r 
 
 SRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 ; i 
 
 Deceived 
 Successions 
 
 MAR '23 1&94 
 
 189 
 
 No 
 
 Class No. 
 
ORIGINAL PAPERS 
 
 ON 
 
 DYNAMO MACHINERY 
 
 AND ALLIED SUBJECTS. 
 
 BY 
 
 JOHN HOPKINSON, M.A., D.So., F.B.S. 
 
 NEW YORK : 
 THE W. J. JOHNSTON COMPANY, LIMITBB, 
 
 41 PARK Row (TIMES BUILDING). 
 
 LONDON : 
 WHITTAKER & CO., 
 
 2, WHITEHART STREET, PATERNOSTER SQUARE. 
 
 1893. 
 

 AUTHORIZED AMERICAN EDITIOK 
 
PEEFACE. 
 
 THE following short collection of papers includes all that 
 I have written of an original character on electrotechnical 
 subjects. Here and there errors have been corrected; 
 otherwise the papers are republished exactly as they 
 first appeared. The chronological order is not . strictly 
 adhered to. The papers are arranged rather according to 
 subject. Thus, five papers relating wholly or in part to the 
 continuous current dynamo come first; then follow four 
 on converters ; lastly, there are a note on the theory of al- 
 ternate current machines and a paper on the applications 
 of electricity to lighthouses. 
 
 The motive of this publication has been that I have 
 understood that one or two of these papers are out of 
 print and are not so accessible to American readers as an 
 author who very greatly values the good opinion of Ameri- 
 can electrical engineers would desire. 
 
 J. HOPKI^SOtf. 
 LONDON, September, 1892. 
 
 3 
 
CONTENTS. 
 
 PAGE 
 
 I. ON ELECTRIC LIGHTING, . . . - 7 
 
 (Proceedings of the Institution of Mechanical Engineers, April 25, 1879.) 
 
 II. ON ELECTEIC LIGHTING, (Second Paper) . . 26 
 
 (Proceedings of the Institution of Mechanical Engineers, April 23, 1880.) 
 
 III. SOME POINTS IN ELECTRIC LIGHTING, ... 40 
 
 (Proceedings of the Institution of Civil Engineers, April 5, 1883.) 
 
 IV. DYNAMO-ELECTRIC MACHINERY, 79 
 
 (Philosophical Transactions of the Royal Society, May 6, 1886.) 
 
 V. DYNAMO-ELECTRIC MACHiNERY,(Second Paper) 134 
 
 (Proceedings of the Royal Society, February 15, 1892.) 
 
 VI. THEORY or ALTERNATING CURRENTS, . . . 148 
 
 (Institution of Electrical Engineers, November 13, 1884.) 
 
 VII. AN UNNOTICED DANGER IN CERTAIN APPA- 
 RATUS FOR DISTRIBUTION OF ELECTRICITY, 177 
 
 (Philosophical Magazine, September, 1885.) 
 
 VIII. INDUCTION COILS OR TRANSFORMERS, . . .182 
 
 (Proceedings of the Royal Society, February 17, 1887.) 
 
 IX. EEPORT TO THE WESTINGHOUSE COMPANY OF 
 THE TEST OF Two 6,500-WATT TRANS- 
 FORMERS, MAY 31, 1892, .187 
 
 X. THEORY OF THE ALTERNATE CURRENT DYNAMO, 211 
 
 (Proceedings of the Royal Society, February 17, 1887.) 
 
 XL THE ELECTRIC LIGHTHOUSES OF MACQUARIE 
 
 AND OF TINO, 217 
 
 (Proceedings of the Institution of Civil Engineers, December 7, 18S6.) 
 
 5 
 
ORIGINAL PAPEES 
 
 ON 
 
 DYNAMO MACHINERY 
 
 AND ALLIED SUBJECTS. 
 
 ON ELECTRIC LIGHTING. 
 
 FIRST PAPER. 
 
 DURIKG the last year much has been written and much 
 information communicated concerning the production of 
 light from mechanical power by means of an electric cur- 
 rent. The major portion of what has appeared has been 
 either descriptive of particular machines for producing the 
 current, and of lamps for manifesting a portion of its 
 energy as light, or a statement of practical results con- 
 necting the light obtained with the power applied and the 
 money expended in producing it. 
 
 While fully appreciating the present value of such in- 
 formation, the author has felt that it did not tell all that 
 was interesting or practically useful to know. It is de- 
 sirable to know what the various machines can do with 
 varied and known resistances in the circuit, and with va- 
 ried speeds of rotation; and what amount of power is 
 absorbed in each case. It is a question of interest whether 
 
 7 
 
8 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 a machine intended for one light can or cannot produce 
 two in the same circuit, and if not, why not ; whether a 
 machine such as the Wallace-Farmer, intended as it is for 
 many lights, will give economical results when used for 
 one; and so on. It is clear that the attempt to examine 
 all separate combinations of so many variables would be 
 hopeless, and that the work must be systematized. 
 
 The mechanical energy communicated by the steam en- 
 gine or 'other motor is not immediately converted into the 
 energy of heat, but is first converted into the energy of 
 an electric current in a conducting circuit; of this a 
 portion only becomes localized as heat between the car- 
 bons of the electric arc ; and of this again a part only be- 
 comes sensible to the eye as light. The whole of what we 
 need to know may be more easily ascertained and more 
 shortly expressed if the inquiry is divided into two parts : 
 (a) What current will a machine produce under various 
 conditions of circuit, and at what expenditure of mechani- 
 cal power ? (b) Having given the electric conditions under 
 which the arc is placed, no matter how these conditions 
 are produced, what light will be obtained therefrom ? 
 Parts of the subject have been treated more or less in this 
 sense by Edlund (Pogg. Ann., 1867 and 1868), Houston 
 and Thomson in America, Mascart (Journal de Physique, 
 March, 1878), Abney (Proceedings of the Royal Society, 
 1878), Trowbridge (Philosophical Magazine, March, 1879), 
 Schwendler (Report on Electric Light Experiments), etc., 
 but not so completely that nothing remains to be done ; 
 nor does the author doubt that a great deal of information 
 is in the hands of makers of machines, which they have 
 not thought it necessary to make known. The present 
 
ON ELECTRIC LIGHTING. 9 
 
 communication is limited to an account of some experi- 
 ments on the production of currents by a Siemens medium- 
 sized machine; that is, the machine which is advertised to 
 produce a light of 6,000 candles by an expenditure of 3J 
 horse power. 
 
 All the machines for converting mechanical power into 
 an electric current consist ultimately of a conducting wire 
 moving in a magnetic field; and approximately the elec- 
 tromotive force of the machine will be proportional to the 
 velocity with which the circuit moves through the field, 
 and to the intensity of the field. In general the intensity 
 of the field is not constant; and in such machines as the 
 Siemens and the ordinary Gramme machine it may be re- 
 garded as a function of the current passing. We must 
 learn what this function is for the machine in question ; 
 or which comes to exactly the same thing, and is better 
 so long as the facts are merely the result of experiment 
 we must construct a curve in which the abscissae represent 
 the intensities of currents passing, and the ordinates the 
 corresponding electromotive forces for a given speed of 
 rotation. But the power of a current, that is, its energy 
 per second, is the product of the electromotive force and 
 the intensity, or, in the case of the curve, the product of 
 the ordinate and the abscissa; this is in all cases less than 
 the power required to drive the machine, and the ratio be- 
 tween the two may fairly be called the efficiency of the 
 machine. 
 
 The object of the inquiry may perhaps be made clearer 
 by an illustration. Consider the case of a pump forcing 
 water through a pipe against friction; then the electric 
 current corresponds to the volume of water passing per 
 
10 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 second, and the electromotive force to the difference of 
 pressure on the two sides of the pump; and just as the 
 product of pressure and volume per second is power, so 
 the product of electromotive force and current is power, 
 which is directly comparable with the power expended in 
 driving the machine or the pump,, as the case may be. 
 The peculiarity of the so-called dynamo-electric machine 
 lies in this, that what corresponds to the difference of 
 pressure (the electromotive force) depends directly on 
 what corresponds to the volume passing (the current). 
 
 Each experiment requires the determination of the 
 speed, the driving power, the resistances in circuit, and 
 the current passing; or of the difference of potential be- 
 tween the two ends of a known resistance of the circuit. 
 
 The apparatus employed by the author was arranged, 
 not alone with an aim to accuracy, but in part to make use 
 of such instruments as he happened to possess or could 
 easily construct, and in part with a view to ready erection 
 and transportation. Much more accurate results may be 
 obtained by any one who will arrange apparatus with a single 
 aim to attain the greatest accuracy possible. The author's 
 apparatus will, however, be briefly described, that others 
 may form their own opinion of the importance of the va- 
 rious sources of error. 
 
 The speed counter was that supplied with the electric 
 machine. 
 
 Concerning the steam engine nothing need be said, save 
 that its speed was maintained very constant by means of a 
 governor, shown in Fig. 1, specially arranged for great 
 sensibility. By placing the joint A above the joint B, in- 
 stead of below it, as in Porter's governor, any degree of 
 
ON ELECTRIC LIGHTING. 
 
 11 
 
 FIG. 1. GOVERNOR. 
 
 sensibility up to instability may be obtained. The speed 
 was varied by means of a weight and a spring attached to 
 a lever on the throttle valve 
 spindle. The ungainly ap- 
 pearance of this governor could 
 easily be remedied by any one 
 proposing to manufacture it. 
 
 The power is transmitted 
 from the engine to a counter- 
 shaft by means of a strap, and 
 by a second strap from the 
 countershaft to the pulley of 
 the electric machine. On this 
 second strap is the dynamom- 
 eter shown in Fig. 2. 
 
 This dynamometer has for some time been used by 
 Messrs. Siemens, and was also used by Mr. Schwendler; its 
 invention is due to Herr von Hefner- Alteneck. A is the 
 driving pulley ; B the pulley of the electric machine ; C C 
 are a pair of loose pulleys between which the strap passes ; 
 these are carried in a double triangular frame, which can 
 turn about a bar D. This bar might form part of a per- 
 manent structure ; but in order to place the dynamometer 
 readily on any strap, the bar was in this case provided with 
 eyes at either end, and secured in position by six or eight 
 ropes. This plan answers well, as there is very little stress 
 on the bar. Immediately above the pulleys C C a cord 
 leads from the frame through a Salter spring balance over 
 snatch blocks to a back balance weight ; the tension of this 
 cord is read on the spring balance. At first the spring 
 balance was omitted, and the weight at the end of the cord 
 
12 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
ON ELECTKIC LIGHTING. 13 
 
 was observed ; but the friction of the snatch block pulleys 
 was found objectionable. The pulley frame carries a 
 pointer, which is adjusted so as to coincide with a datum 
 mark when the line A B bisects the distance between the 
 loose pulleys. Let W be the tension of the cord required 
 to bring the pulley frame to its standard position when no 
 work is being transmitted, W" the tension which is 
 required to bring the pointer back to the datum mark when 
 an observation is made, and let W = W W". Let 
 T', T" be the tensions on the tight and slack halves of the 
 strap; R l9 # 2 , r the radii of the pulleys A, B and C, plus 
 half the thickness of the strap; c,, e a the distances AJ, 
 J B; 2d the distance apart of the centres (7, C; a l} # 2 the 
 inclinations of the two parts of the strap, on either side of 
 C, C, to the line A B. Then 
 
 (T f - T")(sin a, + sin a,) = W; 
 
 R, + r - d . d (R, + r - dV 
 and sm a. = --- \- - -- , 
 
 c l 2<?,\ c l I ' 
 
 R, + r - d , d fR, + r - 
 
 -- 
 
 very nearly. 
 
 The value of T' T" and the velocity of rotation of the 
 electric machine being known, the power received by it is 
 readily obtained, expressed in gram-centimetres per second. 
 Multiplying by 981, the value of gravity in centimetres 
 and seconds, the power is then expressed in ergs* per 
 
 * The dyne is the force which will in one second impart to one gram a 
 velocity of one centimetre per second, and an erg is. the work done by a dyne 
 working through a centimetre; a horse power may be taken as three-quarters 
 
14 DYXAMO MACHINERY AND ALLIED SrBJBCTS. 
 
 is ready for comparison with the results of the 
 electrical experiments. 
 
 As already stated, the dynamo-electric machine in the 
 present case was a Siemens medium size; the armature coil 
 has fifty-ax divisions, and the brushes are single, not 
 divided, that is, each brash is in connection with one 
 segment of the commutator at any instant 
 
 The leading wire is 100 yards of Siemens No. 90, con- 
 sisting of seven copper wires, insulated with tape and India 
 rubber, and having a diameter of about 9J mm. 
 
 The method of determining the current is shown in the 
 diagram, Fig. 3. The current is conveyed from the 
 machine A through a set of coils of brass wire r, and in 
 some eases through a resistance coil placed in a calorimeter 
 B, and so back to the machine, the connections being 
 made through cups of mercury excavated in a piece of 
 wood />. The current passing may be ascertained by the 
 heating of the calorimeter, or by measuring the difference 
 of potential at the extremities of the resistance r. all the 
 resistances of the circuit being supposed known. This 
 difference of potential could of course be very easily 
 measured by "means of a quadrant electrometer; but, as 
 the instrument had to be frequently removed, a galva- 
 nometer appeared more convenient. The two points to be 
 measured are connected to the ends of two series of resist- 
 ance coils a. b. The galvanometer G is placed in a second 
 derived current, passing from a junction in a b through a 
 battery H 9 then through a set of high resistances J for 
 
 being M"erg. Bee Report of fW Brit. 
 G. S- System of Unto," pvJbfiaked by tfce 
 
OS KLECTB1C UGHTIXG. 
 
 15 
 
 
 _ 
 
 : ~" 
 
16 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 adjusting sensibility, a reversing key K, the galvanometer 
 6r, the reversing key K again, and so to the other extremity 
 of b. The electromotive force is ascertained by adjusting 
 the resistance b so that the deflection of the galvanometer 
 is nil. 
 
 The resistance coils c comprise ten coils of common 
 brass wire, each wound round a couple of wooden uprights 
 driven into a baseboard common to the set; each wire is 
 about 60 metres long, and of No. 17 Birmingham wire 
 gauge (.06 inch or 1-J mm. diameter), weighing about 14.6 
 grams per metre. Each terminal is connected to a cup of 
 mercury excavated in the baseboard, so that the coils can 
 be placed in series or in parallel circuit at pleasure. The 
 resistance of each coil being about 3 ohms, this set may be 
 arranged to give resistances varying from 0.3 to 30 ohms. 
 
 The calorimeter B is a Siemens pyrometer with the top 
 scale removed; a resistance coil of uncovered German 
 silver wire nearly 2 m. long, 1J mm. in diameter, and 
 having a resistance of about 0.2 ohm, is suspended within 
 it from an ebonite cover, which also carries a little brass 
 stirrer, and the calorimeter is filled with water to a level 
 determined by the mark of a scriber. It was of course 
 necessary to know the capacity of the calorimeter for heat. 
 It was filled with warm water up to the mark, and the coil 
 placed in position ; 120 grams of water were then with- 
 drawn, and the temperature of the calorimeter was ob- 
 served to be 58.8 C. ; after the lapse of one minute it was 
 58.3 C.; after a second minute 57.9 0.; 120 grams of 
 cold water, temperature 13.3 C., were then suddenly in- 
 troduced through a hole in the ebonite cover, and it was 
 found that, two minutes after the reading of 57.9 C., the 
 
ON ELECTEIC LIGHTING. 17 
 
 temperature was 50.0 C.; hence we may infer that the 
 capacity of the calorimeter is equal to that of 740 grams of 
 water. Two similar experiments at lower temperatures 
 gave respectively the numbers 749 and 750. Estimating 
 the capacity from the weight of the copper cylinder sup- 
 plied with the pyrometer, it should be 747, to which must 
 be added the capacity of the German silver wire and 
 stirrer. Taking everything into consideration, 750 grams 
 may be assumed as the most probable result. 
 
 The resistance coils a, b are of German silver, made by 
 Messrs. Elliott Brothers ; they are on the binary scale from 
 -J ohm to 1,024 ohms. Separate coils were used, instead of 
 a regular resistance box, because they were more readily 
 applicable to any other purpose for which they might be 
 required; and the binary scale was adopted, because the 
 coils could at once be used as conductivity coils in parallel 
 circuit, also on the binary scale. Each coil as supplied 
 terminated in two stout copper legs ; these were fitted with 
 cups of india rubber tubing for mercury, whereby any con- 
 nections whatever could readily be made. This arrange- 
 ment, though rude, was very convenient, and perhaps even 
 safer from error than a box with brass plugs to make the 
 connections. By a slight alteration of the connections the 
 whole was instantly available as a Wheatstone bridge to 
 determine resistances. 
 
 The battery H is a single element of Daniell's battery, 
 in which the sulphate of zinc solution floats on the sul- 
 phate of copper; its electromotive force is assumed to be 
 | volt. 
 
 The resistances J added in the battery circuit are pencil 
 lines on glass, such as are described in the Philosophical 
 
18 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 Magazine of February, 1879. Three were used, giving a 
 range of sensibility approximately in the proportions 1, 25, 
 170, 700 the last figure being when all were short cir- 
 cuited ; they are very useful in adjusting the resistance b 
 so as to give no deflection of the galvanometer. 
 
 The reversing key K belongs to Sir W. Thomson's elec- 
 trometer, and is quite suitable when high resistances and 
 nil methods are used. 
 
 The galvanometer G is far more sensitive than necessary, 
 and has a resistance of 7,000 ohms. 
 
 Preliminary to experiments on the current, determina- 
 tions of resistances were made. The resistance of each 
 brass coil c was first determined, to afford the means of. 
 calculating the value of this resistance in any subsequent 
 experiment. When the ten coils were coupled in parallel 
 circuit, the calculated resistance was 0.29 ohm, while 0.292 
 was obtained by direct measurement. The leading wire 
 was then examined; the further ends being disconnected, 
 the insulation resistance was found to be over 60,000 ohms ; 
 how much over, it was immaterial to learn. When the 
 ends of the wire were connected, the resistance was found 
 to be 0.129 ohm. The resistances in the dynamo-electric 
 machine A were found to be as follows when cold: magnet 
 coils, 0.156 and 0.152 respectively; armature coil, 0.324; 
 total, 0.632 ohm. Direct examination was made of the 
 whole machine in eight positions of the commutator, 
 giving 0.643 ohm, with a maximum variation of 0.6 per 
 cent, from the mean. After running the machine for 
 some time the resistance was found to be 0.683, an increase 
 which would be accounted for by a rise of temperature of 
 12 0. or thereabouts. The resistance of the calorimeter 
 
Otf ELECTKIC LIGHTING. 19 
 
 B is 0.20 ohm, without its leading wire, which may be 
 taken as 0.01. We have then in circuit three resistances 
 which must be considered: (1) The resistance of the 
 machine A and leading wire, assumed throughout as 
 together 0.81 ohm, and denoted bye,; (2) the resistance 
 of the brass coils c, calculated from the several determina- 
 tions, with the addition of 0.02 ohm, the resistance of the 
 leading wire, and denoted by c 2 ; (3) when present, the 
 resistance of the calorimeter B and leading wire, denoted 
 by c 3 . 
 
 Two approximate corrections were employed, and should 
 be detailed. The first is the correction for the consider- 
 able heating of the resistance coils c. These were arranged 
 in two sets of five each, five being in parallel circuit, and 
 the two sets in series. The current from the machine, 
 being about 7.4 webers in each wire, was passed for three 
 or four minutes; the circuit was then broken, and the 
 resistance c 2 was determined within one second of breaking 
 circuit, when it was found to be about 5 per cent, greater 
 than when cold. As the resistance was falling, the follow- 
 ing was adopted as a rule of correction : square the current 
 in a single wire, and increase the resistance c 2 by ^ per 
 cent, for every unit in the square. The second correction 
 is due to the fact that the calorimeter was losing heat all 
 the time it was being used. It was assumed that it loses 
 0.01 C. per minute for every 1 0. by which the tempera- 
 ture of the calorimeter exceeds that of the air; this cor- 
 rection is of course based on the experiment already 
 mentioned. 
 
 The method of calculation may now be explained: 
 
20 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 R is the total resistance of the circuit in ohms, equal to 
 
 CI + C.H-CS; 
 
 Q is the current passing in webers; 
 E is the electromotive force round the circuit in volts; 
 W l is the work per second converted into heat in the 
 circuit, as determined by the galvanometer, measured 
 in erg-tens per second ; 
 W a is the work per second as determined by the 
 
 calorimeter; 
 
 TF 3 is the work per second as determined by the dyna- 
 mometer, less the power required to drive the machine 
 when the circuit is open; 
 HP is the equivalent of W 3 in horse power; 
 n is the number of revolutions per minute of the 
 
 armature. 
 
 As already mentioned, the standard resistance coils a, b 
 are adjusted in each experiment so that the galvanometer 
 gives no deflection, and the value of b is then noted. 
 The values of c lt c 2 , c 3 are known from previous observa- 
 tions. Then 
 
 _ 
 ~' 
 
 E = Q x R, 
 W, = E x Q, 
 
 mechanical equivalent of heat 
 generated per second in calorimeter. 
 
 The results of the experiments are given in the accom- 
 panying table. 
 
ON ELECTRIC LIGHTING. 
 
 oM 
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 11 
 
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 t Ci O CO CO T"* ^ 
 t i - GO O? i OO O 
 
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 5 . 3 X 
 
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 6 o o 
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 i-ii-ti-tojwcjeocoioeootcoosTfeoO'? 
 
 .29, 
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 g S ?2 
 
 "ooi eo t^ 
 
 |O-*T#cO(NOOOp<NlOi-jOOi-HOl-.t-OOOT-( 
 
 l d " ^ S SS ^ ^ SI 35 e5 S 5 % $ 5 3 S 
 
 858lil8988S85S8^$8 
 
 j rr eo eo eo o c* ei ai i-J oi oj <N oi oi w ci 
 
 spfoocsOTHWeo^jo 
 
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22 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 A power of 0.21 erg-ten, or 0.28 horse power, was re- 
 quired to drive the machine at 720 revolutions on open 
 circuit. An examination of the table shows that the 
 efficiency of the machine is about 90 per cent., exclusive 
 of friction. Comparing experiments 11 and 13, and also 
 the last four experiments, it is seen that the electromotive 
 force is proportional to the speed of rotation within the 
 errors of observation. Experiments 14, 15, and 16 were 
 intended to ascertain the effect of displacing the com- 
 mutator brushes. 
 
 The principal object of the experiments was to ascertain 
 how the electromotive force depended on the current. 
 This relation is represented by the curve shown in Fig. 4, 
 
 Curves of Force and Current 
 Speed 720 revolutions per minute 
 
 40 50 60 TOWebcrs 
 
 FIG. 4. CURVE OF FORCE AND CURRENT. 
 
 in which the abscissae represent the currents flowing, or the 
 values of Q in the table, and the ord mates the electro- 
 motive forces, or the values of E reduced to a speed of 720 
 revolutions per minute. The curve may also be taken to 
 represent the intensity of the magnetic field, It will be. 
 
ON ELECTRIC LIGHTING. 23 
 
 remarked that there is a point of inflection in the curve 
 somewhere near the origin. The experiments 1 to 5 indi- 
 cate that this is the true form of the curve, and it is con- 
 firmed in a remarkable manner by a special experiment. 
 A resistance intermediate between 5J and 4 (experiments 
 3 and 4) was used in circuit, and E and Q were determined 
 in two different ways: first, by starting with an open 
 circuit, which was then closed ; secondly, by starting with 
 a portion of the resistance short circuited, and a very 
 powerful current passing, and then breaking the short 
 circuit. It was found that ' E and Q were four times as 
 great in the latter case as in the former. Unfortunately 
 the numbers are not sufficiently accurate to be given, as 
 the solutions of the standard battery had become mixed. 
 
 The curve really gives a great deal more information 
 than appears at first sight. It will determine what current 
 will flow at any given speed of rotation of the machine, 
 and under any conditions of the circuit, whether of resist- 
 ances or of opposed electromotive forces. It will also give 
 very approximate indications of the corresponding curve 
 for other machines of the same configuration, but in which 
 the number of times the wire passes round the electro- 
 magnet or the armature is different. 
 
 It will be well to compare these results with those 
 obtained by others. M. Mascart worked on a Gramme 
 machine with comparatively low currents: he represents 
 his results approximately by the formula 
 
 E = n (a + b Q), 
 
 where a and b are constants. This corresponds to the 
 rapidly rising part of the curve in Fig. 4, Mr, Trowbridge 
 
24 DYNAMO MACHINEBY AND ALLIED SUBJECTS. 
 
 with a Siemens machine obtained a maximum efficiency of 
 76 per cent., and states that the machine was running 
 below its normal velocity. Mr. Schwendler's results, when 
 fully published, will probably be found to be the most 
 complete and most accurate existing. In the precis he 
 states that the loss of power with a Siemens machine in 
 producing currents of over 20 webers is 12 per cent. 
 Now, taking the author's experiments 4 to 19, the mean 
 value of W, is 3.027 erg-tens and of W 3 3.304; adding to 
 the latter 0.21, the power required to drive the machine 
 when no current passes, it appears that 13.8 per cent, of 
 the power applied is wasted. Again, taking experiments 
 4, 6, 8, 10, and 12, the mean value of JF 2 is 2.888 erg-tens 
 and of W s 3.076, indicating a waste of power amounting to 
 12 per cent. Of this, as already stated, 0.21 erg-ten, or 
 0.28 horse power, is accounted for by friction of the 
 journals and commutator brush; the remainder is ex- 
 pended in local currents, or by loss of kinetic energy of 
 current when sparks occur at the commutator. 
 
 According to Weber's theory of induced magnetism, as 
 set forth in Maxwell's "Electricity and Magnetism," 
 vol. II., if X be the magnetizing force and / the intensity 
 of magnetization, 
 
 2 X 
 1= a , until X rises to the value b, 
 
 6 o 
 
 and I= 
 
 where a and b are constants. We should naturally expect 
 that a similar formula would be approximately applicable 
 to dynamo-electric machines. 
 
ON ELECTKIC LIGHTING. 25 
 
 In the present experiments, let 1 be the electromotive 
 force, X the current passing, and assume a to be 60 and b 
 to be 15; we then obtain results not far from those of 
 experiment. The capacity of any continuous current 
 machine may thus be shortly stated by giving the values of 
 a and b; or, which comes to the same thing, by stating the 
 electromotive force at a given speed when the -current is 
 as great as possible, and also the total resistance through 
 which the machine will exert an electromotive force two- 
 thirds of this greatest electromotive force. To this should 
 be added a statement of the resistance of the machine, 
 and of the power it absorbs, with known conditions of the 
 circuit. 
 
 The author has not yet tried any quantitative experi- 
 ments with the electric light, but hopes shortly to do so. 
 In the meantime he would remark that, as the lamp is 
 usually adjusted, only half the energy of the current 
 appears in the arc, or 44 per cent, of the energy trans- 
 mitted to the machine by the strap. 
 
 In conclusion the author would express the obligation 
 he is under to Messrs. Chance Brothers & Co., on account 
 of the facilities he has enjoyed for making these experi- 
 ments at their works. It may be mentioned that one 
 principal object of the research of which this is a beginning 
 is to obtain a minute knowledge of the electric light, with 
 a view to lighthouse illumination. 
 
26 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 ON ELECTRIC LIGHTING. 
 
 SECOND PAPER. 
 
 Dynamo-Electric Machines. Since the date of the 
 author's former paper in April, 1879, other observers have 
 published the results of experiments similar to those de- 
 scribed by him. It may be well to exhibit some of these 
 
 '0 Webers 
 
 FIG. 5. CURVES OF ELECTROMOTIVE FORCE AND CURRENT OP SIEMENS MEDIUM 
 SIZE MACHINE. 
 
 results reduced to the form he has adopted, namely, a curve, 
 such as that previously shown in Fig. 4 of the preceding 
 paper, and now reproduced, with slight alterations, in Fig. 
 5. Here any abscissa represents a current passing through 
 the dynamo-electric machine, and the corresponding ordi- 
 
ON ELECTRIC LIGHTING. 27 
 
 nate represents the electromotive force of the machine for 
 a certain speed of revolution, when that current is passing 
 through it. It will be found (1) that with varying speed 
 the ordinate, or electromotive force, corresponding to any 
 abscissa or current is proportional to the speed; (2) that 
 the electromotive force does not increase indefinitely with 
 increasing current, but that the curve approaches an asymp- 
 tote; (3) that the earlier part of the curve is, roughly 
 speaking, a straight line, until the current attains a certain 
 value, and that at that point the electromotive force has 
 reached about two-thirds of its maximum value. When the 
 current is such that the electromotive force is not more 
 than two-thirds of its maximum, a very small change in the 
 resistance with speed of engine constant, or in the speed of 
 the engine with resistance constant, causes a great change 
 in the current. For this reason the greatest of these cur- 
 rents, which is that corresponding to the point where the 
 curve breaks away from a straight line, and which is the 
 same for all speeds of revolution, since the curves for dif- 
 ferent speeds differ only in the scale of ordinates, may be 
 called the " critical current " of the machine. The effect 
 of a change of speed is exhibited in Fig. 5, where the lower 
 dotted line represents the curve for a speed of 660 revolu- 
 tions per minute, instead of 720. The resistance, varying as 
 
 electromotive force . . -, 41 i 4. ,-, v ^ n 
 
 , is given by the slope of the line P. 
 current 
 
 But since the resistance is constant, the slope of this line 
 must be constant; and it will be seen that it cuts the 
 upper curve at a point corresponding to a current of 15 
 webers, and the lower at a point corresponding to a current 
 of 5 webers only. 
 
28 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 In Germany, Auerbach and Meyer ( Wiedemann Annalen, 
 Nov., 1879) have experimented fully on a Gramme machine 
 at various speeds, and with various external resistances. 
 The resistance of the machine was 0.97 ohm. Their results 
 are summarized in a table at the end of their paper, which 
 gives the current passing, with resistances in circuit from 
 1.75 to 200 Siemens units, and at speeds from 20 to 800 
 revolutions per minute. In the accompanying diagram, 
 Fig. 6, the curve G expresses the relation between electro- 
 
 Current 
 
 70 Webers 
 
 FIG. 6. CURVES OP ELECTROMOTIVE FORCE AND CURRENT : GRAMME MACHINE, 
 G; SIEMENS MEDIUM, SM; SIEMENS SMALLEST, Ss. 
 
 motive force and current, as deduced from some of their 
 observations; the points marked are plotted from their 
 table, making allowance, where necessary, for difference in 
 speed. The curve, as actually constructed, is for a speed 
 of 800 revolutions : at this speed it will be seen that the 
 maximum electromotive force is about 76 volts; and the 
 critical current, corresponding to a force of about 51 volts, 
 is 6.5 webers, with a total resistance of 7.8 ohms. Up to 
 this point there will be great instability, exactly as was the 
 
ON ELECTRIC LIGHTING. 29 
 
 case in the Siemens machine examined by the author, where 
 the resistance was 4 ohms and the speed 720 revolutions. 
 
 The results of an elaborate series of experiments on cer- 
 tain dynamo-electric machines have recently been presented 
 to the Koyal Society by Dr. Siemens. One of the machines 
 examined was an ordinary medium sized machine, substan- 
 tially similar to that tried by the author in 1879. It is 
 described as having 24 divisions of the commutator; 336 
 coils on the armature, with a resistance of 0.4014 Siemens 
 unit; and 512 coils on the magnets, with a resistance of 
 0.3065: making a total resistance of 0.7079 Siemens unit 
 = 0.6654 ohm. The curve 8m, Fig. 6, gives the relation 
 of electromotive force and current, reduced to a speed of 
 700 revolutions per minute, the actual speeds ranging from 
 450 to 800 revolutions. The maximum electromotive 
 force appears to be probably 76 volts, and the critical 
 current 15 webers; which is the same as in the author's 
 first experiments on a similar machine. 
 
 In the summer of 1879 the author examined a Siemens 
 machine of the smallest size. This machine is generally 
 sold as an exciter* for their alternate current machine. It 
 has an internal resistance of 0.74 ohm, of which 0.395 is in 
 the armature or helix. The machine is marked to run at 
 1,130 revolutions per minute. The following Table II. 
 gives, for a speed of 1,000 revolutions, the total resistance, 
 current, electromotive force and horse power developed as 
 current. The horse power expended was not determined. 
 
 The curve S s, Fig. 6, gives as usual the relations olelec- 
 tromotive force and current. From this curve it will be seen 
 that the critical current is 11.2 webers, and the maximum 
 electromotive force, at the speed of 1,000 revolutions, is 
 
30 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 TABLE II. EXPERIMENTS ON SMALLEST-SIZED SIEMENS DYNAMO- 
 ELECTRIC MACHINE. 
 
 Resistance. 
 
 Electric Current. 
 
 Electromotive 
 Force. 
 
 Horse Power Devel- 
 oped as Current. 
 
 2.634 ohms. 
 
 5.10 webers. 
 
 13.2 volts. 
 
 0.09H.P. 
 
 2 221 
 
 
 12.15 
 
 
 27.0 
 
 
 0.44 
 
 
 1.967 
 
 ' 
 
 17.0 
 
 
 33.6 
 
 
 0.76 
 
 
 1.784 
 
 
 20.4 
 
 
 36.4 
 
 
 0.99 
 
 
 1.668 
 
 
 22.3 
 
 
 37.2 
 
 
 1.11 
 
 
 1.579 
 
 
 23.2 
 
 
 36.6 
 
 
 1.14 
 
 
 1.503 
 
 
 25.6 
 
 
 39.3 
 
 
 1.34 
 
 
 1.440 
 
 
 27.8 
 
 40.0 
 
 
 1.49 " 
 
 1.145 
 
 
 36.2 " 
 
 41.5 
 
 
 2.00 " 
 
 about 42 volts. The determinations for this machine were 
 made in exactly the same manner as in the experiments 
 on the medium sized machine, using the galvanometer, but 
 omitting the experiment with the calorimeter (compare 
 Table L, p. 21). 
 
 The time required to develop the current in a Gramme 
 machine has been examined by Herwig (Wiedemann, June, 
 1879). He established the following facts for the machine 
 he examined : A reversed current, having an electromotive 
 force of 0.9 Grove cell, sufficed to destroy the residual 
 magnetism of the electromagnets. If the residual mag- 
 netism was as far as possible reduced, it took a much longer 
 time to get up the current than when the machine was in 
 its usual state. A longer time was required to get up the 
 current when the external resistance was great than when 
 it was small. With ordinary resistance the current required 
 from f second to 1 second to attain its maximum. 
 
 Brightness of the Electric Arc. The measurement of 
 the light emitted by an electric arc presents certain peculiar 
 difficulties. The light itself is of a different color from 
 
ON ELECTRIC LIGHTING. 31 
 
 that of a standard candle, in terms of which it is usual to 
 express luminous intensities. The statement, without 
 qualification, that a certain electric lamp and machine give 
 a light of a specified number of candles, is therefore want- 
 ing in definite meaning. A red light cannot with pro- 
 priety be said to be any particular multiple of a green 
 light; nor can one light which is a mixture of colors be 
 said with strictness to be a multiple of another, unless the 
 proportions of the colors in the two cases are the same. 
 Captain Abney (Proceedings of the Royal Society, March 
 7, 1878, p. 157) has given the results of measurements of 
 the red, blue, and actinic light of electric arcs in terms of 
 the red, blue, and actinic light of a standard candle. The 
 fact that the electric light is a very different mixture of 
 rays from the light of gas or of a candle has long been 
 known, but has been ignored in statements intended for 
 practical purposes. 
 
 Again, the emission of rays from the heated carbons and 
 arc is by no means the same in all directions. Determi- 
 nations have been made in Paris of the intensity in differ- 
 ent directions, in particular cases. If the measurement is 
 made in a horizontal direction, a very small obliquity in 
 the crater of the positive carbon will throw the light much 
 more on one side than on the other, causing great dis- 
 cordance in the results obtained. 
 
 If the electric light be compared directly with a stand- 
 ard candle, a dark chamber of great length is needed a 
 convenience not always attainable. In the experiments 
 made at the South Foreland by Dr. Tyndall and Mr. 
 Douglass, an intermediate standard was employed; the 
 electric light was measured in terms of a large oil lamp, 
 
32 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 and this latter was frequently compared with a standard 
 candle. 
 
 Other engagements have prevented the author from 
 fairly attacking these difficulties; but since May, 1879, he 
 has had in occasional use a photometer with which power- 
 ful lights can be measured in .moderate space. This 
 photometer is shown in Figs. 7 and 8, and an enlargement 
 
 5T 
 
 rU 
 
 ^Longitudinal Section 
 FIG. 7. PHOTOMETER FOR POWERFUL LIGHTS. 
 
 STANDARD 
 
 LIGHT 
 
 of the field piece in Fig. 9. A convex lens A, of short 
 focus, forms an image at B of the powerful source of 
 light which it is desired to examine. The intensity of 
 the light from this image will be less than that of the 
 actual source by a calculable amount; and when the dis- 
 tance of the lens from the light is suitable, the reduction 
 is such that the reduced light becomes 
 comparable with a candle or a carcel 
 lamp. Diaphragms C C are arranged 
 in the cell which contains the lens, to 
 cut off stray light. One of these is 
 placed at the focus of the lens, and has 
 a small aperture. It is easy to see that 
 this diaphragm will cut off all light 
 entering from a direction other than 
 " that of the source; so effectually does it 
 do so, that observations may be made in 
 broad daylight on any source of light, if a dark screen 
 
ON ELECTRIC LIGHTING. 
 
