Electromagnetic Theory, Volume 2Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. His main research activity concerned the theory of electricity and magnetism. This book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912. |
Contents
The dates within brackets are the dates of first publication | 1 |
of Mathematical Methods of Enquiry | 8 |
CHAPTER II | 20 |
Feb 27 1891 Forces and Fluxes | 26 |
March 13 1891 Crossconnections of Electric and Magnetic | 32 |
March 27 1891 Classification of Impressed Forces | 39 |
Variation of the Induction through a Moving Circuit | 45 |
A Moving Source equivalent to a Convection Current and makes | 51 |
March 25 1892 SpaceVariation or Slope VP of a Scalar Function | 186 |
Scalar Product VD The Theorem of Divergence | 188 |
Extension of the Theorem of Divergence | 190 |
Vector Product VVE or the Curl of a Vector The Theorem of Version and its Extension | 191 |
April 8 1892 Five Examples of the Operation of V in Transforming from Surface to Volume Summations | 194 |
Circuital to Surface Summations | 197 |
Nine Examples of the Differentiating Effects of V | 199 |
May 13 1892 The Potential of a Scalar or Vector The Characteristic Equation of a Potential and its Solution | 202 |
Field | 57 |
May 29 1891 General Remarks on the Circuital Laws | 62 |
General Nature of Electrified Spherical Electromagnetic Sheet | 63 |
Introduction of the Second Circuital | 68 |
Examples Convection of Energy and Flux of Energy due to | 74 |
Extension to a Moving Medium Full interpretation of | 80 |
8885 | 87 |
Aug 21 1891 Electric Field disturbed by Foreign Body | 93 |
Movement of Insulators in Electric Field Effect on the Stored | 99 |
Force on Intrinsically Electrised Matter | 107 |
29 | 108 |
The Origin and Spread of the Eruption | 117 |
Oct 30 1891 Rational v Irrational Electric Poles | 123 |
CHAPTER III | 132 |
Abolition of the Minus Sign of Quaternions | 138 |
103 | 139 |
June 10 1892 Energy and other Equivalences in the Diver | 141 |
Application to Physical Vectors Futility of Popular Demon | 147 |
107 | 148 |
Reciprocal of a Vector | 155 |
Jan 1 1892 The Vector Product of Two Vectors Illus trations | 156 |
Combinations of Three Vectors The Parallelepipedal Property | 158 |
SemiCartesian Expansion of a Vector Product and Proof of the Fundamental Distributive Principle | 159 |
Examples relating to Vector Products | 162 |
Jan 29 1892 The Differentiation of Scalars and Vectors | 163 |
SemiCartesian Differentiation Examples of Differentiating Functions of Vectors | 165 |
Motion along a Curve in Space Tangency and Curvature Velocity and Acceleration | 167 |
Tortuosity of a Curve and Various Forms of Expansion | 169 |
Feb 12 1892 Hamiltons Finite Differentials Inconvenient and Unnecessary | 172 |
Determination of Possibility of Existence of Differential Co efficients | 174 |
Variation of the Size and Ort of a Vector | 176 |
March 4 1892 Preliminary on V Axial Differentiation Differentiation referred to Moving Matter | 178 |
Motion of a Rigid Body Resolution of a Spin into other Spins | 180 |
Motion of Systems of Displacement c | 183 |
Motion of a StrainFigure | 185 |
Connections of Potential Curl Divergence and Slope Separa tion of a Vector into Circuital and Divergent Parts A Series of Circuital Vectors | 206 |
May 27 1892 A Series of Divergent Vectors | 209 |
The Operation inverse to Divergence www | 212 |
The Operation inverse to Slope | 213 |
The Operation inverse to Curl | 214 |
Remarks on the Inverse Operations | 215 |
Integration by parts Energy Equivalences in the Circuital Series | 216 |
The Isotropic Elastic Solid Relation of Displacement to Force | 219 |
June 24 1892 The Elastic Solid generalised to include | 226 |
Electromagnetic and Elastic Solid Comparisons First | 232 |
Modification of the Second and Fourth | 239 |
Magnetic Force compared with | 245 |
Unintelligibility of the Rotational Analogue for a Conducting | 252 |
Geometrical Illustrations The Sphere and Ellipsoid Inverse | 259 |
Theory of the Relative Motion of Electrification and | 269 |
Theory of the Relative Motion of Magnetisation and | 277 |
The Dyadical Structure of Linear Operators | 285 |
The Inversion of Linear Operators | 293 |
Dec 9 1892 Summary of Method of Vector Analysis | 301 |
General Notions about Electromagnetic Waves Generation | 310 |
Selfcontained Forced Electromagnetic Vibrations Contrast | 316 |
Jan 27 1893 WaveFronts their Initiation and Progress | 323 |
Feb 24 1893 Conductors at Low Temperatures | 331 |
March 24 1893 The Effect of Conducting Matter | 344 |
April 7 1893 Effect of a Thin Plane Conducting Sheet | 353 |
The Simple Propagation of Waves in a Distortionless Con | 366 |
Application to Waves along Straight Wires | 374 |
The Second Circuital Equation when Penetration is Not | 390 |
The Beneficial Effect of Leakage in Submarine Cables | 417 |
Oct 20 1893 SelfInduction imparts Momentum to Waves | 429 |
Nov 3 1893 Evidence in favour of SelfInduction Con | 437 |
Nov 17 1893 Effective Resistance and Inductance of | 446 |
Application of above Theory to Inductive Leakance | 453 |
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Common terms and phrases
algebra analogy applied axis B₁ body C₁ Cartesian charge circuital law component conduction current conductor connected considered constant curl density dielectric differential distribution disturbances divergence dynamical elastic electric and magnetic electric current electric displacement electric force electrification electromagnetic sheet electromagnetic waves equation equivalent ether express external flux of energy forcive formula gaussage impressed force induction intrinsic isotropic law of circuitation line-integral magnetic conductivity magnetic current magnetic energy magnetic force magnetisation mathematical matter Maxwell Maxwell's theory meaning medium merely moving force non-conducting normal Ohm's law parallel permeance permittivity perpendicular phenomena plane sheet potential Prof propagation quantity quaternion reckoned regards result rotation scalar product side Similarly speed spherical sheet stationary stress vector summation surface tangential tensor tion torque translational force unit area unit vector unit volume vector algebra vector analysis vector product velocity voltage waste whilst wire zero
Popular passages
Page xviii - Owing to the extraordinary complexity of the investigation when written out in Cartesian form (which I began doing, but gave up aghast), some abbreviated method of expression becomes desirable. I may also add, nearly indispensable, owing to the great difficulty in making out the meaning and mutual connections of very complex formulae.