Electromagnetic Theory, Volume 3

Front Cover
American Mathematical Soc., 2003 - Science - 666 pages
Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. However, his main research activity concerned the theory of electricity and magnetism, the area in which he worked for most of his life. Results of this work are presented in his fundamental three-volume ""Electromagnetic Theory"". The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912. One of Heaviside's main achievements was the recasting of Maxwell's theory of electromagnetism into the form currently used by everyone. He is also known for the invention of operational calculus and for major contributions to solving theoretical and practical problems of cable and radio communication.All this is collected in three volumes of ""Electromagnetic Theory"". However, there is even more. For example, Chapter V in Volume II discusses the age of Earth, and several sections in Volume III talk about the teaching of mathematics in school. In addition to Heaviside's writings, two detailed surveys of Heaviside's work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of ""Electromagnetic Theory"") is included in Volume III.
 

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Contents

WAVES FROM MOVING SOURCE
1903
Simple Proof of Fundamental Property of a Plane Wave
1
The General Plane Wave
2
Generation of Waves by a Plane Source of Induction
4
Generation of Waves by a Plane Source of Displacement
6
Comparison of Electromagnetic with Aerial Waves
7
Waves ending perpendicularly upon a Conductor Conduction and Convection
8
Oblique Reflection at a Conducting Surface with H tangential Transformation to a Convection Problem
11
How to have Constant Speed through Space of Plane Radiation Traversing a Moving Compressible Ether
147
Connection Between the Compressed Electromagnetic Wave and Rankines Wave of Compression
150
Theory of the Rankinian Wave of Compression
152
Crossing of Two Waves Riemanns Solution
153
Modification of the Rankmian to make a Compressed Maxwellian Wave
154
The Waste of Energy from a Moving Electron
156
Sound Waves and Electromagnetics The Fanpotential
162
The Radiation from an Electron describing a Circular Orbit
167

