Electromagnetic Theory, Volume 2

Front Cover
American Mathematical Soc., 2003 - History - 547 pages
Oliver 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 This book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.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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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.

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