## Electromagnetic Theory, Volume 3Oliver 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 The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.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work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of ""Electromagnetic Theory"") is included in Volume III.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 | ix |

Simple Proof of Fundamental Property of a Plane Wave | 3 |

The General Plane Wave | 4 |

Generation of Waves by a Plane Source of Induction | 6 |

Generation of Waves by a Plane Source of Displacement | 8 |

Comparison of Electromagnetic with Aerial Waves | 9 |

Waves ending perpendicularly upon a Conductor Conduction and Convection | 10 |

Oblique Reflection at a Conducting Surface with H tangential Transformation to a Convection Problem | 13 |

Connection Between the Compressed Electromagnetic Wave and Rankines Wave of Compression | 152 |

Theory of the Rankinian Wave of Compression | 154 |

Crossing of Two Waves Riemanns Solution | 155 |

Modification of the Rankmian to make a Compressed Maxwellian Wave | 156 |

The Waste of Energy from a Moving Electron | 158 |

Sound Waves and Electromagnetics The Fanpotential | 164 |

The Radiation from an Electron describing a Circular Orbit | 169 |

The Radiation from an Electron moving in an Elliptic or any other Orbit | 173 |

Generation of a Pair of Inclined Plane Waves by Motion of an Electrified Strip uv The applied force required | 15 |

Generation of a Pair of Inclined Plane Waves by a Moving Source of Induction when uv | 18 |

Slanting Plane Waves Generated by a Moving Magnet and by an Electrified Strip moving normally to its Plane | 20 |

Generation of a Single Plane Wave by Motion of an Electrified Electret Also of Two Separated Plane Waves | 23 |

Theory of the Steady Rectilinear Motion of a PointCharge or Electron through the Ether when uv and when uv | 25 |

Construction of the Slanting Plane Waves generated by an Electrified Line by means of the Potential of an Electron | 28 |

The steady Rectilinear Motion in its own line of a Terminated Electrified Live when uv and interpretation of the Impure Conical Wave Following an ... | 30 |

The Wave from a Straight Line Source of Induction in a Nonconducting Dielectric | 33 |

The Wave from a Straight Line Source of Induction In a Conductor | 37 |

The Waves due to a Growing Plane Sheet ot Sources of Induction and to Travelling Filaments at any Speed | 39 |

Reversion to Divergent Plane Waves Is the Ether Fixed? | 43 |

Drag of Matter upon Ether Modified Circuital Equations and the Wavespeed resulting | 44 |

Comparison of Wavespeeds in special Cases | 46 |

Effect of Modified Circuital Equations on Electrical Distributions | 50 |

Lorentzs Equations of a Moving Dielectric | 52 |

The Wavespeed according to Lorentz | 55 |

Possible Equations for a Moving Magnetised Substance | 57 |

Larmors Equations for a Moving Body | 59 |

Theory of Moving Electrified Cones uv The Moving Force upon them and upon an Electrified Line | 61 |

Theory of Electrified Line of Finite Length Moving Transversely uv | 65 |

Motion of Electrified Hyperboloids uv | 69 |

Growing Plane Source of Induction Transition from uv to uv | 72 |

The Waves from a Plane Strip Source of Induction suddenly started | 76 |

Impressed Current along a Straight Axis The Operational Solution in General | 78 |

Algebrisation of the Operational Solution in the case of Steady Motion of an Electron or of an Electrified Line uv | 81 |

Application of Simply Periodic Analysis The Transition fromw to uc | 84 |

Train of Simply Periodic Forced Waves along an Axis The Work done and Waste of Energy | 86 |

Construction of the Simply Periodic Wave Train from the Two Electronic Steady Solutions | 90 |

Connection between Moving Electrification and Moving Electrisation Transition from Cylindrical to Conical Wave | 92 |

Spherical Impulsive Wave dne to sudden Displacement of an Electron | 95 |

Spherical Impulse due to sudden change of Velocity of an Electron Rontgen Rays | 98 |

Wave Train due to Damped Vibrations | 100 |

Investigation of the Electromagnetic Field due to an Impressed Electric Current growing in a Straight Line The Solutions in Sphere and Cone | 102 |

The electric field demands separate consideration to follow The Ellipsoidal and Conical Equipotential Surfaces | 105 |

The Magnetic Force and Electric Current in the Cone and Sphere The Spherical Current Sheet | 107 |

