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 1
... equation d2 u + n2u + → = 0 ; de → being a function of 0 and constants only . Multiply the equation by cos n0 , * d2 u then cos no.- + n2 cos no . u + cos ne . → = 0 ; d0 ° * sinn , sinn0 + D , or cos ne + D , would have served as ...
... equation d2 u + n2u + → = 0 ; de → being a function of 0 and constants only . Multiply the equation by cos n0 , * d2 u then cos no.- + n2 cos no . u + cos ne . → = 0 ; d0 ° * sinn , sinn0 + D , or cos ne + D , would have served as ...
Page 2
... equation by cos2ne : du ᏧᎾ n sin no.u 1 then + + cos no cos2 no cos2 ne fe cos ne . = 0 : น 1 integrating , + Le cos2 ng Se cos no . → = = 0 , cos no - 1 or u = − cosne focos2 , cos nẹ Se cos2ne • Se cos ne . ☺ . du 2 . Case 1. Let ...
... equation by cos2ne : du ᏧᎾ n sin no.u 1 then + + cos no cos2 no cos2 ne fe cos ne . = 0 : น 1 integrating , + Le cos2 ng Se cos no . → = = 0 , cos no - 1 or u = − cosne focos2 , cos nẹ Se cos2ne • Se cos ne . ☺ . du 2 . Case 1. Let ...
Page 4
... equation with greater ease , by assuming an expres- sion with indeterminate coefficients . Thus , if we had the equation du do + n2u + a + b cos m◊ + B + p cos q0 + Q = 0 , we might assume u = - a 22 + A cos ( no + C ) + D cos me + B + ...
... equation with greater ease , by assuming an expres- sion with indeterminate coefficients . Thus , if we had the equation du do + n2u + a + b cos m◊ + B + p cos q0 + Q = 0 , we might assume u = - a 22 + A cos ( no + C ) + D cos me + B + ...
Page 5
... equation . This remark we shall find to be very important . The solution in the 4th case assumes a form different from any of the others : its peculiarity will materially affect our future operations . MOTION OF TWO BODIES . 8. Ir the ...
... equation . This remark we shall find to be very important . The solution in the 4th case assumes a form different from any of the others : its peculiarity will materially affect our future operations . MOTION OF TWO BODIES . 8. Ir the ...
Page 6
... equation above , t d2 u d02 M + M ' + u 0 , h2 the solution of which , by ( 3 ) , is u = M + M ' h9 + A cos 0 - B , 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 ...
... equation above , t d2 u d02 M + M ' + u 0 , h2 the solution of which , by ( 3 ) , is u = M + M ' h9 + A cos 0 - B , 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 ...
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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...