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
1883: On the Highest Wave of Uniform Propagation. (Preliminary notice)
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
There is one particular case of possible wave motion, applicable to a fluid of practically infinite depth, in which all the circumstances of the motion admit of being expressed mathematically in finite terms, the necessary equations being satisfied exactly, and not approximately only; while the general expressions contain an arbitrary constant permitting of making the amplitude any whatsoever up to the extreme limit of cycloidal waves, coming to cusps at the crests. This possible solution of the equations was given first by Gerstner, near the beginning of the present century. The motion however to which it relates is not of the irrotational class, and could not therefore be excited in a fluid previously at rest by forces applied to the surface; nor could it be propagated into still water from a disturbance at first at a distance. In fact, the conditions requisite for its existence are of a highly artificial character; so that the chief interest of the solution is one arising from the imperfection of our mathematics, which makes it desirable to discuss a case of possible motion, however artificial the conditions may be, in which everything relating to the motion can be pretty simply expressed in finite terms.
There can be no question however that it is the irrotational class of possible wave motions which possesses the greatest, almost the only, intrinsic interest; since it is this kind alone which can be excited in a fluid previously at rest by means of forces applied to the surface, such for example as the unequal pressure of the wind on the surface, or propagated into previously still water from a distance.
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- Mathematical and Physical Papers , pp. 140 - 145Publisher: Cambridge University PressPrint publication year: 2009First published in: 1905