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Stan’s Legacy

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A Treatise on Electricity and Magnetism, Vol. 2 (1873) — part 1 of 27

1 January 1873

UNIVERSITY Of I -X CALIFORNIA I

A TREATISE

ON

ELECTRICITY AND MAGNETISM

MAXWELL

VOL. II.

Honfcon MACMILLAN AND CO.

PUBLISHERS TO THE UNIVERSITY OF

Clareniron

A TREATISE

ON

ELECTRICITY AND MAGNETISM

BY

JAMES CLERK MAXWELL, M.A.

LLD. EDIN., F.R.SS. LONDON AND EDINBURGH

HONORARY FELLOW OP TRINITY COLLEGE,

AND PROFESSOR OF EXPERIMENTAL PHYSICS

IN THE UNIVERSITY OF CAMBRIDGE

VOL. II

AT THE CLARENDON PRESS

1873

[All rights reserved]

v.

.

J/VV*Wt

CONTENTS.

PART III.

MAGNETISM. CHAPTER I.

ELEMENTARY THEOEY OF MAGNETISM.

Art. Page

  1. Properties of a magnet when acted on by the earth .. .. 1

  2. Definition of the axis of the magnet and of the direction of

magnetic force 1

  1. Action of magnets on one another. Law of magnetic force .. 2

  2. Definition of magnetic units and their dimensions 3

  3. Nature of the evidence for the law of magnetic force .. .. 4

  4. Magnetism as a mathematical quantity 4

  5. The quantities of the opposite kinds of magnetism in a magnet

are always exactly equal .* .. .; .. 4

  1. Effects of breaking a magnet .. .. 5

  2. A magnet is built up of particles each of which is a magnet .. 5

  3. Theory of magnetic 'matter' 5

  4. Magnetization is of the nature of a vector 7

  5. Meaning of the term 'Magnetic Polarization' 8

  6. Properties of a magnetic particle 8

  7. Definitions of Magnetic Moment, Intensity of Magnetization,

and Components of Magnetization .. .; .. .. .. 8

  1. Potential of a magnetized element of volume 9

  2. Potential of a magnet of finite size. Two expressions for this

potential, corresponding respectively to the theory of polari zation, and to that of magnetic 'matter* 9

  1. Investigation of the action of one magnetic particle on another 10

  2. Particular cases 12

  3. Potential energy of a magnet in any field of force 14

  4. On the magnetic moment and axis of a magnet 15

812246

vi CONTENTS.

Art. Page

  1. Expansion of the potential of a magnet in spherical harmonics 16

  2. The centre of a magnet and the primary and secondary axes

through the centre 17

  1. The north end of a magnet in this treatise is that which points

north, and the south end that which points south. Boreal magnetism is that which is supposed to exist near the north pole of the earth and the south end of a magnet. Austral magnetism is that which belongs to the south pole of the earth and the north end of a magnet. Austral magnetism is con sidered positive 19

  1. The direction of magnetic force is that in which austral mag

netism tends to move, that is, from south to nortb, and this is the positive direction of magnetic lines of force. A magnet is said to be magnetized from its south end towards its north end.. 19

CHAPTER II.

MAGNETIC FORCE AND MAGNETIC INDUCTION.

  1. Magnetic force defined with reference to the magnetic potential 21

  2. Magnetic force in a cylindric cavity in a magnet uniformly

magnetized parallel to the axis of the cylinder 22

  1. Application to any magnet 22

  2. An elongated cylinder. — Magnetic force 23

  3. A thin disk. — Magnetic induction 23

  4. Relation between magnetic force, magnetic induction, and mag

netization 24

  1. Line-integral of magnetic force, or magnetic potential .. .. 24

  2. Surface-integral of magnetic induction 25

  3. Solenoidal distribution of magnetic induction .. .. .. .. 26

  4. Surfaces and tubes of magnetic induction 27

  5. Vector-potential of magnetic induction 27

  6. Relations between the scalar and the vector-potential .. .. 28

CHAPTER III.

PARTICULAR FORMS OF MAGNETS.