 33 
 
 be placed behind it. The long box E E, Fig. 7, of 
 about 7 feet length, is lined with black velvet, the old- 
 fashioned dull velvet, not that now sold with a finish, which 
 reflects a great deal of the light incident at a certain angle. 
 This box serves as a dark chamber, in which the intensity 
 of the image formed by the lens is compared with a stand- 
 
 FIG. 9. FIELD PIECE. 
 
 ard light, by means of an ordinary Btmsen's photometer F, 
 sliding on a graduated bar. 
 
 Mr. Dallmeyer kindly had the lens made for the author: 
 he can therefore rely upon the accuracy of its curvature 
 and thickness; it is plano-convex, the convex side being 
 towards the source of light. The curvature is exactly 1 
 inch radius and the thickness is 0.04 inch; it is made of 
 Chance's hard crown glass, of which the refractive index for 
 the D line in the spectrum is 1.517. The focal length/ is 
 therefore 1.933 inches. 
 
 Let u denote the distance of the source of light from 
 
84: DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the curved surface of the lens, and v the distance of the 
 image B of the source from the posterior focal plane. 
 Neglecting for the moment loss by reflection at the sur- 
 face of the glass, the intensity of the source is reduced by 
 
 the factor ( 1 But | = -r, or v hence the f ac- 
 W v u f u~f 
 
 i f Y 
 
 tor of reduction is I -- > The effect of absorption in so 
 \n fJ 
 
 small a thickness of very pure glass may be neglected ; but 
 the reflection at the surfaces will cause a loss of 8.3 per 
 cent., which must be allowed for. This percentage is 
 calculated from Fresners formulae, which are certainly 
 accurate for glasses of moderate refrangibility, and for 
 moderate angles of incidence. 
 
 Suppose, for example, it is required to measure a light of 
 8,000 candles; if it be placed at a distance of 40 inches, it 
 will be reduced in the ratio 467 to 1, and becomes a con- 
 veniently measurable quantity. By transmitting through 
 colored glasses both the light from an electric lamp and that 
 from the standard, a rough comparison may be made of 
 the red or green in the electric light with the red or green 
 in the standard. 
 
 A dispersive photometer, in which a lens is used in a 
 somewhat similar manner, is described in Stevenson's 
 "Lighthouse Illumination;" but in that case the lens is 
 not used in combination with a Bunsen photometer, nor 
 with any standard light. Messrs. Ayrton and Perry de- 
 scribed a dispersive photometer with a concave lens at the 
 meeting of the Physical Society on December 13, 1879 
 (Proceedings Physical Society, vol. III., p. 184J. The 
 convex lens possesses, however, an obvious advantage in 
 
ON ELECTRIC LIGHTING. 35 
 
 having a real focus, at which a diaphragm to cut off stray 
 light may be placed. 
 
 Efficiency of the Electric Arc. To define the electrical 
 condition of an electric arc, two quantities must be stated 
 the current passing, and the difference of electric 
 potential at the ends of the two carbons. Instead of 
 either one of these, we may, if we please, state the ratio 
 difference of potential d ^ it ^ resistance of the arc> 
 
 current 
 
 that is to say, the resistance which would replace the arc 
 without changing the current. But such a use of the term 
 electric resistance is unscientific; for Ohm's law, on which 
 the definition of electric resistance -rests, is quite untrue of 
 the electric arc; while on the other hand, for a given ma- 
 terial of the electrodes, a given distance between them, 
 and a given atmospheric pressure, the difference of poten- 
 tial on the two sides of the arc is approximately constant. 
 The product of the difference of potential and the current 
 is of course equal to the work developed in the arc; and 
 this, divided by the work expended in driving the ma- 
 chine, may be considered as the efficiency of the whole 
 combination. It is a very easy matter to measure these 
 quantities. The difference of potential on the two sides of 
 the arc may be measured by the method given by the 
 author in his previous paper, or by an electrometer, or in 
 other ways. The current may be measured by an Obach 
 galvanometer, or by a suitable electro-dynamometer, or 
 best of all, in the author's opinion, by passing the whole 
 current, on its way to the arc, through a very small known 
 resistance, which may be regarded as a shunt for a galva- 
 
36 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 nometer of very high resistance, or to the circuit of which 
 a very high resistance has been added. 
 
 It appears that with the ordinary carbons, and at ordi- 
 nary atmospheric pressure, no arc can exist with a less 
 difference of potential than about 20 volts; and that in 
 ordinary work, with an arc about i inch long, the differ- 
 ence of potential is from 30 to 50 volts. Assuming the 
 former result, about 20 volts, for the difference of poten- 
 tial, the use of the curve of electromotive forces may be 
 illustrated by determining the lowest speed at which a 
 given machine can run and yet be capable of producing a 
 short arc. Taking as the origin of co-ordinates, Fig. 
 10, set off upon the axis of ordinates the distance A 
 
 Fio. 10. 
 
 equal to 20 volts ; draw A B to intersect at B the negative 
 prolongation of the axis of abscissae, so that the ratio -^= 
 
 may represent the necessary metallic resistance of the cir- 
 cuit. Through .the point B, thus obtained, draw a tangent 
 to the curve, touching it at C, and cutting A in D. 
 Then the speed of the machine, corresponding to the par- 
 ticular curve employed, must be diminished in the ratio 
 
ON ELECTRIC LIGHTING. 
 
 37 
 
 -- , in order that an exceedingly small arc may be just 
 
 possible. 
 
 The curve may also be employed to put into a somewhat 
 different form the explanation given by Dr. Siemens, at 
 the Koyal Society, respecting the occasional instability of 
 the electric light as produced by ordinary dynamo-electric 
 machines. The operation of all ordinary regulators is to 
 part the carbons when the current is greater than a cer- 
 tain amount, and to close them when it is less; initially 
 the carbons are in contact. Through the origin 0, Fig. 
 11, draw the straight line OA, inclined at the angle repre- 
 
 senting the resistances of the circuit other than the arc, 
 and meeting the curve at A. The abscissa of the point A 
 represents the current which will pass if the lamp be pre- 
 vented from operating. Let N represent the current to 
 which the lamp is adjusted; then if the abscissa of A be 
 greater than N, the carbons will part. Through N draw 
 the ordinate B N 9 meeting the curve in the point B; and 
 parallel to A draw a tangent CD, touching the curve at D. 
 If the point B is to the right of D, or further from the 
 
38 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 origin, the arc will persist; but if B is to the left of D, or 
 nearer to the origin, the carbons will go on parting, till 
 the current suddenly fails and the light goes out. If B, 
 although to the right of D, is very near to it, a very small 
 reduction in the speed of the machine will suffice to ex- 
 tinguish the light. Dr. Siemens gives greater stability to 
 the light by exciting the electromagnets of the machine 
 by a shunt circuit, instead of by the whole current. 
 
 The success of burning more than one regulating lamp 
 in series depends on the use in the regulator of an electro- 
 magnet excited by a high resistance wire connecting the 
 two opposed carbons. The force of this magnet will de- 
 pend upon the difference of potential in the arc, instead 
 of depending, as in the ordinary lamp, upon the current 
 passing. Such a shunt magnet has been employed in a 
 variety of ways. The author has arranged it as an attach- 
 ment to an ordinary regulator; the shunt magnet actuates 
 a key, which short circuits the magnet of the lamp when 
 the carbons are too far parted, and so causes them to close. 
 
 In conclusion the author ventures to remind engineers 
 of the following rule for determining the efficiency of any 
 system of electric lighting in which the electric arc is 
 used, the arc being neither exceptionally long nor excep- 
 tionally short: Measure the difference of potential of the 
 arc, and also the current passing through it, in volts and 
 webers respectively; then the product of these quantities, 
 divided * by 746, is the horse power developed in that arc. 
 
 * With respect to the factor 746, given above, the product of difference of poten- 
 tial and current was power, which could of course be given as so many foot- 
 pounds per minute; but the number that was got by multiplying webers and volts 
 together did not give the power in foot pounds, audit required a factor to reduce 
 
ON ELECTRIC LIGHTING. 39 
 
 It is then known that the difference between the horse 
 power developed in the arc and the horse power expended 
 to drive the machine must be absolutely wasted, and has 
 been expended in heating either the iron of the machine or 
 the copper conducting wires. 
 
 the one to the oth r, just as it required a factor to reduce gramme-centimetres, 
 or any other measure of power, to foot-pounds. The factor in this case hap- 
 pened to be 740, as would be seen by referring to Everett, "Units and Physical 
 Constants." The product of a weber and a volt was 10 7 ergs per second (p. 138), 
 while a horse power was 7.46 x 10 9 = 740 X 10 7 ergs per second (p. 5J5); hence the 
 rule given. 
 
40 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 ARTIFICIAL light is generally produced by raising some 
 body to a high temperature. If the temperature of a body 
 be greater than that of surrounding bodies it parts with 
 some of its energy in the form of radiation. While the 
 temperature is low these radiations are not of a kind to 
 which the eye is sensitive; they are exclusively radiations 
 less refrangible and of greater wave length than red light, 
 and may be called infra red. As the temperature is in- 
 creased the infra red radiations increase, but presently 
 there are added radiations which the eye perceives as red 
 light. As the temperature is further increased, the red 
 light increases, and yellow, green and blue rays are succes- 
 sively thrown off in addition. On pushing the temperature 
 to a still higher point, radiations of a wave length shorter 
 even than violet light are produced, to which the eye is 
 insensitive, but which act strongly on certain chemical 
 substances; these may be called ultra violet rays. It is 
 thus seen that a very hot body in general throws out rays 
 of various wave lengths, our eyes, it so happens, being only 
 sensitive to certain of these, viz., those not very long and 
 not very short, and that the hotter the body the more of 
 every kind of radiation will it throw out ; but the propor- 
 tion of short waves to long waves becomes vastly greater as 
 the temperature is increased, The problem of the artificial 
 
SOME POINTS IN ELECTRIC LIGHTING. 41 
 
 production of light with economy of energy is the same as 
 that of raising some body to such a temperature that it 
 shall give as large a proportion as possible of those rays 
 which the eye happens to be capable of feeling. For prac- 
 tical purposes this temperature is the highest temperature 
 we can produce. Owing to the high temperature at 
 which it remains solid, and to its great emissive power, the 
 radiant body used for artificial illumination is nearly always 
 some form of carbon. In the electric current we have an 
 agent whereby we can convert more energy of other forms 
 into heat in a small space than in any other way; and 
 fortunately carbon is a conductor of electricity as well as a 
 very refractory substance. 
 
 The science of lighting by electricity very naturally 
 divides itself into two principal parts the methods of 
 production of electric currents, and of conversion of the 
 energy of those currents into heat at such a temperature 
 as to be given oif in radiations to which our eyes are sensi- 
 ble. There are other subordinate branches of the subject, 
 such as the consideration of the conductors through which 
 the electric energy is transmitted, and the measurement of 
 the quantity of electricity passing and its potential or elec- 
 tric pressure. Although I shall have a word or two to say on 
 the other branches of the subject, I propose to occupy most 
 of the time at my disposal this evening with certain points 
 concerning the conversion of mechanical energy into elec- 
 trical energy. We know nothing as to what electricity is, 
 and its appeals to our senses are in general less direct than 
 those of the mechanical phenomena of matter. The laws, 
 however, which we know to connect together those phe- 
 nomena which we call electrical are essentially mechanical 
 
42 DYNAMO MACHINEKY AND ALLIED SUBJECTS. 
 
 in form, are closely correlated with mechanical laws, and 
 may be most aptly illustrated by mechanical analogues. 
 For example, the terms " potential/' " current " and " re- 
 sistance/' with which we are becoming familiar in electric- 
 ity, have close analogues respectively in "head," "rate of 
 flow" and "coefficient of friction" in the hydraulic trans- 
 mission of power. Exactly as in hydraulics head multi- 
 plied by velocity of flow is power measured in foot-pounds 
 per second or in horse power, so potential multiplied by 
 current is power and is measurable in the same units. The 
 horse power not being a convenient elec- 
 trical unit, Dr. Siemens has suggested that 
 the electrical unit of power or volt-ampere 
 should be called a watt : 746 watts are equal 
 to one horse power. Again, just as water 
 flowing in a pipe has inertia and requires an 
 expenditure of work to set it in motion, and 
 is capable of producing disruptive effects if 
 its motion is too suddenly arrested, as, for 
 example, when a plug tap is suddenly closed 
 in a pipe through which water is flowing 
 rapidly, so a current of electricity in a wire 
 has inertia; to set it moving electromotive 
 force must work for a finite time, and if we 
 r in iiiiiiim attempt to arrest it suddenly by breaking the 
 
 1 circuit, the electricity forces its way across 
 
 the interval as a spark. Corresponding to 
 mass and moments of inertia in mechanics 
 FIG. 12. we have in electricity coefficients of self 
 induction. We will now show that an 
 electric circuit behaves as though it had inertia. The ap- 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 43 
 
 paratus we shall use is shown diagrammatically in Fig. 12. 
 A current from a Sellon battery A circulates round an 
 electromagnet Z?/ it can be made and broken at pleasure 
 at C. Connected to the two extremities of the wire on the 
 
 FIG. 13. 
 
 magnet is a small incandescent lamp D, lent to me by Mr. 
 Crompton, of many times the resistance of the coil. On 
 breaking the circuit, the current in the coil, in virtue of its 
 momentum, forces its way through the lamp, and renders 
 it momentarily incandescent, although all connection with 
 the battery, which in any case would be too feeble to send 
 sufficient current through the lamp, has ceased. Let us. 
 try the experiment, make contact, break contact. You 
 
44 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 observe the lamp lights up. Compare with the diagram 
 (Fig. 13) ^of the hydraulic analogue, the hydraulic ram. 
 There a current of water suddenly arrested forces a way 
 for a portion of its quantity to a greater height than that 
 from which it fell. A B corresponds to the electromag- 
 net, the valve C to the contact breaker, and D E to the 
 lamp. There is, however, this difference between the in- 
 ertia of water in a pipe and the inertia of an electric cur- 
 rent : the inertia of the water is confined to the water, 
 whereas the inertia of the electric current resides in the 
 surrounding medium. Hence arise the phenomena of in- 
 duction of currents upon currents, and of magnets upon 
 moving conductors phenomena which have no immediate 
 analogues in hydraulics. There is thus little difficulty to 
 any one accustomed to the laws of rational mechanics in 
 adapting the expression of those laws to fit electrical 
 phenomena; indeed we may go so far as to say that the 
 part of electrical science with which we have to deal this 
 evening is essentially a branch of mechanics, and as such 
 I shall endeavor to treat it. 
 
 This is neither the time nor the place for setting forth 
 the fundamental laws of electricity, but I cannot forbear 
 from showing you a mechanical illustration, or set of 
 mechanical illustrations, of the laws of electrical induction, 
 first discovered by Faraday. I have here a model, Fig. 14, 
 which was made to the instructions of the late Professor 
 Clerk Maxwell, to illustrate the laws of induction. It 
 consists of a pulley P, which I now turn with my hand, 
 and which represents one electric circuit, its motion the 
 current therein. Here is a second pulley, S, representing 
 a second electric circuit. These two pulleys are geared 
 
SOME POINTS IN ELECTBIC LIGHTING. 45 
 
 FIGK 14, 
 
46 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 together by a simple differential train, such as is some- 
 times used for a dynamometer. The intermediate wheel 
 of the train, however, is attached to a balanced flywheel, 
 the moment of inertia of which can be varied by moving 
 inwards or outwards these four brass weights. The resist- 
 ances of the two electric circuits are represented by the 
 friction on the pulleys of two strings, the tension of which 
 can be varied by tightening these elastic bands. The dif- 
 ferential train, with its flywheel, represents the medium, 
 whatever it may be, between the two electric conductors. 
 The mechanical properties of this me del are of course 
 obvious enough. Although the mathematical equations 
 which represent the relation between one electric conduct- 
 or and another in its neighborhood are the same in form 
 as the mathematical equations which represent the mechan- 
 ical connection between these two pulleys, it must not be as- 
 sumed that the magnetic mechanism is completely repre- 
 sented by the model. We shall now see how the model 
 illustrates the action of one electric circuit upon another. 
 You know that Faraday discovered that if you have two 
 closed conductors arranged near to and parallel to each 
 other, and if you cause a current of electricity to begin to 
 flow in the first, there will arise a temporary current in the 
 opposite direction in the second. This pulley, marked P 
 on the diagram, represents the primary circuit, and the 
 pulley marked 8 on the diagram the secondary circuit. 
 We cause a current to begin to flow in the primary, or turn 
 the pulley P; an opposite current is induced in the sec- 
 ondary circuit, or the pulley 8 turns in the opposite 
 direction to that in which we began to move the pulley P. 
 The effect is only temporary; resistance speedily stops the 
 
SOME POINTS IN ELECTRIC LIGHTING. 47 
 
 current in the secondary circuit, or, in the mechanical 
 model, friction the rotation of the pulley S. I now grad- 
 ually stop the motion of P; the pulley S moves in the 
 direction in which P was previously moving, just as Far- 
 aday found that the cessation of the primary current in- 
 duced in the secondary circuit a current in the same direc- 
 tion as that which had existed in the primary. If there 
 were a large number of convolutions or coils in the second- 
 ary circuit, but that circuit were not completed, but had 
 an air space interrupting its continuity, an experiment 
 with the well known Kuhmkorff coil would show you that 
 when the current was suddenly made to cease to flow in 
 the primary circuit, so great 'an electromotive force would 
 be exerted in the secondary circuit that the electricity 
 would leap across the space as a spark. I will now show 
 you what corresponds to a spark with this mechanical 
 model. The secondary pulley S shall be held by passing a 
 thread several times round it. I gradually produce the 
 current in the primary circuit. I will now suddenly stop 
 this primary current: you observe that the electromotive 
 force is sufficient to break the thread. The inductive 
 effects of one electric circuit upon another depend not 
 alone on the dimensions and form of the two circuits, but 
 on the nature of the material between them. For example, 
 if we had two parallel circular coils, their inductive effects 
 would be very considerably enhanced by introducing a bar 
 of iron in their common axis. We can imitate this effect 
 by moving outwards or inwards these brass weights. In 
 the experiment I have shown you the weights have been 
 some distance from the axis in order to obtain considerable 
 effect, just as in the Ruhmkorff coil an iron core is intro- 
 
48 DYNAMO MACHINERY A.ND ALLIED SUBJECTS. 
 
 duced within the primary circuit. I will now do what is 
 equivalent to removing the core : I will bring the weights 
 nearer to the axis, so that my flywheel shall have less 
 moment of inertia. You observe that the inductive effects 
 are very much less marked than they were before. With 
 the same electromagnet which we used before, but differ- 
 ently arranged, we will show what we have 
 just illustrated the induction of one 
 circuit on another. Referring to Fig. 15, 
 coil A B corresponds to wheel P ; C D to 
 wheel 8, and the iron core to the fly- 
 wheel and differential gear. The resist- 
 ance of a lamp takes the place of the 
 friction of the string on S. As we make 
 and break the circuit you see the effect 
 of the induced current in rendering the 
 lamp incandescent. So far I have been 
 illustrating the phenomena of the induc- 
 tion of one current upon another. I will 
 now show on the model that a current 
 in a single electric circuit has momen- 
 tum. The secondary wheel shall be 
 firmly held ; it shall have no conductivity 
 at all that is, its electrical effect shall 
 be as though it were not there. I now 
 cause a current to begin to flow in the primary circuit, 
 and it is obvious enough that a certain amount of work 
 must be done to bring it up to a certain speed. The an- 
 gular velocity of the flywheel is half that of the pulley 
 representing the primary circuit. Now suppose that the 
 two pulleys were connected together in such a way that 
 
 FIG. 15. 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 49 
 
 they must have the same angular velocity in the same 
 direction. This represents the coil having twice as many 
 convolutions as it had before. A little 
 consideration will show that I must do 
 four times as much work to give the 
 primary pulley the same velocity that 
 it attained before; that is to say, that 
 the coefficient of self induction of a coil 
 of wire is proportional to the square of 
 the number of convolutions. Again, 
 suppose that these two wheels were so 
 geared together that they must always 
 have equal and opposite velocities, you 
 can see that a very small amount of 
 work must be done in order to give the 
 primary wheel the velocity which we 
 gave to it before. Such an arrangement 
 of the model represents an electric cir- 
 cuit, the coefficient of induction of which 
 is exceedingly small, such as the coils 
 that are wound for standard resistances; 
 the wire is there wound double, and 
 the current returns upon itself, as shown 
 in Fig. 16. 
 
 In the widest sense, the dynamo-electric machine may 
 be defined as an apparatus for converting mechanical 
 energy into the energy of electrostatic charge, or mechan- 
 ical power into its equivalent electric current through a 
 conductor. Under this definition would be included the 
 electrophorus and all f rictional machines ; but the term is 
 used, in a more restricted sense, for those machines which 
 
 FIG. 16. 
 
50 DYtfAMO MACHINEHY AND ALLIED SUBJECTS. 
 
 produce electric currents by the motion of conductors in a 
 magnetic field, or by the motion of a magnetic field in the 
 neighborhood of a conductor. The laws on which the 
 action of such machines is based have been the subject of 
 a series of discoveries. Oersted discovered that an electric 
 current in a conductor exerted force upon a magnet; 
 Ampere that two conductors conveying currents generally 
 exerted a mechanical force upon each other. Faraday dis- 
 covered what Helmholtz and Thomson subsequently 
 proved to be the necessary consequence of the mechanical 
 reactions between conductors conveying currents and mag- 
 nets that if a closed conductor move in a magnetic field, 
 there will be a current induced in that conductor in one 
 direction if the number of lines of magnetic force passing 
 through the conductor was increased by the movement; in 
 the other direction if diminished. Now all dynamo-electric 
 machines are based upon Faraday's discovery. Not only 
 so ; but however elaborate we may wish to make the analysis 
 of the action of a dynamo machine, Faraday's way of pre- 
 senting the phenomena of electromagnetism to the mind 
 is in general our best point of departure. The dynamo 
 machine, then, essentially consists of a conductor made to 
 move in a magnetic field. This conductor, with the exter- 
 nal circuit, forms a closed circuit in which electric currents 
 are induced as the number of lines of magnetic force pass- 
 ing through the closed circuit varies. Since, then, if the 
 current in a closed circuit be in one direction when the 
 number of lines of force is increasing, and in the opposite 
 direction when they are diminishing, it is clear that the 
 current in each part of such circuit which passes through 
 the magnetic field must be alternating in direction, unless, 
 
SOME POINTS IN ELECTRIC LIGHTING. 51 
 
 indeed, the circuit be such that it is continually cutting 
 more and more lines of force, always in the same direction. 
 Since the current in the wire of the machine is alternating, 
 so also must be the current outside the machine, unless 
 something in the nature of a commutator be employed to 
 reverse the connections of the internal wires in which the 
 current is induced, and of the external circuit. We have, 
 then, broadly, two classes of dynamo-electric machines 
 the simplest, the alternating current machine, where no 
 commutator is used; and the continuous current machine, 
 in which a commutator is used to change the connection 
 of the external circuit just at the moment when the direc- 
 tion of the current would change. The mathematical 
 theory of the alternate current machine is comparatively 
 simple. To fix ideas, I will ask you to think of the alter- 
 nate current Siemens machine, which Dr. Siemens exhibited 
 here three weeks ago. We have there a series of magnetic 
 fields of alternate polarity, and through these fields we 
 have coils of wire moving; these coils constitute what is 
 called the armature; in them are induced the currents 
 which give a useful effect outside the machine. Now I 
 am not going to trouble you to go through the mathematical 
 equations, simple though they are, by which the following 
 formulae are obtained: 
 
 n t /T , 
 
 r (I.) 
 
 2 n A 2 Ttt 
 E= --cos- (II.) 
 
52 DYNAMO MACHINERY AND ALLIED 
 
 = (in.) 
 
 (IV.) 
 
 (VL) 
 
 T represents the periodic time of the machine ; that is, in 
 the case of a Siemens machine having eight magnets on 
 each side of the armature, T represents the time of one- 
 fourth of a revolution. / represents the number of lines 
 of force embraced by the coils of the armature at the time 
 t. I must be a periodic function of /, in the simplest form 
 represented by Equation I. Equation II. gives E the elec- 
 tromotive force acting at time / upon the circuit. Having 
 given the electromotive force acting at any time, it would 
 appear at first sight that we had nothing to do but to 
 divide that electromotive force by the resistance R of the 
 whole circuit, to obtain the current flowing at that time. 
 But if we were to do so we should be landed in error, for 
 the conducting circuit has other properties besides resist- 
 ance. I pointed out to you that it had a property of mo- 
 mentum represented by its coefficient of self induction, 
 
LIGHTING. 
 
 53 
 
 with 
 
 it |iijii at important a part as 
 DI. gives die 
 wiD obeerre that it 
 
 Hlesstkanitwoaldbeif 
 
 byfte 
 
 br Foonia IV. 
 of deefetical work 
 
 --;,-_:_, ::::_.: : -^ 
 
54 DYNAMO "MACHINERY AND ALLIED SUBJECTS. 
 
 In some cases this phenomenon is so marked that the 
 machine actually takes more to drive it, when the machine 
 is on open circuit, than when it is short circuited. The ex- 
 planation is that on open circuit currents are induced in 
 the iron cores, but that when the copper coils are closed 
 the current in them diminishes by induction the current in 
 the iron. The effect of currents in the iron cores is not 
 alone to waste eiwrgy and heat the machine; but for a 
 given intensity of field and speed of revolution the exter- 
 nal current produced is diminished. The cure of the evil 
 is to subdivide the moving iron as much as possible, in di- 
 rections perpendicular to those in which the current tends 
 to circulate. 
 
 There remains one point of great practical interest in 
 connection with alternate current machines: How will 
 they behave when two or more are coupled together to aid 
 each other in doing the same work ? With galvanic bat- 
 teries we know very well how to couple them, either in 
 parallel circuit or in series, so that they shall aid, and not 
 oppose, the effects of each other; but with alternate cur- 
 rent machines, independently driven, it is not quite obvi- 
 ous what the result will be, for the polarity of each 
 machine is constantly changing. Will two machines, 
 coupled together, run independently of each other, or will 
 one control the movement of the other in such wise 
 that they settle down to conspire to produce the same 
 effect, or will it be into mutual opposition ? It is obvious 
 that a great deal turns upon the answer to this question, 
 for in the general distribution of electric light it will be 
 desirable to be able to supply the system of conductors 
 from which the consumers draw by separate machines, 
 
SOME POINTS IN ELECTRIC LIGHTING. OO 
 
 which can be thrown in and out at pleasure. Now I know 
 it is a common impression that alternate current machines 
 cannot be worked together, and that it is almost a necessity 
 to have one enormous machine to supply all the consumers 
 drawing from one system of conductors. Let us see how 
 the matter stands. Consider two machines independently 
 driven, so as to have approximately the same periodic time 
 
 FIG. 17. 
 
 and the same electromotive force. If these two machines 
 are to be worked together, they may be connected in one 
 of two ways : they may be in parallel circuit with regard to 
 the external conductor, as shown by the full line in Fig. 1 7, 
 that is, their currents may be added algebraically and sent 
 to the external circuit, or they may be coupled in series, as 
 shown by the dotted line, that is, the whole current may 
 pass successively through the two machines, and the 
 electromotive force of the two machines may be added ? 
 
56 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 instead of their currents. The latter case is simpler. Let 
 us consider it first. I am going to show that if you couple 
 two such alternate current machines in series they will so 
 control each other's phase as to nullify each other, and 
 that you will get no effect from them ; and, as a corollary 
 from that, I am going to show that if you couple them in 
 parallel circuit they will work perfectly well together, and 
 the currents they produce will be added; in fact, that you 
 cannot drive alternate current machines tandem, but that 
 you may drive them as a pair, or, indeed, any number 
 abreast. In diagram, Fig. 18, the horizontal line of ab- 
 
 1JIL11IV 
 
 scissae represents the time advancing from left to right; 
 the full curves represent the electromotive forces of the 
 two machines not supposed to be in the same phase. We 
 want to see whether they will tend to get into the same 
 phase or to get into opposite phases. Now, if the machines 
 are coupled in series, the resultant electromotive force 
 on the circuit will be the sum of the electromotive 
 forces of the two machines. This resultant electromotive 
 force is represented by the broken curve III. By what we 
 have already seen in Formula IV., the phase of the cur- 
 
SOME POINTS IN ELECTRIC LIGHTING. 57 
 
 reut must lag behind the phase of the electromotive force, 
 
 as is shown in the diagram by curve 7F, thus . . 
 
 . Now the work done in any machine is represented 
 
 by the sum of the products of the currents and of the 
 electromotive forces, and it is clear that, as the phase of 
 the current is more near to the phase of the lagging 
 machine // than to that of the leading machine /, the lag- 
 ging machine must do more work in producing electricity 
 than the leading machine; consequently its velocity 
 will be retarded, and its retardation will go on until the 
 two machines settle down into exactly opposite phases, 
 when no current will pass. The moral, therefore, is, do 
 not attempt to couple two independently driven alternate 
 current machines in series. Now for the corollary: A, B, 
 Fig. 17, represent the two terminals of an alternate cur- 
 rent machine; , b the two terminals of another machine 
 independently driven. A and a are connected together, 
 and B and b. So regarded, the two machines are in 
 series, and we have just proved that they will exactly 
 oppose each other's effects, that is, when A is positive, a 
 will be positive also; when A is negative, a is also nega- 
 tive. Now, connecting A and a through the compara- 
 tively high resistance of the external circuit with B and b, the 
 current passing through that circuit will not much disturb, 
 if at all, the relations of the two machines. Hence, when 
 A is positive, a will be positive, and when A is negative, a 
 will be negative also; precisely the condition required that 
 the two machines may work together to send a current into 
 the external circuit. You may, therefore, with confi- 
 dence, attempt to run alternate current machines in 
 parallel circuit for the purpose of producing any external 
 
58 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 effect. I might easily show that the same applies to a 
 larger number; hence there ic no more difficulty in feed- 
 ing a system of conductors from a number of alternate cur- 
 rent machines than there is in feeding it from a number 
 of continuous current machines. A little care is only re- 
 quired that the machine shall be thrown in when it has 
 attained something like its proper velocity. A further 
 corollary is that alternate currents with alternate current 
 machines as motors may theoretically be used for the trans- 
 mission of power.* 
 
 It is easy to see that, by introducing a commutator re- 
 volving with the armature, in an alternate current machine, 
 and so arranged as to reverse the connection between the 
 armature and the external circuit just at the time when 
 the current would reverse, it is possible to obtain a cur- 
 rent constant always in direction; but such a current 
 would be far from constant in intensity, and would cer- 
 tainly not accomplish all the results that are obtained in 
 modern continuous current machines. This irregularity 
 may, however, be reduced to any extent by multiplying 
 the wires of the armature, giving eacli its own connection 
 to the outer circuit, and so placing them that the electro- 
 motive force attains a maximum successively in the several 
 coils. A practically uniform electric current was first com- 
 mercially produced with the ring armature of Pacinotti, 
 as perfected by Gramme. The Gramme machine is repre- 
 sented diagram matically in Fig. 19. The armature consists 
 
 *Of course in applying these conclusions it is necessary to remember that 
 the machines only tend to control each other, and that the control of the 
 motive power may be predominant, and compel th two or more machines to 
 run at different speeds. 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 59 
 
 of an anchor ring of iron wire, the strands more or less 
 insulated from each other. Round this anchor ring is 
 wound a continuous endless coil 
 of copper wire; the armature 
 moves in a magnetic field, pro- 
 duced by permanent or electro- 
 magnets with diametrically oppo- 
 site poles, marked N and S. The 
 lines of magnetic force may be 
 regarded as passing into the ring 
 from N, dividing, passing round 
 the ring and across to S. Thus 
 the coils of wire, both near to N 
 and near to S, are cutting through 
 a very strong magnetic field; con- 
 sequently there will be an intense 
 inductive action. The inductive 
 action of the coils near JV being 
 equal and opposite to the induc- 
 tive action of the coils near S, 
 it results that there will be strong 
 positive and negative electric po- 
 tential at the extremities of a 
 diameter perpendicular to the line 
 NS. The electromotive force pro- 
 duced is made use of to produce a 
 
 current external to the machine; thus the endless coil of 
 the armature is divided into any number of sections, in the 
 diagram into six for convenience, usually into sixty or 
 eighty, and the junction of each pair of sections is con- 
 nected by a wire to a plate of the commutator fixed upon 
 
 FIG. 19. 
 
60 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the shaft which carries the armature; collecting brushes 
 make contact with the commutator, as shown in the 
 diagram. If the external resistance were enormously 
 high, so that very little current, or none at all, passed 
 through the armature, the greatest difference of potential 
 between the two brushes would be found when they made 
 contact at points at right angles to the line between the 
 magnets; but when a current passes in the armature, this 
 current causes a disturbing effect upon the magnetic field. 
 Every time the contact of the brushes changes from one 
 contact plate to the next, the current in a section of the 
 copper coil is reversed, and this reversal has an inductive 
 effect upon all the other coils of the armature. You may 
 take it from me that the net result on any one coil is approxi- 
 mately the same as if that coil alone were moved, and all 
 the other coils were fixed, and there were no reversals of 
 current in them. Now you can easily see that the mag- 
 netic effect of the current circulating in the coils of 
 the armature will be to produce a north pole at n 
 and a south pole at s. This will displace the magnetic 
 field in the direction of rotation. If, then, we were to 
 keep the contact points the same as when no current was 
 passing, we should short circuit the sections of the arma- 
 ture at a time when they were cutting through the lines 
 of magnetic force, with a result that there would be vigor- 
 ous sparks between the collecting brushes and the com- 
 mutator. To avoid this, the brushes must follow the 
 magnetic field, and also be displaced in the direction of 
 rotation, this displacement being greater as the current in 
 the armature is greater in proportion to the magnetic field. 
 The net effect of this disturbing effect of the current in. 
 
SOME POINTS IN ELECTRIC LIGHTING. 61 
 
 the armature reacting upon itself is, then, to displace the 
 neutral points upon the commutator, and consequently 
 somewhat to diminish the effective electromotive force. 
 It is best to adjust the brushes to make contact at a point 
 such that, with the current then passing, flashing is re- 
 duced to a minimum; but this point does not necessarily 
 coincide with the point which gives maximum difference 
 of potential. The magnetic field' in the Gramme and 
 other continuous dynamo-electric machines may be pro- 
 duced in several ways. Permanent magnets of steel may be 
 used, as in some of the smaller machines now made, and in 
 all the earlier machines; these are frequently called mag- 
 neto machines. Electromagnets excited by a current 
 from a small dynamo-electric machine were introduced 
 by Wilde; these may be described shortly as dynamos 
 with separate exciters. The plan of using the whole 
 current from the armature of the machine itself, for 
 exciting the magnets, was proposed almost simultaneously 
 by Siemens, Wheatstone, and S. A. Varley. A dynamo 
 so excited is now called a series dynamo. Another method 
 is to divide the current from the armature, sending the 
 greater part into the external circuit, and a smaller por- 
 tion through the electromagnet, which is then of very 
 much higher resistance. Such an arrangement is called a 
 shunt dynamo. A combination of the last two methods 
 has been recently introduced, for the purpose of main- 
 taining constant potential. The magnet is partly ex- 
 cited by a circuit of high resistance, a shunt to the 
 external circuit, and partly by coils conveying the 
 whole current from the armature. All but the first 
 two arrangements named depend on residual magnetism 
 
62 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 to initiate the current, and below a certain speed of rotation 
 give no practically useful electromotive force. A dynamo 
 machine is, of course, not a perfect instrument for converting 
 mechanical energy into the energy of electric current. Cer- 
 tain losses inevitably occur. There is, of course, the loss 
 due to friction of bearings, and of the collecting brushes 
 upon the commutator; there is also the loss due to the 
 production of electric currents in the iron of the machine. 
 When these are accounted for, we have the actual electrical 
 effect of the machine in the conducting wire; but all of 
 this is not available for external work. The current has to 
 circulate through the armature, which inevitably has elec- 
 trical resistance; electrical energy must, therefore, be con- 
 verted into heat in the armature of the machine. Energy 
 must also be expended in the wire of the electromagnet 
 which produces the field, for the resistance of this also cannot 
 be reduced beyond a certain limit. The loss by the resistance 
 of the wires of the armature and of the magnets greatly 
 depends on the dimensions of the machine. About this 
 I shall have to say a word or two presently. To know the 
 properties of any machine thoroughly, it is not enough to 
 know its efficiency and the amount of work it is capable 
 of doing; wo need to know what it will do under all cir- 
 cumstances of varying resistance or varying electromotive 
 force. We must know, under any given conditions, what 
 will be the electromotive force of the armature. Now this 
 electromotive force depends on the intensity of the mag- 
 netic field, and the intensity of the magnetic field depends 
 on the current passing round the electromagnet and the 
 current in the armature. The current, then, in the machine 
 is the proper independent variable in terms of which to 
 
SOME POINTS IN ELECTRIC LIGHTING. 63 
 
 express the electromotive force. The simplest case is that 
 of the series dynamo, in which the current in the electro- 
 magnet and in the armature is the same, for then we have 
 only one independent variable. The relation between the 
 electromotive force and current is represented by such a 
 curve as is shown in the diagram, Fig. 20. The abscissae, 
 
 Fio. 20. 
 
 measured along X, represent the current, and the ordi- 
 nates represent the* electromotive force in the armature. 
 When four years ago I first used this curve, for the pur- 
 pose of expressing the results of my experiments on the 
 Siemens dynamo machine, I pointed out that it was capable 
 of solving almost any problem relating to a particular 
 machine, and that it was also capable of giving good indi- 
 cations of the results of changes in the winding of the 
 magnets or of the armatures of such machines. Since then 
 M. Marcel Deprez has happily named such curves " char- 
 
64 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 acteristic curves." I will give you one or two illustrations 
 of their use. A complete characteristic of a series dynamo 
 does not terminate at the origin, but has a negative branch, 
 as shown in the diagram ; for it is clear that by reversing 
 the current through the whole machine the electromotive 
 force is also reversed. Suppose a series dynamo is used for 
 charging an accumulator, and is driven at a given speed, 
 what current will pass through it ? The problem is easily 
 solved. Along Y, Fig. 20, set off E to represent the 
 electromotive force of the accumulator, and through ^draw 
 the line C E B A, making an angle with X, such that its 
 tangent is equal to the resistance of the whole circuit, and 
 cutting the characteristic curve, as it in general will do, in 
 three points, A, B, and C. We have, then, three answers to 
 the question. The current passing through the dynamo 
 will be either L, M, or N t the abscissae of the points 
 where the line cuts the curve. L represents the current 
 when the dynamo is actually charging the accumulator. 
 M represents a current which could exist for an instant, 
 but which would be unstable, for the least variation would 
 tend to increase. N is the current which passes if the 
 current in the dynamo should get reversed, as it is very 
 apt to do when used for this purpose. THie next illustration 
 is rather outside my subject, but shows another method of 
 using the characteristic curve. Many of you have heard of 
 Jacobi's law of maximum effect of transmitting work by 
 dynamo machines. It is this: Supposing that the two 
 dynamo machines were perfect instruments for converting 
 mechanical energy into electrical energy, and that the gen- 
 erating machine were run at constant velocity, while the 
 receiving machine had a variable velocity, the greatest 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 65 
 
 amount of work would be developed in the receiving 
 machine when its electromotive force was one-half that of 
 the generating machine; then the efficiency would be one- 
 half, and the electrical work done by the generating machine 
 would be just one-half of what it would be if the receiving 
 machine were forcibly held at rest. Now this law is strictly 
 true if, and only if, the electromotive force of the generat- 
 ing machine is independent of the current passing through 
 
 its armature. What I am now going to do is to give you a 
 construction for determining the maximum work which 
 can be transmitted when the electromotive force of the 
 generating machine depends on the current passing through 
 the armature, as, indeed, it nearly always does. Referring to 
 Fig. 21, PB is the characteristic curve of the generating 
 machine. Construct a derived curve thus: at successive 
 
66 DYNAMO MACHINERY ANt> ALLIED 
 
 points P of the characteristic curve draw tangents P T; 
 draw T N parallel to X, cutting P j^in N; produce M P 
 to L, making L P equal P N; the point L gives the derived 
 curve, which I want. Now, to find the maximum work 
 which can be transmitted, draw A at such an angle with 
 X that its tangent is equal to twice the resistance of the 
 whole circuit, cutting the derived curve in A. Draw the 
 ordinate A C, cutting the characteristic curve in B; bisect 
 A (7 at D. The work expended upon the generating machine 
 would be represented by the parallelogram C B R, the 
 work wasted in resistance by CD S, and the work de- 
 veloped in the receiving machine by the parallelogram 
 SDBR. 
 
