A Treatise on Electricity and Magnetism, Volume 1

Front Cover
Clarendon, 1892 - Electricity
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Contents

Relation between corresponding vectors of the two classes
12
Lineintegration appropriate to forces surfaceintegration to fluxes
13
Lineintegrals and potentials
14
Hamiltons expression for the relation between a force and its potential
16
Cyclic regions and geometry of position
17
The potential in an acyclic region is single valued
18
System of values of the potential in a cyclic region
19
Surfaceintegrals
21
Surfaces tubes and lines of flow
22
Righthanded and lefthanded relations in space
25
Transformation of a lineintegral into a surfaceintegral
27
Eflect of Hamiltons operation V on a vector function
29
CHAPTER I
32
Electrification by induction
33
Electrification by conduction Conductors and insulators
34
In electrification by friction the quantity of the positive elec trification is equal to that of the negative electrification
35
To discharge a conductor completely into a metallic vessel
36
Test of electrification by goldleaf electroscope
37
Electricity may be treated as a physical quantity
38
Theory of Two fluids
40
Theory of One fluid
41
Measurement of the force between electrified bodies
43
Relation between this force and the quantities of electricity
44
Variation of the force with the distance
45
Proof of the law of electric force
46
Electric field
47
Electromotive force and potential
48
Equipotential surfaces Example of their use in reasoning about electricity
49
Lines of force
51
Capacity of a conductor Electric Accumulators
52
PART II
53
Specific Inductive capacity of a dielectric
54
Absorption of electricity
55
Disruptive discharge Glow
57
Brush
60
Electrical phenomena of Tourmaline
61
Plan of the treatise and sketch of its results
62
Electric polarization and displacement
64
6 The motion of electricity analogous to that of an incompressible fluid
67
Peculiarities of the theory of this treatise
68
CHAPTER II
71
Volumedensity surfacedensity and linedensity
72
Definition of the electrostatic nn it of electricity
73
Law of force between electrified bodies
74
Resultant intensity at a point
75
Lineintegral of electric intensity electromotive force
76
Electric potential
77
Resultant intensity in terms of the potential
78
Potential due to an electrified system
80
b Oavendishs experiments repeated in a modified form
81
c d e Theory of the experiments 8385
83
On the superposition of electrified systems Expression for
84
Surfaceintegral of electric induction
87
Poissons extension of Laplaces equation
89
a b c Conditions to be fulfilled at an electrified surface 9092
90
Resultant force on an electrified surface
93
The electrification of a conductor is entirely on the surface
95
A distribution of electricity on lines or points is physically impossible
96
Lines of electric induction
98
a Specific inductive capacity
99
energy of a system of conductors
103
Nature of the operation V 31
104
Theory of a system of conductors Coefficients of potential
109
b Similar determination for two condensers
115
Practical importance of a knowledge of these forms in simple
117
CHAPTER IV
123
a b Applications of Greens method 131
131
ae Thomsons Theorem 138141
138
a Method of finding limiting values of electrical coefficients
148
CHAPTER V
155
Modification of the expressions at the surface of a conductor
161
CHAPTER VI
169
1 Fig I
178
and
182
Method employed in drawing the diagrams
183
Two coaxal cylindric surfaces
190
b There are 2n + 1 independent constants in a solid harmonic
198
Value offY Yds when m n
204
Laplaces coefficient or Biaxal harmonic
210
Figures of various harmonics
216
b When acted on by external electrical force
222
CHAPTER X
232
Continuous transformation into a figure of revolution about
238
THEORY OF ELECTRIC IMAGES Page 155 Thomsons method of electric images
244
When two points are oppositely and unequally electrified the surface for which the potential is zero is a sphere
245
Electric images
246
Distribution of electricity on the surface of the sphere
248
Image of any given distribution of electricity
249
Resultant force between an electrified point and sphere
250
Images in an infinite plane conducting surface
252
Electric inversion
253
Geometrical theorems about inversion
254
Application of the method to the problem of Art 158
255
Finite systems of successive images
257
Enumeration of the cases in which the number of images is finite
259
Case of two spheres intersecting orthogonally
261
Case of three spheres intersecting orthogonally
263
Case of four spheres intersecting orthogonally
265
Infinite series of images Case of two concentric spheres
266
only
284
Conjugate functions
285
