## A Treatise on Electricity and Magnetism, Volume 2 |

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### Contents

MAGNETISM CHAPTER I | 1 |

Action of magnets on one another Law of magnetic force | 2 |

Definition of magnetic units and their dimensions | 3 |

Nature of the evidence for the law of magnetic force | 4 |

Effects of breaking a magnet | 5 |

Theory of magneticmatter | 6 |

Magnetization is of the nature of a vector | 7 |

Meaning of the term Magnetic Polarization | 8 |

Electric potential | 287 |

Magnetic action of a currentsheet with closed currents | 288 |

Magnetic potential due to a currentsheet | 289 |

Induction of currents in a sheet of infinite conductivity | 290 |

Theory of a plane currentsheet | 291 |

Action of a variable magnetic system on the sheet | 293 |

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 | 294 |

The currents excited by the instantaneous introduction of a magnetic system produce an effect equivalent to an image of that system | 295 |

Properties of a magnetic particle | 9 |

Potential of a magnet of finite size Two expressions for this potential corresponding respectively to the theory of polariza tion and to that of magnetic... | 10 |

Investigation of the action of one magnetic particle on another | 11 |

Particular cases | 13 |

Potential energy of a magnet in any field of force | 15 |

On the magnetic moment and axis of a magnet | 17 |

Magnetic force in a cylindric cavity in a magnet uniformly | 23 |

Vectorpotential of magnetic induction | 29 |

tends at the point | 35 |

The potential at a point on the positive side of a shell of strength t exceeds that on the nearest point on the negative side by 4 w | 36 |

Complex lamellar distribution | 37 |

Vectorpotential of a lamellar magnet | 38 |

On the solid angle subtended at a given point by a closed curve | 39 |

The solid angle expressed by the length of a curve on the sphere | 40 |

FI expressed as a determinant | 41 |

The solid angle is a cyclic function | 42 |

Theory of the vectorpotential of a closed curve | 43 |

Potential energy of a magnetic shell placed in a magnetic field | 45 |

CHAPTER IV | 47 |

Magnetic induction in different substances | 49 |

Definition of the coefficient of induced magnetization | 50 |

Faradays method | 53 |

Case of a body surrounded by a magnetic medium | 55 |

Poissons physical theory of the cause of induced magnetism | 57 |

CHAPTER V | 59 |

Case when is large | 61 |

Corresponding case in two dimensions Fig XV | 62 |

Case of a solid sphere the coefficients of magnetization being different in different directions | 63 |

Theory of an ellipsoid acted on by a uniform magnetic force | 66 |

Cases of very flat and of very long ellipsoids | 68 |

Statement of problems solved by Neumann Kirchhoff and Green | 72 |

Method of approximation to a solution of the general problem when K is very small Magnetic bodies tend towards places of most intense magnetic f... | 73 |

On ships magnetism | 74 |

A plane electric circuit A spherical shell An ellipsoidal | 75 |

CHAPTER VI | 79 |

Webers mathematical theory of temporary magnetization | 81 |

Modification of the theory to account for residual magnetization | 85 |

Explanation of phenomena by the modified theory | 87 |

Magnetization demagnetization and remagnetization | 90 |

Effects of magnetization on the dimensions of the magnet | 92 |

Experiments of Joule | 93 |

MAGNETIC MEASUREMENTS 449 Suspension of the magnet | 95 |

Methods of observation by mirror and scale Photographic method | 96 |

Principle of collimation employed in the Kew magnetometer | 101 |

Measurement of the moment of a magnet and of the intensity of the horizontal component of magnetic force | 104 |

Rotation produced by quartz turpentine c independently | 105 |

Observations of deflexion | 108 |

Method of tangents and method of sines | 109 |

Observation of vibrations | 110 |

Elimination of the effects of magnetic induction | 112 |

Statical method of measuring the horizontal force | 114 |

Bifilar suspension | 115 |

System of observations in an observatory | 119 |

Observation of the dipcircle | 120 |

Art Page | 123 |

CHAPTER VIII | 129 |

The solar and lunar variations | 135 |

The action of this current compared with that of a magnetic | 141 |

Reaction on the circuit | 147 |

The wire is urged from the side on which its magnetic action | 153 |

His method of experimenting | 159 |

tralize each other | 160 |

Kinematics analysis of the phenomena 454 | 163 |

Final expressions for electromagnetic force between two ele | 173 |

ON THE INDUCTION OF ELECTRIC CURRENTS Art Fane 528 Faradays discovery Nature of his methods | 175 |

The method of this treatise founded on that of Faraday | 176 |

Phenomena of magnetoelectric induction | 178 |

General law of induction of currents | 179 |

Induction by the motion of the earth | 180 |

The electromotive force due to induction does not depend on the material of the conductor | 181 |

It has no tendency to move the conductor | 182 |

Use of the galvanometer to determine the timeintegral of the electromotive force | 184 |