 When the dynamo machine is not a series dynamo, but 
 the currents in the armature and in the electromagnet, 
 though possibly dependent upon each other, are not nece.s- 
 sarily equal, the problem is not quite so simple. We have, 
 then, two variables, the current in the electromagnet and 
 the current in the armature; and the proper representation 
 of the properties of the machine will be by a characteristic 
 surface such as that illustrated by this model, Fig. 22. Of 
 the three co-ordinate axes, X represents the current in 
 the magnet, Y represents the current in the armature, 
 not necessarily to the same scale, and Z the electromo- 
 tive force. By the aid of such a surface as this, one may 
 deal with any problem relating to a dynamo machine, no 
 matter how its electromagnets and its armature are con- 
 nected together. Let us apply the model to find the 
 characteristic of a series dynamo. Take a plane through 
 Z y the axis of electromotive force, and making such an 
 angle with the plane X, Z that its tangent is equal to 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 67 
 
 current unity on axis Y, divided by current unity on 
 axis X. This plane cuts the surface in a curve. The 
 projection of this curve on the plane OX, OZ is the 
 characteristic curve of the series dynamo. This model only 
 shows an eighth part of the complete surface. If any of 
 you should interest yourselves about the other seven parts, 
 which are not without interest, remember that it is assumed 
 
 FIG. 22. 
 
 that the brushes always make contact with the commu- 
 tator at the point of no flashing, if there is one. Of course 
 in actual practice one would not use the model of the 
 surface, but the projections of its sections. While I am 
 speaking of characteristic curves there is one point I will 
 just take this opportunity of mentioning. Three years ago 
 Mr. Shoolbred exhibited the characteristic curve of a 
 Gramme machine, in which, after the current attained to a 
 
68 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 certain amount, the electromotive force began to fall. I 
 then said that I thought there must be some mistake in the 
 experiment. However, subsequent experiments have veri- 
 fied the fact; and when one considers it, it is not very 
 difficult to see the explanation. It lies in this : after the 
 current attains to a certain amount the iron in the machines 
 becomes magnetically nearly saturated, and consequently 
 an increase in the current does not produce a correspond- 
 ing increase in the magnetic field. The reaction, however, 
 between the different sections of the wire on the armature 
 goes on increasing indefinitely, and its effect is to diminish 
 the electromotive force. 
 
 A little while ago I said that the dimensions of the 
 machine had a good deal to do with its efficiency. Let us 
 see how the properties of a machine depend upon its dimen- 
 sions. Suppose two machines alike in every particular ex- 
 cepting that the one has all its linear dimensions double 
 those of the other; obviously enough all the surfaces in the 
 larger would be four times the corresponding surfaces in 
 the smaller, and the weights and volumes of the larger 
 would be eight times the corresponding weights in the 
 smaller machine. The electrical resistances in the larger 
 machine would be one-half those of the smaller. The cur- 
 rent required to produce a given intensity of magnetic field 
 would be twice as great in the larger machine as in the 
 smaller. In the diagram (Fig. 23) are shown the compara- 
 tive characteristic curves of the two machines, when driven 
 at the same speed. You will observe that one curve 
 is the projection of the other, having corresponding 
 points with abscissae in the ratio of one to two, and the 
 ordinates in the ratio of one to four. Now at first sight it 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 69 
 
 would seem as though, since the wire on the magnet and 
 armature of the larger machine has four times the section 
 of that of the smaller, four times the current could be 
 carried, that consequently the intensity of the magnetic 
 field would be twice as great and its area would be four 
 times as great, and hence the electromotive force eight 
 times as great; and, since the current in the armature also 
 is supposed to be four times as great, that the work done 
 
 by the larger machine would be thirty-two times as much 
 as that which would be done by the smaller. Practically, 
 however, no such result can possibly be obtained, for a 
 whole series of reasons. First of all, the iron of the mag- 
 nets becomes saturated, and consequently, instead of getting 
 eight times the electromotive force, we should only get four 
 times the electromotive force. Secondly, the current which 
 we can carry in the armature is limited by the rate at which 
 we can get rid of the heat generated in the armature. This 
 we may consider as proportional to its surface; consequently 
 
70 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 we must only waste four times as much energy in the arma- 
 ture of the larger machine as in the smaller one, instead of 
 eight times, as would be the case if we carried the current 
 in proportion to the section of the wire. Again, the larger 
 machine cannot run at so great an angular velocity as the 
 smaller one. And lastly, since in the larger machine the 
 current in the armature is greater in proportion to the 
 saturated magnetic field than it is in the smaller one, the 
 displacement of the point of contact of the brushes with 
 the commutator will be greater. However, to cut the 
 matter, about which one might say a great deal, short, one 
 may say that the capacity of similar dynamo machines is 
 pretty much proportionate to their weight, that is, to the 
 cube of their linear dimensions; that the work wasted in 
 producing the magnetic field will be directly as the linear 
 dimensions; and that the work wasted in heating the wires 
 of the armature will be as the square of the linear dimensions. 
 Now let us see how this would practically apply. Suppose 
 we had a small machine capable of producing an electric 
 current of 4 h. p., that of this 4 h. p. 1 was wasted in heat- 
 ing the wires of the armature, and 1 in heating the wires 
 of the magnet; 2 would be usefully applied outside. Now 
 if we doubled the linear dimensions we should have a ca- 
 pacity of 32 h. p., of which 2 only, if suitably applied, would 
 be required to produce the magnetic field, and 4 would be 
 wasted in heating the wires of the armature, leaving 26 h. p. 
 available for useful work outside the machine a very dif- 
 ferent economy from that of the smaller machines. But 
 if we again doubled the linear dimensions of our machine, 
 we should by no means obtain a similar increase of effect. 
 A consideration of the properties of similar machines has 
 
SOME POINTS IN ELECTRIC LIGHTING. 71 
 
 another very important practical use. As you all know, 
 Mr. Froude was able to control the design of ironclad ships 
 by experiments upon models made in paraffin wax. Now 
 it is a very much easier thing to predict what the perform- 
 ance of a large dynamo machine will be, from laboratory 
 experiments made upon a model of a very small fraction of 
 its dimensions. As a proof of the practical utility of such 
 methods, I may say that by laboratory experiments I have 
 succeeded in increasing the capacity of the Edison machines 
 without increasing their cost, and with a small increase of 
 their percentage of efficiency, remarkably high as that 
 efficiency already was. 
 
 I might occupy your time with considerations as to the 
 proper proportion of conductors, and explain Sir W. 
 Thomson's law that the most economical size of a copper 
 conductor is such that the annual charge for interest and 
 depreciation of the copper of which it is made shall be 
 equal to the cost of producing the power which is wasted 
 by its resistance. But the remaining time will, perhaps, be 
 best spent in considering the production of light from the 
 energy of electric currents. You all know that this is done 
 commercially in two ways by the electric arc, and by the 
 incandescent lamp ; as the arc lamp preceded the incandes- 
 cent lamp historically, we will examine one or two points 
 connected with it first. 
 
 I have here all that is necessary to illustrate the electric 
 arc, viz., two rods of carbon supported in line with each 
 other, and so mounted that they can be approached or with- 
 drawn. Each carbon is connected with one of the poles of 
 the Edison dynamo machine which is supplying electricity 
 to the incandescent lamps which illuminate the whole of 
 
72 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 this building. A resistance is interposed in the circuit of 
 the lamp, because the electromotive force of the machine 
 is much in excess of what the lamp requires. I now ap- 
 proach the carbons, bring them into contact, and again 
 separate them slightly; you observe that the break does 
 not stop the current, which forces its way across the space. 
 I increase the distance between the carbons, and you observe 
 the electric arc between their extremities ; at last it breaks, 
 having attained a length of about 1 inch. Now the current 
 has hard work to cross this air space between the carbons, 
 and the energy there developed is converted into heat, 
 which raises the temperature of the ends of the carbon be- 
 yond any other terrestrial temperature. There are several 
 points of interest I wish to notice in the electric arc. Both 
 carbons burn away in the air, but there is also a transference 
 of carbon from the positive to the negative carbon; there- 
 fore, although both waste away, the positive carbon wastes 
 about twice as fast as the negative. With a continuous 
 current, such as we are using now, the negative carbon be- 
 comes pointed, while the positive carbon forms a crater or 
 hollow; it is this crater which becomes most intensely hot 
 and radiates most of the light; hence the light is not by any 
 means uniformly distributed in all directions, but is mainly 
 thrown forward from the crater in the positive carbon. 
 This peculiarity is of great advantage for some purposes, 
 such, for example, as military or naval search lights; but it 
 necessitates, in describing the illuminating power of an arc 
 light, some statement of the direction in which the measure- 
 ment was made. On account of its very high temperature 
 the arc light sends forth a very large amount of visible 
 radiation, and is therefore very economical of electrical 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 73 
 
 energy. For the same reason its light contains a very large 
 proportion of rays of high refrangibility, blue and ultra 
 violet. I have measured the red light of an electric arc 
 against the red of a candle, and have found it to be 4,700 
 times as great, and I have measured the blue of the same 
 arc light against the blue of the same candle, and found it 
 to be 11,380 times as great. The properties of an electric 
 arc are not those of an ordinary conductor. Ohm's law 
 does not apply. The electromotive force and the current 
 do not by any means bear to each other a constant ratio. 
 Strictly speaking, an electric arc cannot be said to have an 
 electric resistance measurable in ohms. We will now ex- 
 amine the electrical properties of the arc experimentally. 
 In the circuit with the lamp is a Thomson graded current 
 galvanometer for measuring the current passing in amperes; 
 connected to the two carbons is a Thomson graded poten- 
 tial galvanometer for measuring the difference of potential 
 between them in volts. We have the means of varying 
 the current by varying the resistance, which I have already 
 told you is introduced into the circuit. We will first put 
 in circuit the whole resistance available, and will adjust 
 the carbons so that the distance between them is, as near 
 as I can judge, inch. We will afterwards increase the cur- 
 rent and repeat the readings. The results are given in 
 Table III. 
 
 TABLE III. 
 
 Current 
 Galvanometer. 
 
 Potential 
 Galvanometer. 
 
 Amperes. 
 
 Volts. 
 
 Watts. 
 
 H. P. 
 
 6.2 
 
 12.0 
 
 9.9 
 
 35 
 
 346 
 
 0.46 
 
 9.3 
 
 12.0 
 
 14.9 
 
 35 
 
 521 
 
 0.70 
 
 11.5 
 
 11.8 
 
 18.4 
 
 34 
 
 626 
 
 0.84 
 
74 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 If the electrical properties of the arc were the same as 
 those of a continuous conductor, the volts would be in pro- 
 portion to the amperes, if correction were made for change 
 of temperature ; you observe that instead of that the poten- 
 tial is nearly the same in the two cases. We may say, 
 with some approach to accuracy, that, with a given length 
 of arc, the arc opposes to the current an electromotive force 
 nearly constant, almost independent of the current. This 
 was first pointed out by Edlund. If you will speak of the 
 resistance of the electric arc, you may say that the resist- 
 ance varies inversely as the current. Take the last exper- 
 iment: by burning 4 cubic feet of gas per hour we should 
 produce heat energy at about the same rate. I leave any 
 of you to judge of the comparative illuminating effects. It 
 is not my purpose to describe the mechanisms which have 
 been invented for controlling the feeding of the carbons as 
 they waste away. Several lamps lent by Messrs. Siemens 
 Brothers to whom I am indebted for the lamp and resist- 
 ance I have just been using lie upon the table for inspec- 
 tion. An electric arc can also be produced by an alternate 
 current. Its theory may be treated mathematically, and is 
 very interesting, but time will not allow us to go into it. 
 I will merely point out this: there is some theoretical reason 
 to suppose that an alternate current arc is in some measure 
 less efficient than one produced by a continuous current. 
 The efficiency of a source of light is greater as the mean 
 temperature of the radiating surface is greater. The max- 
 imum temperature in an arc is limited probably by the 
 temperature of volatilization of carbon; in an alternate 
 current arc the current is not constant, therefore the mean 
 temperature is less than the maximum temperature; in a 
 
SOME POINTS IN ELECTRIC LIGHTING. 75 
 
 continuous current arc, the current being constant, the 
 mean and maximum temperatures are equal, therefore in a 
 continuous current arc the mean temperature is likely to 
 be somewhat higher than in an alternate current arc. 
 
 We will now pass to the simpler incandescent light. 
 When a current of electricity passes through a continuous 
 conductor, it encounters resistance, and heat is generated, 
 as was shown by Joule, at a rate represented by the resist- 
 ance multiplied by the square of the current. If the cur- 
 rent is sufficiently great, the heat will be generated at such 
 a rate that the conductor rises in temperature so far 
 that it becomes incandescent and radiates light. At- 
 tempts have been made to use platinum and platinum- 
 iridium as the incandescent conductor, but these bodies 
 are too expensive for general use, and besides, refractory 
 though they are, they are not refractory enough to stand 
 the high temperature required for economical incandescent 
 lighting. Commercial success was not realized until very 
 thin and very uniform threads or filaments of carbon were 
 produced and enclosed in reservoirs of glass, from which 
 the air was exhausted to the utmost possible limit. Such 
 are the lamps made by Mr. Edison with which this build- 
 ing is lighted to-night. Let us examine the electrical 
 properties of such a lamp. Here is a lamp intended to 
 carry the same current as those overhead, but of half the 
 resistance, selected because it leaves us a margin of electro- 
 motive force wherewith to vary our experiment. Into its 
 circuit I am able to introduce a resistance for checking the 
 current, composed of other incandescent lamps for con- 
 venience, but which I shall cover over that they may not 
 distract your attention. As before, we have two galva- 
 
76 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 nometers one to measure the current passing through the 
 lamp, the other the difference of potential at its terminals. 
 First of all, we will introduce ar considerable resistance; 
 you observe that, although the lamp gives some light, it 
 is feeble and red, indicating a low temperature. We take 
 our galvanometer readings. We now diminish the resist- 
 ance. The lamp is now a little short of its standard in- 
 tensity; with this current it would last 1,000 hours without 
 giving way. We again read the galvanometers. The re- 
 sistance is diminished still further. You observe a great 
 increase of brightness, and the light is much whiter than 
 before. With this current the lamp would not last very 
 long. The results are given in Table IV. 
 
 TABLE IV. 
 
 Current 
 Galvanometer. 
 
 Potential 
 Galvanometer. 
 
 Amperes. 
 
 Volts. 
 
 Watts. 
 
 Resistance, 
 Ohins. 
 
 5.2 
 
 12.8 
 
 0.38 
 
 87 
 
 14 
 
 97 
 
 6.0 
 
 14.3 
 
 (' 11 
 
 41 
 
 18 
 
 93 
 
 11.5 
 
 i 28.4 
 
 0.84 
 
 68 
 
 5? 
 
 81 
 
 There are three things I want you to notice in these 
 experiments: first, the light is whiter as the current in- 
 creases; second, the quantity of light increases very much 
 faster than the power expended increases; and third, the 
 resistance of the carbon filament diminishes as its tem- 
 perature increases, which is just the opposite of what we 
 should find with a metallic conductor. This resistance is 
 given in ohms in the last column. To the second point, 
 which has been very clearly put by Dr. Siemens in his British 
 Association address, I shall return in a minute or two. 
 
SOME POINTS IN ELECTRIC LIGHTING. 77 
 
 The building is this evening lighted by about 200 
 lamps, each giving sixteen candles' light when 75 watts of 
 power are developed in the lamp. To produce the same 
 sixteen candles' light in ordinary flat flame gas burners 
 would require between seven and eight cubic feet of gas per 
 hour, contributing heat to the atmosphere at the rate of 
 3,400,000 foot-pounds per hour, equivalent to 1,250 watts; 
 that is to say, equivalent gas lighting would heat the air 
 nearly seventeen times as much as the incandescent lamps. 
 
 Look at it another way. Practically, about eight of these 
 lamps take one indicated horse power in the engine to supply 
 them. If the steam engine were replaced by a large gas 
 engine this 1 h. p. would be supplied by 25 cubic feet of 
 gas per hour, or by rather less; therefore by burning gas 
 in a gas engine driving a dynamo, and using the electricity 
 in the ordinary way in incandescent lamps, we can obtain 
 more than five candles per cubic foot of gas, a result you 
 would be puzzled to obtain in 10-candle gas burners. 
 With arc lights instead of incandescent Jamps many times 
 as much light could be obtained. 
 
 At the present time, lighting by electricity in London 
 must cost something more than lighting by gas. Let us 
 see what are the prospects of reduction of this cost. Be- 
 ginning with the engine and boiler, the electrician has no 
 right to look forward to any marked and exceptional 
 advance in their economy. Next comes the dynamo; the 
 best of these are so good, converting 80 per cent, of the 
 work done in driving the machine into electrical work out- 
 side the machine, that there is little room for economy in 
 the conversion of mechanical into electrical energy; but 
 the prime cost of the dynamo machine is sure to be greatly 
 
78 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 reduced. Our hope of greatly increased economy must be 
 mainly based upon probable improvements in the incan- 
 descent lamp, and to this the greatest attention ought to 
 be directed. You have seen that a great economy of 
 power can be obtained by working the lamps at high press- 
 ure, but then they soon break down. In ordinary prac- 
 tice from 140 to 200 candles are obtained from a horse 
 power developed in the lamps, but for a short time I have 
 seen over 1,000 candles per horse power from incandescent 
 lamps. The problem, then, is so to improve the lamp in 
 detail that it will last a reasonable time when pressed to 
 that degree of efficiency. There is no theoretical bar to 
 such improvements, and it must be remembered that in- 
 candescent lamps have only been articles of commerce for 
 about three years, and already much has been done. If 
 such an improvement were realized, it would mean that 
 you would get five times as much light for a sovereign as 
 you can now. As things now stand, so soon as those who 
 supply electricity have reasonable facilities for reaching 
 their customers, electric lighting will succeed commercially 
 where other considerations than cost have weight. We 
 are sure of some considerable improvements in the lamps, 
 and there is a probability that these improvements may 
 go so far as to reduce the cost to one-fifth of what it now 
 is. I leave you to judge whether or not it is probable, nay, 
 almost certain, that lighting by electricity is the lighting 
 of the future. 
 
MAOHlNEKY. 
 
 DYNAMO-ELECTKIC MACHINEKY. 
 
 THEORETICAL CONSTRUCTION" OF CHARACTERISTIC CURVE. 
 
 OMITTING the inductive effects of the current in the 
 armature itself, all the properties of a dynamo machine are 
 most conveniently deduced from a statement of the rela- 
 tion between the magnetic field and the magnetizing force 
 required to produce that field, or, which comes to the same 
 thing but more frequently used in practice, the relation 
 between the electromotive force of the machine at a stated 
 speed and the current around the magnets. This relation 
 given, it is easy to deduce what the result will be in all 
 employments of the machine, whether as a motor or to 
 produce a current through resistance, through an electric 
 arc, or in charging accumulators; also the result of vary- 
 ing the winding of the machine, whether in the armature 
 or magnets. The proper independent variable to choose 
 for discussing the effect of a dynamo machine is the cur- 
 rent around the magnets; and the primary relation it is 
 necessary to know concerning the machine is the relation 
 of the electromotive force of the armature to the magnet 
 current. This primary relation may be expressed by a 
 curve (Fig. 4, p. 22 et seq., and Fig. 5, p. 26), now called 
 the characteristic of the machine, and all consequences 
 deduced therefrom graphically; or it may be expressed by 
 
80 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 stating the E.M.F. as an empirical function of the magnet- 
 izing current. Many such empirical formulaB have been 
 proposed; as an instance we may mention that known as 
 Frohlich's, according to whom, if c be the current in the 
 
 magnets, E the resulting E.M.F., E = ~r-. For some 
 
 J. J~ o c 
 
 machines this formula is said to express observed results 
 fairly accurately, but in our experience it does not suf- 
 ficiently approximate to a straight line in the part of the 
 curve near the origin. The character of the error in 
 Frohlich's formula is apparent by reference to Figs. 24 
 and 25, which give a series of observations on a dynamo 
 machine, and for comparison therewith a hyperbola F, 
 drawn as favorably as possible to accord with the observa- 
 tions.* Such empirical formulaB possess no advantage over 
 the graphical method aided by algebraic processes, and 
 tend to mask much that is of importance. 
 
 One purpose of the present investigation is to give an 
 approximately complete construction of the characteristic 
 curve of a dynanlo of given form from the ordinary laws 
 of electromagnetism and the known properties of iron, 
 and to compare the result of such construction with the 
 actual characteristic of the machine. The laws of electro- 
 magnetism needed are simply (Thomson, papers on " Elec- 
 
 * Added Aug. 17. That Frfihlich's formula cannot be a thoroughly satisfac- 
 tory expression of the characteristic of a dynamo machine is evident from the 
 consideration that E should simply change its sign with c, that is, be an odd 
 function of c. There should be a point of inflection in the characteristic curve 
 
 at the origin. Another empirical formula, = tan ~ 1 -, is free from this objec- 
 tion, but still fails to fully represent the approximation of the curve to a 
 straight line on either side of the origin, and it is equally uninstructive with 
 any other purely empirical formula. 
 
DYNAMO-ELECTEIC MACHINERY 
 
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 Fio. 25. APPKOXIMATK SYNTHESIS OF CHARACTERISTIC CURVE. 
 , armature; B, air space; C, magnets; D, deduced curve; ,E, observed 
 results, -f ascending, descending; F, Frfihlich's curve. This figure is 
 the same as the left-hand part of Fig. 24, but on a larger scale. 
 
DYNAMO-ELECTRIC MACHINERY. 83 
 
 trostatics and Magnetism;" Maxwell, "Electricity and 
 Magnetism/' vol. ii., pp. 24, 26, and 143), (1) that the 
 line integral of magnetic force around any closed curve, 
 whether in iron, in air, or in both, is equal to 4;r n c, where 
 c is the current passing through the closed curve, and n is 
 the number of times it passes through; (2) the solenoidal 
 condition for magnetic induction, that is, if the lines of 
 force or of induction be supposed drawn, then the induc- 
 tion through any tube of induction is the same for every 
 section. Regarding the iron itself, we require to know 
 from experiments on the material in any shape the relation 
 between , the induction, and a, the magnetic force at any 
 point; for convenience write a=f~ l (ae), or a = f(a). 
 From these premises, without any further assumption, it is 
 easy to see that a sufficiently powerful and laborious analysis 
 would be capable of deducing the characteristic of any 
 dynamo to any desired degree of accuracy. This we do not 
 attempt, as, even if successful, the analysis would not be 
 likely to throw any useful light on the practical problem. 
 We shall calculate the characteristic, first making certain 
 assumptions to simplify matters. We shall next point out 
 the nature of the errors introduced by these assumptions, 
 and make certain small corrections in the method to ac- 
 count for these sources of error, merely proving that the 
 amount of these corrections is probable or deducing it 
 from a separate experiment, and again compare the theo- 
 retical and the actual characteristic. 
 
 First Approximation. Assume that by some miracle 
 the tubes of magnetic induction are entirely confined to 
 the iron excepting that they pass directly across from the 
 bored faces of the pole pieces to the cylindrical face of the 
 
84 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 armature core. This, we shall find, introduces minor 
 sources of error, affecting different parts of the charac- 
 teristic curve to a material extent. Let / be total in- 
 duction through the armature, A l the area of section of 
 the iron of the armature, 7, the mean length of lines of 
 force in the armature; .1, the area of each of the two 
 spaces between core of armature and the pole pieces of the 
 magnets, 7, the distance between the core and the pole 
 piece; A t the area of core of magnet, 7, the total length of 
 the magnets. All the tubes of induction which pass 
 through the armature pass through the space A 9 and the 
 magnet cores, and by our assumption there are no others. 
 We now assume further that these tubes are uniformly 
 distributed over these areas. The induction per square 
 
 centimetre is then -.- in the armature core, - in the non- 
 A l A 9 
 
 magnetic spaces, -- in the magnet cores; the correspond- 
 ing magnetic forces per centimetre linear must be/( - -), -y-, 
 
 \AJ A t 
 
 The line integral of magnetic force round a closed 
 
 curve must be 7,/f-;- ) + 27, - - + J/(~r ) ^ n this a P - 
 XAJ A t \A t J 
 
 proximation we neglect the force required to magnetize 
 pole pieces and other parts not within the magnet coils, to 
 avoid complication. The equation of the characteristic 
 
 curve is, then, 4* n c = 7,/fl + 27, -.- + 7, f(-\ This 
 
 \AJ A 9 \A 3 / 
 
 curve is, of course, readily constructed graphically from 
 the magnetic property of the material expressed by the 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 85 
 
 curve a =f(a). In Figs. 24 and 25 curve A represents 
 
 x.= Z, f[ -J-), the straight line B x = 2Z,-j-, curve G 
 \AJ Ji 
 
 x = Z, /(?'), and curve D the calculated characteristic. 
 
 When we compare this with an actual characteristic E, we 
 shall see that, broadly speaking, it deviates from truth in 
 
 FIG. 26. 
 
 two respects: (1) it does not rise sufficiently rapidly at 
 first; (2) it attains a higher maximum than is actually 
 realized. Let us examine these errors in detail. 
 
 (1) The angle the characteristic makes with the axis of 
 abscissae near the origin is mainly determined by the line 
 B (Fig. 26). "We have in fact a very considerable exten- 
 
86 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 sion of the area of the field beyond that which lies under 
 the bored face of the pole piece. The following considera- 
 tion will show that the extension may be considerable: 
 Imagine an infinite plane slab, and parallel with it a second 
 slab cut off by a second plane making an angle a. We 
 want a rough idea of the extension of the area between the 
 plates by the spreading of the lines of induction beyond 
 the boundary. We know that the actual extension of the 
 area will be greater than we shall calculate it to be if we 
 prescribe an arbitrary distribution of lines of force other 
 than that which is consistent with Laplace's equation. 
 Assume, then, the lines of force to be segments of circles 
 
 centre 0, and straight lines perpendicular to A. The 
 
 y 
 induction along a line P Q R will be -T r 7-, V 
 
 t 
 
 being difference of potential between the planes; and the 
 added induction from P B will be 
 
 Vdx V (T- a)x + t 
 
 (it - a)x 4- t ~~ n - a g " t 
 
 7t 
 
 Thus, if n = , we have for x = t, 21, etc., 
 
 t 
 2t 
 
 
 a)x -f t 
 
 lUi^ 
 
 TT a 
 0.599 
 0.904 
 1.109 
 1.263 
 , 1.387 
 1.793 
 
 t 
 
V IS 
 
 DYNAMO-ELECTRIC MACHINERY. 87 
 
 showing that the extension of the area of the field is likely 
 to be considerable. 
 
 (2) The failure of the actual curve to reach the max- 
 imum indicated by approximate theory is because the 
 theory assumes that all tubes of induction passing through 
 the magnets pass also through the armature. Familial- 
 observations round the pole pieces of the magnets show 
 that this is not the case. If v be the ratio of the total 
 induction through the magnets to the induction in the 
 armature, we must, in our expression for the line integral of 
 
 magnetizing force, replace the term /f-j-J by /( ~ J : 
 
 not strictly a constant, as we shall see later; it is somewhat 
 increased as / increases, owing to magnetization of the core 
 of the armature, and it is also affected by the current in 
 the armature. For our present purpose we treat it as con- 
 stant. 
 
 There is yet another source of error which it is necessary 
 to examine. Some part of the induction in the armature 
 may pass through the shaft instead of through the iron 
 plates. An idea of the amount of this disturbance may be 
 readily obtained. Consider the closed curve A B C D E F: 
 A B and FED C are drawn along lines of force; A F and 
 B C are orthogonal to lines of force (Fig. 27). Since this 
 closed curve has no currents passing through it, the line 
 integral of force around it is nil; therefore, neglecting 
 force along E D, we have force along A B equal to force 
 along F E and D C. In the machine presently described 
 we may safely neglect the induction through the shaft; 
 the error is comparable with the uncertainty as to the value 
 of ^; but in another machine, ' with magnets of much 
 
88 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 greater section, the effect of the shaft would become very 
 sensible when the core is practically saturated. 
 
 Fio. 27. 
 
 The amended formula now becomes 
 
 n c = 1 . 1 1 
 
 where 1 4 is the mean length of lines of force in the 
 wrought-iron yoke, A 4 the area of the yoke, l t and A t cor- 
 responding quantities for the pole pieces, the last two 
 terms being introduced for the forces required to magnet- 
 ize the yoke and the two pole pieces. 
 
DYNAMO-ELECTRIC MACHINERY. 89 
 
 "We now repeat the graphical method of construction 
 exactly as before, the actual observations of induction in 
 armature and current being plotted on the same diagram, 
 Figs. 28 and 29, in which curve G represents the force 
 required to magnetize the yoke, and curve H that required 
 to magnetize the pole pieces. Before discussing these 
 curves further, and comparing the results with those of 
 actual observation, it may be convenient to describe the 
 machine upon which the experiments have been made, 
 confining the description strictly to so much as is perti- 
 nent to our present inquiry. 
 
 DESCRIPTION OF MACHINE. 
 
 The dynamo has a single magnetic circuit, consisting of 
 two vertical limbs, extended at their lower extremities to 
 form the pole pieces, and having their upper extremities 
 connected by a yoke of rectangular section. Each limb, 
 together with its pole piece, is formed of a single forging 
 of wrought iron. These forgings, as also that for the yoke, 
 are built up of hammered scrap and afterwards carefully 
 annealed, and have a magnetic permeability but little in- 
 ferior to the best Swedish charcoal iron. The yoke is 
 held to the limbs by two bolts, the surfaces of contact 
 being truly planed. In section the limb is oblong, with 
 the corners rounded in order to facilitate the winding of 
 the magnetizing coils. A zinc base, bolted to the bed- 
 plate of the machine, supports the pole pieces. 
 
 The magnetizing coils are wound directly on the limbs, 
 and consist of 11 layers on each limb, of copper wire 2.413 
 mms, diameter (No. 13, B.W.Gr.), making 3,260 convolu- 
 
90 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 
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DYNAMO-ELECTRIC MACHINERY. 
 
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 5000 10000 15000 20000 25000 force 
 
 Fio. 29. CORRECT SYNTHESIS OP CHARACTERISTIC CURVE. 
 A, armature; B, air space; C, magnets; D, calculated curve; 7. observa- 
 tions, -(-ascending, descending; (?, yoke; H, pole piece. This figure 
 is the same as the left-hand part of Fig. 28, but on a larger scale, 
 
92 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 tions in all, the total length being approximately 4,570 
 metres. The pole pieces are bored to receive the arma- 
 ture, leaving a gap above and below, subtending an angle 
 of 51 at the centre of the fields. The opposing surfaces 
 of the gap are 8 mms. deep. 
 
 The following table gives the leading dimensions of the 
 machine: 
 
 cms. 
 
 Length of magnet limb = 45.7 
 
 Width of magnet limb = 22.1 
 
 Breadth of magnet limb = 44.45 
 
 Length of yoke = il 6 
 
 Width of yoke = 48.3 
 
 Depth of yoke = 23 2 
 
 Distances between ceni res of limbs = 88.1 
 
 Bore of fields = 27.5 
 
 Depth of pole piece '. = 25 4 
 
 Width of pole piece measured 'parallel to the shaft = 48.3 
 
 Thickness of zinc base = 12.7 
 
 Width of gap = 12.7 
 
 The armature is built up of about 1,000 iron plates, insu- 
 lated one from another by sheets of paper, and held between 
 two end plates, one of which is secured by a washer 
 shrunk on to the shaft, and the other by a nut and lock- 
 nut screwed on the shaft itself. The plates are cut from 
 sheets of soft iron, having probably about the same mag- 
 netic permeability as the magnet cores. The shaft is of 
 Bessemer steel, and is insulated before the plates are 
 threaded on. 
 
 The following table gives the leading dimensions of the 
 armature : 
 
 cms. 
 
 Diameter of core = 24.5 
 
 Diameter of internal hole = 7.62 
 
 Length of core over the end plates = 50.8 
 
 Diameter of shaft = 6,985 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 93 
 
 The core is wound longitudinally according to the 
 Hefner von Alteneck principle with 40 convolutions, each 
 consisting of 16 strands of wire 1.753 inm. diameter, the 
 convolutions being placed in two layers of 20 each. The 
 commutator is formed of 40 copper bars, insulated with 
 mica, and the connections to the armature so made that 
 the plane of commutation in the commutator is horizontal 
 when no current is passing through the armature. 
 
 Fig. 30 shows a side elevation of the dynamo; Fig* 31 a 
 
 FIG 30. 
 
 cross section through the centres of the magnets; Fig 32 
 a section of the core of the armature, in a plane through 
 the axis of the shaft. 
 
 The dynamo is intended for a normal output of 105 
 volts 320 amperes at a speed of 750 revolutions per minute. 
 
94 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 The resistance of the armature measured between opposite 
 bars of the commutator is 0.009947 ohm, and of the mag- 
 
 Fio. 81. 
 
 net coils 16.93 ohms, both at a temperature of 13.5 Centi- 
 grade; Lord Rayleigh's determination of the ohm being 
 assumed. 
 
 Fio. 32. 
 
 We have now to estimate the lengths and areas required 
 in the synthesis of the characteristic curve. 
 
 -4,; from the length of the core of the armature (50.8 
 cms.) must be deducted 3.4 cms. for the thickness of 
 
DYHAMO-ELECTKIC MACHINERY. 95 
 
 insulating material between the plates ; the resultant area 
 is, on the other hand, as has already been stated, slightly 
 augmented by the presence of the steel shaft. A 1 is taken 
 as 810 sq. cms. 
 
 /! ; this is assumed to be 13 cms., i.e., slightly in excess 
 of the shortest distance (12.6 cms.) between the pole pieces. 
 
 A^j the angle subtended by the bored face of the pole 
 piece at the axis is 129, the breadth of the pole piece is 
 48.3 cms., the diameter of the bore of the field is 27.5 cms., 
 and, as already stated, the diameter of core 24.5 cms.; thus 
 the area of pole piece is 1,513 sq. cms., and the area of 129 
 of the cylinder at the mean radius of 13.0 cms. is 1,410 sq. 
 cms. ; this value is taken for A^ in the curves drawn in Figs. 
 24 and 25. In Figs. 28 and 29 A^ is taken as 1,600, an 
 allowance of 190 sq. cms. being made for the spreading of 
 
 the field at the edges of the pole pieces, or -- = 1.2 cm. all 
 
 1 2 
 
 round the periphery, that is, -^= 0.8 of the distance from 
 
 l.o 
 
 iron of pole pieces to iron of core. 
 
 1 9 is 1.5 cm. 
 
 A 9 is a little uncertain, as the forgings are not tooled 
 all over; it is here taken as 980 sq. cms., 
 but this value may be slightly too high. 
 
 l s is 91.4 cms. 
 