Generation of a Pair of Inclined Plane Waves by Motion of an Electrified Strip uv The applied force required
13
Generation of a Pair of Inclined Plane Waves by a Moving Source of Induction when uv
16
Slanting Plane Waves Generated by a Moving Magnet and by an Electrified Strip moving normally to its Plane
18
Generation of a Single Plane Wave by Motion of an Electrified Electret Also of Two Separated Plane Waves
21
Theory of the Steady Rectilinear Motion of a PointCharge or Electron through the Ether when uv and when uv
23
Construction of the Slanting Plane Waves generated by an Electrified Line by means of the Potential of an Electron
26
The steady Rectilinear Motion in its own line of a Terminated Electrified Live when uv and interpretation of the Impure Conical Wave Following an ...
28
The Wave from a Straight Line Source of Induction in a Nonconducting Dielectric
31
The Wave from a Straight Line Source of Induction In a Conductor
35
The Waves due to a Growing Plane Sheet ot Sources of Induction and to Travelling Filaments at any Speed
37
Reversion to Divergent Plane Waves Is the Ether Fixed?
41
Drag of Matter upon Ether Modified Circuital Equations and the Wavespeed resulting
42
Comparison of Wavespeeds in special Cases
44
Effect of Modified Circuital Equations on Electrical Distributions
48
Lorentzs Equations of a Moving Dielectric
50
The Wavespeed according to Lorentz
53
Possible Equations for a Moving Magnetised Substance
55
Larmors Equations for a Moving Body
57
Theory of Moving Electrified Cones uv The Moving Force upon them and upon an Electrified Line
59
Theory of Electrified Line of Finite Length Moving Transversely uv
63
Motion of Electrified Hyperboloids uv
67
Growing Plane Source of Induction Transition from uv to uv
70
The Waves from a Plane Strip Source of Induction suddenly started
74
Impressed Current along a Straight Axis The Operational Solution in General
76
Algebrisation of the Operational Solution in the case of Steady Motion of an Electron or of an Electrified Line uv
79
Application of Simply Periodic Analysis The Transition fromw to uc
82
Train of Simply Periodic Forced Waves along an Axis The Work done and Waste of Energy
84
Construction of the Simply Periodic Wave Train from the Two Electronic Steady Solutions
88
Connection between Moving Electrification and Moving Electrisation Transition from Cylindrical to Conical Wave
90
Spherical Impulsive Wave dne to sudden Displacement of an Electron
93
Spherical Impulse due to sudden change of Velocity of an Electron Rontgen Rays
96
Wave Train due to Damped Vibrations
98
Investigation of the Electromagnetic Field due to an Impressed Electric Current growing in a Straight Line The Solutions in Sphere and Cone
100
The electric field demands separate consideration to follow The Ellipsoidal and Conical Equipotential Surfaces
103
The Magnetic Force and Electric Current in the Cone and Sphere The Spherical Current Sheet
105
The Manner of Continuity of the Electric Current
108
The Electric Force and Time Integral of Magnetic Force
110
The Distribution of Displacement
112
Solutions for an Electron Jerked Away from a Stationary Compensating Charge The Spherical Pulse
115
Solutions for a Jerked Electron Without Compensating Charge
118
Comparison of two Cases of Motion of Electrification at the Speed of Light
120
Peculiarities at the Speed of Light
123
The Energy Wasted in the Spherical Pulse from a Jerked Electron and the Energy left behind
125
The Potential of a Charged Spheroid moving along its Axis
127
NOTE ON THE SIZE AND INEKTIA OF ELECTEONS
129
VECTOR ANALYSIS
133
WAVES IN THE ETHER Matter Electricity Ether and the Pressure of Radiation
142
The Moving Force Acting on a Deformable Ether
144
The Radiation from an Electron moving in an Elliptic or any other Orbit
171
The Principle of Least Action Lagranges Equations
173
The Principle of Activity and Lagranges Equations Rotation of a Rigid Body
176
The Undistorted Cylindrical Wave
178
Extension of Kelvins Thermoelectric Theory
181
The Pressure of Radiation
184
Electromagnetics in a Moving Dielectric
188
The Charging of a Cable through a Condenser and Resistance
192
Other Critical Cases Mathematical Excursion
203
The Curbing Effect of an Inductance Shunt
207
The Transverse Momentum of an Electron
209
Extension to Helixal Motion
211
Deep Water Waves
212
The Solution of Definite Integrals by Differential Transformation
232
Given the Effect Find the Cause The Inversion of Operations
289
Theory of Electric Telegraphy
329
Some Plane and Cylindrical Waves
344
Plane Waves in a Dielectric Louded in a Certain Way
381
The Generation of Spherical Pulses in an Elastic Solid
386
Plane Waves in moving Mediums The Energy and Forces
399
The Electromagnetic Circuital Equations and Connected Matter
420
Theory of an Electric Charge in Variable Motion
430
Slanting Motion of Electrified Straight Line
496
The Magnetic Inertia of a Charged Conductor in a Field of Force
500
Vectors versus Quaternions
505
Quaternionic Innovations
508
The Teaching of Mathematics
511
The Teaching of Mathematics
513
The PanPotential as a SurfaceIntegral
515
Limitations on Scientific Prediction
516
SOME UNPUBLISHED NOTES OF OLIVER HEAVSIDE
519
INTRODUCTION
521
PHYSICAL MATHEMATICS
559
ELECTRIC CIRCUIT THEORY
573
ELECTROMAGNETIC THEORY It will be recalled that at the turn of the century Heaviside regarded an electron as a very small charged particle Co...
602
UNIFIED FIELD THEORY
630
ACKNOWLEDGMENTS
637
APPENDIX
638
THE HEAVISIDE PAPERS FOUND AT PAIGNTON IN 1957
641
SUMMARY
641
HEAVISIDES DUPLEX EQUATIONS
641
HEAVISIDES UNIFIED FIELD THEORY
644
HEAVISIDES EXPANSION THEOREM
646
HEAMSIDES FRACTIONAL DIFFERENTIATION
646
HEAVISIDES INFINITE INTEGRAL
646
CONCLUSION
646
APPENDICES
646
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