Book contents
- Frontmatter
- Contents
- Notes on Hydrodynamics. III. On the Dynamical Equations
- On the constitution of the Luminiferous Ether
- On the Theory of certain Bands seen in the Spectrum
- Notes on Hydrodynamics. IV. Demonstration of a Fundamental Theorem
- On a difficulty in the Theory of Sound
- On the Formation of the Central Spot of Newton's Rings beyond the Critical Angle
- On some points in the Received Theory of Sound
- On the perfect Blackness of the Central Spot in Newton's Rings, and on the Verification of Fresnel's Formula for the intensities of Reflected and Reflacted Rays
- On Attractions, and on Clairaut's Theorem
- On the Variation of Gravity at the Surface of the Earth
- On a Mode of Measuring the Astigmatism of a Defective Eye
- On the Determination of the Wave Length corresponding with any Point of the Spectrum
- Discussion of a Differential Equation relating to the Breaking of Railway Bridges
- Notes on Hydrodynamics, VI. On Waves
- On the Dynamical Theory of Diffraction
- On the Numerical Calculation of a class of Definite Integrals and Infinite Series
- On the Mode of Disappearance of Newton's Rings in passing the Angle of Total Internal Reflection
- On Metallic Reflection
- On a Fictitious Displacement of Fringes of Interference
- On Haidinger's Brushes
- Index
Notes on Hydrodynamics. III. On the Dynamical Equations
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- Contents
- Notes on Hydrodynamics. III. On the Dynamical Equations
- On the constitution of the Luminiferous Ether
- On the Theory of certain Bands seen in the Spectrum
- Notes on Hydrodynamics. IV. Demonstration of a Fundamental Theorem
- On a difficulty in the Theory of Sound
- On the Formation of the Central Spot of Newton's Rings beyond the Critical Angle
- On some points in the Received Theory of Sound
- On the perfect Blackness of the Central Spot in Newton's Rings, and on the Verification of Fresnel's Formula for the intensities of Reflected and Reflacted Rays
- On Attractions, and on Clairaut's Theorem
- On the Variation of Gravity at the Surface of the Earth
- On a Mode of Measuring the Astigmatism of a Defective Eye
- On the Determination of the Wave Length corresponding with any Point of the Spectrum
- Discussion of a Differential Equation relating to the Breaking of Railway Bridges
- Notes on Hydrodynamics, VI. On Waves
- On the Dynamical Theory of Diffraction
- On the Numerical Calculation of a class of Definite Integrals and Infinite Series
- On the Mode of Disappearance of Newton's Rings in passing the Angle of Total Internal Reflection
- On Metallic Reflection
- On a Fictitious Displacement of Fringes of Interference
- On Haidinger's Brushes
- Index
Summary
In reducing to calculation the motion of a system of rigid bodies, or of material points, there are two sorts of equations with which we are concerned; the one expressing the geometrical connexions of the bodies or particles with one another, or with curves or surfaces external to the system, the other expressing the relations between the changes of motion which take place in the system and the forces producing such changes. The equations belonging to these two classes may be called respectively the geometrical, and the dynamical equations. Precisely the same remarks apply to the motion of fluids. The geometrical equations which occur in Hydrodynamics have been already considered by Professor Thomson, in Notes I. and II. The object of the present Note is to form the dynamical equations.
The fundamental hypothesis of Hydrostatics is, that the mutual pressure of two contiguous portions of a fluid, separated by an imaginary plane, is normal to the surface of separation. This hypothesis forms in fact the mathematical definition of a fluid. The equality of pressure in all directions is in reality not an independent hypothesis, but a necessary consequence of the former. A proof of this may be seen at the commencement of Prof. Miller's Hydrostatics.
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- Mathematical and Physical Papers , pp. 1 - 7Publisher: Cambridge University PressPrint publication year: 2009
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