The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 1 of 35

THE FIRST TRANSFORMER.

The Iron Ring, with insulated Primary and Secondary Coils wound on it, with which Faraday made the discovery of Magneto-Electric Induction. Photographed from the original, preserved in the Museum of the Royal Institution.

\Fronti*piett.

THE ALTERNATE CURRENT TRANSFORMER

IN THEORY AND PRACTICE.

J. A. FLEMING,

M.A., D.SC. (LOND.), F.R.S.,

FROKKSSOK OK ELECTRICAL F.NG I N KICKING IN UNIVERSITY

COLLEGE, LONDON ; I.ATK FF.I.LOXV AND SCHOLAR OF ST. JOHN'S COI.I.F.GE, CAMBRIDGE

FELLOW OF UNIVERSITY COLLEGE, LONDON ; MEMltER OK THE INSTITUTION OF EI.ECTKICAI. ENGINEERS;

MEMliEK OK THE PHYSICAL SOCIETY OF LONDON; MK.MISEU OK THE ROYAL INSTITUTION OF GREAT liRITAIN;

F.TC., El'C.

VOLUME I.

THE INDUCTION OF ELECTRIC CURRENTS.

NEW EDITION.

LONDON:

1 THE ELECTRICIAN " PRINTING AND PUBLISHING COMPANY, LIMITED,

SALISBURY COURT, FLEET STREET.

[All Rights Reserved.]

Printed ami Published by

"THK KLKCTUIOIAN " PRINTING AND PUBLISHING CO..

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PREFACE.

IN the seven years which have elapsed since the first edition of this Treatise was published, the study of the properties and applications of alternating electric currents has made enormous progress. At the outset the aim of the author was to collect, and present in a form suitable for students, a general statement of the facts and principles of electromagnetic induction, and the manner in which these are applied in the design and construction of the Induction Coil and Transformer. At that time most of the practical information on the subject was embedded in technical journals and original papers. Confident that alternating electric currents would play a very important part in the evolution of the electrical industry, the author believed that service would be rendered to engineering students by an attempt, even if an imperfect one, to place a brief systematic treatise on the subject of the Alternating Current Transformer within reach. The result, so far, has justified the belief. At the present time, however,

iv. Preface.

much of the subject matter in the first edition has become antiquated, and it became necessary to revise the book thoroughly, to eliminate those parts which had been seen to be imperfect or unnecessary, and to bring the remainder of the information as far as possible into line with recent views and experience.

The author has, accordingly, rewritten the greater part of the chapters, and availed himself of various criticisms, with the desire of removing mistakes and remedying defects of treatment. In the hope that this will be found to render the book still useful to the increasing numbers of those who are practically engaged in alternating-current work, he has sought, as far as possible, to avoid academic methods and keep in touch with the necessities of the student who has to deal with the subject not as a basis for mathematical gymnastics but with the object of acquiring practically useful knowledge.

It is, perhaps, in some ways, a positive disadvantage that alternating-currents lend themselves so easily to- mathematical treatment and, by a few assumptions akin to that of the perfectly frictionless machine, offer an attractive field for mathematical ingenuity. Real difficulties are thus often passed over, and an intimate knowledge only gained of a perfectly hypothetical transformer.

The ever-increasing progress of electrical knowledge, and the constant necessity for recasting electrical theories, renders it a most difficult matter to secure in an electrical treatise of any length, uniformity of treat- ment ; whilst views must always differ as to the mode in which any special subject should be approached.

Preface. v.

The author ventures to hope, however, that in its revised form, the information here collected may be of use to those who are in any way concerned with alternating-current practice or investigations, and that it may be effective as an introduction to treatises of a more advanced character, which deal with the properties of periodic currents and their utilization in various technical applications.

J. A. F.

University College, London, April, 1896.

A 2

CONTENTS.

CHAPTER I.

