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eBook ISBN:  9781470464080 
Product Code:  CHEL/237.1.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 

Book DetailsAMS Chelsea PublishingVolume: 237; 1971; 504 ppMSC: Primary 78; 01
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 threevolume 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 The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.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work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of Electromagnetic Theory) is included in Volume III.
This item is also available as part of a set: 
Table of Contents

Front Cover

PREFACE TO THE THIRD EDITION

OLIVER HEAVISIDE

PREFACE.

CONTENTS.

CHAPTER I. INTRODUCTION

§ I. Preliminary Remarks.

§ 2.

§ 3.

§ 4.

§ 5.

§ 6.

§ 7.

§ 8.

§ 9.

§ 10.

§ 11.

§ 12.

§ 13.

§ 14.

§ 15.

§ 16.

CHAPTER II. OUTLINE OF THE ELECTROMAGNETIC CONNECTIONS.

§ 20. Electric and Magnetic Force ; Displacement and Induction ; Elastivity and Permittivity, Inductivity and Reluctivity.

§ 21. Electric and Magnetic Energy.

§ 22. Eolotropic Relations.

§ 23. Distinction between Absolute and Relative Permittivity or Inductivity.

§ 24. Dissipation of Energy. The Conductioncurrent ; Conductivity and Resistivity. The Electric Current.

§ 25. Fictitious Magnetic Conductioncurrent and Real Magnetic Current.

§ 26. Forces and Fluxes.

§ 27. Lineintegral of a Force. Voltage and Gaussage.

§ 28. Surfaceintegral of a Flux. Density and Intensity.

§ 29. Conductance and Resistance.

§ 30. Permittance and Elastance.

§ 31. Permeance, Inductance and Reluctance.

§ 32. Inductance of a Circuit.

§ 33. Crossconnections of Electric and Magnetic Force. Circuital Flux. Circuitation.

§ 34. First Law of Circuitation.

§ 35. Second Law of Circuitation.

§ 36. Definition of Curl.

§ 37. Impressed Force and Activity.

§ 38. Distinction between Force of the Field and Force of the Flux.

§ 39. Classification of Impressed Forces.

§ 40. Voltaic Force.

§ 41. Thermoelectric Force.

§ 42. Intrinsic Electrisation.

§ 43. Intrinsic Magnetisation.

§ 44. The Motional Electric and Magnetic Forces. Definition of a. VectorProduct.

§ 45. Example. A Stationary Electromagnetic Sheet.

§ 46. Connection between Motional Electric Force and "Electromagnetic Force."

§ 47. Variation of the Induction through a Moving Circuit.

§ 48. Modification. Circuit Fixed. Induction moving equivalently.

§ 49. The Motional Magnetic Force.

§ 50. The "Magnetoelectric Force."

§ 51. Electrification and its Magnetic Analogue. Definition of "Divergence."

§ 52. A Moving Source equivalent to a, Convection Current, and makes the True Current Circuital.

§ 53. Examples to illustrate Motional Forces in a Moving Medium with a. Moving Source. (1.) Source and Medium with a. Common Motion. Flux travels with them undisturbed.

§ 54. (2.) Source and Medium in Relative Motion. A Charge suddenly jerked into Motion at the Speed of Propagation. Generation of a Spherical Electromagnetic Sheet ; ultimately Plane. Equations of a Pure Electromagnetic Wave.

§ 55. (3.) Sudden Stoppage of Charge. Plane Sheet moves on. Spherical Sheet generated. Final Result, the Stationary Field.

§ 56. (4.) Medium moved instead of Charge. Or both moved with same Relative Velocity.

§ 57. (5,) Meeting of a Pair of Plane Sheets with PointSources. Cancelment of Charges ; or else passage through one another ; different results. Spherical Sheet with two Plane Sheet Appendages.

§ 58. (6.) Spherical Sheet without Plane Appendages produced by sudden jerking apart of opposite Charges.

§ 59. (7.) Collision of Equal Charges of same Name.

§ 60. (8.) Hemispherical Sheet. Plane, Conical and Cylindrical Boundaries.

§ 61. General Nature of Electrified Spherical Electromagnetic Sheet.

§ 62. General Remarks of the Circuital Laws. Ampere's Rule for deriving the Magnetic Force from the Current. Rational Currentelement.

§ 63. The Cardinal Feature of Maxwell's System. Advice to antiMaxwellians.

§ 64. Changes in the Form of the First Circuital Law.

§ 65. Introduction of the Second Circuital Law.

§ 66. Meaning of True Current. Criterion.

§ 67. The Persistence of Energy. Continuity in Time and Space and Flux of Energy.

