which corre- 
 sponds to the frequency of the supply current. At 
 
SELF-STARTING MOTORS. 139 
 
 the moment when this happens, the reversal of cur- 
 rent produced by the commutator coincides exactly 
 with the reversal of the supply current, and the re- 
 sult is that the current flowing through the arma- 
 ture does not any more change its direction. The 
 armature has virtually been transformed into a 
 field magnet, excited by a continuous current, and 
 what was at starting the field magnet has now be- 
 come the armature of an ordinary alternator. The 
 moment when the machine jumps into step can be 
 easily noticed by the behaviour of the brushes. 
 At starting there is violent sparking and a peculiar 
 noise. As the machine gathers speed the sparking 
 gets less, and suddenly there is a kind of jerk, 
 after which both noise and sparking cease and the 
 load may be put on. The motor, when once in 
 step, will even stand a considerable overload. 
 
CHAPTER XIII. 
 
 MULTIPHASE CURRENTS. 
 
 The motor I have just described will start itself, 
 but it will not start with a load. The sparking is 
 also an objection which renders the machine use- 
 less for flour mills, cotton mills, and any works 
 where an explosion may be caused by sparks. We 
 can therefore not regard this motor as the final so- 
 lution of the problem of transmitting power by 
 alternating currents, but must look for the solu- 
 tion in quite another direction. This direction has 
 been first indicated by Professor Galileo Ferraris, 
 of Turin, some six years ago. Quite independent 
 of Ferraris, the same discovery was also made by 
 Nikola Tesla, of New York ; and since the practical 
 importance of the discovery has been recognized, 
 quite a host of original discoverers have come for- 
 ward, each claiming to be the first. With these 
 
 various claims we need not concern ourselves at 
 
 140 
 
MULTIPHASE CURRENTS. 
 
 141 
 
 present. I will merely describe the apparatus used 
 by Ferraris. He employed two vertical coils AB 
 (Fig. 35) set at right angles to each other, and a 
 copper cylinder C suspended between them. Two 
 alternating currents of the same frequency, but 
 with a phase difference of 90 degrees, were sent 
 though the two circuits, and the copper cylinder 
 was thereby set in rotation. The explanation is as 
 
 FIG. 35. 
 
 follows: Each coil taken by itself produces an 
 oscillating magnetic field, the lines of which are at 
 right angles to the face of the coil. The two coils 
 together produce a resultant .field which revolves 
 round the vertical axis of the apparatus. The sur- 
 face of the copper cylinder is therefore being con- 
 
142 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 tinuously cut by lines of force as they sweep round ; 
 currents are induced in the copper which by Lenz's 
 law are in such directions as to resist motion ; and 
 since the cylinder is freely suspended, its endeavour 
 to resist the motion of the field results in its being 
 set in motion itself. 
 
 Experiment Lantern and Model. In translating 
 this laboratory experiment into practical work we 
 must, of course, make many alterations and im- 
 provements. We must, for one thing, employ iron 
 to get a more compact and a stronger apparatus. 
 We must also sub-divide the two coils in order to 
 get a machine which will run at a moderate speed, 
 and finally we must substitute for the plain copper 
 cylinder an armature properly wound. A machine 
 designed on these lines will be, generally speaking, 
 a great improvement on the original apparatus, but 
 in one respect it will not be so good. In Fig. 35 
 the coils are at right angles, and the currents are 
 at right angles. As you have seen by the model, 
 the effect of this combination is an absolutely con- 
 stant magnetic field revolving round the axis with 
 constant speed. But if we split up the two coils 
 into a number of sections, and wind these alter- 
 
