A Treatise on Electricity and Magnetism, Volume 1

Front Cover
Clarendon, 1892 - Electricity
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Contents

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
Specific Inductive capacity of a dielectric
54
Absorption of electricity
55
Art Page 54 Impossibility of an absolute charge
56
Disruptive discha rge Glow
57
Brush
60
Electrical phenomena of Tourmaline
61
Plan of the treatise and sketch of its results
62
Electric polarization and displacement
64
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 unit 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 Cavendishs experiments repeated in a modified form
81
c d e Theory of the experiments 8385
83
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
97
a Specific inductive capacity
99
ON ELECTRICAL WORK AND ENERGY IN A SYSTEM OF CONDUCTORS
103
Page
107
Theory of a system of conductors Coefficients of potential
109
b Similar determination for two condensers
115
Art Page
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
THE ELECTRIC CURRENT
168
CHAPTER VI
169
1 Fig I
178
Art Page 182 Cases in which the quantities are functions of a and
182
Method employed in drawing the diagrams
183
Two coaxal cylindric surfaces
190
a Potential due to a spherical shell
199
Equilibrium of electricity on two spherical conductors
224
CHAPTER X
232
The characteristic equation
240
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
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
Case of two spherical surfaces intersecting at an angle 2
258
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
Any two spheres not intersecting each other
268
Calculation of the coefficients of capacity and induction
270
Calculation of the charges of the spheres and of the force between them
272
Distribution of electricity on two spheres in contact Proof sphere
273
Thomsons investigation of an electrified spherical bowl
276
Induction on an uninsulated disk or bowl by an electrified point in the continuation of the plane or spherical surface
277
The rest of the sphere supposed uniformly electrified
278
The bowl maintained at potential V and uninfiuenced
279
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
302
Method of approximation applied to the case of the grating
314
CHAPTER XIII
317
The electrophorus of Volta
319
Production of electrification by mechanical work Nicholsons Revolving Doubler _
320
Thomsons waterdropping machine
322
Holtzs electrical machine
323
Construction of an artificial solid having given coefficients of longitudinal and transverse conductivity 449
324
On electrometers and electroscopes Indicating instruments and null methods Difference between registration and mea surement
326
215
327
Electrometers for measuring potentials SnowHarriss and Thomsons
331
218
334
Selfacting electrometers Thomsons Quadrant Electrometer
336
Measurement of the electric potential of a small body
339
Measurement of the potential at a point in the air
340
222
341
Measurement of the superficial density of electrification The proof plane
342
A hemisphere used as a test
343
A circular disk
344
On electric accumulators The Leyden jar
346
Accumulators of measurable capacity
347
The guardring accumulator
349
Comparison of the capacities of accumulators
350
Art Bage 230 Current produced when conductors are discharged
354
232
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 Joules Law
363
Analogy between the conduction of electricity and that of heat
364
Differences between the two classes of phenomena
365
CHAPTER III
367
Effect 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
379
Secondary actions observed at the electrodes
381
Conservation of energy in electrolysis
383
Measurement of chemical affinity 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
291
414
RESISTANCE AND CONDUCTIVITY IN THREE DIMENSIONS
418
Relation between any three systems of surfaces of flow
420
CONDUCTION IN DIELECTRICS 325 In a strictly homogeneous medium there can be no internal charge
450
Theory of a condenser in which the dielectric is not a perfect insulator
451
No residual charge due to simple conduction
452
Residual charge and electrical absorption
454
Total discharge
456
414
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
CHAPTER XI
465
Different standards which have been used and different systems which have been proposed
466
Reproduction of standards
467
Forms of resistance coils
468
Coils of great resistance
469
Arrangement of coils in series
470
On the comparison of resistances 1 Ohms method
471
2 By the differential galvanometer
475
Estimation of limits of error in the determination
477
Best arrangement of the conductors to be compared
478
On the use of Wheatstones Bridge
480
Thomsons method for small resistances
482
Appendix to Chap II 101
484
Matthiessen and Hockins method for small resistances
485
Comparison of great resistances by the electrometer
487
Direct electrostatic method
488
Thomsons method for the resistance of a galvanometer
489
Mances method of determining the resistance of a battery
490
Comparison of electromotive forces
493
CHAPTER XII
495
Resistance of metals
496
Resistance of mercury
497
Table of resistance of metals
498
Resistance of electrolytes
499
Experiments of Paalzow
500
Experiments of Kohlrausch and Nippoldt
501
Guttapercha
503
Glass
504
Experiments of Wiedemann and Riihlmann
505

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