§ 68. Examples. Convection of Energy and Flux of Energy due to an active Stress. Gravitational difficulty.

§ 69. Specialised form of expression of the Continuity of Energy.

§ 70. Electromagnetic Application. Medium at Rest. The Poynting Flux.

§ 71. Extension to a Moving Medium. Full interpretation of the Equation of Activity and derivation of the Flux of Energy.

§ 72. Derivation of the Electromagnetic Stress from the Flux of Energy. Division into an Electric and a Magnetic Stress.

§ 73. Uncertainty regarding the General Application of the Electromagneti c Stress.

§ 7 4. The Electrostatic Stress in Air.

§ 75. The moving Force on Electrifi.cation, bodily and superficial .. Harmonisation.

§ 76. Depth of Electrified Layer on a Conductor.

§ 77. Electric Field disturbed by Foreign Body. Effect of a. Spherical Nonconductor.

§ 78. Dynamical Principle. Any Stress Selfequilibrating.

§ 79. Electric Application of the Principle. Resultant Action on Solid Body independent of the Internal Stress, which is · statically indeterminate. Real Surface Traction is the Stress Difference.

§ 80. Translational Force due to Variation of Permittivity. Harmonisation with Surface Traction.

§ 81. Movement of Insulators in Electric Field. Effect on the Stored Energy.

§ 82. Magnetic Stress. Force due to Abrupt or Gradual Change of Inductivity. Movement of Elastically Magnetised Bodies.

§ 82a.. Force on Electric Current Conductors. The Lateral Pressure becomes prominent, but no Stress Discontinuity in general.

§ 83. Force on Intrinsically Magnetised Matter. Difficulty. Maxwell's Solution probably wrong. Special Estimation of Energy of a Magnet and the Moving Force it leads to.

§ 84. Force on Intrinsically Electrized Matter.

§ 85. Summary of the Forces. Extension to include varying States in a Moving Medium.

§ 86. Union of Electric and Magnetic to produce Electromagnetic Stress. Principal Axes.

§ 87. Dependence of the Fluxes due to an Impressed Forcive upon its Curl only. General Demonstration of this Property.

§ 88. Identity of the Disturbances due to Impressed Forcives having the same Curl. Example :A Single Circuital Source of Disturbance.

§ 89. Production of Steady State due to Impressed Forcive by crossing of Electromagnetic Waves. Example of a Circular Source. Distinction between Source of Energy and of Disturbance.

§ 90. The Eruption of "4π"s.

§ 91. The Origin and Spread of the Eruption.

§ 92. The Cure of the Disease by Proper Measure of the Strength of Sources.

§ 93. Obnoxious Effects of the Eruption.

§ 94. A Plea for the Removal of the Eruption by the Radical Cure.

§ 95. Rational v. Irrational Electric Poles.

§ 96. Rational v. Irrational Magnetic Poles.

APPENDIX.

CHAPTER III. THE ELEMENTS OF VECTORIAL ALGEBRA AND ANALYSIS.

§ 97. Scalars and Vectors

§ 98. Characteristics of Cartesian and Vectorial Analysis

§ 99. Abstrusity of Quaternions and Comparative Simplicity gained by ignoring them

§ 100. Elementary Vector Analysis independent of the Quaternion.

§ 101. Tait v. Gibbs and Gibbs v. Tait

§ 102. Abolition of the Minus Sign of Quaternions

§ 103. Type for Vectors. Greek, German, and Roman Letters unsuitable. Clarendon Type suitable. Typographical Backsliding in the Present Generation.

§ 104. Notation. Tensor and Components of a Vector. Unit Vectors of Reference.

§ 105. The Addition of Vectors. Circuital Property.

§ 106. Application to Physical Vectors. Futility of Popular Demonstrations. Barbarity of Euclid.

§ 107. The Scalar Product of Two Vectors. Notation and Illustrations.

§ 108. Fundamental Property of Scalar Products, and Examples.

§ 109. Reciprocal of a Vector.

§ 110. Expression of any Vector as the Sum of Three Independent Vectors.

§ 111. The Vector Product of Two Vectors. Illustrations

§ 112. Combinations of Three Vectors. The Parallelepipedal Property.

§ 113. SemiCartesian Expansion of a Vector Product, and Proof of the Fundamental Distributive Principle.

§ 114. Examples relating to Vector Products.

§ 115. The Differentiation of Scalars and Vectors.

§ 116. SemiCartesian Differentiation. Examples of Differentiating Functions of Vectors.

§ 117. Motion along a Curve in Space. Tangency and Curvature ; Velocity and Acceleration.

§ 118. Tortuosity of a Curve, and Various Forms of Expansion.

§ 119. Hamilton's Finite Differentials Inconvenient and Unnecessary.

