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 6
... tion 1 the rela ! or r = M + M ' h2 2 1 + A cos - B 9 which is the general polar equation to the conic sections , the focus being the pole . 11. The conic section which a planet appears to describe about the Sun , or the Sun about a ...
... tion 1 the rela ! or r = M + M ' h2 2 1 + A cos - B 9 which is the general polar equation to the conic sections , the focus being the pole . 11. The conic section which a planet appears to describe about the Sun , or the Sun about a ...
Page 28
... tion tan tan y = sin - γ reduces this equation to The value found for s or tan the form tank . Therefore , from whatever point of the Moon's path we draw a great circle to a certain point on the ecliptic , the angle at which it meets it ...
... tion tan tan y = sin - γ reduces this equation to The value found for s or tan the form tank . Therefore , from whatever point of the Moon's path we draw a great circle to a certain point on the ecliptic , the angle at which it meets it ...
Page 41
... tion of ( 41 ) , we have d2 u First , + u d02 d2 u + u . d02 du T Second , + + u 2 de So h2u3 = { } 3m3 a { cos ( 2 - 2m ) 0 – 2 ß 2e cos ( 2 - 2m - c ) 0 − 2ß ÷ 0-2ẞ + a } ( Prop . 18. ) Third , P h2u * 3k2 3k2 m2 a ( 1 cos 2g0-27 ) + ...
... tion of ( 41 ) , we have d2 u First , + u d02 d2 u + u . d02 du T Second , + + u 2 de So h2u3 = { } 3m3 a { cos ( 2 - 2m ) 0 – 2 ß 2e cos ( 2 - 2m - c ) 0 − 2ß ÷ 0-2ẞ + a } ( Prop . 18. ) Third , P h2u * 3k2 3k2 m2 a ( 1 cos 2g0-27 ) + ...
Page 50
... tion . The latter depends on the Sun's mean anomaly : it appears that , while the Sun ( apparently ) goes from perigee to apogee , the Moon's true place is behind her mean place : while the Sun goes from apogee to perigee , the Moon's ...
... tion . The latter depends on the Sun's mean anomaly : it appears that , while the Sun ( apparently ) goes from perigee to apogee , the Moon's true place is behind her mean place : while the Sun goes from apogee to perigee , the Moon's ...
Page 53
... tion has to the elliptic inequality ; and the alteration which it produces in the place of the node and the 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 ...
... tion has to the elliptic inequality ; and the alteration which it produces in the place of the node and the 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 ...
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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...