Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 79 On the Determination of the Ohm [B. A. Unit] in Absolute Measure
- ART. 80 Experiments to Determine the Value of the British Association Unit of Resistance in Absolute Measure
- ART. 81 On the Specific Resistance of Mercury
- ART. 82 The Use of Telescopes on Dark Nights
- ART. 83 On a New Form of Gas Battery
- ART. 84 Acoustical Observations. IV
- ART. 85 Further Observations upon Liquid Jets, in Continuation of those recorded in the Royal Society's ‘Proceedings’ for March and May, 1879
- ART. 86 Address to the Mathematical and Physical Science Section of the British Association
- ART. 87 On the Tension of Mercury Vapour at Common Temperatures
- ART. 88 On the Absolute Measurement of Electric Currents
- ART. 89 On the Duration of Free Electric Currents in an Infinite Conducting Cylinder
- ART. 90 On the Equilibrium of Liquid Conducting Masses charged with Electricity
- ART. 91 On an Instrument capable of Measuring the Intensity of Aerial Vibrations
- ART. 92 Comparison of Methods for the Determination of Resistances in Absolute Measure
- ART. 93 On the Dark Plane which is formed over a Heated Wire in Dusty Air
- ART. 94 Experiments, by the Method of Lorenz, for the Further Determination of the Absolute Value of the British Association Unit of Resistance, with an Appendix on the Determination of the Pitch of a Standard Tuning-Fork
- ART. 95 On the Mean Radius of Coils of Insulated Wire
- ART. 96 On the Invisibility of Small Objects in a Bad Light
- ART. 97 On Maintained Vibrations
- ART. 98 The Soaring of Birds
- ART. 99 Distribution of Energy in the Spectrum
- ART. 100 Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
- ART. 101 On the Vibrations of a Cylindrical Vessel containing Liquid
- ART. 102 On the Crispations of Fluid resting upon a Vibrating Support
- ART. 103 On Porous Bodies in Relation to Sound
- ART. 104 Suggestions for Facilitating the Use of a Delicate Balance
- ART. 105 On the Imperfection of the Galvanometer as a Test of the Evanescence of a Transient Current
- ART. 106 On Laplace's Theory of Capillarity
- ART. 107 On the Measurement of Electric Currents
- ART. 108 On the Circulation of Air observed in Kundt's Tubes, and on some Allied Acoustical Problems
- ART. 109 The form of Standing Waves on the Surface of Running Water
- ART. 110 Acoustical Observations.—V
- ART. 111 On the Measurement of the Electrical Resistance between Two Neighbouring Points on a Conductor
- ART. 112 On the Electro-Chemical Equivalent of Silver, and on the Absolute Electromotive Force of Clark Cells
- ART. 113 Presidential Address
- ART. 114 A Lecture Experiment on Induction
- ART. 115 On Telephoning through a Cable
- ART. 116 On a Galvanometer with Twenty Wires
- ART. 117 On Clark's Standard Cells
- ART. 118 On the Constant of Magnetic Rotation of Light in Bisulphide of Carbon
- ART. 119 Optics
- ART. 120 Über die Methode der Dämpfung bei der Bestimmung des Ohms
- ART. 121 On the Theory of Illumination in a Fog
- ART. 122 A Monochromatic Telescope, with application to Photometry
- ART. 123 Self-induction in Relation to Certain Experiments of Mr Willoughby Smith and to the Determination of the Ohm
- ART. 124 Professor Tait's “Properties of Matter”
- ART. 125 A Theorem relating to the Time-Moduli of Dissipative Systems
- ART. 126 On the Accuracy of Focus necessary for Sensibly Perfect Definition
- ART. 127 On an Improved Apparatus for Christiansen's Experiment
- ART. 128 Optical Comparison of Methods for Observing Small Rotations
- ART. 129 On the Thermodynamic Efficiency of the Thermopile
- ART. 130 On Waves propagated along the Plane Surface of an Elastic Solid
- ART. 131 On Prof. Himstedt's Determination of the Ohm
- ART. 132 On the Clark Cell as a Standard of Electro-motive Force
- ART. 133 Testing Dynamos
- ART. 134 The Reaction upon the Driving-Point of a System executing Forced Harmonic Oscillations of Various Periods, with Applications to Electricity
- ART. 135 On the Self-Induction and Resistance of Straight Conductors
- ART. 136 On the Colours of Thin Plates
- ART. 137 Notes, chiefly Historical, on some Fundamental Propositions in Optics
- ART. 138 On the Intensity of Light Reflected from Certain Surfaces at Nearly Perpendicular Incidence
- ART. 139 Notes on Electricity and Magnetism. I. On the Energy of Magnetized Iron
- ART. 140 Notes on Electricity and Magnetism. II. The Self-Induction and Resistance of Compound Conductors
- ART. 141 Notes on Electricity and Magnetism.—III. On the Behaviour of Iron and Steel under the Operation of Feeble Magnetic Forces
ART. 134 - The Reaction upon the Driving-Point of a System executing Forced Harmonic Oscillations of Various Periods, with Applications to Electricity
Published online by Cambridge University Press: 05 December 2011
Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 79 On the Determination of the Ohm [B. A. Unit] in Absolute Measure
- ART. 80 Experiments to Determine the Value of the British Association Unit of Resistance in Absolute Measure
- ART. 81 On the Specific Resistance of Mercury
- ART. 82 The Use of Telescopes on Dark Nights
- ART. 83 On a New Form of Gas Battery
- ART. 84 Acoustical Observations. IV
- ART. 85 Further Observations upon Liquid Jets, in Continuation of those recorded in the Royal Society's ‘Proceedings’ for March and May, 1879
- ART. 86 Address to the Mathematical and Physical Science Section of the British Association