§ 120. Determination of Possibility of Existence of Differential Coefficients.

§ 121. Variation of the Size and Ort of a Vector.

§ 122. Preliminary on ▽. Axial Differentiation. Differentiation referred to Moving Matter.

§ 123. Motion of a Rigid Body. Resolution of a Spin into other Spins.

§ 124. Motion of Systems of Displacement, &c.

§ 125. Motion of a StrainFigure.

§ 126. SpaceVariation or Slope v'P of a Scalar Function.

§ 127. Scalar Product ▽D. The Theorem of Divergence.

§ 128. Extension of the Theorem of Divergence.

§ 129. Vector Product V▽E, or the Curl of a Vector. The Theorem of Version, and its Extension.

§ 130. Five Examples of the Operation of ▽ in Transforming from Surface to Volume Summations.

§ 131. Five Examples of the Operation of ▽ in Transforming from Circuital to Surface Summations.

§ 132. Nine Examples of the Differentiating Effects of ▽

§ 133. The Potential of a Scalar or Vector. The Characteristic Equation of a Potential, and its Solution.

§ 134. Connections of Potential, Curl, Divergence, and Slope. Separation of a Vector into Circuital and Divergent Parts. A Series of Circuital Vectors.

§ 135. A Series of Divergent Vectors.

§ 136. The Operation inverse to Divergence.

§ 137. The Operation inverse to Slope.

§ 138. The Operation inverse to Curl.

§ 139. Remarks on the inverse Operations.

§ 140. Integration "by parts." Energy Equivalences in the Circuital Series.

§ 141. Energy and other Equivalences in the Divergent Ser ies.

§ 142. The Isotropic Elastic Solid. Relation of Displacement to Force through the Potential.

§ 143. The Stored Energy and the Stress in the Elastic Solid. The Forceless and Torqueless Stress.

§ 144. Other Forms for the Displacement in terms of the Applied Forcive.

§ 145. The Elastic Solid generalised to include Elastic, Dissipative, and Inertial Resistance to Translation, Rotation, Expansion, and Distortion.

§ 146. Electromagnetic and Elastic Solid Comparisons. First Example: Magnetic Force compared with Velocity in an incompressible Solid with Distortional Elasticity.

§ 147. Second Example : Same as last, but Electric Force compared with Velocity.

§ 148. Third Example : A Conducting Dielectric compared with a Viscous Solid. Failure.

§ 149. Fourth Example : A Pure Conductor compared with a Viscous Liquid. Useful Analogy.

§ 150. Fifth Example : Modification of the Second and Fourth.

§ 151. Sixth Example : A Conducting Dielectric compared with an Elastic Solid with Translational Friction.

§ 152. Seventh Example : Improvement of the Sixth.

§ 153. Eighth Example : A Dielectric with Duplex Conductivity compared with an Elastic Solid with Translational Elasticity and Friction. The singular Distortionless Case.

§ 153A. The Rotational Ether, Compressible or Incompressible.

§ 154. First Rotational Analogy : Magnetic Force compared with Velocity.

§ 155. Circuital Indeterminateness of the Flux of Energy in general.

§ 156. Second Rotational Analogy : Induction Compared with Velocity.

§ 157. Probability of the Kinetic Nature of Magnetic Energy.

§ 158. Unintelligibility of the Rotational Analogue for a Conducting Dielectric when Magnetic Energy is Kinetic.

§ 159. The Rotational Analogy, with Electric Energy Kinetic, extended to a Conducting Dielectric by means of Translational Friction.

§ 160. Symmetrical Linear Operators, direct and inverse, referred to the principal Axes.

§ 161. Geometrical Illustrations. The Sphere and Ellipsoid. Inverse Perpendiculars and Maccullagh's Theorem.

§ 162. Internal Structure of Linear Operators. Manipulation of several when Principal Axes are Parallel.

§ 163. Theory of Displacement in an Eolotropic Dielectric. The Solution for a PointSource.

§ 164. Theory of the relative Motion of Electrification and the Medium. The Solution for a PointSource in steady rectilinear motion. The Equilibrium Surfaces in General.

§ 165. Theory of the relative Motion of Magnetification and the Medium.

§ 166. Theory of the relative Motion of Magnetisation and the Medium. Increased Induction as well as Eolotropic Disturbance.

§ 167. Theory of the Relative Motion of Electric Currents and the Medium.

§ 168. The General Linear Operator.

§ 169. The Dyadical Structure of Linear Operators.

§ 170. Hamilton's Theorem.

§ 171. Hamilton's Cubic and the Invariants concerned.

§ 172. The Inversion of Linear Operators.

