Book contents
- Frontmatter
- PREFACE
- Contents
- Obituary Notice
- 1876: Note on Certain Formulæ in the Calculus of Operations. (In a letter to Prof. Tait)
- 1876: An Experiment on Electro-Magnetic Rotation
- 1887: On the Foci of Lines seen through a Crystalline Plate
- 1877: On Certain Movements of Radiometers
- 1878: On the Question of a Theoretical Limit to the Apertures of Microscopic Objectives
- 1878: On an Easy and at the same time Accurate Method of Determining the Ratio of the Dispersions of Glasses intended for Objectives
- 1879: On a Method of detecting Inequalities of unknown periods in a series of Observations. (Note appended to a paper by Prof. B. Stewart and W. Dodgson)
- 1880: Description of the Card Supporter for Sunshine Recorders adopted at the Meteorological Office
- 1881: On a Simple Mode of Eliminating Errors of Adjustment in Delicate Observations of Compared Spectra
- 1881: Discussion of the Results of some Experiments with Whirled Anemometers
- 1878: On the Determination of the Constants of the Cup Anemometer by Experiments with a Whirling Machine
- 1881: Note on the Reduction of Mr Crookes's Experiments on the Decrement of the Arc of Vibration of a Mica Plate oscillating within a Bulb containing more or less Rarefied Gas
- 1882: On the Cause of the Light Border frequently noticed in Photographs just outside the Outline of a Dark Body seen against the Sky: with some Introductory Remarks on Phosphorescence
- 1882: Extracts from Reports of the Committee on Solar Physics
- 1882: Memorandum for the use of Observers with Professor Balfour Stewart's Actinometer, prepared by Professor G. G. Stokes, Sec.R.S., and adopted by the Committee on Solar Physics
- 1883: On the Highest Wave of Uniform Propagation. (Preliminary notice)
- 1880: On the Maximum Wave of Uniform Propagation, being a Second Supplement to a Paper on the Theory of Oscillatory Waves. (Not before published)
- 1891: Note on the Theory of the Solitary Wave
- 1895: The Outskirts of the Solitary Wave
- 1885: On a remarkable Phenomenon of Crystalline Reflection
- 1886: The Coefficient of Viscosity of Air
- 1889: Note on the Determination of Arbitrary Constants which appear as Multipliers of Semi-convergent Series
- 1891: On a Graphical Representation of the Results of Dr Alder Wright's Experiments on Ternary Alloys
- 1891: On an Optical Proof of the Existence of Suspended Matter in Flames
- 1891: On the Reactions occurring in Flames
- 1891: The Influence of Surface-Loading on the Flexure of Beams
- 1892: On the best Methods of Recording the direct Intensity of Solar Radiation
- 1896: On the Nature of the Röntgen Rays
- 1897: On the Nature of the Röntgen Rays (Wilde Lecture)
- 1898: Mathematical Proof of the Identity of the Stream Lines obtained by means of a Viscous Film with those of a Perfect Fluid moving in Two Dimensions
- 1902: On the Discontinuity of Arbitrary Constants that appear as Multipliers of Semi-Convergent Series
- 1886: On the Methods of Chemical Fractionation
- 1903: The Ultra-Violet Spectrum of Radium
- APPENDIX (Mathematical Tripos and Smith's Prize questions)
- INDEX
1889: Note on the Determination of Arbitrary Constants which appear as Multipliers of Semi-convergent Series
Published online by Cambridge University Press: 01 June 2011
- Frontmatter
- PREFACE
- Contents
- Obituary Notice
- 1876: Note on Certain Formulæ in the Calculus of Operations. (In a letter to Prof. Tait)
- 1876: An Experiment on Electro-Magnetic Rotation
- 1887: On the Foci of Lines seen through a Crystalline Plate
- 1877: On Certain Movements of Radiometers
- 1878: On the Question of a Theoretical Limit to the Apertures of Microscopic Objectives
- 1878: On an Easy and at the same time Accurate Method of Determining the Ratio of the Dispersions of Glasses intended for Objectives
- 1879: On a Method of detecting Inequalities of unknown periods in a series of Observations. (Note appended to a paper by Prof. B. Stewart and W. Dodgson)