Conjugate positions of two coils | 185 |

Mathematical expression for the total current of induction | 186 |

Faradays conception of an electrotonic state | 188 |

The law of Lenz and Neumanns theory of induction | 189 |

Helmholtzs deduction of induction from the mechanical action of currents by the principle of conservation of energy | 190 |

Thomsons application of the same principle | 191 |

Webers contributions to electrical science | 193 |

CHAPTER IV | 195 |

Difference between this case and that of a tube containing a current of water | 196 |

An electric current has energy which may be called electro kinetic energy | 197 |

Lagranges method furnishes appropriate ideas for the study of the higher dynamical sciences | 199 |

Degrees of freedom of a connected system | 200 |

Generalized meaning of velocity | 201 |

Work done by a small impulse | 203 |

Hamiltons equations of motion | 205 |

Kinetic energy in terms of the velocities and momenta 7 | 206 |

Relations between Tf and Tp and q | 207 |

Moments and products of inertia and mobility | 208 |

Necessary conditions which these coefficients must satisfy | 209 |

CHAPTER VI | 211 |

Work done by electromotive force | 212 |

The most general expression for the kinetic energy of a system including electric currents | 213 |

The electrical variables do not appear in this expression | 214 |

Mechanical force acting on a conductor | 215 |

The part depending on products of ordinary velocities and strengths of currents does not exist | 216 |

Another experimental test | 218 |

Discussion of the electromotive force | 221 |

Art Page 578 The electrokinetic energy of a system of linear circuits | 223 |

Electromotive force in each circuit | 224 |

Electromagnetic force | 225 |

Case of two circuits | 226 |

Mechanical action between the circuits | 227 |

All the phenomena of the mutual action of two circuits depend on a single quantity the potential of the two circuits | 228 |

The electrokinetic momentum of the secondary circuit | 229 |

Expressed as a lineintegral | 230 |

A crooked portion of a circuit equivalent to a straight portion | 231 |

Electrokinetic momentum at a point expressed as a vector 51 | 232 |

Its relation to the magnetic induction SB Equations A | 233 |

Justification of these names | 234 |

Theory of a sliding piece | 235 |

Electromotive force due to the motion of a conductor | 236 |

Electromagnetic force on the sliding piece | 237 |

General equations of electromotive force B | 238 |

Analysis of the electromotive force | 240 |

The general equations referred to moving axes | 241 |

The motion of the axes changes nothing but the apparent value of the electric potential | 243 |

Electromagnetic force on an element of a conducting body Equations C | 244 |

CHAPTER IX | 247 |

Equations of magnetization D | 249 |

Equations of electric currents E | 250 |

Equations of electric displacement F | 252 |

Equations of electric conductivity G | 253 |

Volumedensity of free electricity J | 254 |

Electric currents in terms of electrokinetic momentum | 255 |

Vectorpotential of electric currents | 256 |

Quaternion expressions for electromagnetic quantities | 257 |

Quaternion equations of the electromagnetic field | 258 |

Appendix to Chapter IX | 259 |

CHAPTER X | 263 |

Fifieen relations among these quantities | 264 |

Dimensions in terms of and m | 265 |

Reciprocal properties of the two systems | 266 |

Dimensions of the twelve quantities in the two systems | 267 |

Practical system of electric units Table of practical units | 268 |

Art Pg | 270 |

The force acting on a particle of a substance due to its magnet | 276 |

Force acting on a conductor carrying a current | 282 |

Definition of a currentsheet | 286 |

Trail of images formed by a magnetic system in continuous motion | 296 |

Mathematical expression for the effect of the induced currents | 297 |

Value of the force acting on the magnetic pole 29S 666 Case of curvilinear motion | 299 |

Theory of Aragos rotating disk | 300 |

Trail of images in the form of a helix | 303 |

Spherical currentsheets | 304 |

The vectorpotential | 305 |

To produce a field of constant magnetic force within a spherical shell | 306 |

Currents parallel to a plane | 307 |

Bhell | 308 |

A solenoid | 310 |

A pair of induction coils | 311 |

Proper thickness of wire | 312 |

An endless solenoid | 313 |

CHAPTER XIII | 315 |

fi83 The external magnetic action of a cylindric wire depends only on the whole current through it | 316 |

The vectorpotential | 317 |

Repulsion between the direct and the return current | 318 |

Selfinduction of a wire doubled on itself | 320 |

Relation between the electromotive force and the total current | 322 |

Geometrical mean distance of two figures in a plane | 324 |

Particular cases | 326 |

Application of the method to a coil of insulated wires | 328 |

CHAPTER XIV | 331 |

Solid angle subtended by a circle at any point | 333 |

Potential energy of two circular currents | 334 |

Moment of the couple acting between two coils | 335 |

Values of P | 336 |

Calculation of the coefficients for a coil of finite section | 337 |

Potential of two parallel circles expressed by elliptic integrals | 338 |

Alt Page 702 Lines of force round a circular current Fig XVIII | 340 |

Differential equation of the potential of two circles | 341 |

Approximation when the circles are very near one another | 342 |

Further approximation | 343 |

Coil of maximum selfinduction | 345 |

Appendix I | 347 |

Appendix II | 350 |

CHAPTER XV | 351 |

Construction of a standard coil | 352 |

Mathematical theory of the galvanometer | 353 |

Principle of the tangent galvanometer and the sine galvano meter | 354 |

Gaugains eccentric suspension | 356 |

Galvanometer with four coils | 357 |

Galvanometer with three coils | 358 |

Proper thickness of the wire of a galvanometer | 359 |

Sensitive galvanometers | 360 |

Law of thickness of the wire | 361 |

Galvanometer with wire of uniform thickness | 364 |

Thomsons sensitive coil | 365 |

Determination of magnetic force by means of suspended coil and tangent galvanometer | 366 |