§ 173. Skew Product of a Vector and a Dyadic. The Differentiation of Linear Operators

§ 174. Summary of Method of Vector Analysis.

§ 175. Unsuitability of Quaternions for Physical Needs. Axiom: Once a Vector, always a Vector.

CHAPTER IV. THEORY OF PLANE ELECTROMAGNETIC WAVES

§ 176. Action at a Distance versus Intermediate Agency. Contrast of New with Old Views about Electricity.

§ 177. General Notions about Electromagnetic Waves. Generation of Spherical Waves and Steady States.

§ 178. Intermittent Source producing Steady States and Electromagnetic Sheets. A Train of S.H. Waves.

§ 179. Selfcontained Forced Electromagnetic Vibrations. Contrast with Static Problem.

§ 180. Relations between E and Hin a Pure Wave. Effect of SelfInduction. Fatuity of Mr. Preece's "KR law."

§ 181. WaveFronts; their Initiation and Progress.

§ 182. Effect of a NonConducting Obstacle on Waves. Also of a Heterogeneous Medium.

§ 183. Effect of Eolotropy. Optical WaveSurfaces. Electromagnetic versus Elastic Solid Theories.

§ 184. A Perfect Conductor is a Perfect Obstructor, but does not absorb the Energy of Electromagnetic Waves.

§ 185. Conductors at Low Temperatures.

§ 186. Equilibrium of Radiation. The Mean Flux of Energy.

§ 187. The Mean Pressure of Radiation.

§ 188. Emissivity and Temperature.

§ 189. Internal Obstruction and Superficial Conduction.

§ 190. The Effect of a Perfect Conductor on External Disturbances. Reflection and Conduction of Waves.

§ 191. The Effect of Conducting Matter in Diverting External Induction.

§ 192. Parenhetical Remarks on Induction, Magnetisation, Inductivity and Susceptibility.

§ 193. Effect of a Thin Plane Conducting Sheet on a Wave. Persistence of Induction and Loss of Displacement.

§ 194. The Persistence of Induction in Plane Strata, and in general. Also in Cores and in Linear Circuits.

§ 195. The Laws of Attenuation of Total Displacement and· Total Induction by Electric and Magnetic Conductance.

§ 196. The Laws of Attenuation at the Front of a Wave, due to Electric and Magnetic Conductance.

§ 197. The Simple Propagation of Waves in a Distortionless Conducting Medium.

§ 198. The Transformation by Conductance of an Elastic Wave to a Wave of Diffusion. Generation of Tails. Distinct Effects of Electric and Magnetic Conductance.

§ 199. Application to Waves along Straight Wires.

§ 200. Transformation of Variables from Electric and Magnetic Poree to Voltage and Gaussage.

§ 201. Transformation of the Circuital Equations to the Forms involving Voltage and Gaussage.

§ 202. The Second Circuital Equation for Wires in Terms of V and C when Penetration is Instantaneous.

§ 203. The Second Circuital Equation when Penetration is Not Instantaneous. Resistance Operators, and their Definite Meaning.

§ 204. Simply Periodic Waves Easily Treated in Case of Imperfect Penetration.

§ 205. Long Waves and Short Waves. Identity of Speed of Free and Guided Waves.

§ 206. The Guidance of Waves. Usually Two Guides. One sufficient, though with Loss. Possibility of Guidance within a Single Tube.

§ 207. Interpretation of Intermediate or Terminal Conditions in the Exact Theory.

§ 208. The Spreading of Charge and Current in a long Circuit, and their Attenuation.

§ 209. The Distortionless Circuit. No limiting Distance set by it when the Attenuation is ignored.

§ 210. The two Extreme Kinds of Diffusion in one Theory.

§ 211. The Effect of varying the Four LineConstants as regards Distortion and Attenuation.

§ 212. The Beneficial Effect of Leakage in Submarine Cables.

§ 213. Short History of Leakage Effects on a Cable Circuit

§ 214. Explanation of Anomalous Effects. Artificial Leaks

§ 216. SelfInduction combined with Leaks. The Bridge System of Mr. A. W. Heaviside, and suggested Distortionless Circuit.

§ 217. Evidence in Favour of SelfInduction. Condition of FirstClass Telephony. Importance of the Magnetic Reactance.

§ 218. Various Ways, good and bad, of increasing the Inductance of Circuits.

§ 219. Effective Resistance and Inductance of a Combination when regarded as a Coil, and Effective Conductance and Permittance when regarded as a Condenser.

§220. Inductive Leaks applied to Submarine Cables.

§ 221. General Theory of Transmission of Waves along a Circuit with or without Auxiliary Devices.

§ 222. Application of above Theory to Inductive Leakance.