PAGS

HISTORICAL INTRODUCTION 1

§ 1. Faraday's Discoveries ; His Electrical Researches ; The Discovery of Induced Currents ; The Decisive Experiment with the Iron Ring ; Lines of Magnetic Force. — § 2. Faraday's Theories ; Magneto-Electric Induction ; The Electrotonic State ; Number of Lines of Magnetic Force ; Conduction and Induction ; Views of Maxwell, Helmholtz and Kelvin ; Action at a Distance ; The Electromagnetic Medium. — § 3. Joseph Henry's Investigations ; Henry's Electromagnet ; His Independent Discovery of Electro- magnetic Induction ; Production of Induced Currents from Henry's Large Electromagnet.

CHAPTER II. ELECTROMAGNETIC INDUCTION 13

§ 1. Magnetic Force and Magnetic Fields ; The Magnetic State ; Magnetic Fields ; Magnetic Axis ; Direction of Magnetic Force ; Magnetic Force near a Straight Conductor Conveying a Current ; Ampere's Fundamental Law ; Magnetic Force at the Centre of a Circular Conductor Conveying a Current ; Magnetic Force Due to a Circular Current at a Point on the Axis ; Magnetic Force due to a Straight Helix at Points on Axis ; Magnetic Force of a Circular Solenoid.— § 2. Magnetomotive Force and Magnetic Induction ; Flux of Force ; Magnetic Permeability ; Lines of Induction ; Definition of Unit of Magnetic Induction ; Faraday's Law of Induction ; Electromotive Force due to the Change of Induction.— § 3. The Magnetic Circuit ; Magnetic Resist- ance ; Definition of Magnetic Resistance or Reluctance ; Case of a Circular Ring ; Lines of Induction of Closed and Open Magnetic Circuits; Fundamental Relation between Magnetic

viii. CONTENTS.

CHAPTER II.— ( Continued.)

Force and Magnetic Induction ; A Magnetic Shell ; Intensity of Magnetisation ; Magnetic Moment.— § 4. Lines and Tubes of Magnetic Induction ; Equipotential Surface ; Number of Tubes of Induction ; Surface Integral of Induction ; Linkage of Lines of Induction and Circuits ; Rate of Change of Induction Linked with Circuit. - § 5. Curves of Magnetisation ; Curves of Mag- netisation of Soft Iron Ring ; Permeability Curves ; Determina- tion of Permeability. — § 6. Magnetic Hysteresis ; Hysteresis Curves ; H-B Diagram ; Values of Hysteresis for Various Kinds of Iron and Steel ; Variation of Hysteresis with Speed of Cycle ; Effect of Temperature on Hysteresis ; Experiments of Kunz. — § 7. The Electromotive Force of Induction ; Graphical Repre- sentations ; Electromotive Force of Self-induction.

CHAPTER III.

PAGE

THE THEORY OF SIMPLE PERIODIC CURRENTS 79

§ 1. Variable and Steady Flow ; Periodic Motion.— § 2. Current and Electromotive Force Curves ; Simple and Multiple Valued Functions ; Simple Periodic Curves. — § 3. Simple and Com- pound Periodic Curves. — § 4. Fourier's Theorem ; Mechanical Harmonographs. — § 5. Mathematical Sketch of Fourier's Theorem ; Practical Application of Fourier's Theorem to the Harmonic Analysis of a Periodic Curve.— § 6. Simple Periodic Currents and Electromotive Forces ; Analysis and Synthesis of Compound Periodic Curves. — § 7. Description of a Simple Periodic Curve.— § 8. The Mean Value of the Ordinate of a Sine Curve.— § 9. The Square Root of the Mean of the Squares of the Ordinates of a Simple Periodic Curve ; Mean-Square Value.— §10. Derived Curves. -§ H. Inductance and Inductive Circuits ; Inductance, Resistance, and Capacity of Circuits ; Analogy of Inductance and Inertia ; Inductive and Non- Inductive Circuits ; Faraday's and Henry's Experiments on Self-induction ; Edlund's and Maxwell's Arrangement for Exhibiting the Inductance of Circuits.— § 12. Electromagnetic Momentum ; Electrotonic State and Electromagnetic Momen- tum ; Coefficient of Self-Induction. — § 13. Electromagnetic Energy ; Coefficient of Mutual Induction;. Energy of Two Circuits.— § 14. The Unit of Inductance ; The Henry ; Value of the Self-Induction in Henrys for Various Instruments. — § 15. Current Growth in Inductive Circuit* ; Analogy of Current and Velocity Change : Fundamental Equations for Current Growth in Inductive Circuits. — § 16. Equation for the Establishment of

