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 The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.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work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of ""Electromagnetic Theory"") is included in Volume III.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

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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 |

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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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### Common terms and phrases

applied axis becomes beginning calculation charge circle circuital complete cone connection considered constant continuous convergent corresponding curl density differential direction displacement distance distribution divergent effect electric electrification electromagnetic electron energy equal equations equivalent ether example expanded expression field final finite follows force formula front function give given Heaviside Heaviside's impressed impulse increase induction infinite initial inside integral later limit magnetic magnetic force mathematical matter Maxwell's means method motion moving nature negative notes obtained operator origin plane positive potential powers practical present problem produce pulse reduced reflected regards relation represents resistance result sheet shell shows side simple solution space speed sphere steady surface theorem theory tion true turn unit varies vector volume waste wave wire zero

### Popular passages

Page 1 - There is a time for all things: for shouting, for gentle speaking, for silence; for the washing of pots and the writing of books. Let now the pots go black, and set to work. It is hard to make a beginning, but it must be done' - Oliver Heaviside, Electromagnetic Theory, Vol 3 (1912), Ch 9, 'Waves from moving sources - Adagio.