APPENDIX B. A GRAVITATIONAL AND ELECTROMAGNETICANALOGY.

Part I.

Part II.

THE WORK OF OLIVER HEAVISIDE By B.A. BEHREND

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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 threevolume 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.

Front Cover

PREFACE TO THE THIRD EDITION

OLIVER HEAVISIDE

PREFACE.

CONTENTS.

CHAPTER I. INTRODUCTION

§ I. Preliminary Remarks.

§ 2.

§ 3.

§ 4.

§ 5.

§ 6.

§ 7.

§ 8.

§ 9.

§ 10.

§ 11.

§ 12.

§ 13.

§ 14.

§ 15.

§ 16.

CHAPTER II. OUTLINE OF THE ELECTROMAGNETIC CONNECTIONS.

§ 20. Electric and Magnetic Force ; Displacement and Induction ; Elastivity and Permittivity, Inductivity and Reluctivity.

§ 21. Electric and Magnetic Energy.

§ 22. Eolotropic Relations.

§ 23. Distinction between Absolute and Relative Permittivity or Inductivity.

§ 24. Dissipation of Energy. The Conductioncurrent ; Conductivity and Resistivity. The Electric Current.

§ 25. Fictitious Magnetic Conductioncurrent and Real Magnetic Current.

§ 26. Forces and Fluxes.

§ 27. Lineintegral of a Force. Voltage and Gaussage.

§ 28. Surfaceintegral of a Flux. Density and Intensity.

§ 29. Conductance and Resistance.

§ 30. Permittance and Elastance.

§ 31. Permeance, Inductance and Reluctance.

§ 32. Inductance of a Circuit.

§ 33. Crossconnections of Electric and Magnetic Force. Circuital Flux. Circuitation.

§ 34. First Law of Circuitation.

§ 35. Second Law of Circuitation.

§ 36. Definition of Curl.

§ 37. Impressed Force and Activity.

§ 38. Distinction between Force of the Field and Force of the Flux.

§ 39. Classification of Impressed Forces.

§ 40. Voltaic Force.

§ 41. Thermoelectric Force.

§ 42. Intrinsic Electrisation.

§ 43. Intrinsic Magnetisation.

§ 44. The Motional Electric and Magnetic Forces. Definition of a. VectorProduct.

§ 45. Example. A Stationary Electromagnetic Sheet.

§ 46. Connection between Motional Electric Force and "Electromagnetic Force."

§ 47. Variation of the Induction through a Moving Circuit.

§ 48. Modification. Circuit Fixed. Induction moving equivalently.

§ 49. The Motional Magnetic Force.

§ 50. The "Magnetoelectric Force."

§ 51. Electrification and its Magnetic Analogue. Definition of "Divergence."

§ 52. A Moving Source equivalent to a, Convection Current, and makes the True Current Circuital.

§ 53. Examples to illustrate Motional Forces in a Moving Medium with a. Moving Source. (1.) Source and Medium with a. Common Motion. Flux travels with them undisturbed.

§ 54. (2.) Source and Medium in Relative Motion. A Charge suddenly jerked into Motion at the Speed of Propagation. Generation of a Spherical Electromagnetic Sheet ; ultimately Plane. Equations of a Pure Electromagnetic Wave.

§ 55. (3.) Sudden Stoppage of Charge. Plane Sheet moves on. Spherical Sheet generated. Final Result, the Stationary Field.

§ 56. (4.) Medium moved instead of Charge. Or both moved with same Relative Velocity.

§ 57. (5,) Meeting of a Pair of Plane Sheets with PointSources. Cancelment of Charges ; or else passage through one another ; different results. Spherical Sheet with two Plane Sheet Appendages.

§ 58. (6.) Spherical Sheet without Plane Appendages produced by sudden jerking apart of opposite Charges.

§ 59. (7.) Collision of Equal Charges of same Name.

§ 60. (8.) Hemispherical Sheet. Plane, Conical and Cylindrical Boundaries.

§ 61. General Nature of Electrified Spherical Electromagnetic Sheet.

§ 62. General Remarks of the Circuital Laws. Ampere's Rule for deriving the Magnetic Force from the Current. Rational Currentelement.

§ 63. The Cardinal Feature of Maxwell's System. Advice to antiMaxwellians.

§ 64. Changes in the Form of the First Circuital Law.

§ 65. Introduction of the Second Circuital Law.

§ 66. Meaning of True Current. Criterion.

§ 67. The Persistence of Energy. Continuity in Time and Space and Flux of Energy.

§ 68. Examples. Convection of Energy and Flux of Energy due to an active Stress. Gravitational difficulty.

§ 69. Specialised form of expression of the Continuity of Energy.

