A Treatise on Electricity and Magnetism, Τόμος 1

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Clarendon Press, 1873 - 444 σελίδες
 

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Περιεχόμενα

Relation between corresponding vectors of the two classes
11
Lineintegration appropriate to forces surfaceintegration to fluxes
12
Lineintegrals and potentials
13
Hamiltons expression for the relation between a force and its potential
15
Cyclic regions and geometry of position
16
The potential in an aoyclic region is single valued
17
System of values of the potential in a cyclic region
18
Surfaceintegrals
19
Surfaces tubes and lines of flow
21
Righthanded and lefthanded relations in space
24
Transformation of a lineintegral into a surfaceintegral
25
Effect of Hamiltons operation v on a vector function
27
which the names of Vitreous and Resinous or Positive and Negative have been given
30
Electrification by induction
31
Electrification by conduction Conductors and insulators
32
In electrification by friction the quantity of the positive elec trification is equal to that of the negative electrification
33
To discharge a conductor completely into a metallic vessel
34
called Electricity
35
Electricity may be treated as a physical quantity
36
Theory of Two fluids
37
Theory of One fluid
39
Measurement of the force between electrified bodies
40
Relation between this force and the quantities of electricity
41
Variation of the force with the distance
42
Proof of the law of electric force
43
Electric field
44
Electric potential
45
Lines of force
47
Capacity of a conductor
48
Art Pge 52 Specific Inductive capacity of a dielectric
50
Impossibility of an absolute charge
51
Disruptive discharge Glow
52
Brush
54
Spark
55
Electrical phenomena of Tourmaline
56
Plan of the treatise and sketch of its results
57
GO Electric polarization and displacement
59
The motion of electricity analogous to that of an incompressible
61
fluid
62
CHAPTER II
66
Volumedensity surfacedensity and linedensity
67
Definition of the electrostatic unit of electricity
68
Law of force between electrified bodies
69
Lineintegral of electric force electromotive force
71
Electric potential
72
The potential of all points of a conductor is the same
73
Potential due to an electrified system
74
Surfaceintegral of electric induction
77
Poissons extension of Laplaces equation
79
Conditions to be fulfilled at an electrified surface
80
Resultant force on an electrified surface
82
The electrification of a conductor is entirely on the surface
83
A distribution of electricity on bines or points is physically impossible
84
Lines of electric induction
85
Specific inductive capacity
86
On the superposition of electrified systems
88
Comparison of electrified systems
96
ja + b + cdxdydz
103
Greens functions
113
MECHANICAL ACTION BETWEEN ELECTRIFIED BODIES
119
The hypothesis of stress considered as a step in electrical
126
Statement of the theory of electric polarization
132
Angles at which an equipotential surface intersects itself
138
1 Fig II
144
To analyse a spherical harmonic into a system of conjugate
145
Two concentric spherical surfaces
152
Singular points of different orders defined by their axes
158
Nature of the operation v2 29
160
The zonal tesscral and sectorial types
166
Development of a function in terms of spherical surface har
172
harmonics by means of a finite number of measurements at selected points of the sphere
177
Application to spherical and nearly spherical conductors
178
CHAPTER X
181
The characteristic equation of V in terms of ellipsoidal co ordinates
182
Expression of a 3 y in terms of elliptic functions
183
Particular solutions of electrical distribution on the confocal surfaces and their limiting forms
184
Continuous transformation into a figure of revolution about the axis of z
187
Transformation into a figure of revolution about the axis of x
188
Transformation into a system of cones and spheres
189
CHAPTER XL
191
When two points are oppositely and unequally electrified the surface for which the potential is zero is a sphere
192
Art _ Page 194 Application to two cases of the flow of electricity in a con
194
Distribution of electricity on the surface of the sphere
195
Image of any given distribution of electricity
196
Resultant force between an electrified point and sphere
197
Images in an infinite plane conducting surface
198
Electric inversion
199
Geometrical theorems about inversion
201
Finite systems of successive images
203
Case of two spherical surfaces intersecting at an angle
204
Enumeration of the cases in which the number of images is finite
206
Case of two spheres intersecting orthogonally
207
Case of three spheres intersecting orthogonally
210
Case of four spheres intersecting orthogonally
211
Infinite series of images Case of two concentric spheres
212
Any two spheres not intersecting each other
213
Calculation of the coefficients of capacity and induction
216
Calculation of the charges of the spheres and of the force between them
217
Distribution of electricity on two spheres in contact Proof sphere
219
Thomsons investigation of an electrified spherical bowl
221
Induction on an uninsulated disk or bowl by an electrified point in the continuation of the plane or spherical surface
222
The rest of the sphere supposed uniformly electrified
223
Induction on the bowl due to a point placed anywhere
224
CHAPTER XII
226
Conjugate functions
227
Conjugate functions may be added or subtracted
228
Conjugate functions of conjugate functions arc themselves conjugate
229
Transformation of Poissons equation
231
Additional theorems on conjugate functions
232
Electric images in two dimensions
233
Neumanns transformation of this case
234
Distribution of electricity near the edge of a conductor formed by two plane surfaces
236
Ellipses and hyperbolas Fig X
237
The grating used as a shield to protect a body from electrical influence
249
Method of approximation applied to the case of the grating
251
CHAPTER XIII
254
The electrophorus of Volta
255
Production of electrification by mechanical work Nicholsons Revolving Doubler
256
Thomsons waterdropping machine
259
Holtzs electrical machine
260
On electrometers and electroscopes Indicating instruments and null methods Difference between registration and mea surement
262
Coulombs Torsion Balance for measuring charges
263
Electrometers for measuring potentials Snow Harriss and Thomsons
268
