A Treatise on Electricity and Magnetism: pt. III. Magnetism. pt. IV. Electromagnetism

Front Cover
Clarendon Press, 1881 - Electricity
0 Reviews
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Potential of a magnet of finite size Two expressions for this potential corresponding respectively to the theory of polari zation and to that of magnetic...
10
Particular cases
12
Potential energy of a magnet in any field of force
14
On the magnetic moment and axis of a mngnet
15
Expansion of the potential of a magnet in spherical harmonics
16
Magnetic force in a cylindric cavity in a magnet uniformly
22
Relations between the scalar and the vectorpotential
29
CHAPTER III
31
Another method of proof
33
The potential at a point on the positive side of a shell of strength I exceeds that on the nearest point on the negative side by 47rI
34
Potential of a solenoidal magnet
35
Vectorpotential of a lamellar magnet
36
On the solid angle subtended at a given point by a closed curve
37
The solid angle expressed by the length of a curve on the sphere
38
expressed as a determinant
39
The solid angle is a cyclic function
40
Theory of the vectorpotential of a closed curve
41
Potential energy of a magnetic shell placed in a magnetic field
42
CHAPTER IV
44
Magnetic induction in different substances
45
Definition of the coefficient of induced magnetization
47
Faradays method
49
Case of a body surrounded by a magnetic medium
51
Poissons physical theory of the cause of induced magnetism
53
CHAPTER V
56
Case when k is large
58
Corresponding case in two dimensions Fig XV
60
The nine coefficients reduced to six Fig XVI
61
Statement of problems solved by Neumann Kirchhoff
68
CHAPTER VI
74
Explanation of phenomena by the modified theory
81
Effects of magnetization on the dimensions of the magnet
87
Principle of collimation employed in the Kew magnetometer
94
Observations of deflexion
102
System of observations in an observatory
112
J A Brouns method of correction
116
Combination of the results of the magnetic survey of a country
122
PART IV
128
Potential functiou due to a straight current It is a function
131
Reaction on the circuit
137
The wire is urged from the side on which its magnetic action
143
Art Pn?e
147
The geometrical quantities which determine their relative posi
153
Complete expression for the action between two finite currents
159
ON THE INDUCTION OF ELECTRIC CURRENTS Art Page 528 Faradays discovery Nature of his methods
163
The method of this treatise founded on that of Faraday
164
Phenomena of magnetoelectric induction
165
General law of induction of currents
167
Induction by the motion of the earth
168
The electromotive force due to induction does not depend on the material of the conductor
169
Use of the galvanometer to determine the timeintegral of the electromotive force
171
Conjugate positions of two coils
172
Mathematical expression for the total current of induction
173
Faradays conception of an electrotonic state
174
The law of Lenz and Neumanns theory of induction
177
ELECTROMAGNETIC UNIT OF RESISTANCE
178
Thomsons application of the same principle
179
Shock given by an electromagnet 181
181
Difference between this case and that of a tube containing a current of water
182
An electric current has energy which may be called electro kinetic energy
183
ON THE EQUATIONS OF MOTION OP A CONNECTED SYSTEM Art Page 553 Lagranges method furnishes appropriate ideas for the Btudy of th...
185
Degrees of freedom of a connected system
186
Generalized meaning of velocity
187
Work done by a small impulse
188
Kinetic energy in terms of momenta Tp
189
Hamiltons equations of motion
190
Kinetic energy in terms of the velocities and momenta Tpj
191
Kinetic energy in terms of velocities Tj
192
Moments and products of inertia and mobility
193
Necessary conditions which these coefficients must satisfy
194
Relation between mathematical dynamical and electrical ideas
195
CHAPTER VI
196
Work done by electromotive force
197
The most general expression for the kinetic energy of a system including electric currents
198
The electrical variables do not appear in this expression
199
The part depending on products of ordinary velocities and strengths of currents does not exist
201
Another experimental test
203
Discussion of the electromotive force
205
CHAPTER VII
207
Electromotive force in each circuit
208
Art Pago 580 Electromagnetic force
209
Theory of induced currents
210
Mechanical action between the circuits
211
CHAPTER VIII
212
Any system of contiguous circuits is equivalent to the circuit formed by their exterior boundary
213
A crooked portion of a circuit equivalent to a straight portion
214
Electrokinetic momentum at a point expressed as a vector 91
215
Justification of these names
216
Conventions with respect to the signs of translations and rota tions
217
Theory of a sliding piece
218
Electromotive force due to the motion of a conductor
219
Four definitions of a line of magnetic induction
220
Analysis of the electromotive force
223
The general equations referred to moving axes
224
The motion of the axes changes nothing but the apparent value of the electric potential
225
Electromagnetic force on an element of a conducting body Equations C
227
CHAPTER IX
229
Equations of magnetization D
230
Relation between magnetic force and electric currents
231
Equations of electric currents E
232
Equations of electric displacement F
234
Currents in terms of electromotive force I
235
Amperes theory of magnets
236
Vectorpotential of electric currents
238
Quaternion equations of the electromagnetic field
239
DIMENSIONS OF ELECTRIC UNITS 620 Two systems of units
241
Fifteen relations among these quantities
242
Dimensions in terms of e and m
243
Dimensions of the 12 quantities in the two systems
244
The six derived units
245
Practical system of electric units Table of practical units
246
CHAPTER XI
248
The electrostatic energy expressed in terms of the electromotive force and the electric displacement
249
Electrokinetic energy in terms of electric momentum and electric current
250
Method of this treatise
251
Magnetic energy reduced to electrokinetic energy
252
Art Page
253
Force acting on a conductor carrying a current
259
Magnetic action of a currentsheet with closed currents
265
When there is no external action the currents decay and their