  1. Definition of a magnetic solenoid 31

  2. Definition of a complex solenoid and expression for its potential

at any point 32

CONTENTS. Vll

Art. Page

  1. The potential of a magnetic shell at any point is the product of

its strength multiplied by the solid angle its boundary sub tends at the point 32

  1. Another method of proof 33

  2. The potential at a point on the positive side of a shell of

strength <I> exceeds that on the nearest point on the negative

side by 477$ 34

  1. Lamellar distribution of magnetism .. 34

  2. Complex lamellar distribution 34

  3. Potential of a solenoidal magnet 35

  4. Potential of a lamellar magnet 35

  5. Vector-potential of a lamellar magnet 36

  6. On the solid angle subtended at a given point by a closed curve 36

  7. The solid angle expressed by the length of a curve on the sphere 37

  8. Solid angle found by two line-integrations 38

  9. II expressed as a determinant 39

  10. The solid angle is a cyclic function 40

  11. Theory of the vector-potential of a closed curve 41

  12. Potential energy of a magnetic shell placed in a magnetic field 42

CHAPTER IV.

INDUCED MAGNETIZATION.

  1. When a body under the action of magnetic force becomes itself

magnetized the phenomenon is called magnetic induction .. 44

  1. Magnetic induction in different substances 45

  2. Definition of the coefficient of induced magnetization .. .. 47

  3. Mathematical theory of magnetic induction. Poisson's method 47

  4. Faraday's method 49

  5. Case of a body surrounded by a magnetic medium 51

  6. Poisson's physical theory of the cause of induced magnetism .. 53

CHAPTER V.

MAGNETIC PKOBLEMS.

  1. Theory of a hollow spherical shell 56

  2. Case when K. is large 58

  3. When t = l 58

  4. Corresponding case in two dimensions. Fig. XV 59

  5. Case of a solid sphere, the coefficients of magnetization being

different in different directions 60

viii CONTENTS.

Art. Page

  1. The nine coefficients reduced to six. Fig. XVI 61

  2. Theory of an ellipsoid acted on by a uniform magnetic force .. 62

  3. Cases of very flat and of very long ellipsoids 65

  4. Statement of problems solved by Neumann, Kirchhoff and Green 67

  5. Method of approximation to a solution of the general problem

when K is very small. Magnetic bodies tend towards places of most intense magnetic force, and diamagnetic bodies tend to places of weakest force 69

  1. On ship's magnetism 70

CHAPTER VI.

WEBER'S THEORY OF MAGNETIC INDUCTION.

  1. Experiments indicating a maximum of magnetization .. .. 74

  2. Weber's mathematical theory of temporary magnetization .. 75

  3. Modification of the theory to account for residual magnetization 79

  4. Explanation of phenomena by the modified theory 81

  5. Magnetization, demagnetization, and remagnetization .. .. 83

  6. Effects of magnetization on the dimensions of the magnet .. 85

  7. Experiments of Joule ' 86

CHAPTER VII.

MAGNETIC MEASUREMENTS.

  1. Suspension of the magnet 88

  2. Methods of observation by mirror and scale. Photographic

method 89

  1. Principle of collimation employed in the Kew magnetometer .. 93

  2. Determination of the axis of a magnet and of the direction of

the horizontal component of the magnetic force 94

  1. Measurement of the moment of a magnet and of the intensity of

the horizontal component of magnetic force 97

  1. Observations of deflexion 99

  2. Method of tangents and method of sines 101

  3. Observation of vibrations 102

  4. Elimination of the effects of magnetic induction 105

  5. Statical method of measuring the horizontal force 106

  6. Bifilar suspension 107

  7. System of observations in an observatory Ill

  8. Observation of the dip-circle Ill

CONTENTS. IX

Art. Page

  1. J. A. Broun's method of correction 115

  2. Joule's suspension 115

  3. Balance vertical force magnetometer 117

CHAPTER VIII.

TERRESTRIAL MAGNETISM.

