# 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

Deighton, 1842 - Всего страниц: 390

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Стр. i - 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.
Стр. iv - The undulatory theory of optics is presented to the reader as having the same claims to his attention as the theory of gravitation : namely, that it is certainly true, and that, by mathematical operations of general elegance, it leads to results of great interest. This theory explains with accuracy a vast variety of phenomena of the most complicated kind. The plan of this tract has been to include those phenomena only which admit of calculation, and the investigations are applied only to phenomena...
Стр. 265 - We have, every reason,' he observes, ' to think that a part of the velocity of sound depends upon the circumstance that the law of elasticity of the air is altered by the instantaneous development of latent heat on compression, or the contrary effect on expansion. Now, if this heat required time for its development, the quantity of heat developed would depend...
Стр. 265 - 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...
Стр. 314 - ... 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 wave's motion, and the other perpendicular to that plane ; which...
Стр. iv - ... of the theory : the hypothesis, namely, that light consists of undulations depending on transversal vibrations, and that these travel with certain velocities in different media according to the laws here explained. The mechanical part of the theory, as the suppositions relative to the constitution of the ether, the computation of the intensity of reflected and refracted rays, &c., though generally probable, I conceive to be far from certain.
Стр. 206 - In planetary theory the adopted ratio of the mass of the Earth to the mass of the Moon is...
Стр. 237 - ... intensity of either. These intervals of silence and greatest intensity, called beats, will recur every second, but if the notes differ much from one another, the alternations will resemble a rattle ; and if the strings be in perfect unison, there will be no beats, since there will be no interference. Thus by interference is meant the coexistence of two undulations, in which the lengths of the waves are the same ; and as the magnitude of an undulation may be diminished by the addition of another...