MULTIPHASE CURRENTS. 143 
 
 nately side by side on a cylindrical core, as we 
 wind a Gramme armature, one of our conditions, 
 namely, that of the right angular position of the 
 two coils, has been lost, for the coils are now very 
 nearly in line with each other all the way round, 
 and the result is that the field is not any more ab- 
 solutely constant. I can show you this by means 
 of the model. By setting the cranks at the wrong 
 angle you see immediately that the vector of the 
 resultant field is no longer the radius of a circle, 
 but of a curve resembling an ellipse. To find the 
 variation in the strength of the resultant field we 
 need only draw the two current curves and add 
 up their ordinates as I showed you in Chapter I. 
 If you do this you will find that the maximum 
 strength of the field is about 40 per cent, greater 
 than its minimum value. The field is now not 
 only a rotating one, but it also pulsates. The ro- 
 tation is what we want, but the pulsation is objec- 
 tionable, as, in consequence of it, useless currents 
 are made to circulate in the armature conductors, 
 producing heat but no power. It is the great merit 
 of Herr von Dobrowolsky to have been the first 
 to clearly recognize this defect in machines based 
 
ALTERNATING CURRENTS OF ELECTRICITY. 
 
 he Tesla- Ferraris motor. The evil once un- 
 derstood, a remedy was soon found. Dobrowolsky 
 adopted three currents instead of two, and thus re- 
 duced the pulsation of the field at once to some- 
 thing like 14 per cent. ; but even this was not quite 
 satisfactory. He went, therefore, a step further 
 and re-arranged the winding of the field in such a 
 way as to produce the effect of six distinct currents, 
 though still only using three wires in the line of 
 transmission. A reference to Fig. 36 will make 
 
 this clear. Let abc represent the three coils of a 
 two-pole drum armature, such, for instance, as the 
 armature of a Thomson- Houston machine, but in- 
 stead of joining the coils to a common centre and 
 to a three-part commutator, as is done in this type 
 
MULTIPHASE CURRENTS. 145 
 
 of machine, let them be joined as shown, and let 
 the points of junction ABC be three contact rings 
 by which the currents are received from the line. 
 According to Kirchoff's law, the algebraical sum 
 of the three currents ABC must at all times be 
 ero, for if this were not the case there would be 
 an accumulation of electricity in the machine 
 which is obviously impossible. Any of the cur- 
 rents may therefore be regarded as the resultant of 
 the other two currents. Here we have a simple 
 three-phase winding and a rotating field, the pulsa- 
 tions of which are about 14 per cent, of its mini- 
 mum strength. Now to reduce these pulsations, 
 Dobrowolsky adopts the following expedient. In- 
 stead of bringing the junction between b and c di- 
 rect to the contact ring A, he attaches to the junc- 
 tion a stouter wire and winds this round the 
 armature in a coil placed midway between b and c. 
 Similarly B is wound so as to split up the phase 
 difference between a and c, and C is wound in be- 
 tween a and b. We have now six coils on the 
 armature, but only half the former phase difference 
 between neighbouring coils. Fig. 37 shows a two- 
 pole armature so wound, and in this way the pulsa- 
 10 
 
146 
 
 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 tion is reduced to about 4 per cent. Were the 
 winding not split up in the manner shown, the 
 tendency to produce fluctuations in the strength of 
 
 FIG. 37. 
 
 the resultant field would cause currents to circulate 
 in the induced part of the winding, and these cur- 
 rents would prevent, to a certain extent, the fluctu- 
 ations. But as they must necessarily circulate in 
 coils which at the moment cannot contribute any- 
 thing to the torque by reason of their position at 
 right angles to the resultant field, these currents 
 represent simply so much waste of power by ohmic 
 resistance. Hence Dobrowolsky's method of split- 
 ting up the winding, although not indispensable, 
 
MULTIPHASE CURRENTS. 147 
 
 is a useful device for increasing the out-put obtain- 
 able from a given mass of iron and copper, and for 
 increasing the efficiency. I have called the part of 
 the motor represented by Fig. 37 an armature, but 
 this was merely to point out the analogy with a 
 Thomson- Houston armature. It would be more 
 correct to call this part, which receives the currents 
 from the line, the field, because its function is to 
 produce the revolving field. The armature of the 
 machine is a hollow cylinder of laminated iron, 
 built up of thin plates in the usual way, and pro- 
 vided with a winding which is closed on itself. To 
 understand the principle of this winding, imagine 
 a Gramme ring, the winding of which is altered in 
 the following way. Instead of joining the inner 
 end of each coil with the outer end of the next coil, 
 so as to produce a spiral winding, let the two ends 
 of each coil be joined together. You will then 
 have covered the Gramme core with a number of 
 distinct coils, each closed on itself. Now put a 
 field magnet into the inner space of the armature 
 and revolve this magnet. The poles sweeping past 
 the closed coils of the armature will create in them 
 very powerful currents, and the mechanical reaction 
 