proof plane
277
A hemisphere used as a test
278
A circular disk
279
On electric accumulators The Leyden jar
281
Accumulators of measurable capacity
282
The guardring accumulator
284
Comparison of the capacities of accumulators
285
PART II
288
Description of the voltaic battery
289
Electromotive force
290
Properties of the current
291
Explanation of terms connected with electrolysis
292
Magnetic action of the current
293
The Galvanometer
294
CHAPTER II
295
same temperature
299
Effect of electrolytes
314
Art Pago 269 Dissipation of the ions and loss of polarization
321
Hitters secondary pile compared with the Lcyden jar
322
Constant voltaic elements Darnells cell
325
CHAPTER VI
227
Transformation of this case Fig XI 238
234
Generation of heat by the current Joules Law
242
Thomsons voltaic current in which gravity performs the part
248
Principle of the guardring Thomsons Absolute Electrometer 267
267
Heterostatic method 269
269
Selfacting electrometers Thomsons Quadrant Electrometer 271
271
Measurement of the electric potential of a small body 274
274
Measurement of the potential at a point in the air 275
275
of chemical action 300
291
Analogy between the conduction of electricity and that of heat 297
297
Faradays doctrine of the impossibility of an absolute charge 298
298
Peltiers phenomenon Deduction of the thermoelectric elec tromotive force at a junction 300
300
Seebecks discovery of thermoelectric currents 302
302
Cummings discovery of thermoelectric inversions 304
304
Taits law of the electromotive force of a thermoelectric pair 305
305
CHAPTER IV
307
Clausiuss theory of molecular agitation 309
309
Test of an electrolyte by polarization 310
310
Molecular charges 311
311
Secondary actions observed at the electrodes 313
313
Conservation of energy in electrolysis 315
315
Measurement of chemical affinity as an electromotive force 316
316
CHAPTER V
318
Polarization due to the presence of the ions at the electrodes The ions not in a free state 319
319
Relation between the electromotive force of polarization and the state of the ions at the electrodes 320
320
MATHEMATICAL THEORY OF THE DISTRIBUTION OF ELECTRIC CURRENTS 273 Linear conductors
329
Linear conductors in multiple arc
330
Resistance of conductors of uniform section
331
Dimensions of the quantities involved in Ohms law
332
Specific resistance and conductivity in electromagnetic measure
333
Reciprocal property of any two conductors of the system
335
Conjugate conductors
336
CHAPTER VII
338
Determination of the quantity which flows through any surface
339
Equation of a surface of flow
340
Expression for the components of the flow in terms of surfaces of flow
341
Currentsheets and currentfunctions
342
Quantity of electricity which flows through a given surface
344
Equations of resistance
345
Equations of conduction
346
Conditions of stability
347
Equation of continuity in a homogeneous medium
348
Theory of the coefficient T It probably does not exist
349
Generalized form of Thomsons theorem
350
Proof without symbols
351
Strutts method applied to a wire of variable section Lower limit of the value of the resistance
355
Higher limit
356
CHAPTER IX
360
Spherical surface
363
Spherical shell placed in a field of uniform flow
364
Medium in which small spheres are uniformly disseminated
365
Images in a plane surface
366
Method of inversion not applicable in three dimensions
367
Infinite series of images Application to magnetic induction
368
VOL i
369
If neither of the substances has the rotatory property denoted by T the compound conductor is free from it
370
H the substances are isotropic the direction of greatest resist ance is normal to the strata
371
The rotatory property cannot be introduced by means of con ducting channels
372
Construction of an artificial solid having given coefficients of longitudinal and transverse conductivity
373
charge
374
Theory of a condenser in which the dielectric is not a perfect insulator
375
No residual charge due to simple conduction
376
Residual charge and electrical absorption
378
Total discharge
380
Comparison with the conduction of heat
381
Opinion of Ohm on this subject
384
Mechanical illustration of the properties of a dielectric
385
CHAPTER XI
388
The electromagnetic system of units
389
Reproduction of standards
390
Forms of resistance coils
391
Coils of great resistance
392
Arrangement in multiple arc
393
On the comparison of resistances 1 Ohms method
394
2 By the differential galvanometer
395
3 By Wheatstones Bridge
398
Estimation of limits of error in the determination
399
Best arrangement of the conductors to be compared
400
On the use of Wheatstones Bridge
402
Thomsons method for small resistances
405
Matthiessen and Hockius method for small resistances
406

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Σελίδα 315 - 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 these provisional theories.
Σελίδα 358 - 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.
Σελίδα ix - 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...
Σελίδα xi - Faraday's methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.
Σελίδα 314 - This phrase, gross as it is, and out of harmony with the rest of this treatise, will enable us at least to state clearly what is known about electrolysis, and to appreciate the outstanding difficulties.
Σελίδα 318 - Mag., 1851) established the important theorem that the electro-motive force of an electro-chemical apparatus is, in absolute measure, equal to the mechanical equivalent of the chemical action on one electro-chemical equivalent of the substance.
Σελίδα 134 - I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric.
Σελίδα 5 - ... 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.
Σελίδα ix - 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 either party being wrong. I was first convinced of this by Sir William Thomson », to whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject.
Σελίδα 11 - I am convinced, however, that the introduction of the ideas, as distinguished from the operations and methods of Quaternions, will be of great use to us in the study of all parts of our subject, and especially in electrodynamics, where we have to deal with a number of physical quantities, the relations of which to each other can be expressed far more simply by a few words of Hamilton's, than by the ordinary equations.

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