Webers electrodynamometer | 367 |

Joules currentweigher | 371 |

Suction of solenoids | 372 |

Electrodynamometer with torsionarm | 373 |

CHAPTER XVI | 374 |

Motion in a logarithmic spiral 375 | 375 |

Rectilinear oscillations in a resisting medium | 376 |

Values of successive elongations | 377 |

Determination of the logarithmic decrement | 378 |

Determination of the time of vibration from three transits | 379 |

Two series of observations | 380 |

Dead beat galvanometer | 381 |

To measure a constant current with the galvanometer | 382 |

Best method of introducing the current | 383 |

Measurement of a current by the first elongation | 384 |

Method of multiplication for feeble currents | 385 |

Measurement of a transient current by first elongation | 386 |

Correction for damping | 387 |

Series of observations Zuriickwerfungsmethode | 388 |

If terms involving products of velocities and currents existed they would introduce electromotive forces which are not ob served 221 | 390 |

CHAPTER XVII | 392 |

Determination of gl | 393 |

Determination of the mutual induction of two coils | 395 |

Determination of the selfinduction of a coil | 397 |

Comparison of the selfinduction of two coils | 398 |

Appendix to Chapter XVII | 399 |

Definition of resistance | 402 |

Webers method by transient currents | 404 |

His method of observation | 405 |

Thomsons method by a revolving coil | 408 |

Mathematical theory of the revolving coil | 409 |

Calculation of the resistance | 410 |

Corrections | 411 |

CHAPTER XIX | 413 |

The ratio of the units is a velocity | 414 |

Current by convection | 415 |

Weber and Kohlrauschs method | 416 |

Thomsons method by separate electrometer and electrodyna mometer | 417 |

Maxwells method by combined electrometer and electrodyna mometer | 418 |

Electromagnetic measurement of the capacity of a condenser Jenkins method | 419 |

Method by an intermittent current | 420 |

Condenser and Wippe as an arm of Wheatstones bridge | 421 |

Correction when the action is too rapid | 423 |

Capacity of a condenser compared with the selfinduction of a coil | 425 |

Coil and condenser combined | 427 |

Electrostatic measure of resistance compared with its electro magnetic measure | 430 |

Comparison of the properties of the electromagnetic medium with those of the medium in the undulatory theory of light | 431 |

Energy of light during HB propagation | 432 |

Equation of propagation of an electromagnetic disturbance | 433 |

Solution when the medium is a nonconductor | 434 |

Characteristics of wavepropagation | 435 |

Comparison of this velocity with that of light | 436 |

The specific inductive capacity of a dielectric is the square of its index of refraction | 437 |

Theory of plane waves | 438 |

The electric displacement and the magnetic disturbance are in the plane of the wavefront and perpendicular to each other | 439 |

Energy and stress during radiation | 440 |

Pressure exerted by light | 441 |

Equations of motion in a crystallized medium | 442 |

Propagation of plane waves | 444 |

The theory agrees with that of Fresnel | 445 |

Comparison with facts | 446 |

Solution of the equations when the medium is a conductor | 447 |

Characteristics of diffusion | 448 |

Rapid approximation to an ultimate state | 449 |

CHAPTER XXI | 451 |

The rotation of the plane of polarization by magnetic action | 452 |

Verdets discovery of negative rotation in ferromagnetic media | 453 |

The velocity of a circularlypolarized ray is different according | 455 |

Hypothesis of molecular vortices | 461 |

Note on a mechanical theory of molecular vortices | 468 |

Theory of a current in a perfectly conducting circuit | 474 |

Webers theory of diamaguetism | 475 |

Theory of a perfect conductor | 476 |

Mechanical action of magnetic force on the current which it excites | 477 |

Modifications of Webers theory | 478 |

Consequences of the theory | 479 |

Potential function due to a straight current It is a function | 480 |

Relative motion of four electric particles Fechners theory | 481 |

Two new forms of Amperes formula | 482 |

These are due to Gauss and to Weber respectively | 483 |

Webers formula is consistent with this principle but that of Gauss is not | 484 |

Potential of two currents | 485 |

Webers theory of the induction of electric currents | 486 |

Segregating force in a conductor | 487 |

Case of moving conductors | 488 |

The formula of Gauss leads to an erroneous result | 489 |

Theory of Riemann | 490 |

Theory of Betti | 491 |

Repugnance to the idea of a medium | 492 |