CONTENTS. ix.

CHAPTER III.— (Continued.)

a Steady Current in an Inductive Circuit ; Time Constant of an Inductive Circuit. — § 17. Logarithmic Curves ; Law of Growth of Current in Inductive Circuit. — § 18. Instantaneous Value of Simple Periodic Current ; Solution of Current Equation ; Impe- dance of Inductive Circuit; Relations of Impressed Electromotive Force, Current and Impedance. — § 19. Geometrical Illustrations; Clock Diagrams. — § 20. Graphical Representation of Periodic Currents ; Laws of Vector Addition. — § 21. Impressed and Effective Electromotive Forces ; Clock Diagram of Electromotive Forces in Inductive Circuit ; Triangle Representing Resistance, Impedance, and Reactance of Circuit. — § 22. The Mean Value of the Power of a Periodic Current ; Geometrical Theorem.— § 23. Power Curves for Inductive and Non-inductive Circuits. — § 24. The Experimental Measurement of Periodic Currents and Electromotive Forces ; Mean-Square Value. — § 25. Method of Measuring the True Mean Power Given to an Inductive Circuit ; Theory of the Wattmeter ; Divided Circuits ; Important Trigo- nometrical Lemma. — § 26. Impedance of Branched Circuits. — § 27. Wattmeter Measurement of Periodic Power.— § 28. Correct- ing Factor of a Wattmeter.— § 29. Mutual Induction of Two Circuits of Constant Inductance ; Effect of Closed Secondary on the Resistance and Inductance of a Primary Circuit. — § 30. The Flow of Simple Periodic Currents into a Condenser ; Time- Constant of a Condenser ; Charging a Condenser Through a Resistance ; Admittance ; Condenser Equation. — § 31. A Shunted Condenser in Series with an Inductive Resistance ; Annulment of Inductance by Capacity. — § 32. Representation of Periodic Currents by Polar Diagrams ; Determination of Mean-Square Value of a Periodic Quantity from the Polar Diagram.— § 33. Initial Conditions on Starting Current Flow in Inductive Circuits ; Increased Initial Amplitude of Current.— § 34. Initial Conditions in Circuits having Capacity, Inductance and Resis- tance.— § 35. Complex Periodic Functions ; Apparent and True Power Given to Inductive Circuits ; Power Factor.

CHAPTEE IV.

PACK MUTUAL AND SELF-INDUCTION 207

§ 1. Researches of Prof. Joseph Henry on Self and Mutual Induc- tion ; Experiments with Coils and Bobbins ; Discovery of Self- induction. — § 2. Mutual Induction. — § 3. Induction at a Dis- tance ; Induction between Telephone Circuits ; Induction Over Great Distances ; Communication with Moving Railway Trains. — § 4. Induced Currents of Higher Orders ; Secondary. Tertiary

x. CONTENTS.