 A 4 is 1,120 sq. cms, 
 
 1 4 is 49 cms., being measured along a 
 quadrant from the centre of the magnet 
 (see Fig. 33). FIG. 33. 
 
 AI is 1,230 sq. cms., intermediate between the area of 
 magnet and face of pole piece. 
 
96 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 1 6 is 11 cms. 
 
 v was determined by experiment as described below, and 
 its value is taken as 1.32; when the magnetizing current is 
 more than 5.62 amperes its value should be a little greater. 
 
 The function/(rt) is taken from Hopkinson, Phil. Trans., 
 vol. clxxvi, 1885, p. 455 ; the wrought iron there referred 
 to was not procured at the same time as, and its properties 
 may differ to a certain extent from, the wrought iron of 
 these magnets. 
 
 The curves now explain themselves : the abscissas in each 
 case represent the line integral of magnetizing force in the 
 part of the magnetic circuit referred to; the ordinates, the 
 number of lines of induction which also pass through the 
 armature. 
 
 The results of the actual observations on the machine 
 are indicated, those when the magnetizing force is increas- 
 ing +> when it is decreasing . The measurements of the 
 currents in the magnets which were separately excited, and 
 of the potential difference between the bmshes, the circuit 
 being open, were made with Sir W. Thomson's graded 
 galvanometers, standardized at the time of use. The irreg- 
 ularities of the observations are probably due to the varia- 
 tion of speed, the engine being not quite perfectly governed. 
 The second construction exhibits quite as close an agree- 
 ment between observation and calculation as could be 
 expected; the deviation at high magnetizing forces is 
 probably due to three causes increase in the value of v 
 when the core of the armature is partially saturated, un- 
 certainty as to the area J 3 , difference in the quality of the 
 iron. It is interesting to see how clearly theory predicts - 
 the difference between the ascending and descending curves 
 
DYNAMO-ELECTRIC MACHINERY. 97 
 
 of a dynamo. Consideration of the diagram proves that 
 this machine is nearly perfect in its magnetic proportions. 
 The core might be diminished without detriment by in- 
 creasing the hole through it to a small, but very small, 
 extent. Any reduction of area of magnets would be inju- 
 rious ; they might, indeed, be slightly increased with advan- 
 tage. An increase in the length of the magnets would be 
 very distinctly detrimental. Again, little advantage results 
 from increasing the magnetizing force beyond the point at 
 which the permeability of the iron of the magnets begins 
 to rapidly diminish. For iron of the same quality as that of 
 the machine under consideration, a magnetizing force of 
 2.6x10' or 28.4 per centimetre is suitable. To get the 
 same induction in other parts of the circuit, the diagram 
 shows that for the air space a magnetizing force of 21 X 10 s 
 is required, for the pole pieces 0.1 X 10 8 , for the armature 
 0.2 XlO 3 , for the yoke 0.6X10 8 ; making a total force re- 
 quired of 24.5 X 10". Any alteration in the length of the 
 area of any portion of the magnetic circuit entails a corre- 
 sponding alteration in the magnetizing forces required for 
 that portion, at once deducible from the diagram. Similar 
 machines must have the magnetizing forces proportional 
 to the linear dimensions, and consequently, if the electro- 
 motive force of the machines is the same, the diameter of 
 the wire of the magnet coils must be proportional to the 
 linear dimensions. If the lengths of the several portions 
 of the magnetic circuit remain the same, but the areas are 
 similarly altered, the section of the wire must be altered in 
 proportion to the alteration in the periphery of the section. 
 
DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 EXPERIMENT TO DETERMINE V. 
 
 Around the middle of one of the magnet limbs a single 
 coil of wire was taken, forming one complete convolution, 
 and its ends connected to a Thomson's mirror galvanom- 
 eter rendered fairly ballistic. If the circuit of the field 
 magnets, while the exciting current is passing, be suddenly 
 short circuited, the elongation of the galvanometer is a 
 measure of the total induction within the core of the 
 limbs, neglecting the residual magnetization. If the short 
 circuit be suddenly removed, so that the current again 
 passes round the field magnets, the elongation of the 
 galvanometer will be equal in magnitude and opposite in 
 direction. 
 
 The readings taken were : 
 
 Zero 71 left. 
 
 Deflection .... 332 " magnets made. 
 
 " .... 196 right; magnets short circuited, 
 
 llence, deflection to right = 267 
 left = 261 
 Mean deflection = 264 
 
 To determine the induction through the armature, the 
 leads to the ballistic galvanometer were soldered to con- 
 secutive bars of the commutator, connected to that convo- 
 lution of the armature which lay in the plane of commu- 
 tation. 
 
DYNAMO-ELECTKIC MACHINERY. 99 
 
 The readings taken were : 
 
 Zero 23 left. 
 
 Deflection .... 223 " magnets made. 
 
 ' ' ' ' j- right ; magnets short circuited. 
 
 Hence, deflection to right and left = 200 
 
 It thus appears that out of 264 lines of force passing 
 through the cores of the magnet limbs at their centre, 200 
 go through the core of the armature, whence v equals 1.32. 
 The magnetizing current round the fields during these 
 experiments was 5.G amperes. 
 
 EXPERIMENTS ON" WASTE FIELD NOT PASSING THROUGH 
 ARMATURE. 
 
 As in the determination of v, a single convolution was 
 taken around the middle of one of the limbs, and con- 
 nected to the ballistic galvanometer; the deflections, when 
 a current of 5.6 amperes was suddenly passed through the 
 fields or short circuited, were : 
 
 Zero 34 left. 
 
 Deflection .... 148 " magnets made. 
 
 " .... 82 right; magnets short circuited. 
 
 Hence, deflection to right =116 
 left = 114 
 Mean deflection = 115 
 
 I. Four convolutions were then wound round the zinc 
 plate and the cast-iron bed in a vertical plane, passing 
 
100 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 through the axis of the armature; and the deflections 
 noted were: 
 
 Zero. .' . . ... . 15 left. 
 
 Deflection 61 " magnets short circuited. 
 
 " 40 right; magnets made. 
 
 Zero 11 left. 
 
 Deflection 64 " magnets short circuited. 
 
 " 36 right; magnets made. 
 
 Hence, deflection to right = 55 
 left = 46 
 
 and " right = 47 
 
 left =53 
 
 in the two observations respectively, giving a mean = 50.25; 
 or, reducing to one convolution, = 12.6. 
 
 II. A square wooden frame, 38 cms. x 38 cms., on which 
 were wound ten convolutions, was then inserted between 
 the magnet limbs, with one side resting on the armature, 
 and an adjacent side projecting 5 cms. beyond the coils on 
 the limbs, or about 7.6 cms. beyond the cores of the limbs. 
 The deflections were: 
 
 Zero 34 left. 
 
 Deflection 98 " magnets made. 
 
 " 22 right; magnets short circuited. 
 
 21 " <s " 
 
 " 81 left; magnets made. 
 
 Hence, deflection to right = 56 
 left = 64 
 
 and " right = 55 
 
 left = 47 
 
DYNAMO-ELECTRIC MACHINERY. 101 
 
 in the two observations respectively, giving a mean = 55 ; 
 or, reducing to one convolution, = 5.5. 
 
 III. The same frame was raised a height of 6.35 cms. 
 above the armature in a vertical plane. The deflections 
 were: 
 
 Zero ...... 21 left. 
 
 Deflection .... 98 " magnets made. 
 
 Zero ...... 35 left. 
 
 Deflection .... 8 right; magnets short circuited. 
 
 Hence, deflection to left = 50 
 right = 43 
 
 and mean deflection = 46.5 
 or, reducing to one convolution, = 4.6 
 
 IV. The same frame was again lowered on the armature 
 and pushed inwards so as to lie symmetrically within the 
 space between the limbs. The deflections were : 
 
 Zero ...... 32 right. 
 
 Deflection .... 112 " magnets made. 
 
 " .... 48 left; magnets short circuited. 
 
 Giving a mean of 80; or, reducing to one convolution, 
 = 8.0. 
 
 Let G represent the leakage through a vertical area 
 bounded by the armature and a line 7.6 cms. above the 
 armature and of the same width as the pole pieces; let R 
 be the remainder of the leakage between the limbs; then 
 II. and III. give 
 
 f * = 4.6; 
 
102 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 whence 
 
 G = 1.35, 
 R = 6.9. 
 Again, IV. gives 
 
 |(fl< + *) = 8.0; 
 
 therefore 
 
 G + R = 9.6, 
 
 which shows an agreement as near as might be expected 
 considering the rough nature of the experiment and that 
 the leakage is assumed uniform over the areas considered. 
 We take 
 
 G = 1.6, 
 R = 8.0. 
 
 Reducing these losses to percentages we have 
 
 i c 
 
 G = T 1.4 per cent. 
 
 lio 
 
 *-ra - ' 
 
 And from I. the leakage through the ) .103 
 
 zinc plate and iron base . . . . ) 
 
 Hence the two gaps account for . . . 2.8 " 
 
 The zinc plate and iron base account for 10.3 " 
 
 And the area between the limbs . . . 7.0 " 
 
 Making a total loss accounted for . . 20.1 " 
 
 Out of an observed loss of 24.24 " 
 
 The leakage through the shaft and from pole piece to 
 yoke, and one pole piece to the other by exterior lines, 
 will account for the remainder. 
 
DYNAMO-ELECTRIC MACHINERY. 103 
 
 EFFECT OF THE CURRENT IN THE ARMATURE. 
 
 The currents in the fixed coils around the magnets are 
 not the only magnetizing forces applied in a dynamo 
 machine ; the currents in the moving coils of the armature 
 have also their effect on the resultant field. There are in 
 general two independent variables in a dynamo machine 
 the current around the magnets and the current in the 
 armature; and the relation of E.M.F. to currents is fully 
 represented by a surface. In well-constructed machines 
 the eifect of the latter is reduced to a minimum, but it 
 can be by no means neglected. When a section of the 
 armature coils is commutated, it must inevitably be 
 momentarily short circuited; and if at the time of commu- 
 tation the field in which the section is moving is other 
 than feeble, a considerable current will arise in that see- 
 tion, accompanied by waste of power and destructive 
 sparking. It may be well at once to give an idea of the 
 possible magnitude of such effects. In the machine al- 
 ready described the mean E.M.F. in a section of the arma- 
 ture at a certain speed may be taken as 6 volts, its resist- 
 ance 0.000995 ohm. Setting aside, then, for the moment 
 questions of self induction, if a section were commutated 
 at a time when it was in a field of one tenth part of the 
 mean intensity of the whole field, there would arise in that 
 section, while short circuited by the collecting brush, a 
 current of 600 amperes, four times the current when the 
 section is doing its normal work. The ideal adjustment 
 of the collecting brushes is such that during the time they 
 short circuit the sections of the armature the magnetic 
 
104 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 forces shall just suffice to stop the current in the section, 
 and to reverse it to the same current in the opposite direc- 
 tion. 
 
 Suppose the commutation occurs at an angle A in ad- 
 vance of the symmetrical position between the fields, and 
 
 Fio. 34. 
 
 that the total current through the armature be (7, reckoned 
 positive in the direction of the resultant E.M.F. of the 
 machine, i.e., positive when the machine is used as 
 a generator of electricity. Taking any closed line 
 through magnets and armature, symmetrically drawn as 
 AB C D E FA (Fig. 34), it is obvious that the line in- 
 tegral of magnetic force is diminished by the current in 
 the armature included between angle. A in front and angle 
 
DYNAMO-ELECTRIC MACHINERY. 105 
 
 A behind the plane of symmetry. If m be the number of 
 convolutions of the armature, the value of this magnetizing 
 
 force is n C^ = kmC opposed to the magnetizing 
 
 Z 7t 
 
 force of the fixed coils on the magnets. Thus if we know 
 the lead of the brushes and the current in the armature we 
 are at once in a position to calculate the effect on the 
 electromotive force of the machine. A further effect of 
 the current in the armature is a material disturbance in 
 the distribution of the induction over the bored face of 
 the pole piece; the force along B C (Fig. 34) is by no 
 means equal to that along D E. Draw the closed curve 
 B C G H B: the line integral along C G and H B is negli- 
 gible. Hence the difference between force H G and B C 
 
 is equal to 4;r (7 = %Km C, where K is\the angle COG. 
 
 This disturbance has no material effect upon the perform- 
 ance of the machine. Hut the current in the armature 
 also distorts the arrangement of the comparatively weak 
 field in the gap between the pole pieces, displacing the 
 point of zero field in the direction of rotation in a gener- 
 ator and opposite to the direction of rotation in a motor; 
 and it is due to this that the non-sparking point of 
 the brushes is displaced. A satisfactory mathematical 
 analysis of the displacement of the field in the gap be- 
 tween the pole pieces by the current in the armature 
 would be more troublesome than an a priori analysis of 
 the distribution of field in this space when the magnet 
 current is the only magnetizing force. Owing to the fact 
 that the armature is divided into a finite number of sec- 
 tions, there is a rapid diminution of the displacement of 
 
106 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the field during the time that a section is being commu- 
 tated, the diminution being recovered while the brush is 
 in contact with only one bar of the commutator. The 
 field thus oscillates slightly, owing to the disturbance 
 caused by reversing the direction of the current in tin- 
 successive sections of the armature. The number of oscil- 
 lations in a Gramme armature or in a Siemens armature 
 with an even number of sections will be p m, where p is 
 the number of revolutions per second; but in a Siemens 
 armature with an odd number of sections it will be 2p m.* 
 This oscillation of the field is only another way of express- 
 ing the effect of the self induction of the section, but it 
 must be remembered that if the self induction, multiplied 
 by change of current, is expressed as a change in the field 
 we must omit self induction as a separate term in our 
 electrical equations. The precise lead to be given to the 
 brushes in order to avoid spa_rking in any given case 
 depends on many circumstances the form and extent of 
 the pole pieces, the number of sections in the armature, 
 and the duration of the short circuit which the brushes 
 cause in any section of the armature. The adjustment of 
 the position of the collecting brushes is generally made by 
 
 * Added Aug. 1?. Armatures with an odd number of convolutions are open 
 to one theoretical objection, which would be a practical one if the number of 
 convolutions were very small The 2m 1 convolutions constitute in them- 
 selves a closed circuit, having a resistance four times the mean actual resist- 
 ance of the armature measured between the collecting brushes. When any 
 one convolution is exactly in the middle of the field, the E.M.F. of the other 2m 
 convolutions exactly balance, so that there is upon the closed circuit an E.M.F. 
 
 due to the single convolution somewhat in excess of part of the actual 
 
 E.M.F. of the ?nachine. Thus there will be an alternating E.M.F. around the 
 closed circuit of the armature capable of causing a considerable waste of 
 power. This waste is materially checked by the sHf induction of the circuit. 
 
DYNAMO-ELECTRIC MACHINERY. 107 
 
 hand at the discretion of the attendant, and is in some 
 cases fixed once for all to suit an average condition of the 
 machine. We shall, therefore, treat A. the lead as an inde- 
 pendent variable, controlled by the attendant. 
 
 Let / be total induction through the armature, /-j- 1' 
 total induction through the magnets, /' being the waste 
 field. Let C be current in armature, c in the magnets. 
 Let g 1' be the line integral of magnetic force from a point 
 on one pole piece to a point on the other; the line being 
 drawn external to the armature, g will be approximately 
 constant. Omitting as comparatively unimportant the 
 magnetizing force in the pole pieces and iron core of the 
 armature, we have the following equations : 
 
 / 
 
 4 A, m C -f 21 9 -r g I' = 0; 
 
 4\mC+2l,~ 
 ~t 
 
 When C = 0,vf& observed 
 1 = 
 
 r 1 
 whence 
 
 g= * 8*. 
 
 eliminating /', 
 
 4-Trnc 
 
108 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 The characteristic curve when C = being 7 = F( nnc), 
 we may write the above as the equation of the character- 
 istic surface thus: 
 
 4XrnC 
 
 In applying this equation it must not be forgotten that 
 the E. M. F. of the machine cannot be determined from / 
 
 Fio. 35. 
 
 unless the commutation occurs at such a time that the coil 
 being commutated embraces all, or nearly all, the lines of 
 induction in the armature. 
 
 This equation enables the characteristic surface to be 
 
DYNAMO-ELECTRIC MACHINERY. 109 
 
 constructed from the characteristic curve. Let L = 4 n n c 
 (Fig. 35), LM=m\C; draw MK so that j^=\\ 
 
 through ./Tdraw ordinate KR, meeting characteristic curve 
 in R ; draw R Q parallel to L, meeting ordinate Q L in Q ; 
 
 p c 
 
 draw Q S parallel to L M\ draw Q P so that 
 
 . ^y . Then P is a point on the characteristic 
 
 surface. 
 
 A very important problem is to deduce the characteristic 
 curve of a series- wound machine from the normal charac- 
 teristic; in this case c = C, and we have 
 
 taking PR (Fig. 36) as ordinate of any point in the nor- 
 
 v \ A 
 
 mal characteristic, cut off QR equal to -4Afw(7 * 
 
 "V t ' 
 
 that is, draw Q so that 
 
 tan$0= \mC^/n(n - \C 
 
 _v IA, Am 
 
 r 2L A m 
 
 * nn 
 
 v 
 
 Then P Q will represent the induction corresponding to 
 magnetizing force n\n ^j G. It is noteworthy that as 
 
110 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the current C, and therefore R, increases, PQ, the induc- 
 tion, will attain a maximum and afterwards diminish, van- 
 ish, and become negative. That in series-wound machines 
 the E. M. F. has a maximum value has been many times 
 observed. The cause lies in the existence of a waste field 
 
 Fio. 86. 
 
 not passing through the armature, and in the saturation of 
 the magnet core. 
 
 The effect of the current in the armature on the poten- 
 tial between the brushes of any machine is the same as 
 that of an addition to the resistance of the armature pro- 
 portional to the lead of the brushes and to the ratio of the 
 waste field to the total field, combined with that of taking 
 
 the main current times round the magnets in direction 
 
DYNAMO-ELECTRIC MACHINERY. Ill 
 
 opposite to the current c. The preceding investigation tells 
 the whole story of a dynamo machine, excepting only the 
 relation of A to C in order that the brushes may be so 
 placed as to avoid sparking. The only constant or func- 
 tion which has to be determined experimentally for any 
 particular machine is v, the ratio of total to effective field; 
 all the rest follows from the configuration of the iron and 
 the known properties of the material. 
 
 The following illustrations of the effect of the current 
 in the armature and the lead of the brushes are interesting. 
 In both cases the magnet coils are supposed to be entirely 
 disconnected, so that c is zero. First, let A be negative, 
 short circuit the brushes, and drive the machine at a cer- 
 tain speed; a large current will be produced, the current in 
 the armature itself forming the magnet.* Second, let A, 
 be positive, cause a current to pass through the armature: 
 the armature will turn in the positive direction and will act 
 as a motor capable of doing work. In either case, partic- 
 ularly the former, such use of the machine would not be 
 practical, owing to violent sparking on the commutator. 
 The following is a further illustration of the formula 
 given above : If we could put up with the sparking which 
 
 * Added Aug. 17. This experiment was tried upon a dynamo machine of 
 construction generally similar to that shown in Figs. 30, 31, and 32, but with an 
 armature of half the length intended in normal work to give 400 amperes, 50 
 volts, at 1,000 revolutions. The magnet coils were disconnected, and the termi- 
 nals of the armature were connected through a Siemens electrodynamometer, 
 and the machine was run at 1,380 revolutions. When the brushes were placed in 
 the normal position (A = 0) the current due to residual magnetism was 52 am- 
 peres. By giving the brushes a small positive lead the current was reduced to 
 nearly zero. By giving the brushes a small negative lead a current of over 234 
 amperes, the maximum measured by the dynamometer, was obtained, and by 
 varying the lead it was easy to maintain a steady current of any desired 
 amount. 
 
DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 would ensue, it would be possible to make A negative in a 
 generator of electricity, and thereby obtain by the reactions 
 of the armature itself all the results usually obtained by 
 compound winding. 
 
 EFFICIENCY EXPERIMENTS. 
 
 Having discussed the relations subsisting between the 
 configuration of the magnetic circuit of a dynamo machine 
 and the induction obtained for given magnetizing forces, 
 and having compared the results obtained by direct calcu- 
 lation with the results of actual observation on a partic- 
 ular machine, the construction of which we have described 
 at length, it appeared of importance to determine the 
 efficiency of the machine under consideration 'as a con- 
 verter of energy, when used either as a generator of elec- 
 tricity or as a motor. An accurate determination of the 
 mechanical power transmitted to a dynamo by a driving 
 belt, or of the power given by a motor, presents formidable 
 experimental difficulties. Moreover, if the mechanical 
 power absorbed in driving the dynamo be measured di- 
 rectly, any error in measurement will involve an error of 
 the same magnitude in the determination of the efficiency. 
 To avoid this difficulty, we employed the following device: 
 
 Let two dynamos, approximately equal in dimensions 
 and power, have their shafts coupled by a suitable coup- 
 ling, which may serve also as a driving pulley ; and let the 
 electrical connections between the dynamos be made so that 
 the one drives the other as a motor. If the combination 
 be driven by a belt passing over the coupling pulley, the 
 power transmitted by the belt is the waste in the two dyn- 
 
DYNAMO-ELECTRIC MACHINERY. 113 
 
 amos and the connections between them. By suitably 
 varying the magnetic field of one of the dynamos, the 
 power passing between the two machines can be adjusted 
 as desired. If, then, the electrical power given out by the 
 generator is measured, and also the power transmitted by 
 the belt, the efficiency of the combination can be at once 
 determined. By this arrangement the measurement, which 
 presents experimental difficulties, viz., the power trans- 
 mitted by the belt, is of a small quantity. Consequently 
 even a considerable error in the determination hasXbtfta. 
 small effect on the ultimate result. On the other h^Qd 
 the measurement of the large quantity involved, viz., the 
 electrical power passing between the two machines, can 
 without difficulty be made with great accuracy. 
 
 The second machine was similar in all respects to that 
 already described, and each is intended for a normal out- 
 put of 105 volts, 320 amperes, at a speed of 750 revolutions 
 per minute. 
 
 The power transmitted by the belt was measured by a 
 dynamometer of the Hefner-Alteneck type, the general 
 arrangement being as shown in the diagram, Fig. 37. A 
 is the driving pulley of the engine, B the driven coupling 
 of the dynamos; /), D are the guide pulleys of the dyna- 
 mometer, carried on a double frame turning about the ful- 
 crum C, and supported by a spiral spring, the suspension 
 of which can be varied by a pair of differential pulley 
 blocks attached to a fixed support overhead. When a read- 
 ing is made, the suspension of the spring is adjusted until 
 the index of the dynamometer comes to a fiducial mark on 
 a fixed scale; the extension of the spring is then read by a 
 second index attached to its upper extremity. F 9 F are two 
 
114 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 fixed guide pulleys of the same diameter as the pulleys D, 
 D, and having the same distance between their centres, in 
 order that the two portions of the belt may be parallel and 
 the sag as far as possible taken up. The normal from G 
 
 Fio. 87. 
 
 to the centre line of either portion of the belt between the 
 pulley B and the guide pulleys = 31.9 cms. The normal 
 from C to the centre line of either of the parallel por- 
 tions of the belt = 2.4 cms., and from C to the centre line 
 of the spring = 92.7 cms. 
 
 Take moments about (7; then 
 
 92.7 
 
 Tension of the belt = j" X tension of spring, 
 o4.o 
 
 = 2.7 X tension of spring. 
 
 Also the diameter of the pulley B = 33.6 cms. and the 
 thickness of the belt = 1.6 cm. 
 
 Hence the velocity of the centre of the belt in centime- 
 
DYNAMO-ELECTKIC MACHINERY. 115 
 
 tres per second = 1.845 X revolutions of dynamo per minute, 
 and, therefore, 
 
 Power transmitted by the belt in ergs per second = 2.7 X 
 1.845 X 981 X tension of spring X revolutions per minute, 
 assuming the value of g to be 981. 
 
 We may more conveniently express the power in watts 
 (= 10 7 ergs per second), and write 
 
 Power in watts = 0.0004887 X tension of spring 
 
 X revolutions per minute. 
 
 The potential between the terminals of the generator 
 was measured by one of Sir William Thomson's graded 
 galvanometers, previously standardized by a Clark's cell, 
 which had been compared with other Clark's cells, of which 
 the electromotive force was known by comparison with 
 Lord Rayleigh's standard. The current between the two 
 machines was measured by passing it through a known re- 
 sistance, the difference of potential between the ends of the 
 resistance being determined by direct comparison with the 
 Clark's standard cell, according to Poggendorff's method. 
 As experiments were made with currents of large magni- 
 tude, it was important that the temperature coefficient of 
 the resistance should be as low as possible. To this end 
 we found a resistance frame constructed of platinoid wire 
 of great value. The temperature coefficient of this alloy 
 is only 0.021 per cent, per degree Centigrade. (Proc. Roy. 
 Soc., vol. xxxviii, 1885, p. 265.) 
 
 The resistances of the armatures and magnets of the 
 two machines are as follows : 
 
110 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 Ohms. 
 Generator, . . . armature, . . . 0.009947 
 
 magnets, . . . 16.93 
 Motor, .... armature, . . . 0.009947 
 
 magnets, . . . 16.44 
 
 The resistance of the leads connecting the two machines 
 was 0.00205 ohm, and of the standard resistance 0.00586 
 ohm. 
 
 In all determinations of resistance the value of the B. A. 
 
 TERMINALS Of MACHINE 
 ACTINGAS MOTOR 
 
 Fio. 88. 
 
 ohm was taken as 0.9867 X 10' C. G. S. units, according to 
 Lord Rayleigh's determination. 
 
 The diagram, Fig. 38, shows the electrical connections 
 between the two machines with the rheostat r inserted in 
 the magnets of the motor dynamo. 
 
DYNAMO- ELECTRIC MACHINERY. 117 
 
 In order to ascertain the friction of bending the belt 
 round the pulley B, and of the journals of the dynamo, a 
 preliminary experiment was made with the dynamometer. 
 The combination was run at a speed of 814 revolutions per 
 minute with the dynamos on open circuit, and the tension 
 of the spring observed 9,979 grams. The engine was then 
 reversed and the dynamos run at the same speed, and the 
 tension of the spring again observed 3,629 grams. The 
 difference of the two readings gives twice the power ab- 
 sorbed in friction, viz., 1,262 watts for the two machines, 
 or 631 watts per machine. This is excluded entirely from 
 the subsequent determinations of efficiency, as being a 
 quantity dependent on such arbitrary conditions as the 
 lubrication of the journals, the weight of the belt, and the 
 angle it makes with the horizontal. 
 
 In Table V., column I. is the speed of the dynamos; 
 column II. is the reading of the spring in grams; column 
 
 III. is the power transmitted by the belt in watts; column 
 
 IV. is the potential at the terminals of the generator; 
 column V. is the current passing in the external circuit be- 
 tween the two machines; column VI. is the resistance in- 
 troduced into the magnets of the motor by the rheostat; 
 column VII. is the power absorbed in the armature of the 
 generator; column VIII. is the power absorbed in the 
 armature of the motor; column IX. is the power absorbed 
 in the magnets of the generator; column X. is the power 
 absorbed in the magnets of the motor; column XI. is the 
 power absorbed in the connecting leads between the two 
 dynamos, in the rheostat resistance r, and in the standard 
 resistance used for measuring the current; column XII. is 
 the total electrical power developed in the generator; col- 
 
118 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 TABLE V. 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 vn. 
 
 
 Revolutions 
 
 
 
 
 
 
 
 
 per 
 
 Grams. 
 
 Watts. 
 
 Volts. 
 
 Amperes. 
 
 Ohms. 
 
 Watts. 
 
 
 minute. 
 
 
 
 
 
 
 
 1 
 
 810 
 
 8,392 
 
 3,322 
 
 129.1 
 
 21.6 
 
 1.39 
 
 13 
 
 * 
 
 801 
 
 9,299 
 
 3,640 
 
 127.2 
 
 72.0 
 
 1.89 
 
 75 
 
 3 
 
 811 
 
 11,113 
 
 ,"> 
 
 125.8 
 
 150.0 
 
 2.72 
 
 267 
 
 4 
 
 808 
 
 10,433 
 
 4,119 
 
 124.4 
 
 186.0 
 
 2.72 
 
 8'.>7 
 
 5 
 
 792 
 
 10,000 
 
 4,124 
 
 116.5 
 
 211.0 
 
 2.72 
 
 4y 
 
 6 
 
 798 
 
 ltt,S97 
 
 t;.:,y. 
 
 110.6 
 
 351.0 
 
 4.59 
 
 1,309 
 
 7 
 
 764 
 
 17,0<JO 
 
 .;..,,:, 
 
 110.12 
 
 358.0 
 
 4 c'.i 
 
 1,300 
 
 8 
 
 706 
 
 17,804 
 
 6,065 
 
 110.6 
 
 360.0 
 
 4.59 
 
 1,875 
 
 9 
 
 778 
 
 16,556 
 
 6,294 
 
 102 3 
 
 369.0 
 
 4.09 
 
 1,430 
 
 10 
 
 756 
 
 20,412 
 
 7,541 
 
 90.8 
 
 i ; o 
 
 4.59 
 
 2,070 
 
 11 
 
 NIS 
 
 9,52(5 
 
 3,765 
 
 119.3 
 
 36.8 
 
 2.72 
 
 25 
 
 12 
 
 802 
 
 3,855 
 
 1,512 
 
 113.5 
 
 No current 
 
 .... 
 
 
 13 
 
 814 
 
 8,175 
 
 1,262 
 
 .... 
 
 .... 
 
 
 .... 
 
 
 VIII. 
 Watts. 
 
 IX. 
 
 Watts. 
 
 X. 
 
 Watts. 
 
 XI. 
 Watts. 
 
 XII. 
 Watts. 
 
 XIII. 
 Watts. 
 
 XIV. 
 Watte. 
 
 1 
 
 4 
 
 984 
 
 861 
 
 77 
 
 4,?a) 
 
 691 
 
 5,411 
 
 2 
 
 51 
 
 955 
 
 837 
 
 112 
 
 11.096 
 
 805 
 
 11,901 
 
 3 
 
 223 
 
 985 
 
 709 
 
 295 
 
 20,8% 
 
 9K8 
 
 21>S| 
 
 4 
 
 344 
 
 914 
 
 BBS 
 
 388 
 
 85,266 
 
 691 
 
 2.v.y 
 
 5 
 
 443 
 
 801 
 
 608 
 
 453 
 
 26..V.K) 
 
 BOO 
 
 gr,tto 
 
 6 
 
 1,222 
 
 722 
 
 455 
 
 1,101 
 
 41.433 
 
 no 
 
 42,323 
 
 7 
 
 1,268 
 
 716 
 
 473 
 
 1.131 
 
 42.087 
 
 828 
 
 42.915 
 
 8 
 
 1 289 
 
 722 
 
 455 
 
 1,152 
 
 42, 194 
 
 Kili 
 
 18,880 
 
 9 
 
 1 354 
 
 618 
 
 408 
 
 1,178 
 
 40,314 
 
 SAO 
 
 40.984 
 
 10 
 
 1979 
 
 554 
 
 848 
 
 1,670 
 
 46.244 
 
 459 
 
 M.7M 
 
 11 
 
 13 
 
 841 
 
 637 
 
 116 
 
 5,998 
 
 1,006 
 
 7,064 
 
 12 
 
 
 
 
 
 
 
 756 
 
 
 13 
 
 ... 
 
 
 
 
 .... 
 
 
 631 
 
 
 
 umn XIII. is half the power absorbed by the combination 
 less the known losses in the armatures, magnets, and ex- 
 ternal connections of the two machines; column XIV. is 
 the total mechanical power given to the generator, being 
 the sum of the powers given in columns XII. and XIII. 
 
 In Table VI. the percentage losses in the armature and 
 magnets of the generator are given, as also the sum of all 
 
DYNAMO-ELECTRIC MACHINERY. 
 TABLE VI. 
 
 119 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 
 Per cent. 
 
 Per cent. 
 
 Per cent 
 
 Per cent. 
 
 Per cent. 
 
 Per cent. 
 
 1 
 
 0.24 
 
 18.20 
 
 12.76 
 
 68.8 
 
 57.28 
 
 39.40 
 
 2 
 
 0.63 
 
 8.93 
 
 6.76 
 
 84.58 
 
 82.99 
 
 70.19 
 
 3 
 
 1.88 
 
 4.27 
 
 4.52 
 
 90.00 
 
 90.15 
 
 81 . 13 
 
 4 
 
 1.53 
 
 3 52 . 
 
 2.66 
 
 92.28 
 
 92.65 
 
 85.49 
 
 5 
 
 1.83 
 
 2.94 
 
 2.415 
 
 92.80 
 
 93.12 
 
 86.42 
 
 6 
 
 3.09 
 
 1.71 
 
 2.10 
 
 93.10 
 
 93.30 
 
 86.86 
 
 7 
 
 3.17 
 
 1.67 
 
 1.93 
 
 93 23 
 
 93.39 
 
 87.07 
 
 8 
 
 3.17 
 
 1.67 
 
 1.93 
 
 93.23 
 
 93.43 
 
 87.10 
 
 9 
 
 3.51 
 
 1.75 
 
 1.59 
 
 93.39 
 
 93.50 
 
 87.32 
 
 10 
 
 4.43 
 
 1.19 
 
 0.98 
 
 93.39 
 
 93.36 
 
 87.19 
 
 11 
 
 0.35 
 
 11.9 
 
 15.1 
 
 72.65 
 
 65.77 
 
 47.78 
 
 other losses as obtained from column XIII. in Table V.; 
 also the percentage efficiency of the generator, of the motor, 
 and of the double conversion. Column I. is the percentage 
 loss in the generator armature; column II. is the percent- 
 age loss in the generator magnets; column III. is the per- 
 centage sum of all other losses in the generator; column 
 
 IV. is the percentage efficiency of the generator; column 
 
 V. is the percentage efficiency of the motor; column VI. 
 is the percentage efficiency of the double conversion. 
 
 In this series of experiments, in all cases from Nos. 1 to 
 10 inclusive, the brushes, both of the generator and motor, 
 were set at the non-sparking point; but in No. 11 no lead 
 was given to the brushes of the generator, and consequently 
 there was violent sparking throughout the duration of the 
 experiment. 
 
 In No. 12 the magnets were separately excited with a 
 current giving 113.5 volts across their terminals. The 
 power absorbed must be due entirely to local currents in 
 the core of the armature and to the energy for the reversal 
 of magnetization of the core twice in every revolution of 
 the armature. 
 
120 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 No. 13 gives the results of the experiments on the fric- 
 tion of the bearings and in bending the belt already 
 referred to. 
 
 It will be observed that the figures in column XIII. are 
 calculated by deducting the power absorbed in the arma- 
 tures and magnets and by extraneous resistances from the 
 total power given to the combination as measured by the 
 dynamometer. They must therefore include all the energy 
 dissipated in the core of the armature, whether in local 
 currents or in the reversal of its magnetization ; also the 
 energy dissipated in local currents in the pole pieces, if 
 such exist; also the energy spent in reversing the direction 
 of the current in each convolution of the armature as they 
 are successively short circuited by the brushes. Further, 
 it will include the waste in all the connections of the ma- 
 chine from the commutator to its terminals and the friction 
 of the brushes against the commutator. A separate experi- 
 ment was made to determine the amount of this last 
 constituent, but it was found to be too small to be capable 
 of direct measurement by the dynamometer. Moreover, 
 from the manner in which the figures in this column are 
 deduced, any error in the dynamometric measurement will 
 appear wholly in them. Since, undoubtedly, the first two 
 components enumerated are the most important, and the 
 conditions determining their amount are practically the 
 same throughout the series, the close agreement of the 
 figures in the column is a fair criterion of the accuracy 
 of the observations. Probably 100 watts is the limit of 
 error in any of the measurements. Such an error would 
 affect the determination of the efficiency when the machines 
 were working up to their full power by less than per cent. 
 
 It has been assumed that the sum of these losses is 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 equally divided between the two machines. This will not 
 accurately represent the facts, as the intensities of the 
 fields and the currents passing through the armatures 
 differ to some extent in the two machines. The inequality, 
 however, cannot amount to a great quantity, and if it 
 diminishes the efficiency of the generator it will increase 
 the efficiency of the motor by a like amount, and contrari- 
 wise. In No. 11 of the series the effect of the sparking at 
 the brushes of the generator is very marked, the power 
 wasted amounting to at least 250 watts. 
 
 If it be assumed that the dissipation of energy is the 
 same whether the magnetization of the core is reversed by 
 diminishing and increasing the intensity of magnetization 
 without altering its direction, or whether it is reversed by 
 turning round its direction without reducing its amount 
 to zero, a direct approximation may be made to the value of 
 this component. (J. Hopkinson, Phil. Trans., vol. clxxvi, 
 1885, p. 455.) 
 
 The core has about 16,400 cubic centimetres of soft iron 
 plates; hence loss in magnetizing and demagnetizing when 
 the speed is 800 revolutions per minute = 16,400 X *f- X 
 13,356 ergs per second = 292 watts. 
 
