Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 197 Density of Nitrogen
- ART. 198 On the Intensity of Light reflected from Water and Mercury at nearly Perpendicular Incidence
- ART. 199 On the Interference Bands of Approximately Homogeneous Light; in a Letter to Prof. A. Michelson
- ART. 200 On the Influence of Obstacles arranged in Rectangular Order upon the Properties of a Medium
- ART. 201 On the Densities of the Principal Gases
- ART. 202 Interference Bands and their Applications
- ART. 203 On the Theory of Stellar Scintillation
- ART. 204 Astronomical Photography
- ART. 205 Grinding and Polishing of Glass Surfaces
- ART. 206 On the Reflection of Sound or Light from a Corrugated Surface
- ART. 207 On a Simple Interference Arrangement
- ART. 208 On the Flow of Viscous Liquids, especially in Two Dimensions
- ART. 209 The Scientific Work of Tyndall
- ART. 210 On an Anomaly encountered in Determinations of the Density of Nitrogen Gas
- ART. 211 On the Minimum Current audible in the Telephone
- ART. 212 An Attempt at a Quantitative Theory of the Telephone
- ART. 213 On the Amplitude of Aerial Waves which are but just Audible
- ART. 214 Argon, a New Constituent of the Atmosphere. By LORD RAYLEIGH, Sec. R.S., and PROFESSOR WILLIAM RAMSAY, F.R.S.
- ART. 215 Argon
- ART. 216 On the Stability or Instability of Certain Fluid Motions. III
- ART. 217 On the Propagation of Waves upon the Plane Surface separating Two Portions of Fluid of Different Vorticities
- ART. 218 On some Physical Properties of Argon and Helium
- ART. 219 On the Amount of Argon and Helium contained in the Gas from the Bath Springs
- ART. 220 The Reproduction of Diffraction Gratings
- ART. 221 The Electrical Resistance of Alloys
- ART. 222 On the Theory of Optical Images, with Special Reference to the Microscope
- ART. 223 Theoretical Considerations respecting the Separation of Gases by Diffusion and Similar Processes
- ART. 224 The Theory of Solutions
- ART. 225 Observations on the Oxidation of Nitrogen Gas
- ART. 226 On the Passage of Electric Waves through Tubes, or the Vibrations of Dielectric Cylinders
- ART. 227 On the Passage of Waves through Apertures in Plane Screens, and Allied Problems
- ART. 228 The Limits of Audition
- ART. 229 On the Measurement of Alternate Currents by means of an obliquely situated Galvanometer Needle, with a Method of Determining the Angle of Lag
- ART. 230 On the Incidence of Aerial and Electric Waves upon Small Obstacles in the Form of Ellipsoids or Elliptic Cylinders, and on the Passage of Electric Waves through a Circular Aperture in a Conducting Screen
- ART. 231 On the Propagation of Electric Waves along Cylindrical Conductors of any Section
- ART. 232 The Electro-Chemical Equivalent of Silver
- ART. 233 On an Optical Device for the Intensification of Photographic Pictures
- ART. 234 On the Viscosity of Hydrogen as affected by Moisture
- ART. 235 On the Propagation of Waves along Connected Systems of Similar Bodies
- ART. 236 On the Densities of Carbonic Oxide, Carbonic Anhydride, and Nitrous Oxide
- ART. 237 Röntgen Rays and Ordinary Light
- ART. 238 Note on the Pressure of Radiation, showing an Apparent Failure of the Usual Electromagnetic Equations
- ART. 239 Some Experiments with the Telephone
- ART. 240 Liquid Air at one Operation
- ART. 241 On the Character of the Impurity found in Nitrogen Gas Derived from Urea [with an Appendix containing details of Refractometer]
- ART. 242 On Iso-periodic Systems
- ART. 243 On James Bernoulli's Theorem in Probabilities
- ART. 244 On the Cooling of Air by Radiation and Conduction, and on the Propagation of Sound
- ART. 245 On the Conduction of Heat in a Spherical Mass of Air confined by Walls at a Constant Temperature
- ART. 246 Transparency and Opacity
- ART. 247 On the Transmission of Light through an Atmosphere containing Small Particles in Suspension, and on the Origin of the Blue of the Sky
- ART. 248 The Interferometer
- ART. 249 On the Calculation of the Frequency of Vibration of a System in its Gravest Mode, with an Example from Hydrodynamics
- ART. 250 The Theory of Anomalous Dispersion
- ART. 251 Investigations in Capillarity
- ART. 252 The Mutual Induction of Coaxial Helices
- ART. 253 The Law of Partition of Kinetic Energy
- ART. 254 On the Viscosity of Argon as affected by Temperature
- ART. 255 On the Passage of Argon through Thin Films of Indiarubber
- ART. 256 On the Weight of Hydrogen desiccated by Liquid Air
- ART. 257 The Mechanical Principles of Flight
- ART. 258 On the Law of Reciprocity in Diffuse Reflexion
- ART. 259 On the Viscosity of Gases as Affected by Temperature
- ART. 260 Remarks upon the Law of Complete Radiation
- ART. 261 On Approximately Simple Waves
- ART. 262 On a Theorem analogous to the Virial Theorem
- ART. 263 On Balfour Stewart's Theory of the Connexion between Radiation and Absorption
- ART. 264 Spectroscopic Notes concerning the Gases of the Atmosphere
- ART. 265 On the Stresses in Solid Bodies due to Unequal Heating, and on the Double Refraction resulting therefrom
- ART. 266 On a New Manometer, and on the Law of the Pressure of Gases between 1·5 and 0·01 Millimetres of Mercury
- ART. 267 On a Problem relating to the Propagation of Sound between Parallel Walls
- ART. 268 Polish
- ART. 269 Does Chemical Transformation influence Weight?