148 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 of these currents on the poles will require the ap- 
 plication of a considerable twisting couple or torque 
 to keep up even a moderate speed. You can test 
 this for yourselves very easily by means of any 
 continuous current dynamo. Excite its field sepa- 
 rately, and short-circuit the brushes by a thick 
 wire. If you then turn the armature by hand you. 
 will find that even exerting considerable force it 
 will only creep round slowly, and you will thus 
 realize how a great torque may be developed by a 
 small angular speed of the armature in relation to 
 the field magnet. This is an important fact, and 
 helps us to understand two things in connection 
 with rotary field motors. The first is that the 
 speed of such a motor does not vary much when 
 the load varies, since small variations of the rela- 
 tive speed between field and armature produce large 
 variations in the torque ; and the second is that the 
 torque at starting is very large, the reason being 
 that at starting the relative speed between arma- 
 ture and field is a maximum. It is, however, neces- 
 sary to observe here that to get this large torque, 
 resistance must be inserted in the armature circuit, 
 for were this not done, the current in the armature 
 
MULTIPHASE CURRENTS. 149 
 
 coils would be so strong as to demagnetize the re- 
 volving field, thus again reducing the torque. We 
 may now go back to Fig. 37, and see how this 
 works out in practice. You have seen how a three- 
 phase current passing through the winding pro- 
 duces a sensibly constant field, which revolves 
 round the centre with a speed corresponding to 
 the frequency. The armature surrounds the part 
 shown in Fig. 37, but is omitted from the diagram. 
 The lines of the field, in sweeping past the arma- 
 ture conductors, create in them very strong cur- 
 rents, and the mechanical reaction between these 
 currents and the lines of the field tends to rotate 
 the armature with great force. If the armature 
 were movable it would thereby be set in rotation. 
 But in the particular machine I am describing, the 
 armature is fixed, whilst the field magnet, that is, 
 the part shown in Fig. 37, can rotate. We have 
 then a twisting couple between the armature and 
 field ; the armature cannot move, and therefore the 
 field must move. Let us now see what is the effect 
 of this movement. Say that the direction of the cur- 
 rents is such as to produce, when the central part of 
 the machine is at rest, a clockwise rotation of the 
 
150 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 lines of force. The speed of rotation between the 
 lines and the wires corresponds, of course, always to 
 the frequency. If the wires are stationary the 
 lines revolve in relation to any fixed object in space 
 (for instance, the wires of the armature) with the full 
 speed given by the frequency, say, for instance, 
 thirty revolutions per second if the frequency is 
 thirty and our machine is wound for two poles, as 
 shown in Fig. 37. Each wire of the armature will 
 therefore be cut thirty times by a north field, and 
 thirty times by a south field in each second, and 
 the torque produced will set the central drum rotat- 
 ing counter-clockwise. Say, for instance, that the 
 central drum runs backwards with a speed of twenty 
 revolutions per second. The relative speed be- 
 tween the central drum and the lines of force is, of 
 course, still thirty revolutions per second, but of 
 these thirty revolutions twenty revolutions are made 
 up by the backward rotation of the drum, leaving 
 only ten revolutions of forward speed for the lines 
 of force in relation to any fixed point in space. 
 The wires of the armature are now cut only ten 
 times per second by a north field, and ten times 
 per second by a south field. If we allow the drum 
 