 Eeferring to Table VI., it appears that the efficiency ap- 
 proaches a maximum when the current, passing externally 
 between the two machines, is about 400 amperes. Let C 
 be the current in the armature, p its resistance, W the 
 power absorbed in all parts of the machine other than the 
 armature; then, if the speed is constant, the efficiency is 
 
 . EC -W-(?p . _ . ,, 
 
 approximately - =-~ , where E is the electro- 
 
 & L> 
 
 W 
 
 motive force, This is a maximum when 7* + C p is a 
 
 
 
122 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 minimum, which occurs when W= C*p; when the loss in 
 the armature is equal to the sum of all other losses. For 
 the machines under consideration the experimental results 
 verify this deduction. But in actual practice the rate of 
 generation of heat in the armature conductors, when a 
 current of 400 amperes was passed for a long period, would 
 be so great as to trench upon the margin of safety de- 
 sirable in such machines. Of the total space, however, 
 available for the disposition of the conductors, only about 
 one fourth part is actually occupied by copper, the re- 
 mainder being taken up with insulation and the inter- 
 stices left by the round wire. If the space occupied by 
 the copper should be increased to three fourths of the total 
 space available, while the cooling surface remained the 
 same, the current could be increased 75 per cent, and the 
 efficiency increased 1.3 per cent, approximately, as all 
 losses other than that in the armature wires would not be 
 materially altered. 
 
 The loss in the magnets is also susceptible of reduction. 
 It has already been shown that for a given configuration 
 of the magnetic circuit and a given electromotive force the 
 section of the wire of the magnet coils is determinate. 
 The length is, however, arbitrary, since within limits the 
 number of ampere convolutions is independent of the 
 length. An increase in the length will cause a propor- 
 tionate diminution in the power absorbed in the magnet 
 coils. If the surface of the magnets is sufficient to dissi- 
 pate all the heat generated, then the length' of wire is 
 properly determined by Sir William Thomson's rule that 
 the cost of the energy absorbed must be equal to the con- 
 tinuing cost of the conductor. 
 
DYNAMO-ELECTRIC MACHINERY. 123 
 
 APPENDIX. 
 (Added Aug. 17.) 
 
 Since the reading of the present communication experi- 
 ments have been tried on machines having armatures 
 wound on the plan of Gramme and with differently ar- 
 ranged magnets; the experiments were carried out in a 
 closely similar manner to that already described. 
 
 DESCRIPTION OF MACHINES. 
 
 The construction of these machines is shown in Figs. 39, 
 
 Fio. 39. 
 
 40, and 41, of which Fig. 39 shows an elevation, Fig. 40 a 
 section through the magnets, Fig. 41 a longitudinal sec- 
 tion of the armature. It will be observed that the magnetic 
 circuit is divided. The pole pieces are of cast iron and 
 
124 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 are placed above and below the armature and are extended 
 laterally. The magnet cores are of wrought iron of cir- 
 cular section and fit into the extensions of the east iron 
 
 Fio. 40. 
 
 pole pieces, so that the area of contact of the cast iron is 
 greater than the area of section of the magnet. The mag- 
 netizing coils consist of 2,196 convolutions on each limb 
 
 Fio. 41. 
 
 of copper wire, No. 17, B.W.G., in No. 1 machine, and 
 2,232 convolutions in No. 2 machine. The pole pieces are 
 bored to receive the armature, leaving a gap on either side 
 subtending an angle of 41 at the axis. 
 
MACIUNEkY. 125 
 
 The bearings are carried upon an extension of the lower 
 pole piece. 
 
 The following table gives the principal dimensions of 
 the magnets in No. 1 machine : 
 
 cms. 
 
 Length of magnet limbs between pole pieces 26.0 
 
 Diameter of magnet, limb 15.24 
 
 Boreof fields 26.7 
 
 Width of pole piece parallel to the shaft 24.1 
 
 Width of gap between poles 8.6 
 
 The armature is built up of plates as in the machine al- 
 ready described, and is carried from the shaft by a brass 
 frame between the arms of which the wires pass. 
 
 The principal dimensions are as follows: 
 
 cms. 
 
 Diameter of core 24.1 
 
 Diameter of hole through core I 14.0 
 
 Length of core over end plates 24.1 
 
 The core is wound on Gramme's principle with 160 con- 
 volutions, each consisting of a single wire, No. 9, B.W.G., 
 the wire lying on the outside of the armature in a single 
 layer. The commutator has 40 bars. 
 
 This dynamo is compound wound, and is intended for a 
 normal output of 105 volts, 130 amperes, at a speed of 
 1,050 revolutions per minute. The resistance of the 
 armature is 0.047 ohm, and of the magnet shunt coils 26.87 
 ohms. 
 
 There is here no yoke, and consequently A t and l t do not 
 appear in the equation. 
 
 It is necessary to bear in mind that the magnetizing 
 force is that due to the convolutions on one limb, and that 
 the areas are the sums of the areas of the two limbs. In cal- 
 
126 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 dilating induction from E.M.F. it is also necessary to remem- 
 ber that two convolutions in a Gramme count as one in a 
 Hefner-Alteneck armature. 
 
 A^y the section of the core is 245 sq. cms.; allowances 
 for insulation reduce this to 220.5 sq. cms. 
 
 /, ; this is assumed to be 10 cms., but it will be seen 
 that an error in this value has a much more marked 
 effect on the characteristic in this machine than in the 
 other. 
 
 A t ; the angle subtended by the bored face of the 
 pole pieces is 139; the mean of the radii of the pole pieces 
 and the core is 12.45 cms. Hence the area of 139 of 
 the cylinder of this radius is 768.3 sq. cms. ; add to this a 
 fringe of a width 0.8 of the distance from core to 
 pole pieces, as already found necessary for the other 
 machine, and we have 839.5 sq. cms. as the value of A t . 
 
 J, is 0.8 cm. 
 
 A t is 365 sq. cms. (i.e., the area of two magnet cores). 
 
 l t is 26.0 cms. 
 
 A t is taken to be 532 sq. cms., viz., double the smallest 
 section of the pole piece. 
 
 7, is a very uncertain quantity; it is assumed to be 15 
 cms. 
 
 The expression already used requires slight modification. 
 Inasmuch as the pole pieces are of cast iron, a different 
 function must be used. Different constants for waste field 
 must be used for the field, the pole pieces, and the magnet 
 core. We write 
 
DYNAMO-ELECTRIC MACHINERY. 127 
 
 The function f is taken from Hopkinson, Phil. Trans., vol. 
 clxxvi, 1885, p. 455, Plate 52. v^ v w and v b were deter- 
 mined by experiment, as described below; their values are 
 
 v t = 1.05 
 v, = 1.18 
 r b = 1.49 
 
 Comparing the curves in Figs. 28 and 29 with that in 
 Figs. 42 and 43, the most notable difference is that in the 
 present case the armature core is more intensely magnetized 
 than the magnet cores. No published experiments exist 
 giving the magnetizing force required to produce the in- 
 duction here observed in the armature core, amounting to 
 a maximum of 20,000 per sq. cm. We might, however, 
 make use of such experiments as the present to construct 
 roughly the curve of magnetization of the material; thus 
 we find that with this particular sample of iron a force of 
 740 per cm. is required to produce induction 20,000 per sq. 
 cm. : this conclusion must be regarded as liable to consider- 
 able uncertainty. 
 
 The observations on the two machines are plotted to- 
 gether, but are distinguished from each other as indicated. 
 They are, unfortunately, less accurate than those of Figs. 28 
 and 29, and are given here merely as illustrating the method 
 of synthesis. 
 
 EXPERIMENTS TO DETERMINE 
 
 The method was essentially the same as is described on 
 pp. 96 to 99, and was only applied to No. 1 machine. 
 
128 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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DYNAMO-ELECTKIO MACHINERY. 129 
 
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 f 
 
 
 
 
 
 
 
 
 
 X 
 
 ^ 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 X 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 /*- 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 % 
 
 / 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 ^ 
 
 y 
 
 
 
 
 
 
 
 
 j 
 
 
 
 
 !^ 
 ^ 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 lane 
 
 ntegra 
 
 ofila 
 
 netiein 
 
 fbrce 
 
 FIG. 43. SYNTHESIS OF CHARACTERISTIC CURVE WITH GRAMME ARMATURE. 
 This figure is the same as the left-hand part of Fig. 42, but on a larger scale. 
 
130 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 Keferring to Fig. 44, a wire A A was taken four times round 
 the middle of one limb of the magnet, a known current was 
 suddenly passed round the magnets, and the elongation of 
 the reflecting galvanometer was observed : it was found to 
 be 214 scale divisions, giving 107 as the induction through 
 
 Fio. 44. 
 
 the two magnet limbs in terms of an arbitrary unit. The 
 coil was moved to the top of the limb as at B B ; the elon- 
 gation was reduced to 206, or 103 for the two limbs; we 
 take the mean induction in the magnet to be 105. A wire 
 was taken three times round the whole armature in a hori- 
 zontal plane as at C C\ the elongation observed was 222 
 divisions or 74 in terms of the same units. A wire was 
 taken four times round one half of the armature as at D D\ 
 
DYNAMO-ELECTRIC MACHINERY. 131 
 
 the elongation was 141, or induction in the iron of the 
 armature 70.5, whence we have 
 
 74 :=1.05. 
 
 70.5 
 
 It may be well to recall here that r t is essentially depend- 
 ent on the intensity of the field; strictly the line B in 
 Figs. 42 and 43 should not be straight, but slightly curved. 
 
 Four coils were taken round the upper pole piece at E E\ 
 the elongation was 159, giving 79.5 on the two sides. Coils 
 at F F give a higher result, 87.5, owing to the lines of in- 
 duction which pass round by the bearings of the machine, 
 and across to the upper ends of the magnets. v 6 is taken 
 
 to be = 1.18. 
 
 EFFICIENCY EXPERIMENTS. 
 
 The method and instruments were those already de- 
 scribed, pp. 110 to 112, excepting that the current was 
 measured by a Thomson's graded galvanometer, which had 
 been standardized against a Clark's cell in the position and 
 at the time when used. The resistance of leading wires 
 and galvanometer was 0.034 ohm, the series coils introduced 
 for compounding the machines were also brought into use, 
 and the losses due to their resistance (0.024 ohm) find a place 
 in columns XII. and XIII. of Table VII., in which column 
 I. is lead of brushes of the dynamo, positive for the gene- 
 rator, negative for the motor; column II., revolutions per 
 minute; column III., deflection of spring in grams; column 
 
132 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 TABLE VII. 
 
 I. 
 
 n. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 Degrees. 
 
 Revolutions. 
 
 Grains. 
 
 Watts. 
 
 Volts. 
 
 Amperes 
 
 Ohms. 
 
 Watts. 
 
 17.5 
 
 1098 
 
 7711 
 
 4419 
 
 100.1 
 
 139.0 
 
 00 
 
 955 
 
 5 
 
 1094 
 
 2722 
 
 1554 
 
 103.8 
 
 41.2 
 
 18.8 
 
 10:. 
 
 
 
 1114 
 
 1814 
 
 1063 
 
 104.7 
 
 7.85 
 
 
 
 11 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 xm. 
 
 XIV. 
 
 XV. 
 
 XVI. 
 
 XVII. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 Watts. 
 
 895 
 
 872 
 
 
 
 497 
 
 464 
 
 657 
 
 16,395 
 
 289 
 
 16,684 
 
 78 
 
 400 
 
 138 
 
 5ft 
 
 41 
 
 146 
 
 5.015 
 
 294 
 
 r,.:xi 
 
 3 
 
 408 
 
 406 
 
 6 
 
 1 
 
 2 
 
 1,687 
 
 128 
 
 1,765 
 
 * In this experiment the direction of the current had become reversed, and 
 No. 2 machine was generator. 
 
 IV., watts by dynamometer; column V., volts at terminals of 
 generator; column VI., amperes in external circuit; column 
 VII., rheostat resistance; column VIII., watts in generator 
 armature; column IX., watts in motor armature; column 
 X., watts in generator shunt magnet coils; column XL, 
 watts in motor shunt; column XII., watts in generator 
 series magnet coils; column XIII., watts in motor series; 
 column XIV., watts in external resistances; column XV., 
 total electrical power of generator; column XVI., half the 
 sum of losses unaccounted for; column XVII., total me- 
 chanical power applied to generator. 
 
 TABLE VIII. 
 
 Generator Generator 
 Armature; Shunt 
 
 Generator 
 Series 
 Coils. 
 
 Other 
 Losses. 
 
 Efficiency 
 of 
 Generator. 
 
 Efficiency 
 of 
 Motor. 
 
 Efficiency 
 of Double 
 Conversion. 
 
 5.8 
 2.0 
 
 2.2 
 7.5 
 
 3.0 
 1.0 
 
 1.9 
 5.5 
 
 87.1 
 84.0 
 
 89.0 
 92.0 
 
 77.5 
 77.8 
 
DYNAMO-ELECTRIC MACHINERY. 133 
 
 Table VIII. gives the losses and efficiencies as percent- 
 ages in exactly the same way as in Table VI., excepting 
 that another column is introduced for the loss in the series 
 coils of the magnets of the generator. 
 
 The core of the armature contains about 6,500 cub. cms. 
 of iron. Hence energy of magnetizing and demagnetizing 
 when the speed = 1,100 revolutions per minute = 6,500 X 
 
 ' X 13,356 in ergs per second = 159 watts. 
 
134 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 DYNAMO-ELECTRIC MACHINERY.* 
 
 THE following is intended as the completion of a Paperf 
 by Drs. J. and E. Hopkinson (Phil Trans., 1886). f The 
 motive is to verify by experiment theoretical results con- 
 cerning the effect of the currents in the armature of dyna- 
 mo machines on the amount and distribution of the mag- 
 netic field which were given in that Paper, but which were 
 left without verification. For the sake of completeness, 
 part of the work is given over again. 
 
 The two dynamos experimented upon were constructed 
 by Messrs. Siemens Brothers & Co., and are identical as 
 far as it is possible to make them. They are mounted 
 upon a common base plate, their axles being coupled to- 
 gether, and are referred to in this Paper respectively as 
 No. 1 and No. 2. 
 
 Each dynamo has a single magnetic circuit consisting of 
 two vertical limbs extended at their lower extremities to 
 form the pole pieces, and having their upper extremities 
 connected by a yoke of rectangular section. Each limb, 
 
 * It must not be supposed from his name not appearing in this short Paper 
 that my brother. Dr. E. Hopkinson. had a minor part in the earlier Paper. He 
 not only did the most laborious part of the experimental work, but contributed 
 his proper share to whatever there may be of merit in the theoretical part of 
 the Paper. J. H. 
 
 t The Paper here referred to is that reprinted on pages 79 to 133 of this 
 volume. 
 
DYNAMO-ELECTRIC MACHINERY. 135 
 
 together with its pole piece, is formed of a single forging 
 of wrought iron. These forgings, as also that of the yoke, 
 are built up of hammered scrap iron, and afterwards care- 
 fully annealed. Gun-metal castings bolted to the base 
 plate of the machine support the magnets. 
 
 The magnetizing coils on each limb consist of sixteen 
 layers of copper wire 2 mms. in diameter, making a total of 
 3,968 convolutions for each machine. The pole pieces are 
 bored out to receive the armature, leaving a gap above and 
 below subtending an angle of 68 at the centre of the shaft. 
 The opposing surfaces of the gap are 1.4 cm. deep. 
 
 The following table gives the leading dimensions of the 
 machine: 
 
 cms. 
 
 Length of magnet limb 66.04 
 
 Width of inaguet limb 11.48 
 
 Breadth of magnet limb 38.10 
 
 Length ofyoke 38.10 
 
 Width of yoke 12.06 
 
 Depth ofyoke 11.43 
 
 Distance between centres of limbs 23.50 
 
 Bore of fields 21.21 
 
 Depth of pole piece 20.32 
 
 Thickness of gun-metal base 10.80 
 
 Width of gap 12.06 
 
 The armature core is built up of soft iron disks, No. 24 
 B. W. G., which are held between two end plates screwed on 
 the shaft. 
 
 The following table gives the leading dimensions of the 
 armature : 
 
 cms. 
 
 Diameter of core 18.41 
 
 Diameter of shaft. 4.76 
 
 Length of core , 38,10 
 
136 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 The core is wound longitudinally according to the Hef- 
 ner von Alteneck principle with 208 bars made of copper 
 strip, each 9 mms. deep by 1.8 mm. thick. The commuta- 
 tor is formed of fifty-two hard drawn copper segments in- 
 sulated with mica, and the connections to the armature so 
 made that the plane of commutation in the commutator is 
 vertical when no current is passing through the armature. 
 
 Each dynamo is intended for a normal output of 80 am- 
 peres, 140 volts, at 880 revolutions per minute. The resist- 
 ance of the armature measured between opposite bars of 
 the commutator is 0.042 ohm, and of each magnet coil 
 13.3 ohms. 
 
 In the machine the armature core has a greater cross 
 section than the magnet cores, and consequently the mag- 
 netizing force used therein may be neglected. The yoke 
 has the same section as the magnet cores, and is therefore 
 included therein, as is also the pole piece. The formula 
 connecting the line integral of the magnetizing force and 
 the induction takes the short form 
 
 where 
 
 n is the number of turns round magnet; 
 
 c is the current round magnet in absolute measure; 
 
 / Q the distance from iron of armature to rim of magnet; 
 
 AI the corrected area of field; 
 
 /the total induction through armature; 
 
 l a the mean length of lines of magnetic force in magnets ; 
 
 A a the area of section of magnets; 
 
 * Phil. Trans., 188(5; page 88 of this volume. 
 
DYNAMO-ELECTRIC MACHINERY. 137 
 
 v the ratio of induction in magnets to induction in ar- 
 mature; 
 
 / the function which the magnetizing force is of the in- 
 duction in the case of the machine actually taken 
 from Dr. J. Hopkinson on the " Magnetization of 
 Iron," Phil. Trans., 1885, Figs. 4 and 5, Plate 47. 
 
 In estimating A^ we take the mean of the diameter of 
 the core and of the bore of the magnets 19.8 cms., and the 
 angle subtended by the pole face 112, and we add a fringe 
 all round the area of the pole face equal in width to the 
 distance of the core from the pole face. This is a wider 
 fringe than was used in the earlier experiments,* because 
 the form of the magnets differs slightly. The area so 
 estimated is 906 sq. cms. 
 
 Z 3 is taken to be 108.8 cms. 
 
 A 3 is 435.5 sq. cms. 
 
 v was determined by the ballistic galvanometer to be 
 1.47. It is to be expected that, as the core is actually 
 greater in area than the magnets, v will be more nearly 
 constant than in the earlier experiments. It was found to 
 be constant within the limits of errors of observation. 
 
 Referring to Fig. 45, the curve C is the curve x I 3 f f -jH, 
 and the straight line B is the curve x = 2 /, -j-, while the 
 
 ^2 
 
 full line D is the characteristic curve of the machine, 
 
 as given by calculation. 
 
 * Phil. Trans., 1886; page 95 of this volume, 
 
138 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 The marks -j- indicate the results of actual observations 
 on machine No. 1, and the marks the results on machine 
 No. 2, the total induction / being given by the equation : 
 
 potential difference in volts X 10 8 
 208 X revolutions per second 
 
 Experiments made upon the power taken to drive the 
 machine under different conditions show that it takes about 
 
 Line! rteeral of Mae letisinaf Force 
 
 *0000 
 
 250 watts more power to turn the armature at 660 revolu- 
 tions when the magnets are normally excited than when 
 they are not excited at all. The volume of the core is 
 9,465 cub. cms., or in each complete cycle the loss per cubic 
 
 950 ^ ^Q* 
 
 centimetre is n x 9 465 = 24 > 000 er g 8 - 
 
 The loss by hysteresis is about 13,000 (Phil. Trans., 
 1885, p. 463) if the reversals are made by variation of in- 
 tensity of the magnetizing force and the iron is good 
 wrought iron. This result is similar to that in the earlier 
 
DYNAMO-ELECTRIC MACHINERY. 139 
 
 Paper,* where it is shown that the actual loss in the core, 
 when magnetized, is greater than can be accounted for 
 by the known value of hysteresis. 
 
 EFFECTS OF THE CURRENT IN THE ARMATURE. 
 
 Quoting from the Royal Society Paper [page 103 of this 
 volume], " The currents in the fixed coils around the mag- 
 nets are not the only magnetizing forces applied in a 
 dynamo machine the currents in the moving coils of the 
 armature have also their effect on the resultant field. 
 There are in general two independent variables in a 
 dynamo machine the current around the magnets and 
 the current in the armature; and the relation of E. M. F. 
 to currents is fully represented by a surface. In well con- 
 structed machines the effect of the latter is reduced to a 
 minimum, but it can be by no means neglected. When a 
 section of the armature coils is commutated, it must inevi- 
 tably be momentarily short circuited ; and if at the time of 
 commutation the field in which the section is moving is 
 other than feeble, a considerable current will arise in that 
 section, accompanied by waste of power and destructive 
 sparking. . . . 
 
 " Suppose the commutation occurs at an angle A in advance 
 of the symmetrical position between the fields, and that the 
 total current through the armature be C, reckoned positive 
 in the direction of the resultant E. M. F. of the machine, 
 i.e., positive when the machine is used as a generator of 
 electricity. Taking any closed line through magnets and 
 
 * See page 121 of this volume. 
 
140 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 armature, symmetrically drawn asABCDJS FA [Fig. 46], 
 it is obvious that the line integral of magnetic force is di- 
 minished by the current in the armature included between 
 angle A in front and angle X behind the plane of symme- 
 try. If m be the number of convolutions of the armature, 
 
 the value of this magnetizing force \& 
 
 C - = 
 
 
 opposed to the magnetizing force of the fixed coils on the 
 
 Fio. 46. 
 
 magnets. Thus if we know the lead of the brushes and the 
 current in the armature we are at once in a position to cal- 
 culate the effect on the electromotive force of the machine. 
 A further effect of the current in the armature is a material 
 disturbance of the distribution of the induction over the 
 
DYNAMO-ELECTRIC MACHINERY. 141 
 
 bored face of the pole piece; the force along BC [Fig. 
 46] is by no means equal to that along D E. Draw the 
 closed curve B C G H B, the line integral along G, and HB 
 is negligible. Hence the difference between force H G and 
 
 777 1C 
 
 B G is equal to 4 n G -= = 2 K m G, where K is the angle 
 
 COG." 
 
 To verify this formula is one of the principal objects of 
 this Paper. 
 
 A pair of brushes having relatively fixed positions near 
 together, and insulated from the frame and from one 
 another, are carried upon a divided circle, and bear upon 
 the commutator. The difference of potential between these 
 brushes was measured in various positions round the com- 
 mutator, the current in the armature, the potential differ- 
 ence of the main brushes, and the speed of the machine 
 being also noted. 
 
 The results are given in Figs. 47, 48, 49, and 50, in 
 which the ordinates are measured potential differences, 
 and the abscissae are angles turned through by the ex- 
 ploring brushes. The potential differences in Fig. 47 
 were measured by a Siemens voltmeter, and eacli ordi- 
 nate is therefore somewhat smaller than the true value, 
 owing to the time during which the exploring brashes 
 were not actually in contact with the commutator seg- 
 ments. But this does not affect the results, because the 
 area is reduced in the same proportion as the potential 
 differences. In Figs. 48, 49, and 50 the potential differ- 
 ences were taken on one of Sir William Thomson's quad- 
 rant electrometers, and are correct. 
 
 Take Fig. 47, in which machine No. 1 is a generator. A 
 
142 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 centimetre horizontally represents 10 of lead, and the 
 ordinates represent differences of potential between the 
 brushes. The area of the curve is 61.3 sq. cms., and repre- 
 sents 130 volts and a total field of ? X ^ X 10' 
 
 = 4.31 X 10* lines of induction. This is, of course, not the 
 actual field, which is 3 per cent, greater on account of the 
 
 
 
 
 +~^* 
 
 >T*~ 
 
 +^ 
 
 *~~~^ 
 
 \ 
 
 
 
 
 f 
 
 *~**^ 
 
 
 
 
 
 \ 
 
 
 
 
 I 
 
 
 
 
 
 
 
 \^ 
 
 **^ 
 
 6O 1OO ISO 2OO 
 FlO. 47. 
 
 resistance of the armature, but is represented by an area 3 
 per cent, greater. An ordinate of 1 cm. will represent an 
 
 1 ' ' 1 
 
 induction of - - x 10" = 7.0 X 10* lines in 10. The area 
 
 01. o 
 
 of 10 is 39.5 X 1.73 = 68.3 sq. cms.* Hence an ordinate 
 of 1 cm. represents an induction of 1,024 lines per square 
 centimetre. The difference between ordinates at 50 and 
 140 is 2.5; hence the difference of induction is actually 
 2,560. Theoretically, we have K = n m = 104 C = 9.4. 
 Therefore 2 K m C = 3,072, and this is the line integral of 
 magnetizing force round the curve. 
 
 Let A be the induction at 50 and A + 6 at 140: these 
 
 * In calculating this area, the allowance for fringe at ends of armature is 
 taken less than before, because the form of opposing faces differs. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 143 
 
 also are the magnetizing forces. Hence (^4 -f d) 1.4 A 1.4 
 = 2 x: w (7 ; 6 = 2,200, as against 2,560 actually observed. 
 Take Fig. 48, in which No. 2 machine is a motor. The 
 
 total field = x . x i 8 = 5.15 x 10' lines of indue- 
 104 /wO 
 
 tion. Since the area of the diagram is 53.5 sq. cms., an 
 
 5 15 
 
 ordinate of 1 cm. = -^ X 10" = 96 X 10 4 lines of induc- 
 oo.o 
 
 
 
 
 *-H 
 
 '"'"* s 
 
 
 
 
 
 c 
 
 
 
 / 
 
 
 
 
 
 t *"*^ 
 
 N 
 
 
 
 X 
 
 
 
 
 
 
 
 s 
 
 \ 
 
 310 260 210 
 FlO. 48. 
 
 tion in 10. Hence an ordinate of 1 cm. represents an 
 
 9.6 X 10* 
 induction of ' Q Q = 1,400 lines per square centimetre. 
 
 Do.o 
 
 The difference between ordinates at 320 and at 230 is 2.0; 
 hence the difference of induction is actually 2,800. Theo- 
 
 2*mC 3| X 104 X 11.4 
 retically, we have - = - - = 2,666, as 
 
 I 1.4 
 
 against 2,800 actually observed. 
 
 In Fig. 49 No. 1 machine is a generator. The total field 
 
 = jjjj X jig X 10" = 3.97 X 10" lines. The area of the 
 diagram is 90.9 sq. cms., and therefore an ordinate of 1 cm. 
 
 O Qiy 
 
 = - - x 10" = 4.37 X 10* lines in 10. Hence an ordi- 
 
144 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 4 37 X 10 4 
 nate of 1 cm. represents an induction of - - = 639 
 
 Oo.O 
 
 lines per square centimetre. The difference between ordi- 
 
 200 
 
 nates at 50 and at 140 is 4.5; hence the difference of 
 induction is actually 2,877. Theoretically, we have - 
 
 _ 3} X 104 X 12.9 
 
 1.4 
 
 In Fig. 50 No. 2 machine is a motor. The total field 
 63.5 
 
 x 
 
 " " 4 ' 9G x 10 " lines * The area of the 
 
 diagram is 112.2 sq. cms., and therefore an ordinate of 1 cm. 
 4.96 
 
 112.2 
 
 X 10' = 4.42 X 10 4 lines in 10. Hence an ordi- 
 
 4 42 
 nate of 1 cm. represents an induction of - ~ X 10 4 = 647 
 
 Oo.o 
 
 lines per square centimetre. The difference between ordi- 
 nates at 323 and at 233 is 4.2; hence the difference 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 145 
 
 of induction is actually 2,718. Theoretically, we have 
 
 2*mC 3! X 104 X 12.3 
 
 j = - -j-j = 2,870, as against 2,718 act- 
 ually observed. 
 
 7 
 
 310 
 
 26O 
 
 810 
 
 FIG. 50. 
 
 At page 108 of the preceding Paper on Dynamo-Electric 
 Machinery it is shown that 
 
 C\ 
 J, 
 
 where /= F(4 7tnc)is the characteristic curve when C= 0, 
 and X is the lead of the brushes. 
 
 The following is an endeavor to verify this formula. 
 The potentials both upon the magnets and upon the 
 brushes were taken by a Siemens voltmeter, and are rough. 
 The speeds were taken by a Buss tachometer, and there is 
 some uncertainty' about the precise lead of the brushes, 
 owing to the difficulty in determining the precise position 
 
146 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 of the symmetrical position -between the fields, and also to 
 the width of the contacts on the commutator. 
 
 It was necessary, in order to obtain a marked effect of 
 the armature reaction, that the magnet field should bo 
 comparatively small, that the current in the armature 
 should be large, and the leads of the brushes should be 
 large. 
 
 The two machines had their axles coupled so that No. 1 
 could be run as a generator, and No. 2 as a motor. The 
 magnets were in each case coupled parallel, and excited by 
 a battery each through an adjustable resistance. The two 
 armatures were coupled in series with another battery, and 
 the following observations were made : 
 
 
 Potential on 
 Magnets in volts. 
 
 Potential on 
 Brushes. 
 
 Speed per 
 Minute. 
 
 Current in 
 Amperes. 
 
 Lead of 
 Brushes. 
 
 No. 1 
 No. 2 
 
 24-24 
 2929 
 
 86-67 
 86-84 
 
 880 
 880 
 
 10-2-108 
 102-103 
 
 26 
 29 
 
 Prom which we infer: 
 
 
 Current in 
 Magnets. 
 
 4wnc. 
 
 Corrected Poten- 
 tial for Resistance 
 of Armature. 
 
 Total 
 Induction. 
 /. 
 
 No. 1 
 No. 2 
 
 1.78 
 2.15 
 
 8,900 
 10,750 
 
 70.8 
 80.7 
 
 2.80xlO 
 2.65x10* 
 
 As there was uncertainty as to the precise accuracy of 
 the measurements of potential, it appeared best to remeas- 
 ure the potentials with no current through the armature 
 with the Siemens voltmeter placed as in the last experi- 
 ment. Each machine was therefore run on open circuit 
 with its magnets excited, and its potential was measured. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 14? 
 
 
 Potential on Mag- 
 nets in volts. 
 
 Potential on 
 Brushes. 
 
 Speed per 
 Minute. 
 
 Potential at 
 880 Revs. 
 
 No. I 
 No. 2 
 
 25-25 
 2828 
 
 90-90 
 79-80 
 
 880 
 715-710 
 
 90.0 
 98.2 
 
 From which, since the formula is reduced to 
 
 the characteristic being practically straight, we infer : 
 
 
 Potential on 
 Magnets. 
 
 Potential on 
 Brushes. 
 
 Induction, 
 I=F(4irnc). 
 
 No. 1 
 No. 2 
 
 24 
 29 
 
 86.4 
 101.7 
 
 2.82xlO 
 3.30xlO 
 
 We have further : 
 .\ = 0.45 for No. 1; 
 
 - = 2,920; 
 
 A = 0.5 for No. 2; 
 
 -4m C = 443,800. 
 
 
 
 
 
 
 4Am(7\ 
 
 
 4Xm(7 
 
 "~~*4x r> A ' 2 
 
 4XmC 
 
 / 4\mC\ 
 
 \ v ' 
 
 
 v 
 
 v 2l t 
 
 V 
 
 \ v ' 
 
 ^-^- 
 
 1 
 
 2 
 
 1,314 
 1,460 
 
 199,700 
 221,900 
 
 7,586 
 9,290 
 
 2.41xlO 
 2.90xlO 
 
 2.21xlO 
 2.68xlO 
 
 It has already appeared that experiment gives for / in 
 No. 1 2.3 X 10 6 , and in No. 2 2.65 X 10*. The difference 
 is probably due to error in estimating the lead of the 
 brushes, which is difficult, owing to uncertainty in the 
 position of the neutral line on open circuit. 
 
148 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 THEORY OF ALTERNATING CURRENTS, PAR- 
 TICULARLY IN REFERENCE TO TWO 
 ALTERNATE CURRENT MACHINES CON- 
 NECTED TO THE SAME CIRCUIT. 
 
 IN my lecture on Electric Lighting, delivered before the 
 Institution of Civil Engineers last year,* I considered the 
 question of two alternate current dynamo machines con- 
 nected to the same circuit, but having no rigid mechanical 
 connection between them ; and I showed that, if two such 
 machines be coupled in series, they will tend to nullify 
 each other's effect ; if parallel, to add their effects. f The 
 subject is one which already has practical importance and 
 application, and may have much more in the future; it is 
 also one suited for discussion, and upon which discussion 
 is desirable. I therefore venture to bring before the 
 Society what I said in my lecture some other ways of look- 
 ing at the same subject, and an experimental verification, 
 
 * This Paper is reprinted on pag*>s 40 to 78 of this volume. 
 
 t November 22, 1884. My attention has only to-day been called to a paper by 
 Mr. Wilde, published by the Literary nnd Philosophical Society of Manchester, 
 December 15, 1868, also Philosophical Magazine, January, 1869. Mr. Wilde 
 fully describes observations of the synchronizing control between two or more 
 alternate current machines connected together. I am sorry I did not know of 
 his observations when I lectured before the Institution of Civil Engineers, that 
 I might have given him the honor which was his due. If his paper had been 
 known to those who have lately been working to produce large alternate cur- 
 rent machines, it would have saved them both labor and money. 
 
THEORY OF ALTEENATING CURRENTS. 149 
 
 together with solutions of other problems requiring similar 
 treatment. 
 
 The general explanation, amounting to proof so far as 
 machines in series are concerned, is given in the following 
 extract from my lecture : 
 
 " There remains one point of great practical interest in 
 connection with alternate current machines: How will 
 they behave when two or more are coupled together to aid 
 each other in doing the same work ? With galvanic bat- 
 teries we know very well how to couple them, either in 
 parallel circuit or in series, so that they shall aid, and not 
 oppose, the effects of each other; bnt with alternate cur- 
 rent machines, independently driven, it is not quite ob- 
 vious what the result will be, for the polarity of each 
 machine is constantly changing. Will two machines 
 coupled together run independently of each other, or will 
 one control the movement of the other in such wise that 
 they settle down to conspire to produce the same effect, or 
 will it be into mutual opposition ? It is obvious that a 
 great deal turns upon the answer to this question, for in 
 the general distribution of electric light it will be desirable 
 to be able to supply the system of conductors from which 
 the consumers draw by separate machines, which can be 
 thrown in and out at pleasure. Now I know it is a com- 
 mon impression that alternate current machines cannot be 
 worked together, and that it is almost a necessity to have 
 one enormous machine to supply all the consumers draw- 
 ing from one system of conductors. Let us see how the 
 matter stands. Consider two machines independently 
 driven, so as to have approximately the same periodic time 
 and the same electromotive force, If these two machines 
 
150 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 are to be worked together, they may be connected in one 
 of two ways : they may be in parallel circuit with regard 
 to the external conductor, as shown by the full line in 
 Fig. 51, that is, their currents may be added algebraically 
 and sent to the external circuit, or they may be coupled in 
 series, as shown by the dotted line, that is, the whole cur- 
 rent may pass successively through the two machines, and 
 the electromotive force of the two machines may be added, 
 
 instead of their currents. The latter case is simpler. Let 
 us consider it first. I am going to show that if you couple 
 two such alternate current machines in series they will so 
 control each other's phase as to nullify each other, and 
 that you will get no effect from them; and, as a corollary 
 from that, I am going to show that if you couple them in 
 parallel circuit they will work perfectly well together, and 
 the currents they produce will be added; in fact, that you 
 
THEORY OF ALTERNATING CURRENTS. 
 
 151 
 
 cannot drive alternate current machines tandem, but that 
 you may drive them as a pair, or, indeed, any number 
 abreast. In diagram, Fig. 52, the horizontal line of abscissae 
 represents the time advancing from left to right; the full 
 curves represent the electromotive forces of the two 
 machines not supposed to be in the same phase. We want 
 to see whether they will tend to get into the same phase or 
 to get into opposite phases. Now, if the machines are 
 coupled in series, the resultant electromotive force on the 
 circuit will be the sum of the electromotive forces of the 
 
 nur 
 
 two machines. This resultant electromotive force is rep- 
 resented by the broken curve ///; by what we have already 
 seen in Formula IV. [p. 52, this volume], the phase of 
 the current must lag behind the phase of the electro- 
 motive force, as is shown in the diagram by curve IV, thus 
 
 . . . Now the work done in any machine is 
 
 represented by the sum of the products of the currents 
 and of the electromotive forces, and it is clear that, as the 
 phase of the current is more near to the phase of the lag- 
 ging machine // than to that of the leading machine /, the 
 lagging machine must do more work in producing elec- 
 
152 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 tricity than the leading machine; consequently its velocity 
 will be retarded, and its retardation will go on until the 
 two machines settle down into exactly opposite phases, 
 when no current will pass. The moral, therefore, is, do not 
 attempt to couple two independently driven alternate cur- 
 rent machines in series. Now for the corollary: A, B, 
 Fig. 51, represent the two terminals of an alternate cur- 
 rent machine; a, b, the two terminals of another machine 
 independently driven. A and a are connected together, 
 and B and b. So regarded, the two machines are in series, 
 and we have just proved that they will exactly oppose each 
 other's effects, that is, when A is positive, a will be 
 positive also; when A is negative, a is also negative. 
 Now, connecting A and a through the comparatively high 
 resistance of the external circuit with B and b, the cur- 
 rent passing through that circuit will not much disturb, if 
 at all, the relations of the two machines. Hence, when A 
 is positive, a will be positive, and when A is negative, a 
 will be negative also; precisely the condition required that 
 the two machines may work together to send a current 
 into the external circuit. You may, therefore, with con- 
 fidence, attempt to run alternate current machines in 
 parallel circuit for the purpose of producing any external 
 effect. I might easily show that the same applies to a 
 larger number; hence there is no more difficulty in feed- 
 ing a system of conductors from a number of alternate 
 current machines than there is in feeding it from a num- 
 ber of continuous current machines. A little care only is 
 required that the machine shall be thrown in when it has 
 attained something like its proper velocity. A further 
 corollary is that alternate currents with alternate current 
 
THEORY OF ALTERNATING CURRENTS. 
 
