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 15
... inclined to the ecliptic , the disturbing force draws the Moon from the plane in which she is moving , and thus the plane of her orbit is perpetually changing . There appears to be no better mode of estimating the disturbing force ...
... inclined to the ecliptic , the disturbing force draws the Moon from the plane in which she is moving , and thus the plane of her orbit is perpetually changing . There appears to be no better mode of estimating the disturbing force ...
Page 26
... inclination of the lunar orbit to the ecliptic : m the ratio of the Sun's mean motion to the Moon's mean motion * . Here e-- 1 1 e = nearly ; e ' = ; k = 60 1 ; m = 12 1 13 20 taking e , then , as our standard , e , k , and m , are ...
... inclination of the lunar orbit to the ecliptic : m the ratio of the Sun's mean motion to the Moon's mean motion * . Here e-- 1 1 e = nearly ; e ' = ; k = 60 1 ; m = 12 1 13 20 taking e , then , as our standard , e , k , and m , are ...
Page 47
... + e cos co - a ) = 1 EM If now an ellipse a Mb be described similar and equal to Am B , whose major axis ab is inclined to AB at an angle 2 nation w १ce equal to mEM , or ( 1. EXPLANATION OF THE EFFECT OF DIFFERENT TERMS . 47.
... + e cos co - a ) = 1 EM If now an ellipse a Mb be described similar and equal to Am B , whose major axis ab is inclined to AB at an angle 2 nation w १ce equal to mEM , or ( 1. EXPLANATION OF THE EFFECT OF DIFFERENT TERMS . 47.
Page 53
... inclination of the orbit , may be found in the same manner . Thus , y is the longitude of the node , if the second term did not exist , and B the longitude of the Sun , when 00. ( ca. ) . Now , during the description of a portion only ...
... inclination of the orbit , may be found in the same manner . Thus , y is the longitude of the node , if the second term did not exist , and B the longitude of the Sun , when 00. ( ca. ) . Now , during the description of a portion only ...
Page 54
... inclination of the orbit 3m k { 1+ cos 2. ( y - B ) } . 8 When therefore the longitude of the node is found on the supposition of its uniform retrogradation , we must subtract from it 3 m 8 sin 2 ( long . node - long . Sun ) ; and ...
... inclination of the orbit 3m k { 1+ cos 2. ( y - B ) } . 8 When therefore the longitude of the node is found on the supposition of its uniform retrogradation , we must subtract from it 3 m 8 sin 2 ( long . node - long . Sun ) ; and ...
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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...