CHAPTER TV.— (Continued.)

and Quarteuary. Currents.— § 5. Inductive Effects Produced by Transient Electric Currents, such as Leyden Jar Discharges ; Magnetic Screening ; Direction of Induced Currents ; Various Qualities of an Induced Current. — § 6. Elementary Theory of Mutual Induction of Two Circuits ; Theory of Induction Coil with Non-Magnetic Core.— § 7. Comparison of Theory and Experiment ; Duration of Induced Currents ; Researches of Blaserna, Bernstein, and Helmholtz. — § 8. Magnetic Screening of Good Conducting Masses ; Faraday's and Henry's Experi- ments ; Wilioughby Smith's Investigations on Magnetic Screen- ing ; Dove's Experiments on the same ; Henry's Views on Magnetic Screening. — § 9. The Reaction of the Secondary Currents on the Primary Circuit in the Case of an Induction Coil ; Elihu Thomson's Experiments. — § 10. Hughes's Induction .Balance and Sonometer. — §11. The Transmission of Rapidly Intermittent or Alternating Currents through Conductors ; Induction Bridges ; Hughes's Experiments with the Induction Bridge ; Lord Rayleigh's Researches ; Experimental Confirmation of Theory ; Flow of Current Through a Conductor ; Surface Flow of Alternating Currents ; Increased Resistance of Con- ductor for Alternating Currents of High Frequency ; Lord Rayleigh's Form of Induction Bridge ; Limiting Size of Con- ductors for Conveyance of Alternating Currents ; Stefan's Analogies. — § 12. Electromagnetic Repulsion ; Elihu Thomson's Experiments on Electromagnetic Repulsion ; Copper Rings Projected from the Pole of an Alternating Current Magnet ; Copper Disk Galvanometer; Electromagnetic Rotations Produced by a " Shaded Pole " ; Electromagnetic Gyroscope ; Rotations Produced by Magnetic Leakage Field — § 13- Symmetry of Current and Induction.

CHAPTER V.

PAGE

DYNAMICAL THEORY OF INDUCTION 833

§ 1. Electromagnetic Theory ; Faraday's Conception of an Electro- magnetic Medium ; Maxwell's Suggestion ; The Lumeuiferous Ether ; Maxwell's Theory of Electric Displacement ; Electric Elasticity of the Medium ; The Displacement Current ; The Con- duction Current : Electromotive Intensity.— § 2- Displacement Currents and Displacement Waves.— § 3. Maxwell's Theory of Molecular Vortices ; Mechanical Analogy.— § 4- Comparison of Theory and Experiment ; Maxwell's Law Connecting Dielectric Constant and Refractivity of a Dielectric ; Tables of Comparison. — § 5. Velocity of Propagation of an Electromagnetic Disturbance ;

CONTENTS. xl.

CHAPTER V.— (Continued.)

Two Systems of Measurement of Electric Quantities; Electromag- netic and Electrostatic ; Ratio of the Units Defined as a Velocity ; Velocity of Light ; Determinations of the Electromagnetic "V" ; Table of Results ; Explanation of Meaning of Vector Potential ; Operation called " Curling " ; Vector Potential of a Current ; Relation of Vector Potential and Induction ; Fundamental Equation for Propagation of Vector Potential. — § 6. Electrical Oscillations ; Charge and Discharge of Leyden Jar ; Oscillations in Discharging Circuit ; Experiments on Discharge of Jar ; Oscillatory and Dead-beat Discharge : Influence of Self-induction on Rate of Discharge ; Conditions of Quickest Discharge. — § 7. The Function of the Condenser in an Induction Coil ; Time of Free Electrical Oscillation in a Circuit ; Conditions under which Inductance can Neutralize Capacity. — § 8. Impulsive Discharges and Relation of Inductance Thereto ; Lodge's Experiments on the Alternative Path of Discharge ; Lightning Protectors ; Side Flashing ; Conditions of Impulsive Discharge ; Electrical Surgings. — § 9. Theory of Experiments on the Alternative Path ; Electromagnetic Radiation from Oscillating Discharges ; Syntonic Circuits. — § 10. Impulsive Impedance.— § 11. Hertz's Experi- ments, Researches on the Propagation of Electromagnetic Induc- tion ; Preliminary Experiments ; Electric Resonator Circuit ; Experiments with Induction Coil and Oscillating Discharge ; Induction Phenomena in Open Circuits ; Resonance Phenomena ; Oscillations in Iron Wires ; Propagation of Electromagnetic and Electrostatic Effects ; Electromagnetic Waves ; Influence of Dielectrics ; Interference Phenomena ; Reflection ; Refraction and Polarization of Electromagnetic Waves. — § 13. Propagation of Electromagnetic Energy through Space ; Poynting's Views and Law ; The Importance of the Effects in the Medium. — § 14. Propagation of Currents along Conductors ; Hertz's Experiments ; Energy Penetrates into the Conductor from the Dielectric. — § 15. Experimental Determination of Electromagnetic Wave Velocity ; Photographing Electromagnetic Waves.