- 1880: Description of the Card Supporter for Sunshine Recorders adopted at the Meteorological Office
- 1881: On a Simple Mode of Eliminating Errors of Adjustment in Delicate Observations of Compared Spectra
- 1881: Discussion of the Results of some Experiments with Whirled Anemometers
- 1878: On the Determination of the Constants of the Cup Anemometer by Experiments with a Whirling Machine
- 1881: Note on the Reduction of Mr Crookes's Experiments on the Decrement of the Arc of Vibration of a Mica Plate oscillating within a Bulb containing more or less Rarefied Gas
- 1882: On the Cause of the Light Border frequently noticed in Photographs just outside the Outline of a Dark Body seen against the Sky: with some Introductory Remarks on Phosphorescence
- 1882: Extracts from Reports of the Committee on Solar Physics
- 1882: Memorandum for the use of Observers with Professor Balfour Stewart's Actinometer, prepared by Professor G. G. Stokes, Sec.R.S., and adopted by the Committee on Solar Physics
- 1883: On the Highest Wave of Uniform Propagation. (Preliminary notice)
- 1880: On the Maximum Wave of Uniform Propagation, being a Second Supplement to a Paper on the Theory of Oscillatory Waves. (Not before published)
- 1891: Note on the Theory of the Solitary Wave
- 1895: The Outskirts of the Solitary Wave
- 1885: On a remarkable Phenomenon of Crystalline Reflection
- 1886: The Coefficient of Viscosity of Air
- 1889: Note on the Determination of Arbitrary Constants which appear as Multipliers of Semi-convergent Series
- 1891: On a Graphical Representation of the Results of Dr Alder Wright's Experiments on Ternary Alloys
- 1891: On an Optical Proof of the Existence of Suspended Matter in Flames
- 1891: On the Reactions occurring in Flames
- 1891: The Influence of Surface-Loading on the Flexure of Beams
- 1892: On the best Methods of Recording the direct Intensity of Solar Radiation
- 1896: On the Nature of the Röntgen Rays
- 1897: On the Nature of the Röntgen Rays (Wilde Lecture)
- 1898: Mathematical Proof of the Identity of the Stream Lines obtained by means of a Viscous Film with those of a Perfect Fluid moving in Two Dimensions
- 1902: On the Discontinuity of Arbitrary Constants that appear as Multipliers of Semi-Convergent Series
- 1886: On the Methods of Chemical Fractionation
- 1903: The Ultra-Violet Spectrum of Radium
- APPENDIX (Mathematical Tripos and Smith's Prize questions)
- INDEX
Summary
In three papers communicated at different times to the Society, I have considered the application of divergent series to the actual and easy calculation, to an amply sufficient degree of accuracy, of certain functions which occur in physical investigations, but which can of course be considered quite apart from their applications. These functions present themselves as the complete integrals of certain linear differential equations, or it may be as definite integrals which lead to such differential equations, of which they form particular integrals; and as of course the theory of the complete integrals includes that of any particular integrals, the subject is best regarded from the former, and more general, point of view.
The independent variable was taken as in general a mixed imaginary, and the complete integral was expressed in two ways, either by ascending series which were always convergent, or by exponentials multiplied by descending series which were always divergent (except in very special cases in which they might terminate), though when the divergent series were practically useful they were of the kind that has been called semi-convergent. In either form of the complete integral, the arbitrary constants appeared as multipliers of the infinite series (of the ascending or descending as the case might be), or it might be, in part, of a function in finite terms.
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- Mathematical and Physical Papers , pp. 221 - 225Publisher: Cambridge University PressPrint publication year: 2009First published in: 1905