- ART. 270 Acoustical Notes. VI
- ART. 271 On the Magnetic Rotation of Light and the Second Law of Thermodynamics
- ART. 272 On the Induction-Coil
- CLASSIFIED TABLE OF CONTENTS
- INDEX OF NAMES
- Plate section
ART. 200 - On the Influence of Obstacles arranged in Rectangular Order upon the Properties of a Medium
Published online by Cambridge University Press: 05 July 2011
Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 197 Density of Nitrogen
- ART. 198 On the Intensity of Light reflected from Water and Mercury at nearly Perpendicular Incidence
- ART. 199 On the Interference Bands of Approximately Homogeneous Light; in a Letter to Prof. A. Michelson
- ART. 200 On the Influence of Obstacles arranged in Rectangular Order upon the Properties of a Medium
- ART. 201 On the Densities of the Principal Gases
- ART. 202 Interference Bands and their Applications
- ART. 203 On the Theory of Stellar Scintillation
- ART. 204 Astronomical Photography
- ART. 205 Grinding and Polishing of Glass Surfaces
- ART. 206 On the Reflection of Sound or Light from a Corrugated Surface
- ART. 207 On a Simple Interference Arrangement
- ART. 208 On the Flow of Viscous Liquids, especially in Two Dimensions
- ART. 209 The Scientific Work of Tyndall
- ART. 210 On an Anomaly encountered in Determinations of the Density of Nitrogen Gas
- ART. 211 On the Minimum Current audible in the Telephone
- ART. 212 An Attempt at a Quantitative Theory of the Telephone
- ART. 213 On the Amplitude of Aerial Waves which are but just Audible
- ART. 214 Argon, a New Constituent of the Atmosphere. By LORD RAYLEIGH, Sec. R.S., and PROFESSOR WILLIAM RAMSAY, F.R.S.
- ART. 215 Argon
- ART. 216 On the Stability or Instability of Certain Fluid Motions. III
- ART. 217 On the Propagation of Waves upon the Plane Surface separating Two Portions of Fluid of Different Vorticities
- ART. 218 On some Physical Properties of Argon and Helium
- ART. 219 On the Amount of Argon and Helium contained in the Gas from the Bath Springs
- ART. 220 The Reproduction of Diffraction Gratings
- ART. 221 The Electrical Resistance of Alloys
- ART. 222 On the Theory of Optical Images, with Special Reference to the Microscope
- ART. 223 Theoretical Considerations respecting the Separation of Gases by Diffusion and Similar Processes
- ART. 224 The Theory of Solutions
- ART. 225 Observations on the Oxidation of Nitrogen Gas
- ART. 226 On the Passage of Electric Waves through Tubes, or the Vibrations of Dielectric Cylinders
- ART. 227 On the Passage of Waves through Apertures in Plane Screens, and Allied Problems
- ART. 228 The Limits of Audition
- ART. 229 On the Measurement of Alternate Currents by means of an obliquely situated Galvanometer Needle, with a Method of Determining the Angle of Lag
- ART. 230 On the Incidence of Aerial and Electric Waves upon Small Obstacles in the Form of Ellipsoids or Elliptic Cylinders, and on the Passage of Electric Waves through a Circular Aperture in a Conducting Screen
- ART. 231 On the Propagation of Electric Waves along Cylindrical Conductors of any Section
- ART. 232 The Electro-Chemical Equivalent of Silver
- ART. 233 On an Optical Device for the Intensification of Photographic Pictures
- ART. 234 On the Viscosity of Hydrogen as affected by Moisture
- ART. 235 On the Propagation of Waves along Connected Systems of Similar Bodies
- ART. 236 On the Densities of Carbonic Oxide, Carbonic Anhydride, and Nitrous Oxide
- ART. 237 Röntgen Rays and Ordinary Light
- ART. 238 Note on the Pressure of Radiation, showing an Apparent Failure of the Usual Electromagnetic Equations
- ART. 239 Some Experiments with the Telephone
- ART. 240 Liquid Air at one Operation
- ART. 241 On the Character of the Impurity found in Nitrogen Gas Derived from Urea [with an Appendix containing details of Refractometer]