§ 70. Electromagnetic Application. Medium at Rest. The Poynting Flux.

§ 71. Extension to a Moving Medium. Full interpretation of the Equation of Activity and derivation of the Flux of Energy.

§ 72. Derivation of the Electromagnetic Stress from the Flux of Energy. Division into an Electric and a Magnetic Stress.

§ 73. Uncertainty regarding the General Application of the Electromagneti c Stress.

§ 7 4. The Electrostatic Stress in Air.

§ 75. The moving Force on Electrifi.cation, bodily and superficial .. Harmonisation.

§ 76. Depth of Electrified Layer on a Conductor.

§ 77. Electric Field disturbed by Foreign Body. Effect of a. Spherical Nonconductor.

§ 78. Dynamical Principle. Any Stress Selfequilibrating.

§ 79. Electric Application of the Principle. Resultant Action on Solid Body independent of the Internal Stress, which is · statically indeterminate. Real Surface Traction is the Stress Difference.

§ 80. Translational Force due to Variation of Permittivity. Harmonisation with Surface Traction.

§ 81. Movement of Insulators in Electric Field. Effect on the Stored Energy.

§ 82. Magnetic Stress. Force due to Abrupt or Gradual Change of Inductivity. Movement of Elastically Magnetised Bodies.

§ 82a.. Force on Electric Current Conductors. The Lateral Pressure becomes prominent, but no Stress Discontinuity in general.

§ 83. Force on Intrinsically Magnetised Matter. Difficulty. Maxwell's Solution probably wrong. Special Estimation of Energy of a Magnet and the Moving Force it leads to.

§ 84. Force on Intrinsically Electrized Matter.

§ 85. Summary of the Forces. Extension to include varying States in a Moving Medium.

§ 86. Union of Electric and Magnetic to produce Electromagnetic Stress. Principal Axes.

§ 87. Dependence of the Fluxes due to an Impressed Forcive upon its Curl only. General Demonstration of this Property.

§ 88. Identity of the Disturbances due to Impressed Forcives having the same Curl. Example :A Single Circuital Source of Disturbance.

§ 89. Production of Steady State due to Impressed Forcive by crossing of Electromagnetic Waves. Example of a Circular Source. Distinction between Source of Energy and of Disturbance.

§ 90. The Eruption of "4π"s.

§ 91. The Origin and Spread of the Eruption.

§ 92. The Cure of the Disease by Proper Measure of the Strength of Sources.

§ 93. Obnoxious Effects of the Eruption.

§ 94. A Plea for the Removal of the Eruption by the Radical Cure.

§ 95. Rational v. Irrational Electric Poles.

§ 96. Rational v. Irrational Magnetic Poles.

APPENDIX.

CHAPTER III. THE ELEMENTS OF VECTORIAL ALGEBRA AND ANALYSIS.

§ 97. Scalars and Vectors

§ 98. Characteristics of Cartesian and Vectorial Analysis

§ 99. Abstrusity of Quaternions and Comparative Simplicity gained by ignoring them

§ 100. Elementary Vector Analysis independent of the Quaternion.

§ 101. Tait v. Gibbs and Gibbs v. Tait

§ 102. Abolition of the Minus Sign of Quaternions

§ 103. Type for Vectors. Greek, German, and Roman Letters unsuitable. Clarendon Type suitable. Typographical Backsliding in the Present Generation.

§ 104. Notation. Tensor and Components of a Vector. Unit Vectors of Reference.

§ 105. The Addition of Vectors. Circuital Property.

§ 106. Application to Physical Vectors. Futility of Popular Demonstrations. Barbarity of Euclid.

§ 107. The Scalar Product of Two Vectors. Notation and Illustrations.

§ 108. Fundamental Property of Scalar Products, and Examples.

§ 109. Reciprocal of a Vector.

§ 110. Expression of any Vector as the Sum of Three Independent Vectors.

§ 111. The Vector Product of Two Vectors. Illustrations

§ 112. Combinations of Three Vectors. The Parallelepipedal Property.

§ 113. SemiCartesian Expansion of a Vector Product, and Proof of the Fundamental Distributive Principle.

§ 114. Examples relating to Vector Products.

§ 115. The Differentiation of Scalars and Vectors.

§ 116. SemiCartesian Differentiation. Examples of Differentiating Functions of Vectors.

§ 117. Motion along a Curve in Space. Tangency and Curvature ; Velocity and Acceleration.

§ 118. Tortuosity of a Curve, and Various Forms of Expansion.

§ 119. Hamilton's Finite Differentials Inconvenient and Unnecessary.

§ 120. Determination of Possibility of Existence of Differential Coefficients.

§ 121. Variation of the Size and Ort of a Vector.

