Book contents
- Frontmatter
- PREFACE
- Contents
- 1853. On the Change of Refrangibility of Light.—II
- 1852. On the Optical Properties of a recently discovered Salt of Quinine
- 1853. On the Change of Refrangibility of Light and the exhibition thereby of the Chemical Rays
- 1853. On the Cause of the Occurrence of Abnormal Figures in Photographic Impressions of Polarized Rings
- 1853. On the Metallic Reflexion exhibited by certain Non-Metallic Substances
- 1854. Extracts from Letter to Dr W. Haidinger: on the Direction of the Vibrations in Polarized Light: on Shadow Patterns and the Chromatic Aberration of the Eye: on Haidinger's Brushes
- 1854. On the Theory of the Electric Telegraph. By Prof. W. Thomson. (Extract)
- 1855. On the Achromatism of a Double Object-glass
- 1856. Remarks on Professor Challis's paper, entitled “A Theory of the Composition of Colours, etc.”
- 1856. Supplement to the “Account of Pendulum Experiments undertaken in the Harton Colliery…”. By G. B. Airy, Esq., Astronomer Royal
- 1857. On the Polarization of Diffracted Light
- 1857. On the Discontinuity of Arbitrary Constants which appear in Divergent Developments
- 1857. On the Effect of Wind on the Intensity of Sound
- 1859. On the Existence of a Second Crystallizable Fluorescent Substance (Paviin) in the Bark of the Horse-Chestnut
- 1859. On the bearing of the Phenomena of Diffraction on the Direction of the Vibrations of Polarized Light, with Remarks on the Paper of Professor F. Eisenlohr
- 1860. Note on Paviin
- 1860. On the Colouring Matters of Madder. By Dr E. Schunck (Extract)
- 1860. Extracts relating to the Early History of Spectrum Analysis
- 1861. Note on Internal Radiation
- 1862. On the Intensity of the Light reflected from or transmitted through a Pile of Plates
- 1862. Report on Double Refraction
- 1862. On the Long Spectrum of Electric Light
- 1863. On the Change of Form assumed by Wrought Iron and other Metals when heated and then cooled by partial Immersion in Water. By Lieut.-Col. H. Clark, R.A., F.R.S. Note appended by Prof. Stokes
- 1864. On the supposed Identity of Biliverdin with Chlorophyll, with remarks on the Constitution of Chlorophyll
- 1864. On the Discrimination of Organic Bodies by their Optical Properties
- 1864. On the Application of the Optical Properties of Bodies to the Detection and Discrimination of Organic Substances
- 1864. On the Beduction and Oxidation of the Colouring Matter of the Blood
- 1867. On a Property of Curves which fulfil the condition
- 1867. On the Internal Distribution of Matter which shall produce a given Potential at the surface of a Gravitating Mass
- 1868. Supplement to a paper on the Discontinuity of Arbitrary Constants which appear in Divergent Developments
- 1868. On the Communication of Vibration from a Vibrating Body to a surrounding Gas
- 1868. Account of Observations of the Total Eclipse of the Sun….By J. Pope Hennessy. Note added by Prof. Stokes
- 1869. On a certain Reaction of Quinine
- 1872. Explanation of a Dynamical Paradox
- 1872. On the Law of Extraordinary Refraction in Iceland Spar
- 1873. Sur 1'emploi du prisme dans la vérification de la loi de la double réfraction
- 1871. Notice of the Researches of the late Rev. W. Vernon Harcourt on the Conditions of Transparency in Glass and the Connexion between the Chemical Constitution and Optical Properties of Different Glasses
- 1873. On the Principles of the Chemical Correction of Object-glasses
- 1874. On the Improvement of the Spectroscope. By Thomas Grubb, F.R.S. Note appended by Prof. Stokès
- 1874. On the Construction of a perfectly Achromatic Telescope
- 1875. On the Optical Properties of a Titano-Silicic Glass
- 1876. On a Phenomenon of Metallic Reflection
- 1876. Preliminary Note on the Compound Nature of the Line-Spectra of Elementary Bodies. By J. N. Lockyer, F.R.S. (Extract)
- APPENDIX (Correspondence of Prof. G. G. Stokes and Prof. W. Thomson on the nature and possibilities of Spectrum Analysis)
- INDEX
1868. Supplement to a paper on the Discontinuity of Arbitrary Constants which appear in Divergent Developments
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- PREFACE
- Contents
- 1853. On the Change of Refrangibility of Light.—II
- 1852. On the Optical Properties of a recently discovered Salt of Quinine
- 1853. On the Change of Refrangibility of Light and the exhibition thereby of the Chemical Rays
- 1853. On the Cause of the Occurrence of Abnormal Figures in Photographic Impressions of Polarized Rings
- 1853. On the Metallic Reflexion exhibited by certain Non-Metallic Substances
- 1854. Extracts from Letter to Dr W. Haidinger: on the Direction of the Vibrations in Polarized Light: on Shadow Patterns and the Chromatic Aberration of the Eye: on Haidinger's Brushes
- 1854. On the Theory of the Electric Telegraph. By Prof. W. Thomson. (Extract)
- 1855. On the Achromatism of a Double Object-glass
- 1856. Remarks on Professor Challis's paper, entitled “A Theory of the Composition of Colours, etc.”
