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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Page 84
... curve . The solution = A ' . cos ( n t − B ' ) , if we look no further , merely asserts that the place of the pendulum at the time t may be expressed by means of the same for- mula as that which expresses the place in undisturbed vibra ...
... curve . The solution = A ' . cos ( n t − B ' ) , if we look no further , merely asserts that the place of the pendulum at the time t may be expressed by means of the same for- mula as that which expresses the place in undisturbed vibra ...
Page 86
... curve de- scribed , and a ,, e ,, w , for the variable elements which will represent the place and velocity of the planet in the curve described , provided the calculation be made for any instant as if they were invariable . Now upon ...
... curve de- scribed , and a ,, e ,, w , for the variable elements which will represent the place and velocity of the planet in the curve described , provided the calculation be made for any instant as if they were invariable . Now upon ...
Page 142
... curve , as fig . 10 , in which the abscissa is e , and the ordinate is proportionate to the value of the first side of the equation , fli suffrued 1- >> we find that the curve cannot cut the axis 142 FIGURE OF THE EARTH.
... curve , as fig . 10 , in which the abscissa is e , and the ordinate is proportionate to the value of the first side of the equation , fli suffrued 1- >> we find that the curve cannot cut the axis 142 FIGURE OF THE EARTH.
Page 143
... curve cannot cut the axis in more than two points , and therefore there can be but two forms of the oblate spheroid , which are figures of equilibrium . " If in one of these forms e be small , in the other it will be very nearly 1 ...
... curve cannot cut the axis in more than two points , and therefore there can be but two forms of the oblate spheroid , which are figures of equilibrium . " If in one of these forms e be small , in the other it will be very nearly 1 ...
Page 144
... curve will touch the line of abscissæ : and upon increasing q the curve will not meet the line of abscissæ at all . In the former case , then , there is but one form of equilibrium , and , in the latter , equilibrium is not possible ...
... curve will touch the line of abscissæ : and upon increasing q the curve will not meet the line of abscissæ at all . In the former case , then , there is but one form of equilibrium , and , in the latter , equilibrium is not possible ...
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Common terms and phrases
analyzing plate angle angular velocity attraction axis bright co-ordinates coefficient common light Consequently cos² crystal curve different colours differential direction displacement distance disturbing force dR dR dt dt dt Earth ellipticity equal equation expression extraordinary ray front ƒ² glass Hence integration intensity investigation length longitude lunar lunar precession motion multiplied nearly Newton's rings node nutation ordinary ray parallel particles perigee perihelion perpendicular plane of incidence plane of polarization plane of reflection precession principal plane produced PROP proportion quantity radius vector refraction rhombohedron rings shew sin² spheroid suppose surface theory tion undulation vibration vt-x wave
Popular passages
Page 257 - 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 257 - 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 306 - ... 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 198 - In planetary theory the adopted ratio of the mass of the Earth to the mass of the Moon is...
Page 229 - ... 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...