§ 122. Preliminary on ▽. Axial Differentiation. Differentiation referred to Moving Matter.

§ 123. Motion of a Rigid Body. Resolution of a Spin into other Spins.

§ 124. Motion of Systems of Displacement, &c.

§ 125. Motion of a StrainFigure.

§ 126. SpaceVariation or Slope v'P of a Scalar Function.

§ 127. Scalar Product ▽D. The Theorem of Divergence.

§ 128. Extension of the Theorem of Divergence.

§ 129. Vector Product V▽E, or the Curl of a Vector. The Theorem of Version, and its Extension.

§ 130. Five Examples of the Operation of ▽ in Transforming from Surface to Volume Summations.

§ 131. Five Examples of the Operation of ▽ in Transforming from Circuital to Surface Summations.

§ 132. Nine Examples of the Differentiating Effects of ▽

§ 133. The Potential of a Scalar or Vector. The Characteristic Equation of a Potential, and its Solution.

§ 134. Connections of Potential, Curl, Divergence, and Slope. Separation of a Vector into Circuital and Divergent Parts. A Series of Circuital Vectors.

§ 135. A Series of Divergent Vectors.

§ 136. The Operation inverse to Divergence.

§ 137. The Operation inverse to Slope.

§ 138. The Operation inverse to Curl.

§ 139. Remarks on the inverse Operations.

§ 140. Integration "by parts." Energy Equivalences in the Circuital Series.

§ 141. Energy and other Equivalences in the Divergent Ser ies.

§ 142. The Isotropic Elastic Solid. Relation of Displacement to Force through the Potential.

§ 143. The Stored Energy and the Stress in the Elastic Solid. The Forceless and Torqueless Stress.

§ 144. Other Forms for the Displacement in terms of the Applied Forcive.

§ 145. The Elastic Solid generalised to include Elastic, Dissipative, and Inertial Resistance to Translation, Rotation, Expansion, and Distortion.

§ 146. Electromagnetic and Elastic Solid Comparisons. First Example: Magnetic Force compared with Velocity in an incompressible Solid with Distortional Elasticity.

§ 147. Second Example : Same as last, but Electric Force compared with Velocity.

§ 148. Third Example : A Conducting Dielectric compared with a Viscous Solid. Failure.

§ 149. Fourth Example : A Pure Conductor compared with a Viscous Liquid. Useful Analogy.

§ 150. Fifth Example : Modification of the Second and Fourth.

§ 151. Sixth Example : A Conducting Dielectric compared with an Elastic Solid with Translational Friction.

§ 152. Seventh Example : Improvement of the Sixth.

§ 153. Eighth Example : A Dielectric with Duplex Conductivity compared with an Elastic Solid with Translational Elasticity and Friction. The singular Distortionless Case.

§ 153A. The Rotational Ether, Compressible or Incompressible.

§ 154. First Rotational Analogy : Magnetic Force compared with Velocity.

§ 155. Circuital Indeterminateness of the Flux of Energy in general.

§ 156. Second Rotational Analogy : Induction Compared with Velocity.

§ 157. Probability of the Kinetic Nature of Magnetic Energy.

§ 158. Unintelligibility of the Rotational Analogue for a Conducting Dielectric when Magnetic Energy is Kinetic.

§ 159. The Rotational Analogy, with Electric Energy Kinetic, extended to a Conducting Dielectric by means of Translational Friction.

§ 160. Symmetrical Linear Operators, direct and inverse, referred to the principal Axes.

§ 161. Geometrical Illustrations. The Sphere and Ellipsoid. Inverse Perpendiculars and Maccullagh's Theorem.

§ 162. Internal Structure of Linear Operators. Manipulation of several when Principal Axes are Parallel.

§ 163. Theory of Displacement in an Eolotropic Dielectric. The Solution for a PointSource.

§ 164. Theory of the relative Motion of Electrification and the Medium. The Solution for a PointSource in steady rectilinear motion. The Equilibrium Surfaces in General.

§ 165. Theory of the relative Motion of Magnetification and the Medium.

§ 166. Theory of the relative Motion of Magnetisation and the Medium. Increased Induction as well as Eolotropic Disturbance.

§ 167. Theory of the Relative Motion of Electric Currents and the Medium.

§ 168. The General Linear Operator.

§ 169. The Dyadical Structure of Linear Operators.

§ 170. Hamilton's Theorem.

§ 171. Hamilton's Cubic and the Invariants concerned.

§ 172. The Inversion of Linear Operators.

§ 173. Skew Product of a Vector and a Dyadic. The Differentiation of Linear Operators

§ 174. Summary of Method of Vector Analysis.

§ 175. Unsuitability of Quaternions for Physical Needs. Axiom: Once a Vector, always a Vector.