MULTIPHASE CURRENTS. 151 
 
 to run faster still, the speed of cutting lines will be 
 still further reduced. If, for instance, the central 
 drum is so lightly loaded that it can acquire a speed 
 of twenty-nine revolutions, the absolute speed of 
 the field in relation to the armature will be reduced 
 to one revolution, and each armature wire will be 
 cut by a north field only once a second, and by a 
 south field also once a second. You see, therefore, 
 that the less the load on the motor the faster it will 
 run, and this is precisely the same condition as ob- 
 tains in an ordinary continuous current motor. At 
 starting, when the drum is at rest, we have the 
 greatest torque, and as the speed increases the 
 torque diminishes. This is a very important prop- 
 erty cf the three-phase motor, since in consequence 
 of it the machine not only becomes a self-starting 
 motor, but one which will start with a large load. 
 How large the starting load may be depends on the 
 more or less skilful design of the motor. There 
 are, as already pointed out, certain reactions of the 
 armature on the field which tend to decrease the 
 starting torque, but the subject is too difficult and 
 intricate to be treated in the limited time at my 
 disposal. I have merely given you a bare outline 
 
152 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 of the action of this class of machine, so that you 
 may understand in a general way the principle of 
 working. 
 
 The difference in speed of the drum and the field 
 is technically termed the magnetic slip of the mo- 
 tor, and you will easily see that, to obtain a small 
 magnetic slip, and therefore a close approach to a 
 constant speed, we must employ an armature of 
 small resistance. Here, again, there is a close 
 analogy between the three-phase motor and an or- 
 dinary continuous current motor with shunt or sepa- 
 rately excited magnets. In practice, the magnetic 
 slip need never exceed 10 per cent., and is generally 
 between 3 and 5 per cent. This means that the 
 speed of the motor only varies 5 per cent, between 
 full load and no load. 
 
 In the machine which I have described the inner 
 revolving part is the field magnet, but you will easily 
 understand that the design could also be reversed 
 by making the outer ring the fixed field magnet, 
 and the inner drum the revolving armature. This 
 arrangement is, in fact, adopted for small motors, 
 because in this way we avoid altogether the neces- 
 sity of using rubbing contacts, but it has the disad- 
 
MULTIPHASE CURRENTS. 153 
 
 vantage of increasing the loss from hysteresis. I 
 have shown you that the speed with which the field 
 sweeps through the iron of the armature is very 
 small, namely, that corresponding to magnetic slip, 
 whereas the speed with which the field sweeps 
 through the iron of the field magnet is that due to 
 the frequency, or about twenty times as great. 
 The hysteresis loss in the armature is therefore 
 trifling as compared with that of the field, and it is 
 obviously of advantage to have less iron in the 
 field than in the armature, which is done by mak- 
 ing the inner drum the field, and the outer cylinder 
 the armature. In small machines, where efficiency 
 is not of paramount importance, the opposite ar- 
 rangement is adopted, because of its greater sim- 
 plicity and reduced cost. 
 
 The three-phase motor has several advantages 
 over its two rivals, the ordinary continuous current 
 motor and the ordinary alternate current motor, 
 whilst, in a certain measure, it combines the good 
 qualities of both. It is better than the continuous 
 current motor, because of its greater simplicity. 
 There is no commutator, and there are no brushes. 
 There can be no sparking, and the motor may 
 
154 ALTERNATING CURRENTS OF ELECTRICITY. 
 
 therefore safely be used in coal mines and other 
 places where a machine that is liable to sparking 
 would be dangerous. As a matter of fact ; Mr. 
 Tesla has already constructed motors for coal-cut- 
 ting machines. Its greater simplicity, and more 
 robust construction, renders it also applicable on 
 board ship and other places where it is exposed to 
 rough usage. It would, for instance, be perfectly 
 feasible to design a three-phaser which will stand 
 being drenched with sea- water, and yet work on as 
 if nothing had happened. Another advantage is 
 that the distance over which power has to be trans- 
 mitted can be much increased. With ordinary 
 continuous current motors this distance is limited, 
 because we cannot make such machines, especially 
 if of small power, for high voltages. With a three- 
 phaser there is no such narrow limit to the voltage, 
 for it is always possible to work through transform- 
 ers, raising the voltage at the generating station, 
 and letting it down again at the motor station, and 
 this can be done with very small loss. Thus, in 
 the Lauffen transmission of power, the voltage of 
 the generating machine was only 50 volts (meas- 
 ured from any of the three terminals to earth), 
 
MULTIPHASE CURRENTS. 155 
 
 whilst the voltage of any line wire measured in the 
 same way was 160 times as great in some experi- 
 ments, and 320 times as great in others. 
 