  1. Elements of the magnetic force 120

  2. Combination of the results of the magnetic survey of a country 121

  3. Deduction of the expansion of the magnetic potential of the

earth in spherical harmonics 123

  1. Definition of the earth's magnetic poles. They are not at the

extremities of the magnetic axis. False poles. They do not exist on the earth's surface 123

  1. Grauss' calculation of the 24 coefficients of the first four har

monics 124

  1. Separation of external from internal causes of magnetic force .. 124

  2. The solar and lunar variations 125

  3. The periodic variations 125

  4. The disturbances and their period of 11 years 126

  5. Keflexions on magnetic investigations 126

PART IV.

ELECTROMAGNET ISM. CHAPTER I.

ELECTROMAGNETIC FORCE.

  1. Orsted's discovery of the action of an electric current on a

magnet 128

  1. The space near an electric current is a magnetic field .. .. 128

  2. Action of a vertical current on a magnet 129

  3. Proof that the force due to a straight current of indefinitely

great length varies inversely as the distance 129

  1. Electromagnetic measure of the current 130

X CONTENTS.

Art. Page

  1. Potential function due to a straight current. It is a function

of many values 130

  1. The action of this current compared with that of a magnetic

shell having an infinite straight edge and extending on one side of this edge to infinity 131

  1. A small circuit acts at a great distance like a magnet .. .. 131

  2. Deduction from this of the action of a closed circuit of any form

and size on any point not in the current itself 131

  1. Comparison between the circuit and a magnetic shell .. .. 132

  2. Magnetic potential of a closed circuit 133

  3. Conditions of continuous rotation of a magnet about a current 133

  4. Form of the magnetic equipotential surfaces due to a closed

circuit. Fig. XVIII 134

  1. Mutual action between any system of magnets and a closed

current 135

  1. Reaction on the circuit 135

  2. Force acting on a wire carrying a current and placed in the

magnetic field 136

  1. Theory of electromagnetic rotations .. .. 138

  2. Action of one electric circuit on the whole or any portion of

another 139

  1. Our method of investigation is that of Faraday 140

  2. Illustration of the method applied to parallel currents .. .. 140

  3. Dimensions of the unit of current 141

  4. The wire is urged from the side on which its magnetic action

strengthens the magnetic force and towards the side on which

it opposes it 141

  1. Action of an infinite straight current on any current in its

plane .. • 142

  1. Statement of the laws of electromagnetic force. Magnetic force

due to a current 142

  1. Generality of these laws .. 143

  2. Force acting on a circuit placed in the magnetic field .. ..144

  3. Electromagnetic force is a mechanical force acting on the con

ductor, not on the electric current itself 144

CHAPTER II.

MUTUAL ACTION OF ELECTRIC CURRENTS.

  1. Ampere's investigation of the law of force between the elements

of electric currents .. 146

CONTENTS. xi

Art. Page

  1. His method of experimenting 146

  2. Ampere's balance 147

  3. Ampere's first experiment. Equal and opposite currents neu

tralize each other 147

  1. Second experiment. A crooked conductor is equivalent to a

straight one carrying the same current ..148

  1. Third experiment. The action of a closed current as an ele

ment of another current is perpendicular to that element .. 148

  1. Fourth experiment. Equal currents in systems geometrically

similar produce equal forces 149

  1. In all of these experiments the acting current is a closed one .. 151

  2. Both circuits may, however, for mathematical purposes be con

ceived as consisting of elementary portions, and the action

of the circuits as the resultant of the action of these elements 151

  1. Necessary form of the relations between two elementary portions

of lines 151

  1. The geometrical quantities which determine their relative posi

tion 152

  1. Form of the components of their mutual action 153

  2. Kesolution of these in three directions, parallel, respectively, to

the line joining them and to the elements themselves .. .. 154

  1. General expression for the action of a finite current on the ele

ment of another 154

  1. Condition furnished by Ampere's third case of equilibrium .. 155

  2. Theory of the directrix and the determinants of electrodynamic

action 156

  1. Expression of the determinants in terms of the components

of the vector-potential of the current 157

  1. The part of the force which is indeterminate can be expressed

as the space-variation of a potential 157

  1. Complete expression for the action between two finite currents 158

  2. Mutual potential of two closed currents 158

  3. Appropriateness of quaternions in this investigation .. .. 158

  4. Determination of the form of the functions by Ampere's fourth

case of equilibrium 159

  1. The electrodynamic and electromagnetic units of currents .. 159

  2. Final expressions for electromagnetic force between two ele

ments 160

  1. Four different admissible forms of the theory 160

  2. Of these Ampere's is to be preferred 161

xii CONTENTS.