The Manner of Continuity of the Electric Current | 110 |

The Electric Force and Time Integral of Magnetic Force | 112 |

The Distribution of Displacement | 114 |

Solutions for an Electron Jerked Away from a Stationary Compensating Charge The Spherical Pulse | 117 |

Solutions for a Jerked Electron Without Compensating Charge | 120 |

Comparison of two Cases of Motion of Electrification at the Speed of Light | 122 |

Peculiarities at the Speed of Light | 125 |

The Energy Wasted in the Spherical Pulse from a Jerked Electron and the Energy left behind | 127 |

The Potential of a Charged Spheroid moving along its Axis | 129 |

NOTE ON THE SIZE AND INEKTIA OF ELECTEONS | 131 |

VECTOR ANALYSIS | 135 |

WAVES IN THE ETHER Matter Electricity Ether and the Pressure of Radiation | 144 |

The Moving Force Acting on a Deformable Ether | 146 |

How to have Constant Speed through Space of Plane Radiation Traversing a Moving Compressible Ether | 149 |

The Principle of Least Action Lagranges Equations | 175 |

The Principle of Activity and Lagranges Equations Rotation of a Rigid Body | 178 |

The Undistorted Cylindrical Wave | 180 |

Extension of Kelvins Thermoelectric Theory | 183 |

The Pressure of Radiation | 186 |

Electromagnetics in a Moving Dielectric | 190 |

The Charging of a Cable through a Condenser and Resistance | 194 |

Other Critical Cases Mathematical Excursion | 205 |

The Curbing Effect of an Inductance Shunt | 209 |

The Transverse Momentum of an Electron | 211 |

Extension to Helixal Motion | 213 |

Deep Water Waves | 214 |

The Solution of Definite Integrals by Differential Transformation | 234 |

Given the Effect Find the Cause The Inversion of Operations | 291 |

Theory of Electric Telegraphy | 331 |

Some Plane and Cylindrical Waves | 346 |

Plane Waves in a Dielectric Louded in a Certain Way | 383 |

The Generation of Spherical Pulses in an Elastic Solid | 388 |

Plane Waves in moving Mediums The Energy and Forces | 401 |

The Electromagnetic Circuital Equations and Connected Matter | 422 |

Theory of an Electric Charge in Variable Motion | 432 |

Slanting Motion of Electrified Straight Line | 498 |

The Magnetic Inertia of a Charged Conductor in a Field of Force | 502 |

Vectors versus Quaternions | 507 |

Quaternionic Innovations | 510 |

The Teaching of Mathematics | 513 |

The Teaching of Mathematics | 515 |

The PanPotential as a SurfaceIntegral | 517 |

Limitations on Scientific Prediction | 518 |

SOME UNPUBLISHED NOTES OF OLIVER HEAVSIDE | 521 |

INTRODUCTION | 523 |

INFINITE INTEGRALS | 526 |

PHYSICAL MATHEMATICS | 561 |

ELECTRIC CIRCUIT THEORY | 575 |

ELECTROMAGNETIC THEORY It will be recalled that at the turn of the century Heaviside regarded an electron as a very small charged particle Co... | 604 |

UNIFIED FIELD THEORY | 632 |

ACKNOWLEDGMENTS | 639 |

APPENDIX | 640 |

THE HEAVISIDE PAPERS FOUND AT PAIGNTON IN 1957 | 643 |

SUMMARY | 645 |

HEAVISIDES DUPLEX EQUATIONS | 646 |

HEAVISIDES UNIFIED FIELD THEORY | 650 |

HEAVISIDES EXPANSION THEOREM | 653 |

HEAMSIDES FRACTIONAL DIFFERENTIATION | 655 |

HEAVISIDES INFINITE INTEGRAL | 657 |

CONCLUSION | 659 |

APPENDICES | 660 |

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### Common terms and phrases

applied axis Bessel Bessel functions calculation charge circle circuital equations circuital law condensed conductor cone connection constant convergent convergent series curl cylindrical definite integrals density differential displacement distance distribution divergent series effect electric and magnetic electric current electric force electrification electrified line Electromagnetic Theory electromagnetic wave electron equivalent ether Euler integral expansion expression finite formula function given Heaviside's impressed force impulse increase induction infinite initial inside integral J. J. Thomson limit line source magnetic energy magnetic force mathematical matter Maxwell's means medium momentum motion moving force negative obtained operator outward Paignton permittivity plane waves positive potential problem Prof pulse quaternionic radiation reduced regards resistance result sheet shell shows side simple slab solution speed sphere spherical steady surface theorem tion varies vector velocity waste wave front whilst wire zero