CHAPTER VI.

PAGE

THE INDUCTION COIL AND TRANSFORMER 514

§ 1. General Description of the Action of the Transformer or Induction Coil ; Air Core and Iron Core Transformers ; Classification of Transformers ; Problems of the Transformer. — § 2. The Delinea- tion of Periodic -Curves of Current and Electromotive Force ; Curve Tracing ; Joubert's Method of Delineating Alternating Current Curves ; Fleming's Curve Tracer ; Transformer Diagrams ;

lii. CONTENTS.

CHAPTEE VI.— (Continued.)

Bloudel's Oscillograph ; Various Curve Tracers.— § 3. Discussion of Transformer Diagrams ; Curves of Electromotive Force, Current and Induction in Case of Various Transformers taken off Various Alternators ; Open Circuit Current of Transformers ; Various Diagrams ; Symmetry of Transformer Curves ; Ryan's Diagrams ; Effect of Loading-up Transformer on Position of the Curves of Current ; Harmonic Analysis of Transformer Curves ; Only Odd Harmonics Present. — § 4. Derivation of Curves of Power and Hysteresis ; Hysteresis Curves of Various Trans- formers.— § 5. The Efficiency of Transformers ; Efficiency 'Curves of Closed and Open Circuit Transformers ; Table of Efficiencies. — § 6. Current Diagrams of a Transformer ; Open and Closed Circuit Transformers ; Tables of Complete Tests.— § 7. Power Factor of Transformers ; Table of Power Factors ; Influence of Form of E.M.F. Curve on the Power Factor ; Tables of Tests ; Relation of Power Factor to Output — § 8. Magnetic Leakage and Secondary Drop ; Various Causes of Secondary Drop ; Transformation Ratio of a Transformer ; Determination of Magnetic Leakage.— § 9. Effect of the Form of the Curve of Primary Electromotive Force on the Transformer Efficiency and Currents ; Investigations of the Author and of Dr. Roessler. — § 10. The Form Factor and Amplitude Factor of a Periodic Curve. — § 11. General Analytical Theory of the Transformer and Induction Coil.

APPENDIX.

NOTE A. (page 19) 597

The Magnetic Force at any point in the Plane of a Circular Current

NOTE B. (page 35) 599

The Total Induction in a Circular S.jleuoM.

-NOTE C. (page 52) 600

The Calibration of the Ballistic Galvanometer.

ERRATA,

63 In the table at the bottom of page 63, for the power wasted in watts per cubic centimetre per 100 cycles per second, in all the laumerical values except the first for very soft annealed iron, the decimal point is displaced. The numbers should be divided by ten.

117. Line  6  from  top,  for  lies  down  at  b  read  dies  down  at  b. 
     

118. Line  7  from  top,  for  109  linkages  of  current  and  magnetic 
     

force read 10s linkages of current and magnetic force ;

^

B S \ also, in equation (25), for _— ~ read --

and in line 7 from bottom,

162. The  equation  numbered  (12)  should  be  numbered  (39). 
     

163. Equation (47), instead ofv = V(l+e~ ^ read t» = V(l + «~5o).

_ R

195. Last line equation (64),/br i = A.e L« + , &c., read i = Ae~^-t +, <fec.

196. Line  11  from  bottom,  for  of  the  mean  is  -  read  of  the 
     

mean is J.