CHAPTER III.

INDUCTION OF ELECTRIC CUEEENTS.

Art. Page

  1. Faraday's discovery. Nature of his methods 162

  2. The method of this treatise founded on that of Faraday .. .. 163

  3. Phenomena of magneto-electric induction 164

  4. General law of induction of currents 166

  5. Illustrations of the direction of induced currents .. *. .. 166

  6. Induction by the motion of the earth 167

  7. The electromotive force due to induction does not depend on

the material of the conductor 168

  1. It has no tendency to move the conductor 168

  2. Felici's experiments on the laws of induction 168

  3. Use of the galvanometer to determine the time-integral of the

electromotive force 170

  1. Conjugate positions of two coils 171

  2. Mathematical expression for the total current of induction .. 172

  3. Faraday's conception of an electrotonic state 173

  4. His method of stating the laws of induction with reference to

the lines of magnetic force 174

  1. The law of Lenz, and Neumann's theory of induction .. .. 176

  2. Helmholtz's deduction of induction from the mechanical action

of currents by the principle of conservation of energy .. .. 176

  1. Thomson's application of the same principle 178

  2. Weber's contributions to electrical science 178

CHAPTER IV.

INDUCTION OF A CUEEENT ON ITSELF.

  1. Shock given by an electromagnet 180

  2. Apparent momentum of electricity 180

  3. Difference between this case and that of a tube containing a

current of water 181

  1. If there is momentum it is not that of the moving electricity .. 181

  2. Nevertheless the phenomena are exactly analogous to those of

momentum 181

  1. An electric current has energy, which may be called electro-

kinetic energy 182

  1. This leads us to form a dynamical theory of electric currents .. 182

CONTENTS. xiii CHAPTER V.

GENERAL EQUATIONS OF DYNAMICS.

Art. Page

  1. Lagrange's method furnishes appropriate ideas for the study of

the higher dynamical sciences 184

  1. These ideas must be translated from mathematical into dy

namical language 184

  1. Degrees of freedom of a connected system 185

  2. Generalized meaning of velocity 186

  3. Generalized meaning of force , .. ..186

  4. Generalized meaning of momentum and impulse ,. ,. .. 186

  5. Work done by a small impulse .. ., 187

  6. Kinetic energy in terms of momenta, (Tp) .. .. ,. .. 188

  7. Hamilton's equations of motion .. .. , 189

  8. Kinetic energy in terms of the velocities and momenta, (Tp,j) .. 190

  9. Kinetic energy in terms of velocities, (T^) ,, ., .. .. 191

  10. Relations between Tp and T^, p and q 191

  11. Moments and products of inertia and mobility .. .. ,. 192

  12. Necessary conditions which these coefficients must satisfy .. 193

  13. Relation between mathematical, dynamical, and electrical ideas 193

CHAPTER VI.

APPLICATION OF DYNAMICS TO ELECTROMAGNETISM.

  1. The electric current possesses energy 195

  2. The current is a kinetic phenomenon 195

  3. Work done by electromotive force 196

  4. The most general expression for the kinetic energy of a system

including electric currents ., .. .. 197

  1. The electrical variables do not appear in this expression .. .. 198

  2. Mechanical force acting on a conductor 198

  3. The part depending on products of ordinary velocities and

strengths of currents does not exist 200

  1. Another experimental test , ,, ., .. 202

  2. Discussion of the electromotive force 204

  3. If terms involving products of velocities and currents existed

they would introduce electromotive forces, which are not ob served ,. ,. ,. 204

CHAPTER VII.

ELECTROKINETICS.

