A Treatise on Electricity and Magnetism, 2. köide

Front Cover
Clarendon, 1892 - 23 pages
 

Contents

Vectorpotential of a lamellar magnet
38
On the solid angle subtended at a given point by a closed curve
39
The solid angle expressed by the length of a curve on the sphere
40
expressed as a determinant
42
Theory of the vectorpotential of a closed curve
43
Potential energy of a magnetic shell placed in a magnetic field
45
CHAPTER IV
47
Magnetic induction in different substances
49
Definition of the coefficient of induced magnetization
50
Faradays method
53
Case of a body surrounded by a magnetic medium
55
Poissons physical theory of the cause of induced magnetism
57
CHAPTER V
59
Case when x is large K
61
Corresponding case in two dimensions Fig XV
62
Case of a solid sphere the coefficients of magnetization being different in different directions
63
72
69
Theory of an ellipsoid acted on by a uniform magnetic force 438 Cases of very flat and of very long ellipsoids 439 Statement of problems solved by ...
72
On ships magnetism 12742
75
CHAPTER VI
79
79
81
CHAPTER VII
95
Definition of the earths magnetic poles
132
PART IV
138
Conditions of continuous rotation of a magnet about a current
144
Theory of electromagnetic rotations
150
Kinematical analysis of the phenomena
163
ON THE INDUCTION OF ELECTRIC CURRENTS
175
Faradays conception of an electrotonic state
188
CHAPTER IV
195
ON THE EQUATIONS OF MOTION OF A CONNECTED SYSTEM
199
Kinetic energy in terms of momenta T₂
205
CHAPTER VI
211
Another experimental test
218
Art Page 578 The electrokinetic energy of a system of linear circuits
223
Electromotive force in each circuit
224
Electromagnetic force
225
Case of two circuits
226
Mechanical action between the circuits
227
All the phenomena of the mutual action of two circuits depend on a single quantity the potential of the two circuits
228
CHAPTER VIII
229
Expressed as a lineintegral
230
Electrokinetic momentum expressed as a surfaceintegral 589 A crooked portion of a circuit equivalent to a straight portion
231
Electrokinetic momentum at a point expressed as a vector A
232
Its relation to the magnetic induction B Equations A
233
Justification of these names
234
Theory of a sliding piece
235
Electromotive force due to the motion of a conductor
236
Electromagnetic force on the sliding piece
237
General equations of electromotive force B
238
Analysis of the electromotive force
240
The general equations referred to moving axes
241
Art Page 602 Electromagnetic force on a conductor
243
Electromagnetic force on an element of a conducting body Equations C
244
CHAPTER IX
247
Equations of magnetization D
249
Equations of electric currents E
251
Equations of electric displacement F
252
Equations of electric conductivity G
253
Volumedensity of free electricity J
254
Electric currents in terms of electrokinetic momentum
255
Vectorpotential of electric currents
256
Quaternion expressions for electromagnetic quantities
257
Quaternion equations of the electromagnetic field
258
Appendix to Chapter IX
259
CHAPTER X
263
Fifteen relations among these quantities
264
Dimensions in terms of e and m
265
Reciprocal properties of the two systems
266
Dimensions of the twelve quantities in the two systems
267
Practical system of electric units Table of practical units
268
The electrostatic energy expressed in terms of the electromotive
271
CHAPTER XIII
315
The external magnetic action of a cylindric wire depends only on the whole current through it
316
The vectorpotential
317
Repulsion between the direct and the return current
318
Selfinduction of a wire doubled on itself
320
The motion of the axes changes nothing but the apparent value of the electric potential 243
321
Relation between the electromotive force and the total current
322
Geometrical mean distance of two figures in a plane
324
Particular cases
326
Application of the method to a coil of insulated wires
328
CHAPTER XIV
331
Solid angle subtended by a circle at any point
333
Potential energy of two circular currents
334
Moment of the couple acting between two coils
335
Values of P
336
Calculation of the coefficients for a coil of finite section
337
Potential of two parallel circles expressed by elliptic integrals
338
CHAPTER XV
351
ments
352
Properties of a magnet when acted on by the earth
371
CHAPTER XVI
374
Motion in a logarithmic spiral
375
Rectilinear oscillations in a resisting medium
376
The quantities of the opposite kinds of magnetism in a magnet
377
Determination of the logarithmic decrement
378
Determination of the time of vibration from three transits
379
Two series of observations
380
Dead beat galvanometer
381
To measure a constant current with the galvanometer
382
Best method of introducing the current
383
Definitions of Magnetic Moment Intensity of Magnetization
384
Method of multiplication for feeble currents
385
Measurement of a transient current by first elongation
386
Correction for damping
387
Series of observations Zurückwerfungsmethode
388
On the magnetic moment and axis of a magnet
390
CHAPTER XVII
392
Determination of G₁
393
Determination of 91
394
Determination of the mutual induction of two coils
395
Determination of the selfinduction of a coil
397
Comparison of the selfinduction of two coils
398
Appendix to Chapter XVII
399
Definition of a magnetic solenoid
407
Thomsons method by a revolving coil
408
Nature and importance of the investigation
414
Capacity of a condenser compared with the selfinduction
425
Comparison of the properties of the electromagnetic medium
431
Comparison of this velocity with that of light
437
The theory agrees with that of Fresnel
445
Methods of observation by mirror and scale Photographic method
450
Principle of collimation employed in the Kew magnetometer
451
Determination of the axis of a magnet and of the direction of the horizontal component of the magnetic force
452
Measurement of the moment of a magnet and of the intensity of the horizontal component of magnetic force
453
Observations of deflexion
454
Method of tangents and method of sines
455
Observation of vibrations
456
Elimination of the effects of magnetic induction
457
Statical method of measuring the horizontal force
458
Bifilar suspension
459
System of observations in an observatory
460
Observation of the dipcircle
461
The magnetic rotation
468
Örsteds discovery of the action of an electric current on
475
Relative motion of four electric particles Fechners theory
481
Segregating force in a conductor
489
Dimensions of the unit of current
495
109
496
112
497
120
499
His method of experimenting
503
Theory of stress in a medium as stated by Faraday