219. In  the  first  line  of  paragraph  §  4,  for  1888  read  1838. 
     

220. Line  7  from  bottom,  for   then   Sir  William   Thomson 
     

read then Prof. William Thomson.

377. In  equation  (116),  for  q  =  A  «-'«"  +  B  em*  read  q  =  \e"^ 
     

38:?. At the end of line 7 insert a full stop, and in line 8 for when t = Q read When t = 0.

58H. Equation (156), for N, S ^ mid N, S ^1 ; (It dt

also, in equation (157), for + N, S 1^1 r«id - N2 S ^?,

in line 7 from bottom, /or N, 8^ read N S^l '/ « d f '

and in line 4 from bottom, for - N, S-^rawJN S^?

rf«'

CHAPTER I.

HISTOEICAL INTRODUCTION.

§ 1. Faraday's Discoveries.— The autumn days of the year 1831 are ever memorable in the annals of electrical discovery. At that time Faraday, then in the prime of his intellectual powers, began the continuous series of " Electrical Researches," which enriched physical science with discoveries of far-reaching importance, and laid the firm foundations on which much of the modern applications of electricity rests. Looking on the whole of electrical phenomena with an eye eager to see physical analogies, and confident that where these exist they may prove suggestive for further research, he had already asked himself if it were possible there was any effect in the case of electric currents analogous to that known as electrostatic induction. An insulated conductor possessing an electric charge when introduced into a closed chamber having conducting walls calls forth upon them an equal charge of an opposite sign. This induced electrification is invariably present, 110 matter how far off the walls of the enclosing chamber may be, and all sur- rounding conductors share in the duty of carrying a portion of the induced charge. At a later date, when Faraday viewed this phenomenon of electrostatic induction by the aid of the education he had received in dealing with magnetic lines of force, he was able to picture to himself lines of electrostatic force proceeding in all directions from the surface of a charged body. Wherever they terminated, whether on neighbouring con- ductors or on the walls of an enclosing chamber, they developed on these " corresponding points " a charge equal and opposite to that of the surface at the point from which they took their rise. Just eleven years previously H. C. Oersted had made

2 HISTORICAL INTRODUCTION.

Copenhagen famous as the birthplace of the discovery that an electric current passing through a metallic wire magnetises it circularly and creates round it a magnetic field, the direction of the lines of magnetic force being closed curves surrounding the axis of the wire. Faraday placed these two phenomena side by side before his mental vision, and he asked himself whether it was possible that the magnetic field of force gene- rated round a current-carrying conductor could develop in an adjacent circuit an induced current just as the charged body calls forth an induced electrostatic charge on the neighbouring conductors.

Some notions on this subject of electric current induction had before 1831 occupied his mind at intervals, but these early experiments did not lead to any satisfactory results.

In 1825, in the month of November, Faraday stretched alongside of a wire connected with a galvanometer another through which an electric current was flowing, but both then and on December 2, 1825, and on April 22, 1828, he had to record of his experiment that it gave "no result." A very little step in experimental research often separates failure from success. A reversal of operations, a change of some dimension, an alteration of some proportion, is often all that is needed to step from the region of failure into the field of discovery and achievement. In this case it may have been the apparently trivial one of starting the electric current in one wire before completing the circuit of the galvanometer.

The one thing, it seemed, that this preliminary work did dis- prove was the notion that a continuous steady current in one conductor could generate a continuous current in another adjacent conductor relatively at rest to the first. It is possible that some conception of the above nature had been dominant in the mind of Faraday before these trials had convinced him that the effect, if existing at all, was not detectable with his apparatus. Three years later he returned to the attack, and we cannot describe the experimental results of the autumn months of 1831 better than they have been given in Faraday's own words in the laboratory note-books of the Royal Insti- tution.* On the 29th day of August, 1831, he thus records the epoch-making discovery by which he will be for ever

• See Dr. Bence Jones's " Life of Faraday,' Vol. II., p. 2.