  1. The electrokinetic energy of a system of linear circuits .. .. 206

  2. Electromotive force in each circuit . . 207

xiv CONTENTS.

Art. Page

  1. Electromagnetic force 208

  2. Case of two circuits 208

  3. Theory of induced currents 209

  4. Mechanical action between the circuits 210

  5. All the phenomena of the mutual action of two circuits depend

on a single quantity, the potential of the two circuits .. .. 210

CHAPTER VIII.

EXPLOBATION OF THE FIELD BY MEANS OF THE SECONDARY CIRCUIT.

  1. The electrokinetic momentum of the secondary circuit .. .. 211

  2. Expressed as a line-integral 211

  3. Any system of contiguous circuits is equivalent to the circuit

formed by their exterior boundary 212

  1. Electrokinetic momentum expressed as a surface -integral .. .212

  2. A crooked portion of a circuit equivalent to a straight portion 213

  3. Electrokinetic momentum at a point expressed as a vector, Ql .. 214

  4. Its relation to the magnetic induction, 3B. Equations (A) .. 214

  5. Justification of these names 215

  6. Conventions with respect to the signs of translations and rota

tions 216

  1. Theory of a sliding piece 217

  2. Electromotive force due to the motion of a conductor .. .. 218

  3. Electromagnetic force on the sliding piece ..218

  4. Four definitions of a line of magnetic induction 219

  5. General equations of electromotive force, (B) 219

  6. Analysis of the electromotive force 222

  7. The general equations referred to moving axes 223

  8. The motion of the axes changes nothing but the apparent value

of the electric potential 224

  1. Electromagnetic force on a conductor 224

  2. Electromagnetic force on an element of a conducting body.

Equations (C) 226

CHAPTER IX.

GENERAL EQUATIONS.

  1. Recapitulation 227

  2. Equations of magnetization, (D) 228

  3. Relation between magnetic force and electric currents .. •• 229

  4. Equations of electric currents, (E) 230

  5. Equations of electric displacement, (F) 232

CONTENTS. xv

Art. Page

  1. Equations of electric conductivity, (G) 232

  2. Equations of total currents, (H) 232

  3. Currents in terms of electromotive force, (I) .. .. .. .. 233

  4. Volume-density of free electricity, (J) 233

  5. Surface-density of free electricity, (K) 233

  6. Equations of magnetic permeability, (L) 233

  7. Ampere's theory of magnets 234

  8. Electric currents in terms of electrokinetic momentum .. .. 234

  9. Vector-potential of electric currents 236

  10. Quaternion expressions for electromagnetic quantities .. .. 236

  11. Quaternion equations of the electromagnetic field 237

CHAPTER X.

DIMENSIONS OF ELECTKIC UNITS.

  1. Two systems of units .. .. 239

  2. The twelve primary quantities 239

  3. Fifteen relations among these quantities 240

  4. Dimensions in terms of [e] and [m] 241

  5. Reciprocal properties of the two systems 241

  6. The electrostatic and the electromagnetic systems 241

  7. Dimensions of the 12 quantities in the two systems .. .. 242

  8. The six derived units 243

  9. The ratio of the corresponding units in the two systems .. 243

  10. Practical system of electric units. Table of practical units .. 244

CHAPTER XI.

ENERGY AND STRESS.

  1. The electrostatic energy expressed in terms of the free electri

city and the potential 246

  1. The electrostatic energy expressed in terms of the electromotive

force and the electric displacement 246

  1. Magnetic energy in terms of magnetization and magnetic force 247

  2. Magnetic energy in terms of the square of the magnetic force .. 247

  3. Electrokinetic energy in terms of electric momentum and electric

current 248

  1. Electrokinetic energy in terms of magnetic induction and mag

netic force 248

  1. Method of this treatise 249

  2. Magnetic energy and electrokinetic energy compared .. .. 249

  3. Magnetic energy reduced to electrokinetic energy 250

xvi CONTENTS.

