A Treatise on Electricity and Magnetism, Volume 0

Front Cover
Courier Corporation, 1954 - Science - 532 pages

"Maxwell is without a peer … this printing is an opportunity to become thoroughly acquainted with the thought of the greatest of our electrical scientists." — School Science and Math.
Here is the final elaboration of Maxwell's theory of electromagnetism, including the systematic and rigorous derivation of his general equations of field theory. These equations continue to occupy a central position in the modern physicist's view of the physical world. They are a magnificent summary of the fundamental advances in electricity and magnetism, and later inspired the theories of Lorentz on the electron and Einstein on relativity. Einstein himself has said that "The formulation of these equations is the most important event in physics since Newton's time" — The Evolution of Physics.
Volume 2, Part III, "Magnetism," develops a theory of magnetism through the study of solenoids and shells, magnetic induction, methods of observation, and terrestrial magnetism. Part IV, "Electromagnetism," covers the mutual action of electric currents, the equations of motion of a connected system, Maxwell's dynamical theory of electromagnetism, the equations of the electromagnetic field, dimensions of electric units, parallel and circular currents, coils, and the electromagnetic theory of light and foundation of the theory of relativity.

 

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Contents

371
1
381
7
Investigation of the action of one magnetic particle on another
15
396
23
405
29
Another method of proof
35
386
37
Theory of the vectorpotential of a closed curve
43
Relation between the electromotive force and the tota 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 II
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

Magnetic induction in different substances
49
Case of a body surrounded by a magnetic medium
55
CHAPTER
59
Case when k is large
61
Art Page 436 The nine coefficients reduced to six Fig XVI
64
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 x is very small Magnetic bodies tend towards places of most intense magnetic fo...
73
On ships magnetism
74
webERs THEoRY of INDUCED MAGNETISM 442 Experiments indicating a maximum of magnetization
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
93
CHAPTER VII
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
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
on TERRESTRIAL MAGNETISM
129
The solar and lunar variations
135
482
141
490
148
498
155
CHAPTER II
158
Art Page
159
Kinematical analysis of the phenomena 454
163
Determination of the form of the functions by Ampères fourth
172
Thomsons application of the same principle
191
An electric current has energy which may be called electro
197
oN THE EQUATIONs of MoTION of A connecTED systEM Art Page 553 Lagranges method furnishes appropriate ideas for the study of the higher ...
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 Tri
206
Relations between T and Tº p and j
207
Moments and products of inertia and mobility
208
Necessary conditions which these coefficients must satisfy
209
CHAPTER WI DYNAMICAL THEORY OF ELECTRoMAGNETISM 568 The electric current possesses energy
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
Theory of ELECTRIC CIRCUITS 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
Exploration of The FIELD BY MEANS OF THE secondary circuit 585 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 ?
232
Its relation to the magnetic induction B 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
Electromagnetic force on a conductor
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
Fifteen relations among these quantities
264
Dimensions in terms of e 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
Magnetic energy in terms of magnetization and magnetic
271
MAGNETIC Force AND MAGNETIC INDUCTION
273
Electromagnetic force due to an electric current passing
277
Numerical value of magnetic tension
283
Application to any magnet
284
CHAPTER XII
286
Electric potential
287
Magnetic action of a currentsheet with closed currents
288
Magnetic potential due to a currentsheet
289
Lineintegral of magnetic force or magnetic potential
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
295
This image moves away from its original position with velo city R
296
Mathematical expression for the effect of the induced currents
297
Walue of the force acting on the magnetic pole
298
666 Case of curvilinear motion
299
Theory of Aragos rotating disk
300
26
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
A plane electric circuit A spherical shell An ellipsoidal shell
308
A solenoid
309
A long solenoid
310
A pair of induction coils
311
28
312
An endless solenoid
313
CHAPTER XIII
315
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
The motion of the axes changes nothing but the apparent value of the electric potential 243
321
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
Art 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
387
349
CHAPTER XV
351
Construction of a standard coil
352
Mathematical theory of the galvanometer z
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 3 71
371
Suction of solenoids 37 2
373
CHAPTER XVI
374
Motion in a logarithmic spiral
375
Rectilinear oscillations in a resisting medium
376
Walues 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 Zurückwerfungsmethode
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 G
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
CHAPTER XVIII
402
Kirchhoffs method
403
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 o a coil
425
Coil and condenser combined
427
Ampères investigation of the law of force between the elements
428
Electrostatic measure of resistance compared with its electro magnetic measure
430
CHAPTER XX
431
Energy of light during its 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 o its index of refraction
437
142
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
Werdets discovery of negative rotation in ferromagnetic media
453
The velocity of a circularlypolarized ray is different according to its direction of rotation
455
In media which of themselves have the rotatory property the velocity is different for right and lefthanded configurations
456
The luminiferous disturbance mathematically considered is a vector
457
Kinetic and potential energy of the medium
458
Condition of wavepropagation 820 The action of magnetism must depend on a real rotation about the direction of the magnetic force as an axis
459
Statement of the results of the analysis of the phenomenon
460
Wariation of the vortices according to Helmholtzs law
462
Expression in terms of the current and the velocity
463
Velocity of a circularlypolarized ray
464
The magnetic rotation
465
Researches of Werdet
466
Note on a mechanical theory of molecular vortices
468
CHAPTER XXII
471
The phenomena of magnetic molecules may be imitated by electric currents
472
Simplicity of the electric theory
473
Theory of a current in a perfectly conducting circuit
474
Webers theory of diamagnetism
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 Ampères 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
858 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
INDEX
495
143
497
PLATES
501
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About the author (1954)

James Clerk Maxwell: In His Own Words — And Others
Dover reprinted Maxwell's Treatise on Electricity and Magnetism in 1954, surely one of the first classics of scientific literature over a thousand pages in length to be given new life and accessibility to students and researchers as a result of the paperback revolution of the 1950s. Matter and Motion followed in 1991 and Theory of Heat in 2001.

Some towering figures in science have to speak for themselves. Such is James Clerk Maxwell (1813–1879), the Scottish physicist and mathematician who formulated the basic equations of classical electromagnetic theory.

In the Author's Own Words:
"We may find illustrations of the highest doctrines of science in games and gymnastics, in traveling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion."

"The 2nd law of thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again." — James Clerk Maxwell

Critical Acclaim for James Clerk Maxwell:
"From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade." — Richard P. Feynman

"Maxwell's equations have had a greater impact on human history than any ten presidents." — Carl Sagan

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