 Ordinary alternators offer, of course, the same 
 facility of transmitting power at high voltage and 
 utilizing it at low voltage, but they do not offer the 
 same facility for distributing the power in small 
 parcels, because each motor must be provided with 
 some source of independent electrical energy for 
 starting and field excitation. It is also claimed by 
 Her von Dobrowolsky that the total weight of cop- 
 per in the line is better utilized if arranged in three 
 wires for the three-phase current than in two wires 
 for a single-phase current, but on this point I can- 
 not give you my own opinion, as I have not yet in- 
 vestigated it. One of the objections against the 
 three-phase current is that it does not admit of a 
 variable speed of motor, which, for many purposes, 
 especially for traction work, is an absolute necessity. 
 This, no doubt, is a serious drawback, but we may 
 reasonably expect that the men who have succeeded 
 in transmitting something like 200 horse-power 
 over a distance of 1 10 miles will, in time, also suc- 
 ceed in solving this problem. 
 
SHELL TRANSFORMERS, 
 
 OUTPUT OF ALL 6 K. W. 
 
 Plate I 
 
 
 
 
 Item, 96 Ibs". 
 
 
 
 
 Iron, 100 Ibs. 
 Copper, 340 " 
 
 Copper^ 450 u 
 Hygferesisi 1,3* 
 
 ^\ 
 
 Hysteresis, 1.45$ 
 
 Iron, 90 Ibs. 
 
 Copper, 160 " 
 Hysteresis 
 
 Iron, 105 Ibs. 
 
 Copper, 120 " 
 Hysteresis, 
 
 Iron, 
 
 Copper, 
 
 "Hysteresis, 
 
 '102 IBs. 
 
 Iron, 
 
 Copper, 
 
 Hysteresis, 
 
 108 Ibs. 
 
 Iron, 119 Ibs. 
 
 Copper, 54 w 
 Hysteresis,. 
 
 Iron, 154 Ibs. 
 
 Copper, 25 " 
 JHysteresis, 2.2* 
 
SHELL TRANSFORMERS. 
 
 OUTPUT OF ALL 6 K. W. 
 
 jtebH T LEOFFEE r\ i. 
 
 Iron, 94 Ibs. 
 
 Copper, 116 " 
 Hysteresis, 1.3# 
 
 Plate 
 
 Iron, 105 Ibs. 
 
 Copper, 93 " 
 Hysteresis, 1.53* 
 
 Iron, 103 Ibs. 
 
 Copper, 59 " 
 Hysteresis, 1.55* 
 
 Iron, 114 Ibs. 
 
 Copper, 48 " 
 Hysteresis, 1.7* 
 
 D D 
 
 Iron, 120 Ibs. 
 
 Copper, 33 " 
 'Hysteresis, 1..7W 
 
 Iron, 115 Ibs. 
 
 Copper, 19 " 
 'Hysteresis, 
 
 Irpn, 135 Ibs. 
 
 Copper, 27 " 
 Hysteresis, 1.94j< 
 
 Iron, 173 Ibs. 
 
 Copper, 15 " 
 Hysteresis, 2.5556 
 
INDEX. 
 
 AIR-GAP, Resistance of, diminished with iron arma- 
 tures, 80 
 Alternators, Advantages of, 80 
 
 compared with continuous current machines, 
 
 62 
 
 Conductors of, 74 
 Coreless, 79 
 Cores of, 74 
 Description of, 82 
 Design of, 71, 74 
 in parallel, 128 
 
 Experiment with, 130 
 in series, 135 
 
 Mechanical construction of, 73 
 Practical forms of, 62, 63 
 Simple form of, 59 
 
 Alternators, Brown's three-phase, 74, 80 
 Ferranti, 79-82 
 Kapp, 87 
 Kennedy, 89 
 Kingdon, 88 
 Lowrie-Hall, 65 
 Meritens, 79 
 
 159 
 
160 . INDEX. 
 