Art. Page

  1. The force acting on a particle of a substance due to its magnet

ization 251

  1. Electromagnetic force due to an electric current passing through

it 252

  1. Explanation of these forces by the hypothesis of stress in a

medium 253

  1. General character of the stress required to produce the pheno

mena 255

  1. When there is no magnetization the stress is a tension in the

direction of the lines of magnetic force, combined with a pressure in all directions at right angles to these lines, the

magnitude of the tension and pressure being — — • ^2, where •$

O7T

is the magnetic force 256

  1. Force acting on a conductor carrying a current 257

  2. Theory of stress in a medium as stated by Faraday .. .. 257

  3. Numerical value of magnetic tension 258

CHAPTER XII.

CURRENT-SHEETS.

  1. Definition of a current-sheet 259

  2. Current-function 259

  3. Electric potential , 260

  4. Theory of steady currents 260

  5. Case of uniform conductivity 260

  6. Magnetic action of a current-sheet with closed currents .. .. 261

  7. Magnetic potential due to a current-sheet 262

  8. Induction of currents in a sheet of infinite conductivity .. .. 262

  9. Such a sheet is impervious to magnetic action 263

  10. Theory of a plane current-sheet 263

  11. The magnetic functions expressed as derivatives of a single

function 264

  1. Action of a variable magnetic system on the sheet 266

  2. When there is no external action the currents decay, and their

magnetic action diminishes as if the sheet had moved off with constant velocity R 267

  1. The currents, excited by the instantaneous introduction of a

magnetic system, produce an effect equivalent to an image of that system 267

  1. This image moves away from its original position with velo

city R 268

  1. Trail of images formed by a magnetic system in continuous

motion . 268

CONTENTS. xvn

Art. Page

  1. Mathematical expression for the effect of the induced currents 269

  2. Case of the uniform motion of a magnetic pole 269

  3. Value of the force acting on the magnetic pole 270

  4. Case of curvilinear motion 271

  5. Case of motion near the edge of the sheet .. .. ..-'.', 271

  6. Theory of Arago's rotating disk 271

  7. Trail of images in the form of a helix 274

  8. Spherical current-sheets 275

  9. The vector- potential 276

  10. To produce a field of constant magnetic force within a spherical

shell 277

  1. To produce a constant force on a suspended coil 278

  2. Currents parallel to a plane 278

  3. A plane electric circuit. A spherical shell. An ellipsoidal

shell 279

  1. A solenoid 280

  2. A long solenoid 281

  3. Force near the ends 282

  4. A pair of induction coils 282

  5. Proper thickness of wire 283

G81. An endless solenoid 284

CHAPTER XIII.

PAKALLEL CURRENTS.

  1. Cylindrical conductors 286

  2. The external magnetic action of a cylindric wire depends only

on the whole current through it .. 287

  1. The vector-potential 288

  2. Kinetic energy of the current 288

  3. Repulsion between the direct and the return current .. .. 289

  4. Tension of the wires. Ampere's experiment ,. 289

  5. Self-induction of a wire doubled on itself 290

  6. Currents of varying intensity in a cylindric wire 291

  7. Relation between the electromotive force and the total current 292

  8. Geometrical mean distance of two figures in a plane .. ,. 294

  9. Particular cases 294

  10. Application of the method to a coil of insulated wires .. .. 296

CHAPTER XIV.

CIRCULAR CURRENTS.

  1. Potential due to a spherical bowl 299

  2. Solid angle subtended by a circle at any point 301

VOL. II. b

xviii CONTENTS.

Art. Page

  1. Potential energy of two circular currents 302

  2. Moment of the couple acting between two coils 303

  3. Values of Q? 303

  4. Attraction between two parallel circular currents 304

  5. Calculation of the coefficients for a coil of finite section .. .. 304

  6. Potential of two parallel circles expressed by elliptic integrals 305

  7. Lines of force round a circular current. Fig. XVIII .. .. 307

  8. Differential equation of the potential of two circles 307

  9. Approximation when the circles are very near one another .. 309

  10. Further approximation 310

  11. Coil of maximum self-induction 311

CHAPTER XV.

ELECTROMAGNETIC INSTRUMENTS.

