Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the Earth, Precession and Nutation, the Calculus of Variations, and the Undulatory Theory of Optics: Designed for the Use of Students in the University

J. & J.J. Deighton, 1831 - 410 páginas

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Página 12 - The centre of gravity of the Earth and Moon describes about the Sun, very nearly, an ellipse in one plane, and the area passed over by its radius vector is very nearly proportional to the time.
Página 285 - We have every reason to think that a part of the velocity of sound depends on the circumstance that the law of elasticity of the air is altered by the instantaneous developement of latent heat on compression, or the contrary effect on expansion. Now if this heat required time for its developement, the quantity of heat developed would depend on the time during which the particles remained in nearly the same relative state; that is, on the time of vibration. Consequently...
Página 286 - Now, if this heat required time for its development, the quantity of heat developed would depend upon the time during which the particles remained in nearly the same relative state, that is, on the time of vibration. Consequently, the law of elasticity would be different for different times of vibration, or for different lengths of waves ; and therefore the velocity of transmission would be different for waves of different lengths. If we suppose some cause which is put in action by the vibration...
Página 339 - On considering this presumption in conjunction with the second and third conclusions, we easily arrive at this simple hypothesis explaining the whole : Common light consists of undulations in which the vibrations of each particle are in the plane perpendicular to the direction of the wave's motion. The polarization of light is the resolution of the vibrations of each particle into two, one parallel to a given plane passing through the direction of the...
Página 343 - ... that there are three directions^" at right angles to each other, in which if a particle be disturbed, the resultant of the forces * M.
Página 343 - To explain the separation of common light into two pencils by doubly refracting crystals : and to account for the polarization of the two rays in planes at. right angles to each other.
Página 255 - I* when a single undulation' only is considered. It is to be observed that a is the maximum vibration of any particle. PROP. 5. To explain the interference of undulations. 9. By interference is meant the co-existence of two undulations in which the length of a wave is the same. The conception of interference is not in any circumstances...
Página 284 - ... and this will cause a reflected wave. Thus when light passes through glass there will be reflection at both surfaces. But there is this difference between th'e two reflections : one is caused by a vibration in the same direction as that of the incident ray, and the other by a vibration in the direction opposite to that of the incident ray. We shall find this distinction important in explaining a fundamental experiment (65). The same thing may be thus shewn. If we suppose a mass of glass to be...

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