CHAPTER IV. THEORY OF PLANE ELECTROMAGNETIC WAVES

§ 176. Action at a Distance versus Intermediate Agency. Contrast of New with Old Views about Electricity.

§ 177. General Notions about Electromagnetic Waves. Generation of Spherical Waves and Steady States.

§ 178. Intermittent Source producing Steady States and Electromagnetic Sheets. A Train of S.H. Waves.

§ 179. Selfcontained Forced Electromagnetic Vibrations. Contrast with Static Problem.

§ 180. Relations between E and Hin a Pure Wave. Effect of SelfInduction. Fatuity of Mr. Preece's "KR law."

§ 181. WaveFronts; their Initiation and Progress.

§ 182. Effect of a NonConducting Obstacle on Waves. Also of a Heterogeneous Medium.

§ 183. Effect of Eolotropy. Optical WaveSurfaces. Electromagnetic versus Elastic Solid Theories.

§ 184. A Perfect Conductor is a Perfect Obstructor, but does not absorb the Energy of Electromagnetic Waves.

§ 185. Conductors at Low Temperatures.

§ 186. Equilibrium of Radiation. The Mean Flux of Energy.

§ 187. The Mean Pressure of Radiation.

§ 188. Emissivity and Temperature.

§ 189. Internal Obstruction and Superficial Conduction.

§ 190. The Effect of a Perfect Conductor on External Disturbances. Reflection and Conduction of Waves.

§ 191. The Effect of Conducting Matter in Diverting External Induction.

§ 192. Parenhetical Remarks on Induction, Magnetisation, Inductivity and Susceptibility.

§ 193. Effect of a Thin Plane Conducting Sheet on a Wave. Persistence of Induction and Loss of Displacement.

§ 194. The Persistence of Induction in Plane Strata, and in general. Also in Cores and in Linear Circuits.

§ 195. The Laws of Attenuation of Total Displacement and· Total Induction by Electric and Magnetic Conductance.

§ 196. The Laws of Attenuation at the Front of a Wave, due to Electric and Magnetic Conductance.

§ 197. The Simple Propagation of Waves in a Distortionless Conducting Medium.

§ 198. The Transformation by Conductance of an Elastic Wave to a Wave of Diffusion. Generation of Tails. Distinct Effects of Electric and Magnetic Conductance.

§ 199. Application to Waves along Straight Wires.

§ 200. Transformation of Variables from Electric and Magnetic Poree to Voltage and Gaussage.

§ 201. Transformation of the Circuital Equations to the Forms involving Voltage and Gaussage.

§ 202. The Second Circuital Equation for Wires in Terms of V and C when Penetration is Instantaneous.

§ 203. The Second Circuital Equation when Penetration is Not Instantaneous. Resistance Operators, and their Definite Meaning.

§ 204. Simply Periodic Waves Easily Treated in Case of Imperfect Penetration.

§ 205. Long Waves and Short Waves. Identity of Speed of Free and Guided Waves.

§ 206. The Guidance of Waves. Usually Two Guides. One sufficient, though with Loss. Possibility of Guidance within a Single Tube.

§ 207. Interpretation of Intermediate or Terminal Conditions in the Exact Theory.

§ 208. The Spreading of Charge and Current in a long Circuit, and their Attenuation.

§ 209. The Distortionless Circuit. No limiting Distance set by it when the Attenuation is ignored.

§ 210. The two Extreme Kinds of Diffusion in one Theory.

§ 211. The Effect of varying the Four LineConstants as regards Distortion and Attenuation.

§ 212. The Beneficial Effect of Leakage in Submarine Cables.

§ 213. Short History of Leakage Effects on a Cable Circuit

§ 214. Explanation of Anomalous Effects. Artificial Leaks

§ 216. SelfInduction combined with Leaks. The Bridge System of Mr. A. W. Heaviside, and suggested Distortionless Circuit.

§ 217. Evidence in Favour of SelfInduction. Condition of FirstClass Telephony. Importance of the Magnetic Reactance.

§ 218. Various Ways, good and bad, of increasing the Inductance of Circuits.

§ 219. Effective Resistance and Inductance of a Combination when regarded as a Coil, and Effective Conductance and Permittance when regarded as a Condenser.

§220. Inductive Leaks applied to Submarine Cables.

§ 221. General Theory of Transmission of Waves along a Circuit with or without Auxiliary Devices.

§ 222. Application of above Theory to Inductive Leakance.

APPENDIX B. A GRAVITATIONAL AND ELECTROMAGNETICANALOGY.

Part I.

Part II.

THE WORK OF OLIVER HEAVISIDE By B.A. BEHREND

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