  1. Standard galvanometers and sensitive galvanometers .. .. 313

  2. Construction of a standard coil 314

  3. Mathematical theory of the galvanometer 315

  4. Principle of the tangent galvanometer and the sine galvano

meter 316

  1. Galvanometer with a single coil 316

  2. Gaugain's eccentric suspension 317

  3. Helmholtz's double coil. Fig. XIX 318

  4. Galvanometer with four coils 319

  5. Galvanometer with three coils 319

  6. Proper thickness of the wire of a galvanometer 321

  7. Sensitive galvanometers 322

  8. Theory of the galvanometer of greatest sensibility 322

  9. Law of thickness of the wire 323

  10. Galvanometer with wire of uniform thickness 325

  11. Suspended coils. Mode of suspension 326

  12. Thomson's sensitive coil 326

  13. Determination of magnetic force by means of suspended coil

and tangent galvanometer 327

  1. Thomson's suspended coil and galvanometer combined .. .. 328

  2. Weber's electrodynamometer 328

  3. Joule's current -weigher 332"

  4. Suction of solenoids 333

  5. Uniform force normal to suspended coil 333

  6. Electrodynamometer with torsion-arm 334

CONTENTS. xix CHAPTER XVI.

ELECTROMAGNETIC OBSERVATIONS.

Art. Page

  1. Observation of vibrations , ;. 335

  2. Motion in a logarithmic spiral 336

  3. Eectilinear oscillations in a resisting medium 337

  4. Values of successive elongations 338

  5. Data and qusesita 338

  6. Position of equilibrium determined from three successive elon

gations 338

  1. Determination of the logarithmic decrement 339

  2. When to stop the experiment 339

  3. Determination of the time of vibration from three transits .. 339

  4. Two series of observations 340

  5. Correction for amplitude and for damping 341

  6. Dead beat galvanometer 341

  7. To measure a constant current with the galvanometer .. .. 342

  8. Best angle of deflexion of a tangent galvanometer 343

  9. Best method of introducing the current 343

  10. Measurement of a current by the first elongation 344

  11. To make a series of observations on a constant current .. .. 345

  12. Method of multiplication for feeble currents 345

  13. Measurement of a transient current by first elongation .. .. 346

  14. Correction for damping 347

  15. Series of observations. Zurilckwerfungs methode 348

  16. Method of multiplication 350

CHAPTER XVII.

ELECTRICAL MEASUREMENT OF COEFFICIENTS OF INDUCTION.

  1. Electrical measurement sometimes more accurate than direct

measurement 352

  1. Determination of G^ 353

  2. Determination of gl 354

  3. Determination of the mutual induction of two coils .. .. 354

  4. Determination of the self-induction of a coil 356

  5. Comparison of the self-induction of two coils 357

CHAPTER XVIII.

DETERMINATION OF RESISTANCE IN ELECTROMAGNETIC MEASURE.

  1. Definition of resistance 358

  2. Kirchhoff's method 358

XX CONTENTS.

Art. Page

  1. Weber's method by transient currents 360

  2. His method of observation 361

  3. Weber's method by damping 361

  4. Thomson's method by a revolving coil 364

  5. Mathematical theory of the revolving coil ..- 364

  6. Calculation of the resistance 365

  7. Corrections 366

  8. Joule's calorimetric method 367

CHAPTER XIX.

COMPARISON OF ELECTROSTATIC WITH ELECTROMAGNETIC UNITS.

  1. Nature and importance of the investigation 368

  2. The ratio of the units is a velocity 369

  3. Current by convection 370

  4. Weber and Kohlrausch's method 370

  5. Thomson's method by separate electrometer and electrodyna-

mometer 372

  1. Maxwell's method by combined electrometer and electrodyna-

mometer 372

  1. Electromagnetic measurement of the capacity of a condenser.

Jenkin's method 373

  1. Method by an intermittent current 374

  2. Condenser and Wippe as an arm of Wheatstone's bridge .. 375

  3. Correction when the action is too rapid 376

  4. Capacity of a condenser compared with the self-induction of a

coil 377

  1. Coil and condenser combined 379

  2. Electrostatic measure of resistance compared with its electro

magnetic measure 382

CHAPTER XX.