HISTORICAL INTRODUCTION. 3

known. He wrote : — " I have had an iron ring made (soft iron), iron round and fin. thick, and ring Gin. in external diameter. Wound many coils of copper round one-half of it, the coils being separated by twine and calico ; there were three lengths of wire, each about 24ft. long, and they could be con- nected as one length or used as separate lengths. By trials with a trough, each was insulated from the other. Will call this side of the ring A. On the other side, but separated by .an interval, was wound wire in two pieces, together amounting to about 60ft. in length, the direction being as with former coils. This side call B. Charged a battery of ten pairs of plates 4in. square. Made the coil B side one coil, and con- nected its extremities by a copper wire passing to a distance and just over a magnetic needle (3ft. from wire ring), then connected the ends of one of the pieces on A side with battery ; immediately a sensible effect upon needle. It oscillated, and settled at last in original position. On breaking connection of A side with battery, again a disturbance of the needle." (See Frontispiece.)

On September 24th he resumed his attack. He prepared an iron cylinder and wound on it a helix of insulated wire. The ends of the helix were connected with a galvanometer. The iron was then placed between the poles of bar magnets. Every time the magnet poles were brought in contact with the ends of the iron cylinder the galvanometer needle indicated a current, the effect being, as in former cases, not permanent, but a mere momentary impulse or deflection.

But the full meaning of this hardly appeared clear, and on October 1st he once more laid siege to the fortress. Preparing a battery of 100 pairs of plates, each 4in. square, and charged with a mixture of nitric and sulphuric acids, he arranged to send the current from this through a wire of copper 203ft. long wound round a block of wood. Bound the same block, and wound parallel to the first, was a second wire, of equal length to the first, but insulated from it. This second wire he joined up to the terminals of his galvanometer, and then when the battery connection was made or broken with the first wire he noticed a small but sudden jerk of the needle, one way when the current was made, the other way when it was broken. The clue to the real phenomenon was now in his hand, and

B2

4 HISTORICAL INTRODUCTION.

guided by it he stepped over a series of confirmatory experi- ments, and entered as a triumphant conqueror into the stronghold wherein the whole truth lay hid.

Writing on November 29th to his friend, Mr. E. Phillips, he says : — " Now, the pith of all this I must give you very briefly. When the electric current is passed through one of two parallel wires it causes at first a current in the same direction through the other, but this induced current does not last a moment, notwithstanding the inducing current (from the voltaic battery) is continued. All seems unchanged except that the principal current continues its course. But when the current is stopped, then a return current occurs in the wire under induction of about the same intensity and momentary duration, but in the opposite direction to that first formed. Electricity in currents, therefore, exerts an inductive action like ordinary electricity, but subject to peculiar laws. The effects are a current hi the same direction when the induction is estab- lished, a reverse current when the induction ceases, and a peculiar state in the interim."

The path for valuable discovery now lay open. Fully familiar with the work of Ampere and Arago, Faraday knew that a closed circuit conveying an electric current affects all surrounding space with magnetic force, and that, in particular, a small closed circular current can, as far as magnetic action is concerned, be exactly replaced by a very thin disc of steel, whose edge coincides with the line of the closed current, and which is magnetised everywhere in a direction perpen- dicular to its surface. Such a normally magnetised disc is called a magnetic shell. It follows that a helix of wire, which may be regarded as a number of closely approximate circular currents nearly in the same plane, should be magnetically equivalent to a number of magnetic shells piled one above the other, with similar polar faces turned the same way. But such an arrangement of shells would form a cylindrical magnet, and therefore a helix of wire or solenoid in which a current is flow- ing is for all external space the magnetic equivalent of a cylinder of steel of the same dimensions magnetised uniformly in a longitudinal direction. It remained, therefore, to test this hypothesis. The fifth day of his experiments was October 17th, and on that day he thus notes in the laboratory book the

HISTORICAL INTRODUCTION. 5

results: — "A cylindrical bar magnet fin. in diameter and 8|in. in length had one end just inserted into the end of a helix of wire 220ft. long. It was then quickly thrust in the whole length, and the galvanometer needle moved ; then pulled out again, and again the needle moved, but in the opposite direc- tion. This effect was repeated every time the magnet was put in or out, and therefore a wave of electricity was so pro- duced from mere approximation of a magnet."

