A Treatise on Electricity and Magnetism, Volume 1 (Google eBook)

Front Cover
Clarendon, 1892 - Electricity
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Contents

Division of physical vectors into two classes Forces and Fluxes
11
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
20
Surfaces tubes and lines of flow
23
Righthanded and lefthanded relations in space
25
Transformation of a lineintegral into a surfaceintegral
27
Effect of Hamiltons operation V on a vector function
29
Nature of the operation Vs
31
ELECTROSTATICS 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
Specific Inductive capacity of a dielectric
54
Absorption of electricity
55
Art Page 54 Impossibility of an absolute charge
56
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
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
98
a Specific inductive capacity
99
AppendixtoChap il
101
ON ELECTRICAL WORK AND ENERGY IN A SYSTEM OF CONDUCTORS
103
Theory of a system of conductors Coefficients of potential
109
Similar determination for two condensers
115
Practical importance of a knowledge of these forms in simple
117
CHAPTER IV
123
a 6 Applications of Greens method 131132
131
In terms of the potential arising from both systems
156
Discussion of the integral of Art 104 expressing the force
163
CHAPTER VI
169
1 Fig I
178
Art Page 182 Cases in which the quantities are functions of x and
182
Method employed in drawing the diagrams
183
CHAPTER VIII
186
Two coaxal cylindric surfaces
190
a Potential due to a spherical shell
199
Art Page
204
Laplaces coefficient or Biaxal harmonic
210
Figures of various harmonics
216
e When enclosed in a nearly spherical and nearly concentric
223
CHAPTER X
232
Continuous transformation into a figure of revolution about
238
THEORY OF ELECTRIC IMAGES Art 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
Case of two spherical surfaces intersecting at an angle
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 uninfluenced
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
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
ELECTROSTATIC INSTRUMENTS Art Page 207 The frictional electrical machine
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
324
On electrometers and electroscopes Indicating instruments and null methods Difference between registration and mea surement
326
Coulombs Torsion Balance for measuring charges
327
MATHEMATICAL THEORY OF THE DISTRIBUTION OF ELECTRIC
330
Electrometers for measuring potentials SnowHarriss and Thomsons
331
Heterostatic method
335
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
Measurement of the potential of a conductor without touch ing it
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 Page 230 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 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
VOL I
369
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 the 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 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 Darnells cell
394
Linear conductors
399
Linear conductors in multiple arc
400
Resistance of conductors of uniform section
401
Dimensions of the quantities involved in Ohms law
402
Specific resistance and conductivity in electromagnetic measure
403
Reciprocal property of any two conductors of the system
405
a b Conjugate conductors
406
Heat generated in the system
407
Appendix to Chap VI
409
CHAPTER VII
411
Determination of the quantity which flows through any surface
412
Equation of a surface of flow
413
Expression for the components of the flow in terms of surfaces offlow
414
Currentsheets and currentfunctions
415
Quantity of electricity which flows through a given surface
417
RESISTANCE AND CONDUCTIVITY IN THREE DIMENSIONS Art Pne 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
429
Lower limit for the correction for the ends of the wire
431
Higher limit
432
Surfaceconditions
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 parallel planes
443
On stratified conductors Coefficients of conductivity of a con ductor consisting of alternate strata of two different substances
445
If neither of the substances has the rotatory property denoted by T the compound conductor is free from it
446
longitudinal and transverse conductivity
449
CHAPTER X
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
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
Appendix to Chap XI 281
484

Common terms and phrases

Popular passages

Page ix - As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols.
Page 166 - I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric.
Page 430 - Remembering that the joint resistance of two (or more) circuits in parallel is the reciprocal of the sum of the reciprocals of the resistances of the several branches, we have: Fig.
Page viii - One reason of this is that before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday's Experimental Researches in Electricity. I was aware that there was supposed to be a difference between Faraday's way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other's language. I had also the conviction that this discrepancy did not arise from...
Page 406 - ... in a direction opposite to the motion of the hands of a watch.
Page 381 - It is extremely improbable however that when we come to understand the true nature of electrolysis we shall retain in any form the theory of molecular charges, for then we shall have obtained a secure basis on which to form a true theory of electric currents, and so become independent of those provisional theories.
Page 164 - Induction appears to consist in a certain polarized state of the particles, into which they are thrown by the electrified body sustaining the action, the particles assuming positive and negative points or parts, which are symmetrically arranged with respect to each other and the inducting surfaces or particles*.
Page 61 - These and many other phenomena of electrical discharge are exceedingly important, and when they are better understood they will probably throw great light on the nature of electricity as well as on the nature of gases and of the medium pervading space.
Page 3 - ... in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such a standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body.
Page viii - Electricity. I was aware that there was supposed to be a difference between Faraday's way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other's language. I hald also the conviction that this discrepancy did not arise from either party being wrong.

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