ELECTROMAGNETIC THEORY OF LIGHT.

  1. Comparison of the properties of the electromagnetic medium

with those of the medium in the undulatory theory of light 383

  1. Energy of light during its propagation 384

  2. Equation of propagation of an electromagnetic disturbance .. 384

  3. Solution when the medium is a non-conductor 386

  4. Characteristics of wave-propagation 386

  5. Velocity of propagation of electromagnetic disturbances .. .. 387

  6. Comparison of this velocity with that of light 387

CONTENTS. xxi

Art. Page

  1. The specific inductive capacity of a dielectric is the square of

its index of refraction 388

  1. Comparison of these quantities in the case of paraffin .. .. 388

  2. Theory of plane waves 389

  3. The electric displacement and the magnetic disturbance are in

the plane* of the wave-front, and perpendicular to each other 390

  1. Energy and stress during radiation 391

  2. Pressure exerted by light .. .. 391

  3. Equations of motion in a crystallized medium 392

  4. Propagation of plane waves •,. .. 393

  5. Only two waves are propagated 393

  6. The theory agrees with that of Fresnel 394

  7. Relation between electric conductivity and opacity .. .. 394

  8. Comparison with facts 395

  9. Transparent metals 395

  10. Solution of the equations when the medium is a conductor .. 395

  11. Case of an infinite medium, the initial state being given .. 396

  12. Characteristics of diffusion 397

  13. Disturbance of the electromagnetic field when a current begins

to flow 397

  1. Rapid approximation to an ultimate state 398

CHAPTER XXI.

MAGNETIC ACTION ON LIGHT.

  1. Possible forms of the relation between magnetism and light .. 399

  2. The rotation of the plane of polarization by magnetic action .. 400

  3. The laws of the phenomena 400

  4. Verdet's discovery of negative rotation in ferromagnetic media 400

  5. Rotation produced by quartz, turpentine, &c., independently of

magnetism 401

  1. Kinematical analysis of the phenomena 402

  2. The velocity of a circularly-polarized ray is different according

to its direction of rotation , 402

  1. Right and left-handed rays 403

  2. In media which of themselves have the rotatory property the

velocity is different for right and left-handed configurations 403

  1. In media acted on by magnetism the velocity is different for

opposite directions of rotation 404

  1. The luminiferous disturbance, mathematically considered, is a

vector 404

  1. Kinematic equations of circularly-polarized light 405

xxii CONTENTS.

Art. Page

  1. Kinetic and potential energy of the medium 406

  2. Condition of wave-propagation 406

  3. The action of magnetism must depend on a real rotation about

the direction of the magnetic force as an axis 407

  1. Statement of the results of the analysis of the phenomenon .. 407

  2. Hypothesis of molecular vortices 408

  3. Variation of the vortices according to Helmholtz's law .. .. 409

  4. Variation of the kinetic energy in the disturbed medium .. 409 825.- Expression in terms of the current and the velocity .. .. 410

  5. The kinetic energy in the case of plane waves 410

  6. The equations of motion 411

  7. Velocity of a circularly-polarized ray 411

  8. The magnetic rotation 412

  9. Researches of Verdet 413

  10. Note on a mechanical theory of molecular vortices 415

CHAPTER XXII.

ELECTRIC THEOEY OF MAGNETISM.

  1. Magnetism is a phenomenon of molecules 418

  2. The phenomena of magnetic molecules may be imitated by

electric currents 419

  1. Difference between the elementary theory of continuous magnets

and the theory of molecular currents 419

  1. Simplicity of the electric theory 420

  2. Theory of a current in a perfectly conducting circuit .. .. 420

  3. Case in which the current is entirely due to induction .. .. 421

Provenance

Shelf
Reference library
Book
A Treatise on Electricity and Magnetism, Vol. 2 (1873)
Author
James Clerk Maxwell
Rights
Published in 1873, before 1929, and therefore in the public domain in the United States.
Collected By
StanBot reference library