Elements of Theoretical Physics

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Macmillan, 1897 - Mathematical physics - 339 pages
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Contents

Constrained Motion
24
Keplers Laws
29
Universal Attraction
30
Universal Attraction continued
31
The Potential of a System of Masses
34
Examples Calculation of Potentials
36
Gausss Theorem The Equations of Laplace and Poisson
41
Examples of the Application of Laplaces and Poissons Equations
46
Action and Reaction On the Molecular and Atomic Structure of Bodies
48
The Centre of Gravity
50
A Materia System XIX Moment of Momentum
55
The Energy of a System of Masses XXI Conditions of Equilibrium Rigid Bodies XXII Rotation of a Rigid Body The Pendulum I
56
58
58
CHAPTER II
62
Components of Stress
64
Relations among the Components of Stress
67
The Principal Stresses
69
Faradays Views on the Nature of Forces Acting at a Distance
72
Deformation
74
Relations between Stresses and Deformations
79
Conditions of Equilibrium of an Elastic Body
82
Stresses in a Spherical Shell
83
SECTION PAGE CXV The Differential Coefficients 280
84
Torsion
85
Flexure
87
Equations of Motion of an Elastic Body
89
Plane Waves in an Infinitely Extended Body
90
Other Wave Motions
93
Vibrating Strings
95
Potential Energy of an Elastic Body
96
CHAPTER III
99
Examples of the Equilibrium of Fluids
101
Vortex Motions and Currents in a Fluid
107
Steady Motion with VelocityPotential
109
Lagranges Equations of Motion
111
Wave Motions
112
CHAPTER V
115
Equations of Motion of a Viscous Fluid
118
Flow through a Tube of Circular Cross Section
119
CHAPTER VI
121
Conditions of Equilibrium
123
Capillary Tubes
125
CHAPTER VII
127
Electrical Potential
128
The Distribution of Electricity on a Good Conductor 130
130
The Distribution of Electricity on a Sphere and on an Ellipsoid
132
Electrical Distribution
135
Complete Distribution
139
Mechanical Force Acting on a Charged Body
141
Lines of Electrical Force
143
Electrical Energy
145
A System of Conductors
147
Mechanical Forces
150
The Condenser and Electrometer
151
The Dielectric
155
SECTION PAGE LXVI Conditions of Equilibrium
157
CHAPTER VIII
163
The Magnetic Potential L66 LXX The Potential of a Magnetized Sphere lt
166
The Fundamental Equations of ElectroMagnetism
188
Systems of Currents in General
190
The Action of Electrical Currents on each other
192
The Measurement of CurrentStrength on the Quantity of Electricity
194
Ohms Law and Joules Law
197
99
199
101
202
Measurement of Resistance
205
Fundamental Equations of Induction
208
ElectroKinetic Energy
210
Absolute Units
211
CHAPTER IV
215
Calculation of the Period
217
The Fundamental Equations for Electrical Insulators or Dielectrics 219
219
Plane Waves in the Dielectric
221
The Hertzian Oscillations
223
Poyntings Theorem
224
CHAPTER XII
229
FresnePs Formulas
231
XCTX The ElectroMagnetic Theory of Light
235
Equations of the ElectroMagnetic Theory of Light
237
2
242
Double Refraction
246
CHI Discussion of the Velocities of Propagation
249
The Wave Surface
251
The Wave Surface continued
254
The Direction of the Rays
256
Uniaxial Crystals
259
Double Refraction at the Surface of a Crystal
261
Double Refraction in Uniaxial Crystals
264
CHAPTER XIII
266
Ideal Gases
270
Cyclic Processes
272
Carnots and Clausius Theorem
274
Application of the Second Law
279
Liquids and Solids
281
The Development of Heat by Change of Length
282
Van der Waals Equation of State
285
Saturated Vapours
290
The Entropy
292
Dissociation
295
CHAPTER XIV
298
Steady State
300
The Periodic Flow of Heat in a given Direction
301
A Heated Surface
303
The Flow of Heat from a Point
304
The Flow of Heat in an Infinitely Extended Body
305
The Formation of Ice
307
The Flow of Heat in a Plate whose Surface is kept at a Constant Temperature
308
The Development of Functions in Series of Sines and Cosines
312
The Application of Fouriers Theorem to the Conduction of Heat
315
The Cooling of a Sphere
319
The Motion of Heat in an Infinitely Long Cylinder
322
On the Conduction of Heat in Fluids
325
The Influence of the Conduction of Heat on the In tensity and Velocity of Sound in Gases
330
MOTION OF FLUIDS XLI Eiders Equations of Motion XLII Transformation of Eiders Equations 103
336
106
337
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Page 42 - ... only when friction is negligible and when the fluid motion is irrotational. But the air motion in Fig. 135 is due to friction between the air and the spinning ball, and there is only one particular case in which the air whirl in Fig. 135 is irrotational, namely, when the velocity of the air at a point is inversely proportional to the distance of the point from the axis of the spinning ball. Therefore the application of Bernoulli's principle to the air motion in Fig. 136 is very questionable.
Page 83 - Differentiating the first of these equations with respect to x, the second with respect to y, and the third with respect to z...
Page 232 - REFLEXION. (1) The incident ray, the normal to the surface at the point of incidence, and the reflected ray lie in one plane. (2) The angle between the reflected ray and the normal is equal to that between the incident ray and the normal.
Page 31 - These are received according to the square of the distance of the planet from the sun ; that is, they decrease as the square of the distance increases.
Page 154 - The evaluation of this for a thin wire is discussed below. In confirmation of equation (12), Dingle (unpublished) has found by direct integration of the Boltzmann equation for this case...
Page 234 - Hence Fresnel's assumption that the density of the ether is different in different media is inconsistent with the continuity of the ether at right angles to the surface. Adopting the above equations, Neumann and MacCullagh postulate that the density of the ether is the same in all media, but that its elasticity is different.
Page 29 - The squares of the periodic times of the planets are proportional to the cubes of the semimajor axes of their orbits. The first law states a particular case of the result established in Sec.
Page 195 - F is the magnitude of the force, ds is the magnitude of the displacement, and 6 is the angle between the direction of the force and the direction of the displacement.
Page 296 - Hence the entropy of the system is equal to the sum of the entropies of its two sub-systems.
Page 245 - If the angle of incidence is greater than the critical angle, the sine of the angle of refraction, as computed by Snell's law, is greater than unity.

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