 153 
 
 machines as motors may theoretically be used for the 
 transmission of power." * 
 
 Although the proof of this corollary regarding motors is 
 similar to what we have just been going through, it may 
 be instructive to give it. In the accompanying diagrams, 
 Figs. 53 and 54, the full lines / and 21 represent the 
 
 Fio.68. 
 
 electromotive forces of the two machines (generator and 
 receiver) ; the dotted line, curve 777 (. . . .), the resultant 
 electromotive force; and the curve IV, the resulting cur- 
 rent, each in terms of the time, as abscissae. The only dif- 
 ference between the two diagrams is, that in Fig. 53 the 
 two machines have equal electromotive forces, while in 
 Fig. 54 the receiving machine has double the electromotive 
 force of the generator. In both figures the receiving 
 machine lags behind the phase of direct opposition to the 
 generator by one quarter of a period, or something less. 
 Now observe, the resultant electromotive force must be in 
 
 * " Of course in applying these conclusions it is necessary to remember 
 that the machines only tend to control each other, and that the control of the 
 motive power may be predominant and compel the two or more machines to 
 run at different speeds." 
 
154 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 phase behind the receiver, but in advance of the generator. 
 Also observe, the current must be in phase behind the re- 
 sultant electromotive force, and may be one quarter of a 
 period behind, provided only the self induction be large 
 enough compared with the resistance. The current will 
 then be less than a quarter period behind the generator. 
 This machine will do work upon the current, but the cur- 
 
 <J 
 
 FIG. 54. 
 
 rent will be more than a quarter period behind the receiv- 
 ing machine; therefore in the receiver the current does 
 work upon the machine. 
 
 The subject is illustrated by the following problems. Of 
 course any of them may be treated more generally by con- 
 sidering the machines as unequal, or by introducing other 
 periodic terms, but I do not see that this would throw more 
 light on the subject: 
 
 I. Two alternate current machines, equal in all respects, 
 are connected in series and independently driven at the 
 same speed, to determine the current, etc., in each. 
 
THEORY OF ALTERNATING CURRENTS. 155 
 
 Let y be the coefficient of self induction of each, r the 
 
 2 n 
 resistance, x the current at time t, and E sin =- (t -\- T) 
 
 2# 
 
 and E sin -^ (t r) the electromotive forces. Then 
 
 regarding the coefficient of self induction as constant, 
 which it is not exactly, and neglecting the effect of currents 
 other than those in the copper wire, the equation of motion is 
 
 = E \ sm -^ (t + i 
 
 27r 2 TT r 
 or ^ a; '+ r x = 12 sm ~- cos ^ ; 
 
 whence 
 
 I p 27TT V 
 
 ~^~ ( 2 TT/ 27T X 2?r# 
 
 a = /9 ^ -,\ ! sm fff- + ^- cos -^r- 
 
 Work done by the leading machine per second 
 
 ~T~ ( ZTTT Zxy . 
 
 From this it at once follows that the leading machine does 
 
 T 
 
 least work, and will tend to increase its lead until r = - , 
 
156 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 when the two machines will neutralize each other, as al- 
 ready proved geometrically. The leading machine may ac- 
 tually become a motor and do mechanical ivorJc, although 
 its electromotive force is precisely equal to that of the fol- 
 loiving machine. 
 
 Considering the important case when r is negligible, we 
 have 
 
 ZTTT 
 E cos -. cos 
 
 X = 
 
 27TX 
 
 T~ 
 
 T 
 
 rate of working = - . 
 
 4 .'2|Z 
 
 T 
 This is the maximum when r = -, and then it is equal to 
 
 o 
 
 the maximum work which can be obtained from either 
 machine when connected to a resistance only, which occurs 
 
 when that resistance is ~ ; the current, also, is the same 
 as when the maximum work is being done on resistance, 
 and is of the current the machine will give if short 
 
 circuited. The difference of potential between the two 
 leads connecting the machines, whether r = or not, is 
 
 E cos ^-Tff- sin jfr If there be no work done on the re- 
 
 T 
 
 ceiving machine and r = 0, T -, and the amplitude of 
 
THEORY OF ALTERNATING CURRENTS. 157 
 
 the difference of potential between the leads is E\ if, 
 on the other hand, the maximum work is being transmitted, 
 
 the potential measured will be of that observed when 
 
 either machine is run on open circuit. 
 
 II. Two machines are coupled parallel and connected to 
 an external circuit resistance R. 
 
 Let x l , x t be currents in the two machines. The ex- 
 ternal current will be x l -f # a , and consequently the differ- 
 ence of potential at the junction, R (x l -J- # 3 ). 
 
 Let the electromotive forces of the two machines regarded 
 
 in this case as connected parallel be E sin - -i= -- -, and 
 
 let the self induction and resistance of each be $-y and 2 r. 
 The equations of motion then are : 
 
 =E sin - R (x, 
 
 whence 
 
 and 
 
 \ T7 ^ 7ft . 2 TIT 
 
 - X = E cos -- sm --, 
 
168 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 Solving these, 
 
 27TT 
 
 2 arr 
 
 Electrical work done by the leading machiue 
 
 7f y , 7T T 7TT ) 
 
 -- 7^- Bin -^- COS ;- j, 
 
 %7T V . % 
 
THEORY OF ALTERNATING CURRENTS. 159 
 
 This expression shows that the leading machine does most 
 work in all cases. Suppose r is small compared with R 
 
 ~ 
 
 and , also that R = jr~> we have the work done 
 per second 
 
 T 
 
 Make r = --, and we see that the following machine 
 o 
 
 will then do no work; when T exceeds this, the following 
 machine becomes a motor and absorbs electrical work. 
 
 III. Suppose the terminals of an alternate current ma- 
 chine are connected to a pair of conductors, the difference 
 of potential between which is completely controlled by con- 
 nection with other alternate current machines. 
 
 Let y and R be the coefficient of self induction and the 
 resistance of the machine and its own conductors up to the 
 point at which the potential is completely controlled. Let 
 the difference of potential of the main conductors be 
 
 A sin p- , and let the electromotive force of the machine 
 
 , D . 27f(t-r) 
 be B sin - -^ '- . 
 
 Equation of motion is 
 
 2 n (t r) 2 7ft 
 
 yx' + Rx = B sm ^ * A sm 7fr , 
 
160 DYNAMO MACHINERY AND ALLIED SUBJECTS, 
 whence 
 
 _**(t-r) *ny 
 
 cos 
 
 ;r(*-T)) j 27T* 2*x 2*n~| 
 
 -^r- ^ j- - ^4 | R sin -^- ^- cos -^- j- J, 
 
 Electrical work done by the machine in unit of time 
 
 - 
 
 = x B sin - ,., - = 
 
 T 
 
 
 If T be positive, that is, if machine be lagging in its phase, 
 work done is less than if it be negative; hence T will tend 
 to zero, or the machine will tend to adjust itself to add its 
 currents to that of the system of conductors. The machine 
 may act as a motor even though its electromotive force be 
 greater than that of the system, for let 
 
 R %7T 
 
 - = tan 
 
 7' 
 
THEORY OF ALTERNATING CURRENTS. 161 
 work (electric) done by machine 
 
 AB 
 
 T 
 
 T 
 
 this has a minimum value when <f> + f = -j- , and then 
 
 the mechanical work done by machine or electrical work 
 received by the machine 
 
 B ( RB } 
 
 and this is positive, provided 
 ' i> * 
 
 There are two or three other problems of sufficient in- 
 terest to make it worth while giving them here, although 
 not directly relating to alternate current machines coupled 
 together. 
 
 IV. To determine the law of an alternate current 
 through an electric arc. 
 
 It has been shown by Joubert that in an arc the differ- 
 ence of potential is of approximately constant numerical 
 
162 I>YNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 value, reversing its value discontinuously with the reversal 
 of the current, probably at the instant of reversal of cur- 
 rent. We shall assume, then, that there is in the arc a 
 constant electromotive force, A, always opposed to the 
 current, except when the current ceases, and that then its 
 value is zero. 
 
 The equation of motion is 
 
 yx' + ltx = EBin^^A, 
 
 the negative sign being taken when x is + **> the positive 
 when x is negative. Solving generally, 
 
 A E / 27ty 2?rt 
 
 % ~T~ ~/S I /rt _ .. \ I 7fi~ COS rn 
 
 This equation will continuously hold good for a half period 
 from x = to x = again, but at each half period the 
 arbitrary constant C is changed with the sudden change of 
 sign of A. It 'is determined by the consideration that if, 
 for a certain value t of t, x should vanish, it shall vanish 
 
 T 
 
 again when t = t -f- --- . This applies to the case when E 
 
 A 
 
 is sufficiently large, as is practically the case; but if the 
 current should cease for a finite time this condition will be 
 varied, and instead of it we have the condition x = when 
 
 9 "jf / 
 
 E sin -=- = A. This latter case I do not propose to 
 consider further. 
 
THEORY OF ALTERNATING CURRENTS. 163 
 
 Let 
 
 2 n v %7tt. 
 
 T 
 
 Putting * = t and t = t, + -^ , we have 
 
 _R RT 
 
 Ce *' .e 2 Y* 
 
 equations to determine t and C. 
 Eliminating C, 
 
 RE' .27 
 
 - . sin - 
 
 
164 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 Having obtained t , C is given by equation 
 o A R I R 
 
 This gives the complete solution of the problem. 
 
 A case of special importance is that in which R is small ; 
 let us therefore consider the case R = 0; the solution 
 then is 
 
 T 2 nt 
 yx= - .tf cos -~ A t + C. 
 
 In the same way as before, 
 
 2 7t t A 71 
 
 c=. 
 
 The limiting case to which the solution applies is given by 
 x' = when * = *. + 
 
 2 7f t 
 
 Ci% 
 ^ ~^~ T)' 
 
 or A = E X 0.538. 
 
 Roughly, we may say that, in order that the current may 
 not cease for a finite time, E must be at least double of A; 
 
THEORY OF ALTERNATING CURRENTS. 165 
 
 A will of course depend upon the length of the arc. The 
 work done in the arc will be proportional to the arith- 
 metical mean value of the current taken without regard to 
 sign. This is of course quite a different thing from the 
 mean current as measured by an electro-dynamometer. 
 Let us examine what error is caused by estimating the 
 work done in the arc as equal to the current measured by 
 the dynamometer multiplied by the mean difference of 
 potential. 
 
 The actual work done per second 
 , T 
 
 The mean square of the current as measured by the elec- 
 tro-dynamometer is 
 
 2 /^o 
 
 f I 
 
 */* 
 
 and the work done by this current is apparently the square 
 root of the above expression multiplied by A. It is easy 
 to. see that this is greater in all cases than the work done, 
 but it is worth while to examine the extent of the error. 
 If we treated, the arc as an ordinary resistance, we should 
 assume work per second 
 
166 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 2 
 
 Taking a fairly practical case, assume A = E; we have 
 
 actual work per second 
 
 A*T 1 
 
 work done estimated by electro-dynamometer 
 
 25 
 
 = ^ a y 1 7235 
 
 X SOY/ 12"' 
 
 or nearly part too much. This will suffice to show that 
 the matter is not a mere theoretical refinement. Another 
 erroneous method of estimating the power developed in an 
 arc is to replace by a resistance and adjust this resistance 
 till the current as measured by an electro-dynamometer 
 is the same as with the arc, and assume that the work done 
 in the resistance is the same as the work done in the arc. 
 Returning to the expression 
 
 ny 2 
 
 we may inquire, given T A and the dimensions of the ma- 
 chine, how ought it to be wound or its coils connected that 
 
THEORY OF ALTERNATING CURRENTS. 167 
 
 most work may be done in the arc. If the number of con- 
 volutions be varied, E will vary as the convolutions, y as 
 their square; therefore y oc E* ; we are therefore to deter- 
 mine E so that = A IE* is a maximum which 
 
 occurs when E = n A. When the resistance of the circuit 
 is taken into account, this result will be modified. It 
 suffices to prove that it is desirable that the potential of 
 the machine should be materially in excess of that required 
 to maintain the arc. 
 
 V.* In all that precedes it is assumed, not only that y is 
 constant, but that the copper conductor of the armature is 
 the only conductor moving in the field. If there be iron 
 cores in the armature, we shall approximate to the effect 
 by regarding such cores as a second conducting circuit. 
 Slightly changing the notation, let L be coefficient of self 
 induction of the copper circuit, N coefficient of self induc- 
 tion of the iron circuit and R l its resistance, I 1 the mag- 
 netic induction of the field magnets upon the iron circuit, 
 and M the coefficient of mutual induction of the two cir- 
 cuits, y the current in the iron. The equations of motion 
 are obtained from the expression for the energy, viz., 
 
 %{Lx* -j- %Mxy + Ny* 2 Ix 2 1' y}, 
 and are 
 
 r ~/ i i,r / i n d I 2 7t A 27ft 
 
 L x' -f M y' -f- R x = -J-T = =, cos =- , 
 
 d P 27fS 27ft 
 MX' 4- Nyr + R'u = -=-r = m cos ^-, 
 
 * Fide also "Encyclopaedia Britannica," article " Lighting." 
 
168 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 for in general the iron cores and the copper conductor are 
 symmetrically arranged. Assume 
 
 x = a sm 
 
 . 
 = b cos 
 
 27ft 
 
 , . 27ft 
 
 = a' sm -- b' cos 
 
 and substitute in the equations of motion; we have the 
 following four equations to determine the constants , b, 
 a', ': 
 
 A 
 
 or 
 
 and 
 
 = 0, 
 
 = 0. 
 
 These equations contain the solution of the problem, but 
 are too cumbersome to be worth while solving generally; 
 
THEORY OF ALTERNATING CURRENTS. 169 
 
 we will, however, prove the statements made in the lecture 
 before the Civil Engineers. 
 
 1. Compare short circuit and open circuit, that is, R = 
 very nearly, and R = oc*. In the former case 'we find that 
 
 work done in the iron is diminished, and if B = =r- we 
 
 lj 
 
 have the paradoxical result that there are no currents in- 
 duced in the iron of the cores and no work is required to 
 drive the machine. This, of course, can never actually 
 occur, because R can never absolutely vanish. It suffices 
 to show, however, that the current in the copper circuit 
 may diminish the whole power required to drive the ma- 
 chine to an amount less than the power required to drive 
 the machine on open circuit. 
 
 2. The other statement related to the effect of the cur- 
 rents in the iron upon the currents produced in the copper 
 circuit. Assume that the effect is a small one, for a first 
 approximation. Neglect it, that is, treat the currents in 
 the iron and the currents in the copper as independent of 
 each other, and then see how each would disturb the other. 
 
 The first approximation then is 
 
 AL ,_ EN 
 
 /T2 r>2) ** ' rrty pf2> 
 
 '+^4 ^ j +^-i- 
 
 .TR TR' 
 
 ~ 
 
 7,- 
 
 " 
 
170 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 If we substitute these in the general equations as correc- 
 tions, we have 
 
 4;r 
 
 which shows that the disturbing effect of each circuit upon 
 the other is to diminish the apparent electromotive force, 
 but to accelerate its phase. 
 
 VI. A very similar problem is that of secondary genera- 
 tors or induction coils, whether used for the conversion of 
 high potentials to low, or the reverse. To treat it gener- 
 ally, taking the magnetization of the iron cores, which are 
 always used, as a non-linear function of the currents in the 
 coils, would be a matter of much difficulty; we therefore 
 assume, as is usual, that the coefficients of induction are 
 constants, noting in passing that this is not strictly the 
 fact, though it is very nearly the fact, when the cores are 
 not saturated and when the lines of magnetic induction 
 pass through non-magnetic space. 
 
 Let, then, R, r be the resistances of the primary and 
 secondary circuits; 
 
 L coefficient of self induction of the primary; 
 
 ^coefficient of self induction of the secondary; 
 
 M coefficient of mutual induction of the two circuits; 
 
THEORY OF ALTERNATING CURRENTS. 171 
 
 x and y the currents in the two circuits at time t; 
 
 JTihe electromotive force applied in the primary circuit 
 by an alternate current dynamo machine or other- 
 wise; 
 the equations of motion will be 
 
 Lx' + My' + Rx = X, } 
 
 MX' + Ny' + ry = 0. ) 
 
 Various assumptions may be made as to X, but that most 
 likely to be adopted in the practical work of secondary 
 generators is that X is kept so adjusted that 
 
 2 n 
 x = A cos n t where n = , 
 
 and to inquire how X will depend on the resistances 
 Ny' + r y = n A M sin n t, 
 
 y = a - ra . * ( n N cos n t + r sin n t), 
 9 if N* 4- r a v ' 
 
 8 . 
 
 N 
 
172 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 As in the case of the dynamo machine, the work done in 
 the secondary circuit is greatest when r = n N. The ex- 
 pression for X serves to show that when the secondary is 
 short circuited a loiver electromotive force of the generat- 
 ing circuit is required than when it is on open circuit. In 
 induction coils the electrostatic capacity of the coils them- 
 selves has important effects. An illustration of the effect 
 of electrostatic induction is found in the old-fashioned 
 Ruhmkorff coils. These were not wound symmetrically, but 
 in such wise that one end of the secondary coil was on the 
 whole towards the inside, the other towards the outside of 
 the bobbin. In such coils a spark to earth may be obtained 
 from the outside end, but not from the inside. The reason 
 is that the outer convolutions have smaller electrostatic 
 capacity than the inner ones. The terminals may be made 
 to give equal sparks by the simple expedient of laying a 
 piece of tinfoil around the whole coil and connecting it to 
 earth. 
 
 VII. Some time ago Dr. Muirhead told me that he had 
 observed that the effect of an alternate current machine 
 could be increased by connecting it to a condenser. This 
 is not difficult to explain : it is a case of resonance anal- 
 ogous to those which are so familiar in the theory of sound 
 and in many other branches of physics. 
 
 Take the simplest case, though some others are almost 
 as easy to treat. Imagine an alternate current machine 
 with its terminals connected to a condenser; it is required 
 to find the amplitude of oscillation of potential between the 
 two sides of the condenser. Let R y be the resistance and 
 
 2 71 t 
 
 self induction of the machine, E sin -~- its electromotive 
 
THEORY OF ALTERNATING CURRENTS. 173 
 
 force, C the capacity of the condenser, V the difference of 
 potential sought, and x the current in the machine ; then 
 
 C V = x, 
 and 
 
 _ , f* f+ V - 
 
 ~~ -*-* D fwj W J 
 
 whence 
 
 . % X . 27ft 
 + R 0- sin 
 
 . . . T T 27TEC 
 
 amplitude of V is therefore 
 
 Now suppose E = 100 volts, the machine would light up 
 an incandescent lamp of about 69 volts. Let T = -% fa second, 
 
174 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 2 n y 
 C = 100 microfarads, and =~ = 8 ohms, and R = -fa 
 
 ohm, all figures which could be practically realized; we 
 have amplitude of V = 80 E roughly, or the apparent 
 electromotive force would be increased eighty fold. 
 
 We now return to the principal subject of the present 
 communication. Some attempts have been made to verify 
 the proposition that two alternate current machines can 
 be advantageously connected parallel, but, I believe, till 
 recently without success. I had no convenient opportu- 
 nity for testing the point myself till last summer, when I 
 had two machines of De Meritens, intended for the light- 
 house of Tino, in my hands. I have made no determina- 
 tions of the constants of these machines, but between three 
 and four years ago I thoroughly tested a pair of similar 
 machines now in use at a lighthouse in New South Wales. 
 Each machine haa five rings of sixteen sections, and forty 
 permanent magnets. The resistance of the whole machine 
 as connected for lighthouse work (a single arc) was 0.0313, 
 its electromotive force (E ) when running 830 revolutions 
 
 per minute, 95 volts and ( ar-J = 0.044 ohm. It was 
 
 further remarked that the loss of power was least with a 
 maximum load, as is shown in the following table: 
 
 Power applied as measured in belt 3.1 4.8 5.6 6.5 5.4 
 
 Electric power developed 0.7 8.4 4.3 5.7 3.4 
 
 Mean current in amperes 7.7 38.6 51.7 73.6 151 
 
 This result illustrates well the conclusion arrived at in 
 Problem V. above. 
 Last summer the two machines for Tino were driven 
 
THEORY OF ALTERNATING CURRENTS. 175 
 
 from the same countershaft by link bands, at a speed of 
 850 to 900 revolutions per minute; the pulleys on the 
 countershaft were sensibly equal in diameter, but those on 
 the machines differed by rather more than a millimetre, 
 one being 300, the other 299 mms. in diameter (about); 
 thus the two machines had not when unconnected exactly 
 the same speed. The pulleys have since been equalized. 
 The bands were of course put on as slack as practicable, 
 but no special appliance for adjusting the tightness of the 
 bands was used. The experiment succeeded perfectly at 
 the very first attempt. The two machines, being at rest, 
 were coupled in series with a pilot incandescent lamp 
 across the terminals; the two bands were then simulta- 
 neously thrown on : for some seconds the machines almost 
 pulled up the engine. As the speed began to increase, the 
 lamp lit up intermittently, but in a few seconds more the 
 machines dropped into step together, and the pilot lamp 
 lit up to full brightness and became perfectly steady and 
 remained so. An arc lamp was then introduced, and a per- 
 fectly steady current of over 200 amperes drawn off with- 
 out disturbing the harmony. The arc lamp being removed, 
 a Siemens electro-dynamometer was introduced between 
 the machines, and it was found that the current passing 
 was only 18 amperes, whereas, if the machines had been in 
 phase to send the current in the same direction, it would 
 have been more than ten times as great. On throwing off 
 the two bands simultaneously, the machines continued to 
 run by their own momentum, with retarded velocity. It 
 was observed that the current, instead of diminishing from 
 diminished electromotive force, steadily increased to about 
 50 amperes, owing to the diminished electrical control be- 
 
176 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 tween the machines, and then dropped off to zero as the 
 machines stopped. Professor Adams will, I hope, give an 
 account of experiments he has tried wifh me, and on other 
 occasions, at the South Foreland. With De Meritens' 
 machines, I regard coupling two or more machines parallel 
 as practically the best way of obtaining exceptionally great 
 currents when required in a lighthouse for penetrating a 
 thick atmosphere. 
 
AN UNNOTICED DANGER. 177 
 
 AN UNNOTICED DANGER IN CERTAIN APPA- 
 RATUS FOR DISTRIBUTION OF ELECTRICITY. 
 
 MANY plans have been proposed, and several have been 
 to a greater or less extent practically used, for combining 
 the advantage of economy arising from a high potential in 
 the conductors which convey the electric current from the 
 place where it is generated with the advantages of a low 
 potential at the various points where the electricity is used. 
 A low potential is necessary where the electricity is used ; 
 partly because the lamps, whether arc or incandescent, each 
 require a low potential, and partly because a high potential 
 may easily become dangerous to life. Among the plans 
 which have been tried for locally transforming a supply of 
 high potential to a lower and s,afer, the most promising is 
 by the use of secondary generators or induction coils. It 
 has been proved that this method can be used with great 
 economy of electric power and with convenience; under 
 proper construction of the induction coils it may also be 
 perfectly safe. It is, however, easy and very natural so to 
 construct them that they shall be good in all other respects 
 but that of safety to life that they shall introduce an un- 
 expected risk to those using the supply. 
 
 In a distribution of electricity by secondary generators, 
 an alternating current is led in succession through the 
 primary coils of a series of induction coils, one for each 
 
178 DYNAMO MACHINERY AND ALLIED 
 
 group or system of lamps. The lamps connect the two 
 terminals of the secondary coil of the induction coils. It 
 is easy to so construct the induction coils that the differ- 
 ence of potential between the terminals of the secondary 
 coils may be any suitable number of volts, such as 50 or 
 100; while the potential of the primary circuit, as meas- 
 ured between the terminals of the dynamo machine, may 
 be very great, e.g., 2,000 or 3,000 volts. If the electromag- 
 netic action between the primary and secondary coils, on 
 which the useful effect of the arrangement depends, were 
 the only action, the supply would be perfectly safe to the 
 
 n 
 
 7 
 
 
 
 U A 
 
 rt 
 
 Fio. 55. 
 
 user so long as apparatus with which he could not interfere 
 was in proper order. But the electromagnetic action is 
 not the only one. Theoretically speaking, every induction 
 coil is also a condenser, and the primary coil acts electro- 
 statically as well as electromagnetically upon the secondary 
 coil. This electrostatic action may easily become danger- 
 ous if the secondary generator is so constructed that its 
 electrostatic capacity, regarded as a condenser, is other 
 than a very small quantity. 
 
AN UNNOTICED DANGER. 179 
 
 Imagine an alternate current dynamo machine, A, Fig. 
 55, its terminals, B, C, connected by a continuous con- 
 ductor, B D C, on which may be resistances, self induction 
 coils, secondary generators, or any other appliances : at any 
 point is a condenser, E, one coating of which is connected 
 to the conductor, or may indeed be part of it ; the other is 
 connected to earth through a resistance, R. Let K be the 
 capacity of the condenser, Fthe potential at time t of the 
 earth coating of the condenser, U the potential of the other 
 coating, 2 the current in resistance R to the condenser from 
 the earth, being taken as positive, and the earth potential 
 as zero. We have 
 
 , 
 
 whence, since 
 
 U = A sin 2 n n t, 
 
 where A is a constant depending on the circumstances of 
 the dynamo circuit as well as the electromotive force of the 
 machine, and n is the reciprocal of the periodic time of the 
 machine, we have 
 
 KR % + x = 2 n n KA cosZrtn t, 
 9 - a { 2 7t n KR sin 2 n n t -j- cos 2 n n t \ , 
 
 x = 
 
 - 
 mean square of x = . mean square of A. 
 
 Let us now consider the actual values likely to occur in 
 practice. Let the condenser E be a secondary generator; 
 
180 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 let the resistance R be that of some person touching some 
 part of the secondary circuit, and also making contact to 
 earth with some other part of the body ; n may be anything 
 from 100 to 250, say 150; /Twill depend on the construc- 
 tion of the secondary generator it may be as high as 0.3 
 microfarad or even more, but there would be no difficulty 
 even in large instruments in keeping it down to one hun- 
 dredth of this or less. The mean square of A will depend 
 on the circumstances of other parts of the circuit; it might 
 very easily be as great, or very nearly as great, as the mean 
 difference of potential between the terminals of the ma- 
 chine if the primary circuit were to earth at C. Suppose, 
 however, that the circuit B D C is symmetrical, that E is 
 at one end, and that another person of the same resistance 
 as the person at E is touching the secondary circuit of the 
 secondary generator F at the other end of the circuit. In 
 that case, if 2,400 be difference of potential of the machine, 
 mean square of A will be 1,200; in which case we have, 
 taking R as 2,000 ohms, 
 
 mean square of 
 
 2 n X 150 X 0.3 X 10 
 
 , r. 
 
 ==== 
 
 t/(2 n X 150 X 0.3 X 10- 6 X 2,000)' + 1 
 
 = about 0.3 ampere. 
 
 Experiments are still wanting to show what current may 
 be considered as certain to kill a man, but it is very doubtful 
 whether any man could stand 0.3 ampere for a sensible 
 length of time. It is probable that if the two persons both 
 'took firm hold of the secondary conductors of E and F 9 
 both would be killed. If the person at F be replaced by 
 
AN UNNOTICED DANGER. 181 
 
 an accidental dead earth on the secondary circuit of F, the 
 person at E would experience a greater current than 0.3 
 ampere. 
 
 It follows from the preceding consideration that second- 
 ary generators of large electrostatic capacity are essentially 
 dangerous, even though the insulation of the primary cir- 
 cuit and of the primary coils from the secondary coils is 
 perfect. The moral is for the constructor, Take care that 
 the secondary generators have not a large electrostatic 
 capacity, say not more than 0.03 microfarad, better less 
 than -jlnj- microfarad; for the inspector, Test the system 
 for safety. The test is very easy. Place a secondary gen- 
 erator of greatest capacity at one end of the line and con- 
 nect its secondary circuit to earth through any instrument 
 suitable for measuring alternate currents under one am- 
 pere; put the other end of the primary to earth; the read- 
 ing of the current measuring instrument should not exceed 
 such a current as it may be demonstrated a man can en- 
 dure with safety. 
 
182 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 INDUCTION COILS OR TRANSFORMERS. 
 
 THE transformers considered are those having a con- 
 tinuous iron magnetic circuit of uniform section.* 
 Let A be area of section of the core; 
 
 m and u the number of convolutions of the primary 
 
 and secondary coils, respectively; 
 R, r, and p their resistances, p being the resistance 
 
 of the secondary external to the transformer; 
 x and y currents in the two coils; 
 a induction per square centimetre; 
 a the magnetic force; 
 I the length of the magnetic circuit; 
 E = B sin 2 n (t/T), the difference of potentials 
 
 between the extremities of the primary ; 
 T being the periodic time. 
 We have 
 
 4 it (m x + ny) = I a; (1) 
 
 E = R x m A a; 
 = (r + p)y-nAa. 
 
 (2) 
 (3) 
 
 * For a discussion of transformers in which there is a considerable gap in the 
 magnetic circuit, see Ferraris, Torino, Accad. Sci. Mem., vol. 37, 1885 ; also 
 chapter on the " Theory of Alternating Currents," in this volume, 
 
INDUCTION COILS OR TRANSFORMERS. 183 
 
 From (2) and (3), 
 
 n E = n R x m (r + p) y. (4) 
 
 Substituting from (1), 
 
 x\n*R + m*(r + p)\ = <tf E + (la/7t) m(r + p); (5) 
 y{n*R + m*(r + p)} =-nmE+ (lac/7t)nR; (6) 
 
 (r + p)mE laR(r + p) _ , , 
 
 n* 7* + ra* (r + p) T 4 Trjrc 2 7? + m a (/ H- p) {' v ; 
 
 We may now advantageously make a first approximation. 
 Neglect I ty in comparison with knmx, that is, assume the 
 permeability to be very large; we have 
 
 m .. 
 
 * * 
 
 ~ ' *-' 
 
 For practical purposes these equations are really suf- 
 ficient. 
 
 We see first that the transformer transforms the poten- 
 tial in the ratio n/vn, and adds to the external resistance 
 of the secondary circuit p a resistance (n* R/m*} + r. 
 This at once gives us the variation of potential caused by 
 varying the number of lamps used. The phase of the sec- 
 ondary current is exactly opposite to that of the primary. 
 
 In designing a transformer it is particularly necessary to 
 take note of equation (9), for the assumption is that a is 
 limited so that I <x may be neglected, The greatest value 
 
184 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 of a is R/{(2 Tt/T) mA\, and this must not exceed a 
 chosen value. We observe that B varies as the number of 
 reversals of the primary current per unit of time. 
 
 But this first approximation, though enough for practical 
 work, gives no account of what happens when transformers 
 are worked so that the iron is nearly saturated, or how 
 energy is wasted in the iron core by the continual reversal 
 of its magnetism. The amount of such waste is easily 
 
 Fio. 66. 
 
 estimated from Swing's results when the extreme value of 
 a is known, but it is more instructive to proceed to a second 
 approximation, and see how the magnetic properties of the 
 iron affect the value and phase of x and y. We shall, as a 
 second approximation, substitute in equations (5), (6), (7) 
 
INDUCTION COILS OR TRANSFORMERS. 185 
 
 values of a deduced from the value of a furnished by the 
 first approximation in equation (9). 
 
 In the accompanying diagram, Fig. 56, Ox represents or, 
 y represents , and z the time t. 
 
 The curves A B CD represent the relations of a and a. 
 E F G the induction a as a function of the time, and HIK 
 the deduced relation between a and t. We may substitute 
 the values of a obtained from this curve in equations (5) 
 and (6), and so obtain the values of x and y to a higher 
 degree of approximation. If the values of a were expressed 
 
 Fro. 57. 
 
 by Fourier's theorem in terms of the time, we should find 
 that the action of the iron core introduced into the ex- 
 pression for x and y, in addition to a term in cos (2 TC t/T) 
 which would occur if a and a were proportional, terms in 
 sin (2 it t/T) and terms in sines and cosines of multiples 
 of Znt/T. It is through the term in sin (%7tt/T) that 
 the loss of energy by hysteresis comes in. 
 
 A particular case, in which to stay at a first approxima- 
 tion would be very misleading, is worthy of note. Let an 
 attempt be made to ascertain the highest possible values of 
 
186 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 a by using upon a transformer a very large primary current 
 and measuring the consequent mean square of potential in 
 the secondary circuit by means of an electrometer, by the 
 heating of a conductor, or other such device. The value 
 of a will be related to the time somewhat as indicated by 
 AB C D E FO in Fig. 57; for simplicity assume it to bo 
 as in Fig. 58; the resulting relations of potential in the 
 
 Fio. 88. 
 
 secondary and the time will be indicated by the dotted line 
 HIJKOL MNP Q. The mean square observed will be 
 proportional to ML . ^L P ; but ML . L P is proportional 
 to EL, hence the potential observed will vary inversely as 
 ^L P, even though the maximum induction remain con- 
 stant. If, then, the maximum induction be deduced on 
 the assumption that the induction is a simple harmonic 
 function of the time, results may readily be obtained vastly 
 in excess of the truth. 
 
TEST OF WESTINGIIOTJSE TRANSFORMERS. 187 
 
 REPORT TO THE WESTINGHOUSE COMPANY 
 OF THE TEST OF TWO G,500-WATT WEST- 
 INGHOUSE TRANSFORMERS. 
 
 BEFORE giving any of the results of the tests I have 
 made with your tran sformers, it will be well to explain the 
 methods of experiment adopted. The instantaneous value 
 at any epoch in the period of the difference of potential 
 between any two points of a circuit in which the potential 
 difference is varied periodically is made effective on the 
 measuring instrument by means of a rotating contact 
 maker attached to the shaft of the alternate current gen- 
 erator. This contact maker was constructed for the King's 
 College laboratory by Messrs. Siemens Brothers. It makes 
 contact once in each revolution for a period of about three 
 quarters of a degree, and breaks it for the rest of the revo- 
 lution. It is entirely insulated, and so can be connected to 
 any part of the circuit. The position of the contact can 
 be varied, and the variation be read off on a graduated 
 circle of 13J inches diameter divided into degrees, and by 
 estimation the variation can be read to one tenth of a 
 degree. The two points between which it is desired to 
 measure a potential difference are connected through the 
 contact maker to a. condenser and a quadrant electrometer, 
 
188 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 as shown in Fig. 59, in which A and B are the points, the 
 potential difference of which at a stated epoch is to be 
 measured, C the revolving contact maker, D the reversing 
 switch of the electrometer, E the condenser, of which the 
 capacity can be varied, F the quadrant electrometer. It is 
 evident that the quadrant electrometer will give a reading 
 proportional to the potential difference of A and B, when 
 C makes contact. If there were no leakage, it would at 
 
 once give this potential. It is to obviate the effect of 
 leakage that the condenser is introduced, and the amount 
 of the effect was determined by varying the condenser 
 thus: When the condenser had capacity 1, 0.5, and 0.2 
 microfarads, the readings of the electrometer for a given 
 potential difference of an alternating current at the posi- 
 tion in the period of maximum electromotive force were 
 138, 136, and 132, respectively. The rate of loss of poten- 
 tial will be proportional to the reciprocal of the capacity, 
 whence we infer that the true reading, if insulation were 
 perfect, would be 1394, and hence the readings are always 
 corrected by adding one per cent. When the potential 
 difference was too great for the electrometer it was reduced 
 in any desired ratio by two considerable resistances intro- 
 duced between the points to be measured in the usual way 
 (Fig. 60). The potential difference may, of course, be 
 measured in other ways. An ordinary voltmeter may be 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 189 
 
 placed between A and B, in which case it must be standard- 
 ized with the contact breaker in circuit; and it will depend 
 for its constant on the duration of the contact, which may 
 vary. Further, it gives, not the difference of potential 
 
 Fio. 60. 
 
 at any definite epoch, but the mean difference for the 
 whole time of the contact. The condenser may be used 
 and its potential be measured by discharge through a gal- 
 vanometer: this is open to the objection that if there be 
 any leakage, the result will depend on the time at which 
 the contact is broken by the condenser key in relation to 
 the time at which it was made by the revolving contact 
 maker. Lastly, a Clark cell may be used, by a method 
 which Major Cardew pointed out to me (Fig. 61), the re- 
 
 iDJUSTABLt RESISTANCES ' (] GALVANO 
 
 rmmwms Q C V 
 
 FlO. 61. 
 
 sistance being adjusted till there is no deflection. This 
 is open to the same objection as the first, namely, that it 
 gives the mean of the potential differences which occur 
 during the contact. By making use of the first-mentioned 
 method we have the means of measuring accurately any 
 potential difference at any epoch of the period, and of 
 knowing the epoch. 
 
190 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 For these experiments two transformers intended to be 
 identical were available, each transforming between 2,400 
 and 100 volts. It was most convenient on account of the 
 resistance available to couple these" transformers up from 
 100 to 2,400 in the first or No. 1 transformer, then down 
 from 2,400 to 100 in the second or No. 2 transformer, and 
 to take up the energy from the second in a non-inductive 
 resistance. The arrangement is shown in Fig. 62. 
 
 The obvious way in returning the efficiency of the com- 
 bination would be to measure, at various epochs of half a 
 period, the potential differences of the terminals of the 
 
 TRANSFORMED NO. 1. TRANSFORMER NO. 2. 
 
 FM.OL 
 
 machine and the current passing in the No. 1 transformer; 
 in like manner, at the same epochs, to measure either the 
 potential differences or the current passing to the non-in- 
 ductive resistance, thence to deduce the power supplied to 
 the first transformer and taken from the second. This 
 would be open to certain objections: we are comparing 
 two nearly equal magnitudes and desire their ratio; the 
 ratio will be afflicted with the full error arising from an 
 error in the determination of either magnitude, and such 
 errors may be material, as the observations are not simul- 
 taneous, and conditions may change between one series of 
 observations and another. 
 