- 1856. Supplement to the “Account of Pendulum Experiments undertaken in the Harton Colliery…”. By G. B. Airy, Esq., Astronomer Royal
- 1857. On the Polarization of Diffracted Light
- 1857. On the Discontinuity of Arbitrary Constants which appear in Divergent Developments
- 1857. On the Effect of Wind on the Intensity of Sound
- 1859. On the Existence of a Second Crystallizable Fluorescent Substance (Paviin) in the Bark of the Horse-Chestnut
- 1859. On the bearing of the Phenomena of Diffraction on the Direction of the Vibrations of Polarized Light, with Remarks on the Paper of Professor F. Eisenlohr
- 1860. Note on Paviin
- 1860. On the Colouring Matters of Madder. By Dr E. Schunck (Extract)
- 1860. Extracts relating to the Early History of Spectrum Analysis
- 1861. Note on Internal Radiation
- 1862. On the Intensity of the Light reflected from or transmitted through a Pile of Plates
- 1862. Report on Double Refraction
- 1862. On the Long Spectrum of Electric Light
- 1863. On the Change of Form assumed by Wrought Iron and other Metals when heated and then cooled by partial Immersion in Water. By Lieut.-Col. H. Clark, R.A., F.R.S. Note appended by Prof. Stokes
- 1864. On the supposed Identity of Biliverdin with Chlorophyll, with remarks on the Constitution of Chlorophyll
- 1864. On the Discrimination of Organic Bodies by their Optical Properties
- 1864. On the Application of the Optical Properties of Bodies to the Detection and Discrimination of Organic Substances
- 1864. On the Beduction and Oxidation of the Colouring Matter of the Blood
- 1867. On a Property of Curves which fulfil the condition
- 1867. On the Internal Distribution of Matter which shall produce a given Potential at the surface of a Gravitating Mass
- 1868. Supplement to a paper on the Discontinuity of Arbitrary Constants which appear in Divergent Developments
- 1868. On the Communication of Vibration from a Vibrating Body to a surrounding Gas
- 1868. Account of Observations of the Total Eclipse of the Sun….By J. Pope Hennessy. Note added by Prof. Stokes
- 1869. On a certain Reaction of Quinine
- 1872. Explanation of a Dynamical Paradox
- 1872. On the Law of Extraordinary Refraction in Iceland Spar
- 1873. Sur 1'emploi du prisme dans la vérification de la loi de la double réfraction
- 1871. Notice of the Researches of the late Rev. W. Vernon Harcourt on the Conditions of Transparency in Glass and the Connexion between the Chemical Constitution and Optical Properties of Different Glasses
- 1873. On the Principles of the Chemical Correction of Object-glasses
- 1874. On the Improvement of the Spectroscope. By Thomas Grubb, F.R.S. Note appended by Prof. Stokès
- 1874. On the Construction of a perfectly Achromatic Telescope
- 1875. On the Optical Properties of a Titano-Silicic Glass
- 1876. On a Phenomenon of Metallic Reflection
- 1876. Preliminary Note on the Compound Nature of the Line-Spectra of Elementary Bodies. By J. N. Lockyer, F.R.S. (Extract)
- APPENDIX (Correspondence of Prof. G. G. Stokes and Prof. W. Thomson on the nature and possibilities of Spectrum Analysis)
- INDEX
Summary
In a paper “On the Numerical Calculation of a Class of Definite Integrals and Infinite Series,” printed in the ixth volume of the Transactions of this Society, I gave a method by which a definite integral, to which Mr Airy was led in calculating the intensity of light in the neighbourhood of a caustic, may be readily calculated for large values, whether positive or negative, of a certain variable which appears as a constant under the sign of integration. The method consists in forming a differential equation of which the definite integral is a particular solution, obtaining the complete integral of the equation under a form, indicated by the equation itself, involving series according to descending powers of the variable, and determining the arbitrary constants. The equation admits also of integration by means of ascending series multiplied by other arbitrary constants. The ascending series are always convergent, but when the variable is large begin by diverging rapidly: the descending series, on the other hand, are always divergent, but when the variable is large begin by converging rapidly.
The same method was found to apply to several other definite integrals which occur in physical investigations, as well as to differential equations of frequent occurrence. The ascending and descending series are usually both required, the one for application to small, the other to large values of the variable; and it is necessary to connect the arbitrary constants in the descending with those in the ascending series.
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- Chapter
- Information
- Mathematical and Physical Papers , pp. 283 - 298Publisher: Cambridge University PressPrint publication year: 2009First published in: 1904