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 123
... spheroids , made by the same plane , are similar and concentric ellipses , similarly situated . Let BK , CG , ( fig . 1 ) ... spheroid , with N , the center of the ellipse BK , and let ABE , HCD be sections by any plane through NW : these ...
... spheroids , made by the same plane , are similar and concentric ellipses , similarly situated . Let BK , CG , ( fig . 1 ) ... spheroid , with N , the center of the ellipse BK , and let ABE , HCD be sections by any plane through NW : these ...
Page 126
... SPHEROID . 8. PROP . 6. To find the attraction of an oblate spheroid on a particle placed at its pole . Let B , ( fig . 4 ) , be the pole of the spheroid , BD the axis ; let the spheroid be divided into wedges , by planes passing ...
... SPHEROID . 8. PROP . 6. To find the attraction of an oblate spheroid on a particle placed at its pole . Let B , ( fig . 4 ) , be the pole of the spheroid , BD the axis ; let the spheroid be divided into wedges , by planes passing ...
Page 127
... spheroid will be found by putting 2 in the place of w ; that is , the attraction = 2 e3 e3 ) e √ ( 1 - e 4π.kb { .kb - √ ( 1 - e ) tan- e sin - ' e } . = 4π.kb ... spheroid differs very little from a ATTRACTION OF OBLATE SPHEROID . 127.
... spheroid will be found by putting 2 in the place of w ; that is , the attraction = 2 e3 e3 ) e √ ( 1 - e 4π.kb { .kb - √ ( 1 - e ) tan- e sin - ' e } . = 4π.kb ... spheroid differs very little from a ATTRACTION OF OBLATE SPHEROID . 127.
Page 128
... spheroid . Then e 26 , nearly . Hence , the attraction of the pyramid = cos Ꮎ sin Ꮎ Ꮎ 2bkw 1 - 2 € sin * 0 = 2b ... spheroid is found as before , by putting 2 for w , and is , therefore , C = 1 π kb ( 1 + 2 ) . 4 € 3 10. PROP . 7. To ...
... spheroid . Then e 26 , nearly . Hence , the attraction of the pyramid = cos Ꮎ sin Ꮎ Ꮎ 2bkw 1 - 2 € sin * 0 = 2b ... spheroid is found as before , by putting 2 for w , and is , therefore , C = 1 π kb ( 1 + 2 ) . 4 € 3 10. PROP . 7. To ...
Page 129
... spheroid is b2 PN2 = ( 4C " - = √ ( AC® - CO2 - ON2 ) b ? — — 2 ( AC2 – AC – AO3 – ON2 ) , a2 b ? or 2 = - d2 ( 2 a x − x2 — y3 ) ; - putting for x , y , and x , their values r.cose.cos , it becomes b2 r.cose . sin , r . sin 0 , r2 ...
... spheroid is b2 PN2 = ( 4C " - = √ ( AC® - CO2 - ON2 ) b ? — — 2 ( AC2 – AC – AO3 – ON2 ) , a2 b ? or 2 = - d2 ( 2 a x − x2 — y3 ) ; - putting for x , y , and x , their values r.cose.cos , it becomes b2 r.cose . sin , r . sin 0 , r2 ...
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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...
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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...