 These objections are avoided by the method adopted. 
 The current from No. 2 is observed at certain epochs, the 
 
TEST OF WESTINGIIOTJSE TfcANSFOttlVlEfcS. 191 
 
 difference of current between No. 2 and No. 1, and the 
 difference of potential difference of No. 2 and No. 1 at the 
 same epoch. These give the currents and potentials of 
 No. 1 at the same epochs as the corresponding determina- 
 tions of No. 2, and the difference will only be afflicted with 
 the proportion of error of those differences. For example, 
 suppose the efficiency of the combination were 90 per cent., 
 and the possible error of determination of power 1 per 
 cent., our result might be anything from 38 per cent, to 92 
 per cent, if made in the obvious way, but if made by dif- 
 ferences the maximum loss would be 10.1 per cent., and 
 the possible least determination of the efficiency would be 
 89.8 per cent. The method is essentially similar to the 
 
 >TO NON-INDUCTIVE 
 * RESISTANCE 
 
 NO. 2. 1 
 
 TO REVOLVING CONTACT MAKER 
 FIG. 63. 
 
 method I described* and subsequently used for testing 
 dynamos. The measurements for difference of potential 
 differences are made as in Fig. 63. For current differences 
 (Fig. 64), where G is a known small non-inductive resist- 
 
 *TO NON-INDUCTIVE 
 
 TO REVOLVING CONTACT MAKER 
 FIG. 64. 
 
 ance, the two currents will, of course, slightly disturb each 
 other, but this is readily allowed for in the calculations. 
 
 * Phil. Trans., 1886, page 347. 
 
192 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 Another method would be to couple them as in Fig. 
 65, G v and #, being equal non-inductive resistances. 
 This arrangement is quite free from disturbance, but re- 
 quires two resistances adjusted to exact equality. A single 
 transformer can be tested in the same way, though in this 
 
 1 
 
 TO REVOLVING CONTACT'MAKER 
 FIG. 65. 
 
 case reliance must be placed upon resistances to reduce the 
 current of the low potential coil, and to reduce the poten- 
 tial of the high potential coil in the ratio of the number of 
 windings in the two coils. 
 
 The current was throughout generated by a Siemens 
 alternator with 12 magnets, run at a speed between 830 
 and 840 revolutions per minute, which gives a frequency 
 of 5,000 per minute, or 83 to 84 per second. 
 
 The first experiment tried * was with the two transform- 
 ers coupled, but with No. 2 transformer on open circuit, or 
 on nearly open circuit, for a high resistance for purposes 
 of measurement was interposed between the terminals of 
 the low resistance coil of No. 2 transformer. The actual 
 
 * So far as I know, the first discussion of endless magnetic circuit transform- 
 ers, based on the actual properties of the material, is in a note by myself (Proc. 
 Roy. Soc., vol. xui., and Tiie Electrician, vol. xvni., p. 421.) Definite results 
 were obtained by methods generally similar to those now used by Prof. Ryan 
 (The Electrical World, Dec. 28, 1889). The theory of transformers is well set 
 forth by Prof. Fleming (The Electrician, April 22 and 29, 1892). 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 193 
 
 results are given in Table IX., and are expressed in Fig. 66. 
 Tables X., XL, and XII. give the results for half power, 
 
 f 
 
 TABLE IX. 
 
 S3 
 
 
 Potential No. 2. 
 
 Potential No. 1. 
 
 
 
 n 
 
 
 Thick Coils. 
 
 Thick Coils. 
 
 
 
 
 
 
 
 
 
 
 s 
 S . 
 
 m 
 
 go 
 
 No. 1. 
 Thick 
 Coils. 
 
 Amperes. 
 
 
 
 
 Square of 
 Volts. 
 Vmean 2 
 = 101.9. 
 
 Watts 
 supplied to 
 No. 1. 
 
 Volts. 
 
 Square of 
 Volts. 
 
 P. D. 
 
 Sec Nos. 
 1 and 2. 
 
 Volts. 
 
 Vineau 3 
 
 
 
 
 = 101.1 
 
 Volts. 
 
 
 
 
 267 
 
 -2.2 
 
 + 25.4 
 
 645 
 
 
 -0.9 
 
 + 26.3 
 
 692 
 
 - 57.9 
 
 270 
 
 -0.3 
 
 + 70.2 
 
 4,9:28 
 
 
 -1.2 
 
 + 71.4 
 
 5,098 
 
 - 21.4 
 
 273 
 
 4-1.1 
 
 + 95.3 
 
 9,082 
 
 
 -1.1 
 
 + 96.4 
 
 9,292 
 
 + 106.0 
 
 276 
 
 + 2.1 
 
 +120.4 
 
 14,496 
 
 
 -1.1 
 
 --121.5 
 
 14,761 
 
 + 255.1 
 
 279 
 
 + 2.8 
 
 +147.7 
 
 21,816 
 
 
 -1.1 
 
 --148.8 
 
 22,140 
 
 + 416.6 
 
 282 
 
 285 
 
 + 3.2 
 + 3.4 
 
 +147.2 
 +119.8 
 
 21,668 
 14,351 
 
 + 0.9 
 
 + 0.7 
 
 +148.1 
 --120.5 
 
 21,935 
 14,520 
 
 + 473.9 
 + 409.7 
 
 288 
 291 
 294 
 
 + 3.5 
 + 3.7 
 + 3.5 
 
 + 97.8 
 + 26io 
 
 9,565 
 5,084 
 676 
 
 + 0.6 
 + 0.4 
 + 0.3 
 
 + 98.4 
 -- 71.7 
 -- 25.97 
 
 9,683 
 5,140 
 674 
 
 + 344.4 
 + 260.3 
 + 90.9 
 
 
 
 
 102,311 
 
 
 
 
 103,935 
 
 2,282.6 
 
194 DYNAMO MACHINERY AND ALLIED 
 
 nearly full power, and full power, and the sets of curves of 
 Figs. 67, 68 and 69 give the results of the table. In 
 these tables the first column gives the position of the con- 
 tact brush in degrees, so that 60 on this scale corresponds 
 
 with a complete cycle. Three degrees are thus -^-^ 
 
 . Oo.o X <v(J 
 
 of a second. The second column of Table IX. is the cur- 
 rent in the thick coil of No. 1 transformer, as determined 
 by the difference of potential at the two ends of a non- 
 inductive resistance in which the current passes. The 
 third column is the potential difference of No. 2 trans- 
 former, a direct determination. The fourth column is 
 solely for the purpose of determining the square root of 
 the mean of the squares of the third column. This column 
 is a direct determination of the difference of potential of 
 No. 1 and No. 2, obtained in the manner explained with 
 reference to Fig. 63. 
 
 The sixth column is the deduced potential difference of 
 the terminals of the thick wire of No. 1 transformer, being 
 the sum of the third and fifth columns. The seventh col- 
 umn, like the fourth, is merely for the purpose of deter- 
 mining the square root of the mean of the squares of col- 
 umn six, while the eighth gives the rate at which power is 
 given out or received by the pair of transformers. 
 
 If the transformers had been exactly equal, the poten- 
 tials for the two given by Table IX. would have been equal, 
 though they would have differed a little in phase owing to 
 the lines of magnetic induction which pass through the 
 non-magnetic space between the two coils of the trans- 
 former.* The difference shows that No. 1 transformer has 
 
 *Prof. Perry has already pointed out that the effect of such an induction 
 cannot be entirely neglected, even in endless circuit transformers. 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 195 
 
 a ratio of transformation slightly greater than No. 2. If 
 we correct the potential of either No. 1 or No. 2, there 
 
196 DYNAMO MACHINEKY AND ALLIED SUBJECTS. 
 
 still remains a difference between them, but this difference 
 will be greatest about when the potentials are nil. This 
 
 is due to the lost induction just referred to. In order to 
 check the conclusion that the two transformers are not 
 
 KHOM WAyHTNCtERMINXtB 
 
 NAAA/WV \^A/Wv* 
 
 ywvwvwvww /WW.VWWM 
 
 TO CONTACT MAMER iEl.ECTROME.1ER, 
 
 Fio.70 
 
 precisely equal, they were directly compared, as in Fig. 70. 
 The transformers were coupled parallel, as in Fig. 70, and 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 197 
 
 the difference of potential of the two high potential coils 
 was measured : the value of its square root of mean square 
 was 12.5 volts, the potential of the transformer being 2,400. 
 This does not necessarily imply that the potentials of the 
 two transformers differ by one half per cent.; it maybe 
 largely due to a difference of phase between the two. 
 
 The current supplied to the No. 1 transformer is to be 
 accounted for by the currents necessary to magnetize the 
 
 Z 
 
 FIG. 71. 
 
 two transformers, and by the local currents in their cores. 
 To ascertain the former, the curve of magnetization of one 
 of the transformers was determined by the ballistic galva- 
 nometer for nearly the same induction as in Table IX., the 
 changes of current supplied by a battery being made by a 
 reversing switch, or by suddenly introducing resistance 
 
198 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 into the primary circuit, and the consequent changes of 
 induction being measured by the galvanometer. The 
 tardiness of change of current in the transformer due to 
 its self induction was sufficiently reduced by using many 
 cells and a considerable resistance. The results are shown 
 in Fig. 71 for a single transformer. In this curve the 
 abscissae are the currents in the thin coil of the trans- 
 
 former, divided by 24 to reduce it to the same effect as it 
 would have had if it had been in the thick coil. The 
 ordinates are the inductions as measured by the kick on 
 the galvanometer, but reduced to a scale to make them 
 directly comparable with the volts when the transformer is 
 used with an alternating current. These results are not 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 199 
 
 given in absolute units. The procedure to determine 
 points on the curve was: first, pass the maximum current 
 corresponding to the point C\ next, suddenly diminish the 
 current by inserting suitable resistance in the thin coil 
 circuit, and observe the kick the drop of ordinate from 
 C to A corresponds to the kick, and the abscissa of A is 
 the current after it has been reduced; next, reverse the 
 current, and observe the kick the kick corresponds to the 
 further drop of ordinates from A to B. In this manner a 
 series of points are determined on the curve. Fig. 72 
 shows the relation between induction and magnetizing 
 current for the pair of transformers, as deduced from the 
 experiments with alternating currents set forth in Table IX. 
 The ordinates in this curve are the area of the curve of 
 potentials of Fig. 66, for the ordinates of this latter curve 
 are the rates at which the induction is changing, while the 
 abscissae are the currents in the thick wire at corresponding 
 times. The points marked in Fig. 73 give the remainder 
 after deducting the magnetizing current as estimates in 
 Fig. 71 from the currents of Fig. 72 that is to say, Fig. 
 71 is corrected first for the small difference in maximum 
 induction; then, corresponding to any induction, the cur- 
 rent is taken from the curve, it is doubled, as there is only 
 one transformer, and the result is deduced from the cor- 
 responding current of Fig. 72. The differences are, the 
 magnetizing current equivalent and opposite in effect to 
 the local currents in the cores. If the local currents were 
 equivalent to a current in a single secondary circuit, the 
 points of Fig. 73 ought to have had the form of the full 
 line of Fig. 73, drawn through the points -f, in which the 
 abscissae are proportional to the potential difference, and 
 
200 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the ordinates to the induction. Returning to Table IX., we 
 find that the fall of potential difference on open circuit in 
 the whole combination is 0.8 volt, and that the loss of 
 
 power in magnetizing the cores and in local currents is 
 222.86 watts, that is, a loss for each transformer of 114.13 
 watts. The total loss of 228 watts maybe divided into 126 
 watts accounted for by hysteresis and 102 watts due to 
 local currents. 
 
 Referring now to Table XI. and Fig. 68, the earlier col- 
 umns explain themselves, but a word is necessary about 
 the last six columns. The watts supplied to No. 1 are 
 simply the products at each time of the volts at its termi- 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 201 
 
 nals and the amperes passing through, similarly to the 
 watts given out by No. 2. We see first that the efficiency 
 of the whole combination with this load is 93.73 per cent., 
 and hence the efficiency of one transformer, if the losses 
 in the two are equal, may be taken as 96.9 per cent. The 
 fall of potential in the whole combination is 6.1 volts, but 
 the fall with no load is 0.8 volt; hence the variation due to 
 the load with constant potential on the thin coil of No. 1 
 is 5.3 volts, or, if the fall of potential in the two transform- 
 ers were equal, which it is not, for a single transformer 
 2.65 volts. Assuming that the transformers are equal, the 
 power lost in resistance would be expected to be the mean 
 of mean current X the difference of potential difference, 
 or 215.4 watts. It is, in fact, 150 watts, as given by multi- 
 plying the square of currents by resistances. But the 
 transformers are not exactly equal, and there is the waste 
 magnetic field, both of which will have a small effect on 
 the distribution of loss between the two classes of loss, 
 viz., that by hysteresis and local currents, and that by re- 
 sistance, but none upon the gross efficiency. 
 
 The other tables, X. and XII., are arranged in exactly the 
 same way as Table XL, but the number of observations 
 on Table XII. is insufficient to bring out all the peculiari- 
 ties of the transformers. 
 
 It has already been stated that, if the loss of potential 
 due to load in the two transformers be equal, it will amount 
 to 2.65 per cent. The following experiment was tried to 
 ascertain if this loss was equal: The transformers were 
 coupled in series as before. The mean potential difference 
 of the thick wire was measured by Thomson's multicellu- 
 lar, and of the thin wire by Thomson's electrostatic volt- 
 
202 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 meter. The mean of a considerable number of experiments 
 is given in the following table, the load being the same as 
 in Table XL, and the results being corrected to the same 
 potential of the thin wire : 
 
 Number. 
 
 Full Load. 
 
 Open Circuit. 
 
 Thomson's 
 Multicellular. 
 
 Thomson's 
 Electrostatic. 
 
 Thomson's 
 Multicellular. 
 
 Thomson's 
 Electrostatic. 
 
 1 
 2 
 
 2,380 
 2,380 
 
 99.8 
 94.2 
 
 2,380 
 2,380 
 
 97.0 
 96.2 
 
 This shows that of a total drop of 4.8 volts, 2.8 volts oc- 
 curred in No. 1, and 2 volts in No. 2. There is no doubt 
 of the fact that the drop is greater in No. 1 than in No. 2, 
 which is connected with the waste field between the two 
 coils. Of course these transformers are intended to work 
 exactly as No. 2 is working, in which case the drop from 
 no load to nearly full load, as shown by this experiment, is 
 2.0 volts. The way in which this waste field causes ine- 
 quality of drop of potential in the two transformers, coupled 
 as in my experiments, is well worthy of careful considera- 
 tion. The waste field is proportional to the current in the 
 transformers, or, better, to the mean of the two currents in 
 ampere turns. The electromotive force due to this waste 
 field will be proportional to the rate of change of the cur- 
 rent. If the current were expressed by a simple harmonic 
 
 curve, the electromotive force due to the waste field would 
 
 jyr 
 also be a simple harmonic curve differing in phase by . 
 
 The curve of potentials is roughly in the same phase as the 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 203 
 
 curve of current. Let A be the amplitude of potential 
 difference of No. 2 transformer, B be the amplitude of 
 difference of potential difference in No. 2, or the potential 
 difference of the thin wire divided by 24. 2 b will be very 
 nearly the amplitude of difference between the thick wires 
 o'f Nos. 1 and 2. The ratios of potentials in No. 1 and 
 No. 2 will then be 
 
 Va? + b 9 
 
 and 
 
 2 a 
 
 a and 1 
 
 or the drop in the first from this cause is three times as 
 great as in the second transformer. We shall return to the 
 waste field immediately. Putting aside harmonic curves, 
 and returning to the facts as they are, the following table 
 gives: first, half the difference of potential difference 
 
 Half Difference of Potential 
 Difference. 
 
 Volts of High Potential 
 Coil Divided by 24. 
 
 Squares of Volts. 
 
 | 15.6 
 
 -5.0 
 
 25.0 
 
 148 
 
 41.3 
 
 1,706.0 
 
 11.3 
 
 74.3 
 
 5,520.0 
 
 10.8 
 
 102.6 
 
 10,530.0 
 
 11.1 
 
 131.3 
 
 17,240.0 
 
 5.5 
 
 147.1 
 
 21,640.0 
 
 1.1 
 
 137.0 
 
 18,770.0 
 
 - 3.1 
 
 119.3 
 
 14,230.0 
 
 - 5.9 
 
 95.1 
 
 9,040.0' 
 
 -12.1 
 
 53.4 
 
 2,850.0 
 
 Square root of mean square = 100.8. 
 
 taken from Table XI., that is, at each instant the drop of 
 potential in No. 2; secondly, the volts of the thin wire of 
 No, 2 reduced for number of convolutions this is of course 
 
204 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 the mean of potential difference between 1 and 2 ; lastly, 
 the squares of these volts. From this we see a mean square 
 100.8 showing the drop in No. 2 to be 2.6 volts out of a 
 total drop of 6.1, and the remainder 2.5, the drop in No. 1. 
 Diminishing these results by 0.4, the half of 0.8, the fall 
 observed with no load, the actual losses from no load to 
 nearly full load will be 2.2 and 3.1. 
 
 Turn now to the last column of Table XI. This gives 
 the difference of potential differences corrected for the loss 
 of volts by resistance. It is shown dotted on Fig. 68; this 
 curve presents one or two peculiar features. It should be 
 possible to infer the form of this curve from the curve of 
 current. The rates at which the mean current is changing 
 are as follows : 
 
 268* 271* 274* 277* 280* 283* 286* 289* 292* .... 
 30.7 24.2 19.2 18.5 18.9 1.7 -9.8 -12.7 -21.7 -28.1 
 
 which happens to come to a scale which can be at once 
 plotted. The points marked are the points of the curve 
 corresponding with the above rates. The agreement of 
 the points with the curve is remarkably close. This ex- 
 hibits very completely the effect of waste magnetic field in 
 this transformer. 
 
 For half power, as taken from Table X., the rates are as 
 follows : 
 
 268*6 271* 274* 277* 280* 283* 286* 289* 291>* 295* 
 14.6 11.5 9.4 10.6 4.4 -4.6 -7.2 -7.5 -13.6 -17.6 
 
 and in the same way in Fig. G7 the dotted curve represents 
 the difference of electromotive force corrected for resist- 
 ance, and the points correspond with the above rates. 
 
TEST OF WESTINGHOTJSE TRANSFORMERS. 205 
 
 Fig. 74 gives the efficiencies for the combined transform- 
 ers in terms of the load. This curve is the hyperbole : 
 
 Efficiency = 100 . 
 
 where A = 228, the loss by hysteresis; 
 
 B = 0.005, and mainly depends upon the waste 
 
 field; 
 
 C = 0.0000035, and is mainly the loss by resist- 
 ance; 
 
 X = load in watts. 
 
 To sum up, I find that the efficiency of the transformer 
 at full load would be 96.9 per cent. ; at half load, 96 per 
 
 JOOi 
 
 Load in 103 watte. 
 Fio. 74. 
 
 cent.; and at quarter load, over 92 per cent. The magnet- 
 izing current of the transformer amounts to 114 watts, or 
 1.75 per cent. The drop of potential from no load to full 
 load is between 2 per cent, and 2.2 per cent. 
 
 In conclusion, I wish to express my thanks to Mr. Wil- 
 son, of King's College; this gentleman carried out the 
 experiments under my direction, and made nearly all the 
 numerical calculations and drew most of the curves for me. 
 
DYNAMO MACIIINEKY AND ALLIED SUBJECTS. 
 
 x 
 
 ential No. 
 Thick Coil. 
 
 Pot 
 
 SON; in s JII-'.I.HI. > jo n\>.<\ 
 
 Diffe 
 No 
 
 ! 
 
 H-i 
 % 
 
 5* 
 
 uop 
 
 oiaiio papi 
 i aujjojuxg 
 
 no 
 
 i (s r i.i} i aujjojuxg jo spvaq 
 
 e cT o e o co ao ci 
 
 g g a g 5 t 8 li 
 
 ' 
 
 * o ec o> eo t- 
 
 S Si 69 
 
 1 1 
 
 ooooiooooia 
 
 oooomoooifto 
 
 t- CO I- OS C OC 
 
 OOJOOOOO 
 
ST OF WESTINGilOUSE TRANSFORMERS. C J07 
 
 luiiuejoj jo 8ou8jajji(i 
 
 putt sisaaajsA'H 
 
 ss by Res 
 and pro 
 Waste 
 
 -onn sassoq 
 
 + + + + i 1 I 1 
 
 1 1 ++++++++ 
 
 s 8 f.6 6 fe' i 6 
 
 i + + + + + i i i 
 
 " 1 i S i 1 1. i [8 E 
 
 !..** 
 
 
 OX cxj pai[ddns sa^AV 
 
 SIIOQ 
 
 ui 
 
 jo 
 
 SJIOA jo a-mbs 
 
 *M ^ 
 
 ll 
 
 apaiQ papiAtQ uo qsnag 
 Suuo[dxa jo 
 
 to if of 
 
 i 
 
 . 
 oo of 
 
 1 1 1 1 
 
 o o o M e o o o > to 
 
 oooooooooo 
 
 
DYNAMO MACHINERY AND ALLIED SUBJECT* 
 
 looq pins 8;s<u9isA'H A'q asoq 
 
 Loss by 
 ance and 
 ably Wast 
 
 
 pinunooovun 
 
 g -OK A'q ?no U9A 
 
 'I 'ON oj pajiddns KJ;I?M. 
 
 ;o 
 
 +-H-HH-I 1 i i 
 
 + , 
 
 v s 
 
 /-* 
 
 SIS 
 
 1 1 1 1 
 
 o ** it- 
 
 
 
 gg 
 
 Mil +HH-HH- 1 
 
 i i I+++-H- 
 
 tential Diffe 
 ence No 1. 
 Thick Coil. 
 
 S 
 
 r 
 
 8110 A. .'.n:it I s 
 
 81IOA 
 
 S1IOA T.PUH 
 
 -MIIOO 3|0|i|x 
 
 'S'86 = 
 
 SHOO 3pmx 
 PUB i '8o^ uj 3iu).uii k ) jo 
 
 i- c- 1 e o o o 
 
 I I I I 
 
 e8S|lll|5 
 
 ^^S-|$ 
 
 -f-f -H-H-+-H- 
 
 i -f 
 
 80^ 
 
 ? pas [ 
 
 Jjotqj, -5 
 
 o? o - C c 07 ec so 
 
 I I I-HH-M-++ 
 
 SSSteSffigfcSS 
 
 i NT FT-H--H- 
 
 qsnag 
 
 no 
 spwaq 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 209 
 
 Potential No. 2. 
 Thick Coil. 
 
 *6'06 = eiream^ 
 sil A jo Qjtmbs 
 
 rp 1 Q Q eg a 
 
 98893 S 
 
 eT o oo ec ^* 
 
 
 
 i 
 Q 
 
 .S 
 
 2 
 
 Si 
 
 1 
 
 r? c - ?> 
 
 S 8 g g 8 
 
 + -f- + + 4- 
 
 s|U>o sioiqj, 'Z 
 PUB i -so\i u\ ^uajjno jo uB9ft 
 
 * * * 00 Qt 
 
 S2 S 8 S S 
 
 + + + + + 
 
 Current No. 1. Thick Coil. 
 
 saj^dtay 
 
 o o> to e* GO 
 
 a s s a 
 
 + + + + + 
 
 Current Difference. Thick Co. Is. 
 Nos. 1 and 2. 
 
 s.u^duiv 
 
 * o w o o 
 -J c> ot ' eo 
 1 + + + + 
 
 > 
 
 1-1 TH 0> 1> 1-1 
 
 o 1-5 ot co <* 
 + 1 1 1 1 
 
 uonoayaa 
 pjoajjoo 
 
 | fe te | 
 
 uonoatpd 
 paAJdsqo 
 
 fe fe ^ 38 X 
 
 ^H ^ ^-H O| 
 
 Current No. 2. 
 Thick Coil. 
 
 saaedrav 
 
 00 O CO CO 
 
 S S S S 5 
 
 + -f + + + 
 
 uowoagaa ps^oaojoo 
 
 gw o os o 
 8 5! S 8 
 
 uonoayaa pQAjasqo 
 
 SCO f> i-l t-. 
 O C* 00 O 
 <?i ^S* CO d 
 
 "IPO papiAta 
 no qsrug Saijoidxa jo spaq 
 
 O O C*l CO ^* 
 
 S K 8 V i 
 
210 DYNAMO MACHINKRY AND ALLIED SUBJECTS. 
 
 s s 
 
 + i i 
 
 ^-. co o 
 
 iwooq pav sjs^jaja.f H ^q ssoq 
 
 2 
 
 88 g 
 
 + + + -K 
 
 J5f2' 
 
 i 
 
 O O O CO 
 
 'aoj 
 pe?unooovun sassoq 
 
 i 
 
 + Hh + 1 
 
 00 09 CO 
 
 8 i S 
 
 t- 
 
 i 
 
 *l 'OK 0} penddns snAV 
 
 ! ! ! 
 
 I s 
 
 put? i -BOM ai n?nujoa jo UTOK 
 
 8 S 
 
 
 
 ntial Differe 
 Thick Coils. 
 Nos. 1 and 2. 
 
 ei 10 o co o 
 
 8 2 S S 
 
 + + 7 Hh + 
 
 5 s; s s 
 + + + 1 1 
 
 noo papula 
 
 i (<n.i ; | >uijo|' I x [4 jo spvi 
 
 g S 1 
 
THEORY OF THE ALTERNATE CURRENT DYNAMO. 
 
 \ 
 
 THEORY OF THE ALTERNATE CURRENT 
 DYNAMO. 
 
 ACCORDING to the accepted theory of the alternate current 
 dynamo, the equation of electric current in the armature 
 is y y + R y periodic function of t, where y is a constant 
 coefficient of self induction. This equation is not strictly 
 true, inasmuch as y is not in general constant,* but it is a 
 most useful approximation. My present purpose is to in- 
 dicate how the values of y and of the periodic function 
 representing the electromotive force can be calculated in a 
 machine of given configuration. 
 
 To fix ideas, we will suppose the machine considered to 
 have its magnet cores arranged parallel to the axis of rota- 
 tion, that the cores are of uniform section, also that the 
 armature bobbins have iron cores, so that we regard all the 
 lines of induction as passing either through an armature 
 coil or else between adjacent poles entirely outside the 
 armature. The sketch, Fig. 75, shows a development of 
 the machine considered. The iron is supposed to be so 
 arranged that the currents induced therein may be neg- 
 lected. We further suppose for simplicity that the line 
 integral of magnetic force within the armature core may 
 be neglected. 
 
 * See chapter on the " Theory of Alternating Currents" in this volume. 
 
212 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 i 
 
 Let A t be the effective area of the space between the pole 
 piece and armature core when the cores are in line, J, the 
 distance from iron to iron. 
 
 Let A 9 be the section of magnet core, 7, the effective 
 length of a pair of magnet limbs, so that /, may be re- 
 
 Fro. 76. 
 
 garded as the length of the lines of force as measured from 
 one pole face to the next. 
 
 Let m be the number of convolutions in a pair of magnet 
 limbs, and 
 
 n the convolutions in one armature section; 
 
 T the periodic time. 
 
 The time is measured from an epoch when the armature 
 coil we shall consider is in a symmetrical position in a field 
 which we shall regard as positive. 
 
 x and y are the currents in the magnet and armature 
 coils, the positive direction being that which produces the 
 positive field at time zero. 
 
 At time t the armature coil considered has area Af, 
 
 = ft + ft, cos (2 n t/T) + ft, cos (4 it t/T) + etc., 
 
THEORY OF THE ALTERNATE CURRENT DYNAMO. 213 
 in a positive field; and area A" 9 
 
 = b -b, cos (2 n t/T) + b, cos (4 n t/T) - etc., 
 in a negative field, where 
 
 and 
 
 &o ~ &, + t>, + - - - = 0. 
 
 The coefficients b , b } , etc., are deducible by Fourier's 
 theorem from a drawing of the machine under considera- 
 tion. 
 
 Let / be the total induction in the magnet core, and let, 
 at time t, /be distributed into /' through A' 9 I" through 
 A" and /'" as a waste field to the neighboring poles. 
 
 The line integral of magnetic force from the pole to 
 either adjacent pole is /'"/&, where k is a constant. 
 
 We have first to determine /', 1", /'", in terms of x 
 and y. 
 
 Take the line integral of magnetic force in three ways 
 through the magnets, and respectively through area A', 
 through area A", and across between the adjacent poles 
 
 f + 3 l ' ~' = 4 * m X ~~ 4 * H y 
 
214 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 whence 
 
 A,' -A 
 
 When t, x and y are given, this would suffice to determine 
 1 by means of the known properties of the material of the 
 magnets as represented by the function /. We will, how- 
 ever, consider two extreme cases between which other cases 
 will lie. 
 
 First. Suppose that the intensity of induction in the 
 magnet cores is small, so that /,/(//^4 a ) may be neglected, 
 the iron being very far from saturation. We have 
 
 = 2T !m (A ' " A ") x + n - (A * + A 
 
 7t ( (. 27Tt . 67Tt \ 
 
 = -y- 1 m \t t cos -y- -f J, cos -^ + ...) 
 + n -f b, cos -- + . . . 
 
 We see that the coefficient of self induction y in general 
 contains terms in cos (4 n t/T). 
 Second, In actual work it would be nearer the truth to 
 
THEORY OF THE ALTERNATE CURRENT DYNAMO. 215 
 
 suppose that the magnetizing current x is so great that the 
 induction / may be regarded as constant, and the quantity 
 l^f(I/A^ as considerable. But as small changes in / 
 imply very great changes in l^f(I/A^), its value cannot be 
 regarded as known. We have then 
 
 (A* A 
 I-- 1 2l 
 
 A/ -A" 
 - 
 
 whence 
 
 r r , = (A; -A,") i 
 (A: - A,")' 
 
 (A,' - A,") I 
 ~ A^ + AS' + Zkl, 
 
 4 A,' A," + 2 k I, (A,' + A,") titny 
 ' " 
 
\ 
 216 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 For illustration, consider the simplest possible case: let 
 b = b. = $A t , and b 9 = ft, = . . . = 0, and let 2 k Z, be 
 negligible; we have 
 
 T/ , 2jrtf, .2 TT t 47rny 
 
 I - I = Jcos -y- + A l sin 9 ^- . -y^, 
 
 and the equation of current will be 
 
 instead of the simple and familiar linear equation. 
 
THE ELECTRIC LIGHTHOUSE OF MACQUAKIE. 217 
 
 THE ELECTRIC LIGHTHOUSES OF MACQUARIE 
 AND OF TINO. 
 
 THE subject of the use of the electric light in light- 
 houses was fully discussed at the Institution in 1879, when 
 papers by Sir James Douglass, M. Inst. C.E., and by Mr. 
 James T. Chance, Asso. Inst. C.E., were read.* 
 
 The subject has been further elaborately examined by 
 Mr. E. Allard,f and more recently in practical experi- 
 ments made at the South Foreland, exhaustively reported 
 on by a committee of the Trinity House.J The justifica- 
 tion of the present communication is that, at the light- 
 houses of Macquarie and of Tino, the optical apparatus is on 
 a larger scale than has hitherto been used for the electric 
 arc in .lighthouses, and presents certain novel features in 
 the details of construction. Further, as regards the elec- 
 trical apparatus, tests were made upon the machinery for 
 Macquarie when it was in the hands of Messrs. Chance 
 Brothers & Company, which still possess some value, 
 although five years old; and, in the case of Tino, the 
 machines are practically worked together in a manner 
 not previously used otherwise than by way of experiment. 
 
 * Minutes of Proceedings of the Inst. C.E., vol. LVII., pp. 77 and 168. 
 t " M6moire sur leg Phares filectriques," 1881. 
 
 % " Report into the relative merits of Electricity, Gas, and Oil as Lighthouse 
 Illuminants." Parts 1 and 2, PP. 1885, 
 
218 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 In the case of both lighthouses, Messrs. Chance Brothers 
 & Company, of Birmingham, entered into a contract for 
 the supply of all the apparatus required, including engines, 
 machines, conductors, lamps, optical apparatus, and lan- 
 terns; and Sir James Douglass, engineer-in-chief of the 
 Trinity House, acted as inspecting engineer to the respec- 
 tive colonial and foreign governments. 
 
 As these two lighthouses present many features in com- 
 mon, it may be most convenient to give a full description 
 of the earlier lighthouse, and then limit the description of 
 Tino to those points in which it differs from Macquarie. 
 
 MACQUARIE. 
 
 This lighthouse is situated on South Head, near Sydney, , 
 the precise position being shown in a copy from the 
 chart, Fig. 76. A lighthouse was first placed at this im- 
 portant landfall in 1817. The focal plane is 346 feet 
 above the sea, and the distance of the sea horizon is there- 
 fore 21.6 nautical miles, and the range about 27 nautical 
 miles for an observer 1 5 feet above the sea. 
 
 Optical Apparatus. The light is a revolving one, giv- 
 ing a single flash of eight seconds' duration every minute. 
 On account of the considerable altitude of the lighthouse, 
 it was necessary to secure that a substantial quantity of 
 light should be directed to the nearer sea; but it was also 
 essential, on account of the exceptional power of the ap- 
 paratus, that this dipping light should only be a small 
 fraction of that sent to the horizon, otherwise its effect 
 would be excessively dazzling. Many years ago Mr, 
 
THE 
 
 ELECTRIC LIGHTHOUSE OF MACQUARIE. 219 
 
 EAST MAITLAND JN. 
 
 ?/ A NEWCASTLE 
 
 FIG. 7<J. 
 
220 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 James T. Chance urged that it was not wise to make use 
 of very small apparatus for the electric arc, because a 
 larger apparatus renders it possible for the optical engineer 
 to effect with greater precision the distribution of light 
 which is most desirable, and because any trifling error 
 which may occur in the position of the electric arc lias, 
 with the larger apparatus, a less marked effect on the light 
 as seen from the sea. In the lighthouses of Souter Point, 
 the South Foreland, and the Lizard, the third order ap- 
 paratus of 500 millimetre focal length was adopted. 
 Optically, the larger the apparatus used the better, but 
 there might be some question whether, on purely optical 
 grounds, the advantage of going beyond the third order is 
 sufficient to justify the additional expense; but in the case 
 of a revolving apparatus the third order is a very incon- 
 venient size for the service of the lamp it is too large to 
 be conveniently served from the outside, and too small to 
 admit the attendant within it with comfort. With the 
 large currents, which are now easily obtained and are 
 likely to be used in lighthouses, a first or second order 
 apparatus has the further advantage that it is less liable to 
 injury from particles thrown off from the heated carbons. 
 In the case of Macquarie, it was decided to adopt an ap- 
 paratus of the first order, 920 millimetre focal length; it 
 was further decided that the optical apparatus should pro- 
 duce its condensing effect by means of a single agent that 
 is to say, the vertical straight prisms which were used in 
 Souter Point and other revolving electric lighthouses 
 should be dispensed with. The condensation and dis- 
 tribution of light necessary may be obtained by means of 
 a single agent, with apparatus such as has been pro- 
 
THE ELECTRIC LIGHTHOUSE OF MACQCJARLE. 
 
 posed by Mr. Alan Brebner, Jr., Asso. M. Inst. O.E.;* 
 but this construction is open to the objections that it 
 is somewhat costly, and that it increases the length of 
 the path of the rays through the glass, and consequent 
 absorption. A practically better plan is to adopt forms 
 not differing very greatly from those introduced by 
 Fresnel; to specially arrange them for the purpose in 
 hand, and to accept certain consequent minute deviations 
 from a mathematically accurate solution for the sake of 
 advantages of greater importance when all the actual con- 
 ditions are taken into account. Fig. 77 shows the optical 
 apparatus in vertical section: the upper and the lower 
 totally reflecting prisms are, as is usual in revolving lights, 
 forms of revolutions about a horizontal axis; they direct 
 the light incident upon them to the horizon and the dis- 
 tant sea from 10' above the horizon to 30' below; they are 
 specially adjusted to distribute the light in azimuth over 
 the arc of 3 necessary for a proper duration of flash. 
 
 The refracting portion of the apparatus has the profile 
 so calculated that the central lens and the three rings 
 next to the lens above and below direct their light to the 
 horizon without vertical divergence, except what is due to 
 the size of the arc. The light for the nearer sea is obtained 
 from the remaining ten lens segments, Nos. 5 to 9 in- 
 clusive, above and below the centre, counting the centre as 
 No. 1, the distribution being according to the following 
 table, in which the first column gives the denomination* of 
 the elements of the lens in accordance with the numbers 
 marked upon the section ; the second, the angle between 
 
 * Minutes of Proceedings of the Inst. C.E., vol. LXX., p. 386. 
 
222 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 L II. HI. 
 
 O I It O t II 
 
 gtop 10 2 30 59 
 
 8 2 30 59 5 8 52 
 
 7 " 10 2 87 30 
 
 6 10 1 30 
 
 5 " .... 10 100 
 
 Sbottom.. 10 100 
 
 6 " 10 1 30 
 
 7 " 1 80 3 44 27 
 
 8 3 44 27 5 50 41 
 
 9 " 5 50 41 7 46 57 
 
 the direction of the sea horizon and the ray emerging from 
 the upper limit of the element; the third, the angle be- 
 tween the direction of the sea horizon and the ray from 
 the lower limit of the element, the negative sign denoting 
 that the emerging ray is above the horizon. This practice 
 of appropriating certain elements of the apparatus to dif- 
 ferent distances on the sea was first introduced by Mr. 
 James T. Chance, in the lights of the South Foreland ex- 
 hibited in January, 1872. 
 