271
This image moves away from its original position with velo city It
272
Mathematical expression for the effect of the induced currents
273
Value of the force acting on the magnetic pole
274
Case of curvilinear motion
275
Trail of images in the form of a helix
278
Spherical currentsheets
280
The external magnetic action of a cylindric wire depends only on the whole current through it
291
The vectorpotential
292
Eepulsion between the direct and the return current
293
Selfinduction of a wire doubled on itself
294
Currents of varying intensity in a cylindric wire
295
Relation between the electromotive force and the total current
296
Geometrical mean distance of two figures in a plane
298
Particular cases
299
Application of the method to a coil of insulated wires
301
CHAPTER XIV
303
Solid angle subtended by a circle at any point
305
Potential energy of two circular currents
306
Moment of the couple acting between two coils
307
Attraction between two parallel circular currents
308
Potential of two parallel circles expressed by elliptic integrals
309
Lines of force round a circular current Fig XVIII
311
Differential equation of the potential of two circles
312
Approximation when the circles are very near one another
313
Further approximation
314
70G Coil of maximum selfinduction
316
Appendix I
317
Appendix II
320
Appendix III
321
CHAPTER XV
322
Construction of a standard coil
323
Mathematical theory of the galvanometer
324
Principle of the tangent galvanometer and the sine galvano meter
325
Gaugains eccentric suspension
326
Helmholtzs double coil Fig XIX
327
Galvanometer with four coils
328
Proper thickness of the wire of a galvanometer
330
Sensitive galvanometers
331
Law of thickness of the wire
332
Galvanometer with wire o uniform thickness
334
Suspended coils Mode of suspension
335
Determination of magnetic force by means of suspended coil and tangent galvanometer
336
Thomsons suspended coil and galvanometer combined
337
Joules currentweigher
341
Suction of solenoids
342
Uniform force normal to suspended coil 312
343
CHAPTER XVI
344
Motion in a logarithmic spiral
345
Rectilinear oscillations in a resisting medium
346
Values of successive elongations
347
Determination of the logarithmic decrement
348
Two series of observations
350
To measure a constant current with the galvanometer
351
Best angle of deflexion of a tangent galvanometer
352
Measurement of a current by the first elongation
353
To make a series of observations on a constant current
354
Measurement of a transient current by first elongation
355
Correction for damping
356
Series of observations Zuriickwerfunga methode
357
Method of multiplication
359
COMPARISON OF COILS 752 Electrical measurement sometimes more accurate than direct measurement
361
Determination of
363
Determination of the selfinduction of a coil
365
Comparison of the selfinduction of two coils
367
Definition of resistance
368
Webers method by transient currents
370
His method of observation
371
Thomsons method by a revolving coil
374
Calculation of the resistance
375
Corrections
376
Joules calorimetric method
377
COMPARISON OF THE ELECTROSTATIC WITH THE ELECTROMAGNETIC UNITS 768 Nature and importance of the investigation
378
The ratio of the units is a velocity
379
Current by convection
380
Thomsons method by separate electrometer and clectrodyna mometer
382
Electromagnetic measurement of the capacity of a condenser Jenkins method
383
Method by an intermittent current
384
Condenser and Wippe as an arm of Wlieatstones bridge
385
Correction when the action is too rapid
386
Capacity of a condenser compared with the selfinduction of a coil
387
Coil and condenser combined
389
Comparison of the properties of the electromagnetic medium with those of the medium in the undulatory theory of light
393
Energy of light during its propagation
394
Solution when the medium is a nonconductor
396
Velocity of propagation of electromagnetic disturbances
397
The specific inductive capacity of a dielectric is the square of its index of refraction
398
Theory of plane waves
399
The electric displacement and the magnetic disturbance are in the plane of the wavefront and perpendicular to each other
400
Energy and stress during radiation
401
Pressure exerted by light
402
Propagation of plane waves
403
The theory agrees with that of Fresnel
404
Comparison with facts
405
Solution of the equations when the medium is a conductor
406
Characteristics of diffusion
407
Rapid approximation to an ultimate state
408
CHAPTER XXI
410
The rotation of the plane of polarization by magnetic action
411
Rotation produced by quartz turpentine c independently of magnetism
412
Kinematical analysis of the phenomena
413
Right and lefthanded rays
414
Art Page 815 In media acted on by magnetism the velocity is different for opposite directions of rotation
415
Kinematic equations of circularlypolarized light
416
Kinetic and potential energy of the medium
417
The action of magnetism must depend on a real rotation about the direction of the magnetic force as an axis
418
Hypothesis of molecular vortices
419
Variation of the vortices according to Helmholtzs law
420
Expression in terms of the current and the velocity
421
Velocity of a circularlypolarized ray
422
The magnetic rotation
424
Note on a mechanical theory of molecular vortices
426
CHAPTER XXII
429
The phenomena of magnetic molecules may be imitated by electric currents 430
430
Simplicity of the electric theory
431
Case in which the current is entirely due to induction
432
Magnecrystallic induction
433
A medium containing perfectly conducting spherical molecules
434
Theory of a molecule with a primitive current
435
Modifications of Webers theory
436
Art Page 846 Quantities which enter into Amperes formula
437
Relative motion of four electric particles Fechners theory
438
Two new forms of ArapereB formula
439
These are due to Gauss and to Weber respectively
440
Webers formula is consistent with this principle but that of Gauss is not
441
Potential of two currents
442
Segregating force in a conductor
443
Case of moving conductors
444
The formula of Gauss leads to an erroneous result
445
Letter of Gauss to Weber
446
Theory of Betti
447
Kepugnance to the idea of a medium
448

Other editions - View all

Common terms and phrases

Bibliographic information