## 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 |

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accelerating acting alteration angle appears apply attraction axes axis becomes body bright called coefficient colours Consequently consider constant corresponding crystal curve depending described determined differential direction displacement distance disturbing dR dR dt dt Earth effect ellipticity equal equation expression force former front function given gives glass Hence incidence inclined increased instance integration intensity length light limits longitude manner mean Moon Moon's motion multiplied nearly observed orbit ordinary original parallel particles passing period perpendicular plane plate polarized position produced Prop proportion quantity radius reflected refraction represented resolved respect rings seen side similar spheroid substituting suppose surface theory tion true undulation velocity vibration wave whole

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Page 251 - 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...

Page 251 - 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...

Page 300 - ... 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...

Page 192 - In planetary theory the adopted ratio of the mass of the Earth to the mass of the Moon is...

Page 223 - ... 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...