- ART. 87 On the Tension of Mercury Vapour at Common Temperatures
- ART. 88 On the Absolute Measurement of Electric Currents
- ART. 89 On the Duration of Free Electric Currents in an Infinite Conducting Cylinder
- ART. 90 On the Equilibrium of Liquid Conducting Masses charged with Electricity
- ART. 91 On an Instrument capable of Measuring the Intensity of Aerial Vibrations
- ART. 92 Comparison of Methods for the Determination of Resistances in Absolute Measure
- ART. 93 On the Dark Plane which is formed over a Heated Wire in Dusty Air
- ART. 94 Experiments, by the Method of Lorenz, for the Further Determination of the Absolute Value of the British Association Unit of Resistance, with an Appendix on the Determination of the Pitch of a Standard Tuning-Fork
- ART. 95 On the Mean Radius of Coils of Insulated Wire
- ART. 96 On the Invisibility of Small Objects in a Bad Light
- ART. 97 On Maintained Vibrations
- ART. 98 The Soaring of Birds
- ART. 99 Distribution of Energy in the Spectrum
- ART. 100 Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
- ART. 101 On the Vibrations of a Cylindrical Vessel containing Liquid
- ART. 102 On the Crispations of Fluid resting upon a Vibrating Support
- ART. 103 On Porous Bodies in Relation to Sound
- ART. 104 Suggestions for Facilitating the Use of a Delicate Balance
- ART. 105 On the Imperfection of the Galvanometer as a Test of the Evanescence of a Transient Current
- ART. 106 On Laplace's Theory of Capillarity
- ART. 107 On the Measurement of Electric Currents
- ART. 108 On the Circulation of Air observed in Kundt's Tubes, and on some Allied Acoustical Problems
- ART. 109 The form of Standing Waves on the Surface of Running Water
- ART. 110 Acoustical Observations.—V
- ART. 111 On the Measurement of the Electrical Resistance between Two Neighbouring Points on a Conductor
- ART. 112 On the Electro-Chemical Equivalent of Silver, and on the Absolute Electromotive Force of Clark Cells
- ART. 113 Presidential Address
- ART. 114 A Lecture Experiment on Induction
- ART. 115 On Telephoning through a Cable
- ART. 116 On a Galvanometer with Twenty Wires
- ART. 117 On Clark's Standard Cells
- ART. 118 On the Constant of Magnetic Rotation of Light in Bisulphide of Carbon
- ART. 119 Optics
- ART. 120 Über die Methode der Dämpfung bei der Bestimmung des Ohms
- ART. 121 On the Theory of Illumination in a Fog
- ART. 122 A Monochromatic Telescope, with application to Photometry
- ART. 123 Self-induction in Relation to Certain Experiments of Mr Willoughby Smith and to the Determination of the Ohm
- ART. 124 Professor Tait's “Properties of Matter”
- ART. 125 A Theorem relating to the Time-Moduli of Dissipative Systems
- ART. 126 On the Accuracy of Focus necessary for Sensibly Perfect Definition
- ART. 127 On an Improved Apparatus for Christiansen's Experiment
- ART. 128 Optical Comparison of Methods for Observing Small Rotations
- ART. 129 On the Thermodynamic Efficiency of the Thermopile
- ART. 130 On Waves propagated along the Plane Surface of an Elastic Solid
- ART. 131 On Prof. Himstedt's Determination of the Ohm
- ART. 132 On the Clark Cell as a Standard of Electro-motive Force
- ART. 133 Testing Dynamos
- ART. 134 The Reaction upon the Driving-Point of a System executing Forced Harmonic Oscillations of Various Periods, with Applications to Electricity
- ART. 135 On the Self-Induction and Resistance of Straight Conductors
- ART. 136 On the Colours of Thin Plates
- ART. 137 Notes, chiefly Historical, on some Fundamental Propositions in Optics
- ART. 138 On the Intensity of Light Reflected from Certain Surfaces at Nearly Perpendicular Incidence
- ART. 139 Notes on Electricity and Magnetism. I. On the Energy of Magnetized Iron
- ART. 140 Notes on Electricity and Magnetism. II. The Self-Induction and Resistance of Compound Conductors
- ART. 141 Notes on Electricity and Magnetism.—III. On the Behaviour of Iron and Steel under the Operation of Feeble Magnetic Forces
Summary
The object of the present communication is to prove some general mechanical theorems, which may be regarded as in some sort extensions of that of Thomson relating to the energy of initial motions. The question involved in the latter may be thus stated:—
“Given any material system at rest. Let any parts of it be set in motion suddenly with any specified velocities possible, according to the connections of the system; and let its other parts be influenced only by its connections with these. It is required to find the motion.” And the solution is “that the motion actually taken by the system is that which has less kinetic energy than any other motion fulfilling the prescribed velocity conditions.” On the other hand, if the impulses are given, a theorem of Bertrand tells us that the kinetic energy is the greatest possible.
For our present purpose we suppose the system to be set in motion by an impulse of one particular type, which we may call the first. The impulse itself may be denoted by ∫ Ψ1dt, and the corresponding velocity generated by Ψ1. Under any given circumstances as to constraint, the velocity and the impulse are in proportion to one another; and the resulting kinetic energy T is proportional to the square of either, being equal to ½ Ψ1 ∫Ψ1dt.
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- Information
- Scientific Papers , pp. 475 - 485Publisher: Cambridge University PressPrint publication year: 2009First published in: 1900