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Popular passages

Page 294 - If we differentiate the first of these equations with respect to x, and the second with respect to y, and add the...
Page 157 - If the conductor be a rotating disk or a fluid it will move in obedience to this force, and this motion may or may not be accompanied with a change of position of the electric current which it carries. But if the current itself be free to choose any path through a fixed solid...
Page 491 - In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other, for energy, as Torricelli remarked, 'is a quintessence of so subtile a nature that it cannot be contained in any vessel except the inmost substance of material things'.
Page 468 - I think we have good evidence for the opinion that some phenomenon of rotation is going on in the magnetic field, that this rotation is performed by a great number of very small portions of matter, each rotating on its own axis, this axis being parallel to the direction of the magnetic force...
Page 451 - ... theory explains the facts. Faraday has shown, in the nineteenth series of his experimental researches, that a ray of plane-polarized light, when transmitted through any solid (diamagnetic ?) transparent medium under the action of a powerful magnet, has the plane of its polarization rotated in that direction in which a positive current must circulate round the ray in order to produce a magnetic force in the same direction as that which actually exists in the medium. Verdet, however, discovered...
Page 459 - This angular velocity cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis.
Page 179 - The whole of these phenomena may be summed up in one law. When the number of lines of magnetic induction which pass through the secondary circuit in the positive direction is altered, an electromotive force acts round the circuit, which is measured by the rate of decrease of the magnetic induction through the circuit. 532.] For instance, let the rails of a railway be insulated from the earth, but connected at one terminus through a galvanometer, and let the circuit be completed by the wheels and...
Page 175 - The experimental investigation by which Ampere established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the
Page 432 - The general conclusion of philosophers seems to be, that such cases are by far the moat numerous, and for my own part, considering the relation of a vacuum to the magnetic force and the general character of magnetic phenomena external to the magnet, I am more inclined to the notion that in the transmission of the force there is such an action, external to the magnet, than that the effects are merely attraction and repulsion at a distance. Such an action may be a function of the ether ; for it is...
Page 468 - ... of the parts of the electromagnetic field. The problem of determining the mechanism required to establish a given species of connexion between the motions of the parts of a system always admits of an infinite number of solutions.

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