Conjugate functions may be added or subtracted
286
Conjugate functions of conjugate functions are themselves conjugate
287
Transformation of Poissons equation
289
Additional theorems on conjugate functions
290
Electric images in two dimensions
291
Neumanns transformation of this case
292
Distribution of electricity near the edge of a conductor formed by two plane surfaces
294
Ellipses and hyperbolas Fig X
296
Transformation of this case Fig XI
297
Application to two cases of the flow of electricity in a con ducting sheet
299
Capacity of a condenser consisting of a circular disk between two infinite planes
300
Case of a series of equidistant planes cut off by a plane at right angles to them
302
Case of a furrowed surface
303
Case of a single straight groove
304
Modification of the results when the groove is circular
305
Application to Sir W Thomsons guardring
308
Case of two parallel plates cut off by a perpendicular plane Fig XII
309
Case of a grating of parallel wires Fig XIII
310
Case of a single electrified wire transformed into that of the grating
311
The grating used as a shield to protect a body from electrical influence
312
Method of approximation applied to the case of the grating
314
217
317
Medium containing parallelepipeds of another medium 447
323
Construction of an artificial solid having given coefiicients of longitudinal and transverse conductivity 449
324
Principle of the guardring Thomsons Absolute Electro
334
Selfacting electrometers Thomsons Quadrant Electrometer
341
On electric accumulators The Leyden
350
THE ELECTRIC CURRENT Art 236 Current produced when conductors are discharged
354
Description of the voltaic battery
355
Electromotive force
356
Properties of the current
357
Explanation of terms connected with electrolysis
358
Different modes of passage of the current
359
Magnetic action of the current
360
The Galvanometer
361
CHAPTER II
362
Generation of heat by the current J oules Law
363
Analogy between the conduction of electricity and that of heat
364
Differences between the two classes of phenomena
365
CHAPTER III
367
Efiect of electrolytes
368
Seebecks discovery of thermoelectric currents
370
Magnuss law of a circuit of one metal
371
Cummings discovery of thermoelectric inversions
372
Thomsons deductions from these facts and discovery of th reversible thermal effects of electric currents in copper and in iron
373
Taits law of the electromotive force of a thermoelectric pair
374
CHAPTER IV
375
Clausiuss theory of molecular agitation
377
Test of an electrolyte by polarization
378
Molecular charges
380
Secondary actions observed at the electrodes
381
Conservation of energy in electrolysis
383
Measurement of chemical atfinity as an electromotive force
384
CHAPTER V
387
Polarization due to the presence of the ions at the electrodes The ions not in a free state
388
Relation between the electromotive force of polarization and the state of the ions at the electrodes
389
Dissipation of the ions and loss of polarization
390
Limit of polarization
391
Constant voltaic elements Daniells cell
394
CHAPTER VI
399
RESISTANCE AND CONDUCTIVITY IN THREE DIMENSIONS Art Page 297 Equations of resistance
418
Equations of conduction
419
Conditions of stability
420
Equation of continuity in a homogeneous medium
421
Theory of the coefficient T It probably does not exist
422
Generalized form of Thomsons theorem
423
Proof without symbols
425
Lord Rayleighs method applied to a wire of variable section Lower limit of the value of the resistance
426
Higher limit
429
Lower limit for the correction for the ends of the wire
431
Higher limit
432
CHAPTER IX
435
Spherical surface
438
Spherical shell
439
Medium in which small spheres are uniformly disseminated
440
Images in a plane surface
441
Method of inversion not applicable in three dimensions
442
Case of conduction through a stratum bounded by paralle planes
443
Comparison of the capacities of accumulators
445
If neither of the substances has the rotatory property denoted by T the compound conductor is free from it
446
CONDUCTION IN DIELECTRICS 325 In a strictly homogeneous medium there can be no internal charge
450
326
451
No residual charge due to simple conduction
452
Residual charge and electrical absorption
454
Total discharge
456
331
457
Comparison with the conduction of heat
458
Theory of telegraph cables and comparison of the equations with those of the conduction of heat
460
Opinion of Ohm on this subject
461
Advantage of using material standards of resistance in electrical measurements
465
336
466
Reproduction of standards
467
Forms of resistance coils
468
Coils of great resistance
469
Arrangement of coils in series
470
346
472
Appendix to Chap II 101
484

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