 The ray, dipping at an angle of 7 46' 57' below the 
 horizon, will strike the sea at mile, while 5 8' 52' cor- 
 responds to } mile, 2 37' 30' to 1 mile, 1 30' to 2 miles, 
 1 to 2i miles, and 30' to about 4 miles. Thus the direct 
 light begins at about i mile from the lighthouse. From | 
 mile to | mile the sea receives light from one element of 
 the apparatus, from J to 1 mile from two elements, from 
 1J mile to 2 miles from three elements, from 2 to 2 miles 
 from four elements, and beyond 2 miles from six 
 elements; the upper and lower totally reflecting prisms 
 come in aid at about 5 miles. The main power of the ap- 
 paratus is hardly attained till a distance of 8 or 10 miles. 
 Fig. 78 is a sectional plan of the apparatus by a horizontal 
 
THE ELECTRIC LIGHTHOUSE OF MACQITARIE. 
 Fio. 77. Fia. 79. 
 
 FIG. 78. 
 
 FIG. 80. 
 
224 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 plane through the focus. It will be seen that a dioptric 
 mirror is placed on the landward side of the arc. This 
 mirror is arranged to form the image of the arc at one 
 side of the carbons, so avoiding the interception of light 
 which would result if the mirror were used in the ordinary 
 way, and contributing to the horizontal divergence neces- 
 sary. Further horizontal divergence is given by the form 
 of the lens. In the ordinary revolving light the inner face 
 of the lens is plane; here it is cylindrical, the axis of the 
 cylinder being vertical. This method of obtaining hori- 
 zontal divergence is a modification of a proposal of Mr. 
 Thomas Stevenson,* M. Insl. C.E.; it is not mathemati- 
 cally accurate, inasmuch as the cylindrical form of the 
 inner face of the lens not only displaces the emergent ray 
 horizontally, but also, in the case of rays not in the verti- 
 cal nor horizontal plane through the focus, to a small ex- 
 tent vertically; but the error is easily calculable, and is 
 unimportant, provided the lens is narrow, and the hori- 
 zontal divergence of the beam moderate. Fig. 79 shows a 
 complete panel in elevation with revolving carriage. Fig. 
 80 shows the plan of the service table of the pedestal and 
 lamp table. A new construction was adopted for the gnn- 
 metal framework of the optical apparatus to reduce the 
 interception of light by the frame to a minimum. The 
 metal segment A, Fig. 81, forms part of the lower prism 
 frame, B part of the upper frame, while C and D are parts 
 of the frame for the refracting portion of the apparatus; 
 uprights E support the upper prism frames without throw- 
 ing weight on the lens frames. With the ordinary con- 
 
 *" Lighthouse Construction and Illumination," p. 186. 
 
THE ELECTRIC LIGHTHOUSE OF MACQUARIE. 225 
 
 structions of frame, Figs. 82 and 83, the equivalent of these 
 ring segments A and B would intercept about double as 
 much light as in this new construction. 
 
 E 
 
 Fio. 81. 
 
 FIG 82. 
 
 Fio. 83. 
 
 Mechanism for Rotation. The pedestal is similar to 
 those designed by Sir James Douglass to permit the light 
 keeper to obtain access from below to the interior of the 
 apparatus without in any way interfering with its rotation. 
 The clockwork is fitted with the governor, and maintain- 
 ing poweV used by Messrs. Chance Brothers & Company 
 for the last twelve years. The roller ring may be men- 
 tioned as of an improved type, for although it has been 
 used for some years in all Messrs. Chance's lights, it has 
 not been described before. The rollers and roller paths 
 which carry the whole weight of the optical apparatus 
 have long been made conical, so that the surfaces roll 
 
226 DYNAMO MACHINERY AND ALLIED SUfeJECTS. 
 
 upon each other without twisting. There is consequently 
 a very considerable radial force on each roller tending to 
 force it outwards; the reaction against this force causes a 
 very important part of the total frictional resistance. Fig. 
 84 shows a portion of the roller ring and one of the conical 
 
 Fio. 84. Fio. 86. FIG. 86. 
 
 rollers, according to the old construction; Figs. 85, 86, ac- 
 cording to the improved construction; in the former it 
 will be observed that the thrust of the roller is received on 
 a collar; in the latter, on the end of a pin. The reduction 
 of friction is practically very considerable, and although of 
 small importance in a slow-moving apparatus like Mac- 
 quarie, is of great importance in heavier and quicker ap- 
 paratus; for example, the triple flashing light at Bull 
 Point, in Devonshire. 
 
 Lamp*. These are of the Serrin type, and were supplied 
 by Baron De Meritens. 
 
 Lamp Table. The arrangements for rapidly changing 
 electric lamps, and for substituting gas or oil when de- 
 sired, are shown in Figs. 87, 88, 89, and 90. 
 
 The intention was to use a gas lamp in clear weather, 
 and half power or full power electric light in thick 
 weather, according to the opacity of the atmosphere; but 
 the author understands that in practice the electric arc is 
 
THE ELECTRIC LIGHTHOUSE OF MACQUARIE. 227 
 
 always used. The paraffin oil lamp is intended as a re- 
 source in case of failure of the supply of gas. 
 
 FIG. 87. 
 
 Fio. 88. 
 
 FIG. 89. 
 ARRANGEMENT FOR OIL LAMP. 
 
 FIG. 90. 
 ARRANGEMENT FOR GAS BURNER. 
 
 Focussing the Arc. Two approximately rectangular 
 prisms are fixed upon the mirrcr frame at about 90 from 
 
228 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 each other, the longer face of each is plane, the other two 
 faces convex, of such curvature as to form a good image 
 of the arc upon the service table, as shown in Fig. 91. 
 
 Fio. 91. 
 
 During daylight, a pointed sight or focimeter is placed at 
 the position of the image formed by the lens of an object 
 on the horizon; this then is the position which the arc 
 should occupy. A sight is next taken over the focimeter 
 into one of the adjusting prisms, and a bright object such 
 as a threepenny piece placed on the service table, is moved 
 about until its centre is seen in the prism, exactly upon 
 the point of the focimeter; a mark is made in the then 
 position of the object. When the arc is corrootly adjusted, 
 its image on the service table will be at the point where 
 the mark is made. Two prisms are used in order to secure 
 that the arc shall be in the centre of the apparatus as well 
 as at the correct level. 
 
 Lantern. The lantern is of the well known Douglass 
 type.* 
 
 * Minutes of Proceedings of the List. C.E., vol. LVI., p. 77. 
 
THE ELECTRIC LIGHTHOUSE OF MACQUAKIE. 229 
 
 Dynamo-Electric Machines. Two alternate current ma- 
 chines, with permanent magnets manufactured by De 
 Meritens, were supplied. Each machine has five rings in 
 its armature, and in each ring there are sixteen segments. 
 In supplying one arc for a lighthouse the machine runs 
 about 830 revolutions per minute, and gives a current of 
 55 amperes when half the coils are used, and of 110 when 
 the whole of the machine is in action, the internal resist- 
 ance in the two cases being 0.062 and 0.031 ohm. It is 
 unnecessary to give a description of the machine as its 
 general construction and dimensions are well known, but 
 some numerical details are given below. 
 
 Engines. Each machine is driven by an 8 h. p. Crossley 
 gas engine through a belt without countershafting. 
 
 Tests. Whilst the dynamo machines were at the works 
 of Messrs. Chance Brothers & Company, a series of ex- 
 periments was made in March, 1881, to determine their 
 properties. The time is long passed when it would be 
 profitable to give the details of these experiments, but the 
 general conclusions drawn at the time are still interesting. 
 When the external resistance was a metallic conductor 
 with small self induction, it was found that with varying 
 resistance and speed the currents observed agreed fairly 
 
 well with calculation from the formula 
 
 in which R is the total resistance of the circuit, y the self 
 induction, and T the periodic time. When the machine 
 
 * Lectures on the "Practical Application of Electricity. 1 ' Session 1883-83. 
 Paper on " Some Points in Electric Lighting," reprinted in this volume. 
 
230 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 was running 830 revolutions per minute A = 67 volts and 
 
 = -1 9 ? i 11 onm s<i"aivl, hence y = 6.4 x 10* 
 
 centimetres. The eighty sections of the machine ;t it- 
 arranged four in series, twenty parallel. For a single sec- 
 tion the value of y would be 32 x 10* centimetres. The 
 maximum induction in the core, which has an area of 5 
 square centimetres, is 24,600 or 4,920 per square centi- 
 metre. The loss of power was greater when the machine 
 was doing little or no external work than when that work 
 was great. This is clearly seen in the following table : 
 
 Current amperes ............................... ........ 7.70 73. GO 
 
 Electrical work h. p ................................... 0.69 5.66 
 
 Mechanical work applied ............................... 8.09 6.56 
 
 Loss ................................................. 2.40 0.89 
 
 Photometric experiments were made upon the arc, and 
 simultaneous measurements of effective power applied and 
 of current passing. The red light was measured through 
 bright copper ruby glass, and the blue through a solution 
 of sulphate of copper and ammonia. The h. p. was meas- 
 ured by a transmission dynamometer; but the results must 
 be accepted with some reserve, on account of the difficulty 
 of ascertaining the mean tension in a strap which is con- 
 stantly varying. The oscillations of the dynamometer 
 were damped by a dashpot containing tar. 
 
 Half Power. Full Power. 
 Redcandles ........................................ 1,988 I.'"* 
 
 Blue " .......................................... 4,079 11,382 
 
 Current (amperes) .................................... 54.5 105 
 
 Mechanical power applied (h. p.) .................. 4.5 6.9 
 
 Power expended in heating conducting wires (h, p.) 0.34 0.95 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 231 
 
 The results illustrate the fact that, as the current in- 
 creases, the total light increases in a higher ratio, red 
 light in a slightly higher ratio, and blue in a considerably 
 higher. 
 
 The machinery for this lighthouse was sent out to New 
 South Wales in November, 1881, and was put up and 
 started under the superintendence of Mr. J. Burnett, the 
 architect of the colony, to whom is mainly due the success 
 of the whole from the first start. The glare of the light 
 upon the sky is said to have been seen at a distance of 
 over GO miles, far beyond the distance at which it would 
 cease to be directly visible. The only criticism from 
 mariners has been that when somewhat near the light- 
 house the flashes are so bright as to dazzle the eye. This 
 is an excellent proof of the power of the light, as a much 
 smaller proportion of the light is directed upon the nearer 
 sea than in any previous lighthouse. The lesson is that 
 with powerful electric lighthouses almost all the light 
 should, in ordinary weather at least, be directed to the 
 horizon, and that the quantity thrown upon the nearer sea 
 must be strictly limited. This is only possible when the 
 focal length of the apparatus is large. 
 
 TINO. 
 
 This station is on a small island at the mouth of the 
 Gulf of Spezia. Fig. 92 is copied from the chart of the 
 neighborhood. The focus is 386 feet above sea level. The 
 distance of the sea horizon is 22.7 nautical miles, and 
 the range practically 28 miles. The conditions, therefore, 
 
232 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 were very similar to those of Macquarie, with the excep- 
 tion that it was required to throw some light dowii into 
 the channel between Palmaria and Tino. The lighthouse 
 itself presents some interesting historical features. The 
 buildings were originally a place of defence against the 
 pirates who occasionally made descents upon the coast. 
 
 Fio. 92.-(Scale t 22 miles - j i nc h.) 
 
 Subsequently a coal fire lighthouse was established, and in 
 the spring of 1885 part of the stock of lignite was still 
 found to be in some of the buildings, where it had been 
 lying for fifty years. In 1839 a dioptric light was estab- 
 lished, one of the earliest of Fresnel's types, the lens ring 
 being replaced by short straight prisms, which formed by 
 no means a bad approximation, and could be ground with- 
 out special machinery. The present electric lighthouse has 
 been in contemplation for several years. 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 233 
 
 Optical Apparatus. The distinctive character of the 
 light is a triple flash every half minute. The apparatus for 
 producing this effect is of the general form introduced by 
 the author in 1874. In October of that year he issued a 
 pamphlet pointing out the several advantages of group 
 flashing lights, showing for the first time a simple dioptric 
 apparatus suitable to their production, and also pointing 
 out how easy it is to give the group flashing effect with 
 catoptric apparatus. Since that time a large number of 
 dioptric group flashing lights have been made by Messrs. 
 Chance Brothers & Company, and some also in France, 
 and Mr. Allard has incorporated group flashing lights in 
 the system of distinctions he recommends ; also a consider- 
 able proportion of the light vessels on the English coasts 
 have been converted into group flashing lights of the 
 catoptric system. On the ground of economy the second 
 order apparatus of 700 millimetre focus was adopted in the 
 case of Tino. It is just large enough for tolerably con- 
 venient service of the lamp by an attendant entering with- 
 in the apparatus. The apparatus, shown in vertical 
 section in Fig. 93, and in horizontal section through the 
 focus in Fig. 94, has twenty-four sides, eight groups of 
 three; one group of three is shown in elevation in Fig. 95. 
 The horizontal divergence is obtained in exactly the same 
 way as at Macquarie, excepting that no mirror is used. 
 The metal framework, however, approximates to the 
 ordinary type, as the type used at Macquarie would have 
 been costly when applied to a triple flash light. The dis- 
 tribution of light vertically is as follows : upper and lower 
 prisms, and the central lens, with the two lens rings next 
 adjoining it, all to the horizon and most distant sea. The 
 
234 DYNAMO MACHINERY AND ALLIED* SUBJECTS. 
 
 Fio. 94. 
 
 FIG. 93. 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 235 
 
 lens and lens rings direct their rays according to the fol- 
 lowing table, which is arranged in exactly the same way as 
 the table already given for Macquarie: 
 
 i. n. in. 
 
 7 top 31 35 3 16 
 
 6 " .. 200 
 
 5 " .. 1 30 
 
 4 " .. 100 
 
 4 bottom .. 45 
 
 5 " . .. 30 
 
 6 " .. 30 
 
 7 " all to the horizon. 
 
 No. 7 bottom was directed wholly to the horizon, in 
 order to avoid the horizontal bar of the lantern. It will 
 be observed that the quantity of light thrown upon the 
 nearer sea is much less in the case of Tino than in that of 
 Macquarie, and that greater reliance is placed upon the 
 accuracy with which the arc can be kept in focus; ex- 
 perience has justified these changes, as improvements of a 
 perfectly safe nature. 
 
 A small part of each flash is bent downwards and dis- 
 tributed over the channel between Tino and Palmaria, by 
 means of subsidiary prisms fixed upon the lantern, shown 
 at X, Fig. 93. These subsidiary prisms are really super- 
 fluous, as the scattered light from the beams overhead is 
 found to be as effective at this short distance. Fig. 90 
 shows the plan of lamp shunting table and service table. 
 
 Engines. As there is no water upon the island, the 
 practice of the Trinity House was followed, and two of 
 the Brown hot air engines were supplied, each driving 
 through a countershaft one of the machines. The 
 countershafts could be connected by means of a Mather 
 
236 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 and Platt friction coupling, so that the two machines 
 could be driven together, or either machine from either 
 engine. Drawings of the Brown engines are given in Sir 
 
 Fio. 96. 
 
 James Douglass's Paper.* The accompanying indicator 
 diagrams Figs. 97 and 98.were taken from the compressing 
 and working cylinders. Whilst these diagrams were taken, 
 the effective power developed was measured by a friction 
 brake on the driving pulley, and was found to be 9.1 h. p. 
 Thus of 33.1 h. p. indicated in the working cylinder, 17.7 
 h. p. is employed in compressing the air, 6.3 h. p. is wasted 
 in friction in various parts of the machine, and only 9.1 
 h. p. is effective upon the brake. The engines consume 
 about 4 Ibs. of coke per effective h. p. per hour. In future 
 lighthouses, when a steam engine cannot be employed, it 
 would be preferable on every ground to use gas engines, 
 and manufacture on the spot either Dowson gas or 
 
 * Minutes of Proceedings of the Inst. C.E., vol. LVII., Plate 6. 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 
 
 237 
 
 ordinary gas, according to the character of the fuel avail- 
 able. 
 
 Dynamo Machines. There are two machines of exactly 
 
 FIG. 97. Compressor- pump cylinder, 24 inches in diameter. Stroke, 22 inches. 
 Indicated H. P., 17.7. 
 
 Fm. 98.-Workinpr cylinder. 3'.' inches in diameter. Stroke, 20 inches. Indicated 
 H. P., 33.1. Revolutions per minute, 64. Power on brake of fly-wheel, 9.12 H.P. 
 Pressure in reservoir, 19 to 24 Ibs. 
 
 the same type as those supplied for Macquarie, the only 
 novelty lying in the method of using them. In 1868 Mr. 
 Wilde discovered, by experiment, that two alternate 
 
238 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 current dynamos, independently driven at the same speed, 
 would, if electrically connected, so control each other's 
 motions that they would add their currents. The author 
 subsequently arrived at the same conclusion independently, 
 on theoretical grounds, and gave a thorough explanation of 
 the fact.* The result has been put to a practical applica- 
 tion at Tino. The machines are connected to a single 
 switchboard, so that each half of the two machines can at 
 pleasure be connected to, or disconnected from, the main 
 conductors. Thus a current can be supplied from either 
 machine at half power, 55 amperes, or full power, 110 
 amperes, or from the two machines of double power, or 
 about 200 amperes. Further, a change can be made with- 
 out extinction of the light from one dynamo and engine to 
 the other. Thus, suppose one machine is working full 
 power, clutch the countershafts gradually together, so 
 starting the second engine; throw on the band of the 
 second machine, cut out half the first machine, and con- 
 nect half the second machine at the switchboard; the two 
 machines at once synchronize, without affecting the light. 
 Disconnect the remaining half of the first machine, and 
 connect the remaining half of the second, unclutch the 
 countershafts, and stop the first engine. One man can 
 effect the change, with no more disturbance of the light 
 than a change from full to half power for about one 
 second. A further conclusion, deduced from theoretical 
 considerations, was that of two alternate current machines 
 
 * Lectures on the "Practical Applications of Electricity." Session 1882-88. 
 Paper on "Some Points in Electric Lighting," reprinted in this volume. By 
 Dr. John Hopkinson. And Journal of the Society of Telegraph Engineers and 
 Electricians, vol. xni., p. 496. 
 
THE ELECTKtC LIGHTHOUSE OF TINO. 
 
 of equal potential, one coujd be used as a generator of 
 electricity, the other as a motor converting the current 
 generated back into mechanical power. It was found 
 impossible to verify this conclusion with such intermittent 
 driving as that of a hot air engine. But Professor W. G. 
 Adams effected the verification without difficulty at the 
 South Foreland, the motive power being steam. 
 
 Lamps. These are the improved Serrin of Mr. Berjot. 
 One of the three lamps supplied is of larger size, for the 
 double power current from the two machines. This lamp 
 was said to be suitable for a still greater current, but with 
 about 200 amperes it soon became dangerously heated; a 
 simple modification rendered the lamp equal to the actual 
 work it had to do. It is, however, probable that for the 
 occasional circumstances when it is necessary to use so 
 great a current as 200 amperes in a lighthouse, a lamp 
 worked partly by hand would be preferable to a regulator 
 entirely automatic. 
 
 The apparatus was delivered in November, 1884, and 
 was put up by workmen from Messrs. Chance's workshops, 
 under the supervision of Mr. L. Luiggi, of Genoa, to whose 
 ability and energy the complete success of the lighthouse 
 is largely due. A complete test of the performance of the 
 light, as seen from the sea in all grades of its power, was 
 made in April, 1885, by a commission, consisting of Profes- 
 sor Garibaldi, of Genoa; Mr. Giaccone, engineer-in-chief 
 for Italian lighthouses; Captain Sartoris, and Mr. Luiggi, 
 the author attending on behalf of Messrs. Chance. The 
 light was well observed through rain, when distant 32 
 nautical miles, and although below the horizon, the posi- 
 tion was precisely localized, and the triple flash distinction 
 
240 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 unmistakable. At 18 miles distant the illumination of the 
 flash upon white paper was sufficient to make out letters 
 marked in pencil l inch high, and when 14 miles distant 
 it was easy to ascertain the time from a watch. The light 
 is frequently seen at a distance of 50 miles, near to Genoa. 
 
 A review of work which has been carried out naturally 
 suggests many questions as to what conclusions experience 
 has established, and what indications it gives of the prob- 
 able direction for future developments. In the use of 
 electric light in lighthouses, there are many questions 
 upon which there is wide difference of opinion, questions 
 both as to when and where electric light should be 
 adopted, and questions as to the best way of employing it. 
 It may not be unprofitable to allude to some of them. 
 Although English engineers are now well agreed that a 
 large optical apparatus should be used for the electric 
 light, this opinion is not universally accepted. The 
 advantages of a large apparatus have already been men- 
 tioned. To balance them, there is nothing on the other 
 side but the less prime cost of the smaller apparatus. 
 Although the difference of cost appears considerable when 
 attention is confined to the optical apparatus, it is un- 
 important when the whole outlay on the lighthouse is 
 brought into account. Cases are, however, conceivable in 
 which a small optical apparatus such as a fourth order, 
 having a focal distance of 250 millimetres, would be prop- 
 erly preferred ; such, for example, as a harbor light which 
 could be supplied with current from machinery also used 
 for other purposes, but such cases are likely to be excep- 
 tional. 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 241 
 
 When a flame from oil or gas is the source of light, there 
 is of necessity a considerable divergence vertically ; and the 
 distribution of the light through the angle of vertical 
 divergence is not at disposal, except to a very limited 
 extent in some cases, but is determined by the size and 
 character of the flame. With the electric arc and a large 
 optical apparatus it can be determined in considerable 
 measure how the light shall be distributed how much 
 shall be sent to the distant sea, how much to the various 
 distances between the foot of the tower and a distance 
 of some miles. It becomes then a question what use is to 
 be made of this facility. The experience at Macquarie 
 and at Tino is emphatic, that it is in every way advant 
 ous to direct much the greater part of the light to 
 
 horizon with a very small divergence, and to distribute the \^^ 
 comparatively small remainder over the nearer sea with in- 
 tensity increasing with the distance. 
 
 A question allied to the last is this: Whether it be de- 
 sirable to provide means of directing the strongest light 
 downwards on to the nearer sea in time of fog? The 
 answer must depend upon the circumstances of the par- 
 ticular locality. Take the case of a lighthouse on an 
 isolated rock, the purpose of which is primarily to be a 
 beacon to keep ships off that rock; a lighthouse which 
 would not exist were it not more practical or cheaper to 
 build and maintain the lighthouse rather than remove the 
 rock. Here surely it is of the greatest use to provide 
 means whereby, if the light cannot penetrate 2 miles, it 
 shall if possible be visible at 1 mile. But other cases 
 occur in which the lighthouse has to cover a long length 
 of coast, and has almost as much to do with points of the 
 
242 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 coast 10 miles distant as with the point upon which it is 
 placed, cases in which the lighthouse is far more useful in 
 guiding the regular traffic passing within a radius of 20 
 miles or more than in preventing vessels running ashore 
 within a mile of the tower. Such a light fails of its pur- 
 pose if it can only be seen at a distance of a mile, covering 
 less than ^^ part of its normal area of illumination; it 
 becomes comparatively useless unless it penetrates, to 
 something like its normal range, and its efficiency must be 
 measured by the fewness of the occasions when it fails to 
 do this. It is a grave question whether it be prudent in 
 such cases to place upon the light keeper the responsibility 
 of judging when the light should be dipped on to the 
 nearer sea, the fact being that, if his judgment errs, he 
 may actually diminish the range of the light, and cause 
 unnecessarily the lighthouse to fail of fulfilling its most 
 important function. It is easy for him to be misled if the 
 fog is local and does not extend to any great distance from 
 the lighthouse. Another element enters into the con- 
 sideration the height above the sea. If the focus be 100 
 feet above the sea level, the dip of the sea horizon is 9' 
 45", and a ray dipping 9' 45" below the sea horizon will 
 meet the sea at a distance of 3.1 nautical miles from the 
 tower. Even with a first order apparatus, if the arc be a 
 powerful one, it is very difficult to render the light 
 directed to the horizon from an elevation of 100 feet more 
 powerful than that directed to a point distant 4 miles from 
 the tower. Unavoidable divergence will render the two 
 intensities practically equal. 
 
 Passing to questions of another class, what are the rela- 
 tive advantages in an electric lighthouse of continuous and 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 243 
 
 alternating currents? Present practice tends altogether 
 in favor of alternate currents, but this practice largely 
 results from unfavorable experience of the older continu- 
 ous current machines. These machines have in many 
 respects been greatly improved in the last two or three 
 years. The continuous current presents the advantage of 
 greater economy of power in producing the current, less 
 floor space required by the machine, and a smaller prime 
 cost. The alternate current magneto machine, on the 
 other hand, has the advantage that it may be driven with 
 a defectively governed prime mover, with an indifferent 
 lamp, and may suffer neglect with impunity; whereas the 
 more compact and efficient continuous current machine 
 would be in serious peril of destruction. Optical apparatus 
 can be constructed suitable to make the most of either 
 form of arc. Hot air engines have found favor for electric 
 lighthouses, because in many cases there is no available 
 supply of fresh water. The engines of which the author 
 has experience are open to the objection that they take a 
 great deal of room, are not economical of fuel, and do not 
 govern so quickly as is desirable; the wear and tear also, 
 when they are worked to anything like their full power, is 
 very serious. A gas engine, with Dowson or other gas 
 made on the spot, could be used with greater advantage, 
 
 Antecedent to all considerations as to the best apparatus 
 and machinery to be used is the question under what cir- 
 cumstances, if at all, should electric light be used in a 
 lighthouse ? The Trinity House experiments at the South 
 Foreland showed to demonstration that, where the issue to 
 oe decided was how to produce a light which should be ca- 
 pable of penetrating the furthest in all weathers, electric 
 
244 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 light could do that which could be done in no other way, 
 and that it was the cheapest light of all when the price is 
 estimated per unit of light. But the conclusion was also 
 reached that an electric light must inevitably cost a large 
 sum, both in first outlay and in maintenance; therefore 
 that electric light is extravagant unless very extraordinary 
 power is a necessity. This conclusion is doubtless a fair 
 consequence of experience, but it is not an inherent prop- 
 erty of electric light. Both the capital outlay and the cost 
 of maintenance are greatly increased by the practice of so 
 arranging the machinery as to provide, at all times, a light 
 of very great power : whence it follows that the machinery 
 must be placed at some distance from the lantern, and two 
 men must always be on duty; one man in the lantern, and 
 another with the machinery. 
 
 The essentials for a cheap electric lighthouse are, that 
 for ordinary states of the atmosphere there shall be pro- 
 vided a plant under the easy control of the light keeper 
 himself, which shall be precisely adapted to produce that 
 amount of light which is wanted in ordinary states of the 
 atmosphere; but for thick weather there shall be provided 
 a much more powerful engine and dynamo, available also 
 as a reserve in case the smaller machinery from any cause 
 breaks down. The occasional machinery may be more 
 remote from the lantern, as it is a small matter to require 
 a second man to work on the comparatively rare occasions 
 when the maximum power is needed. A small gas engine 
 and a dynamo machine can be placed without any crowd- 
 ing in the room immediately below the lantern, and arrange- 
 ments can be made whereby the light keeper, whether he 
 is in the lantern or in the engine room, can ascertain at a 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 245 
 
 glance whether the arc is in its proper position, with an 
 error of less than 1 millimetre. The attendance on the 
 lamp, rotating apparatus of, the lens (if a revolving light), 
 engine and dynamo, would be easy when the whole is 
 brought together so as to be under observation at once; in 
 fact the gas engine, dynamo, and lamp constitute together 
 a gas burner which, though consisting of many parts, is 
 automatic throughout, and requires nothing but the con- 
 stant presence of a custodian, exactly as the gas lamp in a 
 lighthouse requires a custodian as a guarantee against fail- 
 ure. The same end, viz., the concentration of the whole 
 mechanical and electrical apparatus under one pair of eyes, 
 could be attained, of course, in other ways. Accumulators 
 could be used, or a petroleum engine. 
 
 In order to give definiteness and afford facilities for 
 criticism, the better course will be to describe a suitable 
 machinery; state what it will do, what attendance it will 
 require, and what it will cost. The author proposes, then, 
 for an electric lighthouse where small outlay is essential, 
 the following: A Dowson gas producing apparatus and gas 
 holder, the generator and superheater being in duplicate, 
 each capable of making 1,200 feet of gas per hour, the gas 
 holder having a capacity of 3,000 cubic feet. 
 
 An 8 h. p. nominal Otto gas engine and series wound 
 dynamo machine, placed in a room near the base of the 
 tower, and copper conductors to the lantern, the dynamo 
 having magnet coils, divided 'into sections so as to supply a 
 small current when required. 
 
 A 1 h. p. nominal Otto gas engine and dynamo machine, 
 placed in the room immediately beneath the lantern floor, 
 with gas pipe from the gas holder; three electric lamps, to 
 
246 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 receive either carbons 25 millimetres in diameter or any 
 lesser size, with complete adjustments for accurate focus- 
 sing; one paraffin lamp as a substitute; an optical appara- 
 tus of the second order of 70 centimetre focal distance. 
 The cost of this apparatus would depend upon the charac- 
 ter of the light it was intended to exhibit. To fix ideas, 
 let it be assumed that the light is to be a half minute 
 revolving light, showing all round the lighthouse. There 
 could then be supplied a sixteen sided apparatus with ped- 
 estal and revolving machinery. Provision would be made 
 in the optical apparatus for giving the horizontal and ver- 
 tical divergence desired by the same methods successfully 
 used in the lighthouses of Macquarie and of Tino. 
 
 Two focussing prisms would be fixed to form magnified 
 images of the arc, on pieces of obscured glass let into the 
 pedestal floor, so that the keeper, whether in the lantern or 
 in the engine room, could see at a glance the state of the 
 arc, and observe whether it is of proper length with the 
 carbons in line, whether it is exactly at the right height 
 and in the centre of the apparatus. An error of I millim- 
 etre would bu glaringly apparent, and call for immediate 
 adjustment, although its effect would be only a displace- 
 ment of the beam 5' of angle. 
 
 The lantern would be 10 feet diameter, with bent plate 
 glass. 
 
 The cost of the whole above described would be materi- 
 ally less than the cost of a first order light and lantern 
 with oil lamp and large burners. 
 
 Now what result would be obtained ? In fine weather 
 the small engine would be used. Its effective power on 
 the brake is fully 1 h. p.; from this 1J h. p. the dynamo 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 247 
 
 machine produces considerably over 800 watts, say 800 
 watts in the arc itself, or 20 amperes through a fairly long 
 arc of 40 volts. Of course the value of this in candles de- 
 pends upon the color in which it is measured, and the 
 direction in relation to the axis of the carbons. In red 
 light the mean over the sphere would certainly exceed 
 1,200 candles. In clear weather or in slight haze or rain, 
 the beam of this light through the lenses would be much 
 more powerful at the horizon and on the more distant sea 
 than any single focus light with oil or gas as the illumi- 
 nant, and would at least be fairly comparable with any- 
 thing yet exhibited with oil or gas whether triform or 
 quadriform. But on the nearer sea the illumination 
 would be reduced, so that no annoyance would be caused 
 by dazzling flashes. In thick weather or indeed in any 
 weather when there was a doubt as to the visibility at the 
 horizon of the lower power, the large engine would be 
 used under the superintendence of the second keeper. 
 This engine will give 10 h. p. on the brake, and there is no 
 difficulty in obtaining 85 per cent, of this as useful 
 electrical energy outside the machine, that is, 6,340 watts. 
 From this deduct 10 per cent, for the leads and the lamp 
 and for steadying the arc, leaving 5,710 watts in the arc 
 itself, or 114 amperes, with a difference of potential of CO 
 volts. Having regard to the fact that the optical appa- 
 ratus here proposed acts upon a larger portion of the 
 sphere than that used in the South Foreland experiments, 
 that the vertical divergence is less, and that the potential 
 difference is greater and the current continuous, although 
 less in quantity, it may safely be assumed that the power of 
 the resulting beam would not be inferior. It hence follows, 
 
248 DYNAMO MACHINERY AND ALLIED SUBJECTS. 
 
 from the South Foreland experiments, that in any fog the 
 flashes would penetrate farther than those of any existing 
 gas or oil light. The increased size of crater, compared 
 with that produced by the current of 20 amperes, will give 
 increased vertical divergence, and so cause the maximum 
 illumination to be attained at a less distance from the 
 lighthouse. The attendance of two men would suffice for 
 all the duties of the lighthouse, because under ordinary 
 circumstances one man only need be on duty excepting for 
 two to three hours while gas is being made. The con- 
 sumption of coal would he 4 Ibs. per hour of lighting, of 
 water about gallon, of carbons about 4 inches. The 
 whole cost of maintaining the light would differ little from 
 that of an ordinary oil light of the first order. 
 
 Though it be the fact, that it is possible to exhibit an 
 electric light at moderate cost, it does not follow that it is 
 suitable for all ocean lights. There is no room in a rock 
 lighthouse tower for a gas plant, and few would at present 
 be prepared to recommend a petroleum engine burning oil 
 of a low flashing point. The light keeper again must 
 understand a gas producer, a gas engine, a dynamo, and 
 an arc lamp, instead of only a paraffin lamp and burner, 
 and arrangements must exist for repairing the more ex- 
 tensive machinery. Such considerations will justly weigh 
 against the use of the electric light in remote stations and 
 in countries where the labor available is not capable of 
 much training. 
 
 It may possibly be said that in this paper no definite 
 conclusions are reached as to whether electricity or some 
 other agent is the best source of light in lighthouses 
 
THE ELECTRIC LIGHTHOUSE OF TINO. 249 
 
 generally, nor yet, if electricity be adopted, what is the 
 best way of producing the light and optically dealing with 
 it. The answer is that it is impossible on many points to 
 arrive at general conclusions. Each case must be judged 
 according to its special circumstances. 
 
IF YOU WISH TO KNOW 
 
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EXPERIMENTS WITH 
 
 ALTERNATE CURRENTS 
 
 Of High Potential and High Frequency. 
 By NIKOLA TESLA. 
 
 Cloth. 156 pages, with Portrait and 35 Illustrations. Price, $1.00. 
 
 This book gives in full Mr. Tesla s important lecture before the 
 London Institution of Electrical Engineers, which embodies the 
 results of years of patient study and investigation of the phenomena 
 of Alternating Currents of Enormously High Frequency and Electro- 
 motive Force. 
 
 The book is well illustrated with 35 cuts of Mr. Tesla's experi- 
 mental apparatus, and contains in addition a biographical sketch, 
 accompanied by a full-page portrait, which forms a fitting frontispiece 
 to a lecture which created such widespread interest. 
 
 Every Electrician, Electrical Engineer or Student of Electrical 
 Phenomena who makes any pretensions to thorough acquaintance 
 with recent progress in this important field of research which Mr. 
 Tesla has so ably developed, must read and reread this lecture. 
 
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AN IMPORTANT NEW BOOK. 
 
 ALTERNATING CURRENTS, 
 
 Treated Analytically and Treated 
 Graphically. 
 
 BY 
 
 FREDERIC BEDELL, Ph.D., and A. C. CREHORE, Ph.D., 
 
 (Cornell University.) 
 
 Uniform in size and style with " The Electric Railway in 
 Theory and Practice" by O. T. Crosby 
 and Dr. Louis Bell. 
 
 Cloth. 300 Pages and 112 Illustrations. Price, $2.50. 
 
 While there are many monographs and special treatises on alter- 
 nating currents, they are either fragmentary or special in character, 
 or couched in mathematical language requiring a special mathematical 
 education to interpret. 
 
 In this volume the theory of alternating currents is, for the first 
 time, treated in a connected and logical manner, and in mathematical 
 language familiar to the ordinary mathematical public, while the 
 graphical extension can be followed by those not having a special 
 knowledge of mathematics. 
 
 Some parts of this volume have been published in separate papers, 
 and from the cordial welcome they received it is believed that the 
 present work will fill a distinct want in an important branch of 
 electrical science. 
 
 Mailed prepaid to any address on receipt of the price by the Publishers, 
 
 THE W. J. JOHNSTON COMPANY, Ltd., 
 
 TIMES BUILDING, NEW YORK. 
 
Puicalioi|so[(i|GW.J.Jois(o[iCo.,L(ii. 
 
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 DICTIONARY OF ELECTRICAL WORDS, TERMS 
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 Second Edition, entirely rewritten. 5,000 definitions, 562 
 double column octavo pages, 570 illustrations 5.00 
 
 THE ELECTRIC MOTOR AND ITS APPLICA- 
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 LIGHTNING FLASHES. A Volume of Short, Bright 
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ELECTRICITY AND MAGNETISM. A Series of t Ad- 
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 pages, 116 illustrations $1.00 
 
 RECENT PROGRESS IN ELECTRIC RAILWAYS. 
 
 Being u Summary of Current Advance in Electric Rail- 
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 EXPERIMENTS WITH ALTERNATING CURRENTS 
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 tions 1.00 
 
 LECTURES ON THE ELECTROMAGNET. Author- 
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 WHEELER'S CHART OF WIRE GAUGES 1.00 
 
 PROCEEDINGS OF THE NATIONAL CONFER- 
 ENCE OF ELECTRICIANS IN PHILADELPHIA. 
 
 300 pages 23 illustrations 75 
 
 WIRED LOVE: A Romance of Dots and Dashes. By 
 
 ELLA CHEEVER THAYER. 256 pages 75 
 
 BERING'S TABLES OF EQUIVALENTS OF UNITS 
 
 OF MEASUREMENT.. 50 
 
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OF CALIFORNIA LIBRARY 
 
 
 JUN161990 
 
 LD 21-lOOm 
 
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U.C. BERKELEY 
 
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