- ART. 242 On Iso-periodic Systems
- ART. 243 On James Bernoulli's Theorem in Probabilities
- ART. 244 On the Cooling of Air by Radiation and Conduction, and on the Propagation of Sound
- ART. 245 On the Conduction of Heat in a Spherical Mass of Air confined by Walls at a Constant Temperature
- ART. 246 Transparency and Opacity
- ART. 247 On the Transmission of Light through an Atmosphere containing Small Particles in Suspension, and on the Origin of the Blue of the Sky
- ART. 248 The Interferometer
- ART. 249 On the Calculation of the Frequency of Vibration of a System in its Gravest Mode, with an Example from Hydrodynamics
- ART. 250 The Theory of Anomalous Dispersion
- ART. 251 Investigations in Capillarity
- ART. 252 The Mutual Induction of Coaxial Helices
- ART. 253 The Law of Partition of Kinetic Energy
- ART. 254 On the Viscosity of Argon as affected by Temperature
- ART. 255 On the Passage of Argon through Thin Films of Indiarubber
- ART. 256 On the Weight of Hydrogen desiccated by Liquid Air
- ART. 257 The Mechanical Principles of Flight
- ART. 258 On the Law of Reciprocity in Diffuse Reflexion
- ART. 259 On the Viscosity of Gases as Affected by Temperature
- ART. 260 Remarks upon the Law of Complete Radiation
- ART. 261 On Approximately Simple Waves
- ART. 262 On a Theorem analogous to the Virial Theorem
- ART. 263 On Balfour Stewart's Theory of the Connexion between Radiation and Absorption
- ART. 264 Spectroscopic Notes concerning the Gases of the Atmosphere
- ART. 265 On the Stresses in Solid Bodies due to Unequal Heating, and on the Double Refraction resulting therefrom
- ART. 266 On a New Manometer, and on the Law of the Pressure of Gases between 1·5 and 0·01 Millimetres of Mercury
- ART. 267 On a Problem relating to the Propagation of Sound between Parallel Walls
- ART. 268 Polish
- ART. 269 Does Chemical Transformation influence Weight?
- ART. 270 Acoustical Notes. VI
- ART. 271 On the Magnetic Rotation of Light and the Second Law of Thermodynamics
- ART. 272 On the Induction-Coil
- CLASSIFIED TABLE OF CONTENTS
- INDEX OF NAMES
- Plate section
Summary
The remarkable formula, arrived at almost simultaneously by L. Lorenz and H. A. Lorentz, and expressing the relation between refractive index and density, is well known; but the demonstrations are rather difficult to follow, and the limits of application are far from obvious. Indeed, in some discussions the necessity for any limitation at all is ignored. I have thought that it might be worth while to consider the problem in the more definite form which it assumes when the obstacles are supposed to be arranged in rectangular or square order, and to show how the approximation may be pursued when the dimensions of the obstacles are no longer very small in comparison with the distances between them.
Taking, first, the case of two dimensions, let us investigate the conductivity for heat, or electricity, of an otherwise uniform medium interrupted by cylindrical obstacles which are arranged in rectangular order. The sides of the rectangle will be denoted by α, β, and the radius of the cylinders by a. The simplest cases would be obtained by supposing the material composing the cylinders to be either non-conducting or perfectly conducting; but it will be sufficient to suppose that it has a definite conductivity different from that of the remainder of the medium.
By the principle of superposition the conductivity of the interrupted medium for a current in any direction can be deduced from its conductivities in the three principal directions.
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- Scientific Papers , pp. 19 - 38Publisher: Cambridge University PressPrint publication year: 2009First published in: 1903
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