 Alternators, Mordey, 79, 84 
 Siemens, 79 
 Thomson-Houston, 85 
 Westinghouse, 65, 85 
 Alternating current machines, 57 
 
 motors, 126 
 
 Alternating currents, Clock diagram of, 18 
 Combining, 20 
 described, 11 
 Distribution of, 105 
 Graphical representation of, 15 
 Sinusoidal curve of, 16 
 Zeuner diagram of, 19 
 Ampere-balance, Thomson's, 39 
 Armatures, Advantage of iron cores in, 80 
 Alternating machine, 65-74 
 Coreless, 79 
 
 Losses by hysteresis in, 78 
 of three-phase motors, 147 
 Split up, to avoid eddy currents, 83 
 with no wire, 88 
 Average volts and current, 40, 45 
 
 AILEY'S system of mains, 118 
 
 Blakesley, 37, 41 
 Brown, C. E. L., 6 
 
 Three-phase machine of, 74, 80 
 
 C 
 
 ENTRAL STATION, Cassel, 122 
 Keswick, 120 
 Lynton, 119 
 Sardina St., Met. E. S. Co., 117 
 
INDEX. l6l 
 
 Central stations, 105 
 
 Alternating vs. continuous current, 107, 115 
 Choking coil, 15 
 Coefficient of E. M. F. of alternator, 71 
 
 Numerical values of, 72, 88 
 of self-induction, 28, 35 
 Clock diagram, of alternating currents and E. M. F., 18 
 
 Motor, 127 
 
 Commutator, Advantage of absence of, in alternators, 80 
 Conductors of alternators, 74 
 Construction, Mechanical, of alternators, 73 
 
 Precautions necessary in, 74 
 Cooling surface of transformers, 103 
 Core transformers, 98 
 Cores of alternators, 74 
 Current, Average, 40, 45 
 Effective, 39, 45 
 Work of, 46 
 
 Currents, Alternating, explained, u 
 Conventional view of, 9 
 Direction of flow of, 10 
 Quarter-phase, 5 
 Three-phase, 5 
 Curve, Sinusoidal, 16 
 
 Trapezoidal, of E. M. F., 68 
 
 DESIGN of alternators, 71, 73, 74 
 Dobrowolski, 6 
 
 motor, 143 
 
 EDDY currents, Cure for, 74 
 Losses from, reduced, 83 
 Thomson, Elihu, on, 75 
 ii 
 
162 INDEX. 
 
 Effective currents and E. M. F., 39 
 
 determined analytically, 44, 45 
 determined graphically, 67 
 E. M. F., Average, 40, 44 
 
 Coefficient of, 71, 72 
 Counter, 53 
 
 and self-inductive, Relation between, 54 
 Curve of, actual, 69 
 
 sinusoidal, 16 
 trapezoidal, 68 
 Effective, 39, 45> 6l > 62 
 Expression of, for alternators, 7 1 
 Factors of, of alternators, 70, 71 
 Formula of maximum, 61 
 of self-induction, 28, 53 
 Ewing, 76 
 
 alternator, 79, 82 
 Ferraris, Prof. Galileo, 140 
 
 Motor model of, 141 
 Field, Intensity of, 60 
 
 Strength of, in Mordey alternator, 85 
 Fleming, 34 
 Frequency, 14, 20, 53, 61 
 
 Effect on motor of lowering, 55 
 
 motor, 55 
 
 HEAT developed a measure of E. M. F. and current, 66 
 Hysteresis, 73, 76 
 
 How to reduce loss from, 77 
 
INDEX. 163 
 
 Hysteresis, Losses from, 76, 99, 101, 103, in, 153 
 Loss in kilo-watts, 78 
 
 INDUCTANCE, 32 
 
 * Induction and current curve, 25 
 
 Change of, 25 
 
 Coefficient of self-, 28, 35 
 
 Total, 6 1 
 
 Instantaneous values of current and E. M. F., 28, 29 
 Impedance, 34 
 
 KAPP alternator, 87, 121, 122 
 Kelly, 6 
 
 Kennedy alternator, 89 
 Kingdon alternator, 88 
 
 LAG of E. M. F., 29, 32 
 Angle of, 33, 43 
 Lines of force, 24 
 
 MAGNET poles of alternators, 64, 65 
 Influence of, on shape of curve of E. 
 