Exactly twenty years afterwards, in the 28th and 29th series of his " Researches," Faraday illuminated, by the exactness and clearness of his experimental method, the whole behaviour of magnets towards closed conducting circuits. It is probable that even at this time he had learned to think of a magnet as carrying with it, as part of itself, a whole system of lines of magnetic force, which emanate from it and surround it. The system of lines of force moves with the magnet wherever it goes. Regarding the production of a current in the helix by a magnet thrust into it, Faraday pictured to himself the advanc- ing magnet as pushing its lines of magnetic force across the coils of wire of the helix, and "cutting " or intersecting them in its progress towards its final position in the coil. The conclusion to which he was led by this reflection seemed to be that the very essence of the effect was the movement across one another of a line of force and a portion of a conducting circuit. If this was so, then the result could be obtained by a more simple and obvious method. The ninth day, October 28th, saw these ideas put to further crucial test. Taking the great permanent horse- shoe magnet of the Royal Society, he placed a copper disc so that it was free to revolve on an axis placed in the line of the poles. Soft iron pole pieces were then adjusted to create a powerful magnetic field, the lines of force of which passed through the disc at right angles to its surface. The wires of the galvanometer were made to press against the disc, one near the axis, and the other near the edge. When the disc remained stationary, no current whatever was manifested, but on causing the disc to revolve on its axis a permanent and steady current traversed the galvanometer. This experiment was conclusive. The operation taking place during the revolu- tion of the disc could be viewed as consisting simply in the continual movement of any radial section of the disc across a

6 HISTORICAL INTRODUCTION.

stream of lines of magnetic force flowing at right angles to its surface. The continuous current resulted from the fact that the motion of that radial section of the disc was always the same relatively to the stream of force. On November 4th. Faraday reduced the conception to its utmost simplicity. Taking in his hand the mere closed galvanometer wires, he passed a portion of the loop between the poles of his large permanent magnet in such a way that the direction of that part of the loop between the poles was at right angles to the direction of the magnetic force, and the direction of the move- ment was at right angles to the direction of the force and that portion of the conductor. The galvanometer deflected, and showed the presence of a momentary current at the instant when the intersection took place.

§ 2. Faraday's Theories. — In ten days of splendid and con- clusive experiment in the autumn of 1831, Faraday had there- fore not only discovered the law of induction of currents, but the facts of magneto-electricity as well ; and more, for he had not merely accumulated a mass of experimental results, but had reduced the whole valuable store of knowledge to one fundamental principle of exquisite simplicity, namely, that the passage of a line of magnetic force across a line of a conducting circuit generates in that portion of the circuit an electromotive force, or a force setting electricity, or tending to set electricity, hi motion.

The subsequent work of all experimentalists and mathema- ticians has been to work out the applications of this principle in countless forms ; but no one has since added any essential discovery of fact which is not implicitly contained in the series of discoveries by which, in this short space, Faraday stepped from happy conjectures into possession of facts, which have proved more fertile in far-reaching practical consequences than any of those which even his genius bestowed upon the world. Faraday's theoretical views, however, on the phenomena under- went, in process of time, some modification. He apparently distinguished at first between the induction of currents by a current, which he called i-olta-eleciric induction, and the pro- duction of currents by a conductor moving in a magnetic field, which he called magneto-electric induction. That which seemed

HISTORICAL INTRODUCTION. 7