 M. F., 65, 66 
 Lowrie-Hall type of, 65 
 Mordey form of, 84 
 should be of equal strength, 83 
 Westinghouse type of, 65 
 Magnetic friction or hysteresis, 76 
 leakage, 95 
 
 Effect of, 96 
 slip, 152 
 Measurement of pressure, current and power, 37 
 
164 INDEX. 
 
 Meri ten's alternator, 79, 84 
 Mordey alternator, 79, 84 
 Motor, Dobrowolski, 144 
 Ganz, 55 
 
 Tesla-F'erraris, 143, 154 
 Zipernowsky, 137 
 Motors, Alternating current, 52-55, 126 
 
 Effect of lower frequency on, 55 
 
 Multiphase, 141 
 
 Self-starting, 136, 151 
 
 Starting, 55, 122 
 
 Theory of alternating, 131 
 
 Three-phase, 140 
 
 Two-phase, 140 
 Motor-transformer, 92 
 Multiphase currents, 140 
 
 PARALLEL coupling of alternators, 123 
 
 Theory of, 131 
 Period of current, 53 
 Permeability, 25 
 Phase, 20 
 
 Angle of, 133 
 Power, maximum, Analytical deduction of, 56 
 
 Condition of, 49 
 
 Graphical representation of, 51 
 Pulsation of multiphase current field, 143, 145, 146 
 
 UARTER-PHASE currents, 5 
 
 p OTARY field, Action of, 148 
 
INDEX. 165 
 
 SELF-INDUCTION, 24, 26, 27, 29, 50 
 Coefficient of, 28, 35 
 
 E. M. F. of, 28, 53 
 
 Phenomena of, 30 
 Self-starting motors, 136 
 Shell transformers, 98 
 Siemens alternator, 79 
 
 dynamometer, 39, 40, 43 
 
 Sinusoidal curve of alternating currents and E. M. F., 16 
 Stanley, Wm., Jr., 3-6 
 Steinmetz, 6 
 
 Storage battery for starting motors, 136 
 Sub-stations, Transforming, 109, 114 
 Swineburne's hedgehog transformer, 97 
 Synchronizer, 128 
 
 TESLA motor, 143, 154 
 Nikola, 140 
 
 Thomson's ampere-balance, 39 
 Thomson, Elihu, on eddy currents, 75 
 
 experiments with armature coils, 86 
 Thomson-Houston alternator, 86 
 Three-phase alternator, 74 
 currents, 5 
 motors, 144 
 
 Advantages of, 153 
 Objections to, 155 
 Transformers, 91 
 
 Core, 98 
 Hedgehog, 97 
 Magnetic leakage in, 95 
 Motor- 92 
 
1 66 INDEX. 
 
 Transformers, Principles of, 92, 99 
 
 Relation between dimensions of, 101 
 Shell, 98 
 
 Small vs. large, 109, 113 
 Temperature of, 103 
 Transforming ratio of, 95 
 Variation of E. M. F. in, 94, 97 
 
 Transforming sub-stations, 109 
 
 Transmission of power, Theory of, 131 
 
 Two-phase motors, 140 
 
 motor model, 141 
 
 V 
 
 OLTMETER, Cardew, 39, 66 
 
 Copper-electrolysis, 40 
 
 Correction of readings of, with alternating 
 
 currents, 37, 42 
 measures heat developed, 66 
 
 WATTMETER, 43 
 Correction for, 48 
 Theory of, 47 
 
 Watts, apparent and true, 42, 46 
 Westinghouse alternator, 85, 118 
 
 'TEUNER diagram of alternating currents and E. M. F., 
 
 L, I9 
 
 Zipernowsky motor, 137 
 
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