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 7
... direction , their relative motion will be the same like prop as if that force did not act and if that force be equal and opposite to the force really acting on the Sun , the Sun will be at rest . Or , instead of this , if we add to the ...
... direction , their relative motion will be the same like prop as if that force did not act and if that force be equal and opposite to the force really acting on the Sun , the Sun will be at rest . Or , instead of this , if we add to the ...
Page 12
... direction Em ' m ' is ; therefore the moving force in that direction y2 m ' . E = ; y * therefore the moving force in direction parallel to Gm ' is m ' . E m'H y y m ' . E r ' + GE.cos w 32 y m ' . E ( r ' + GE . cos w ) y3 Similarly ...
... direction Em ' m ' is ; therefore the moving force in that direction y2 m ' . E = ; y * therefore the moving force in direction parallel to Gm ' is m ' . E m'H y y m ' . E r ' + GE.cos w 32 y m ' . E ( r ' + GE . cos w ) y3 Similarly ...
Page 13
... direction perpendicular to m ' . E EH Gm ' is y y that on M : = m ' . E GE sin o = y ' y m ' : E GE.sin w : y3 m ' . M MK y * y ' m ' . M GM.sin w ; y'3 therefore the accelerating force on the center of gravity in direction ...
... direction perpendicular to m ' . E EH Gm ' is y y that on M : = m ' . E GE sin o = y ' y m ' : E GE.sin w : y3 m ' . M MK y * y ' m ' . M GM.sin w ; y'3 therefore the accelerating force on the center of gravity in direction ...
Page 14
... direction Gm ' EM2 + ME2 2/3 9 - + 2w m ' = { 1+ ( E + M ) 3 2'2 4 ? cos 2 % ) + & c . } m ' ME 2.2 = { 1+ √2 ( E + M ) 2 + ( + cos 24 ) . 9 w + & c . } . 4 m ' Now this differs from only by a quantity which is multiplied 2.2 by and by ...
... direction Gm ' EM2 + ME2 2/3 9 - + 2w m ' = { 1+ ( E + M ) 3 2'2 4 ? cos 2 % ) + & c . } m ' ME 2.2 = { 1+ √2 ( E + M ) 2 + ( + cos 24 ) . 9 w + & c . } . 4 m ' Now this differs from only by a quantity which is multiplied 2.2 by and by ...
Page 15
... directions ; so that not only is the force altered in the direction of the radius vector , but a force also acts perpendicular to it . And as the Moon's orbit is inclined to the ecliptic , the disturbing force draws the Moon from the ...
... directions ; so that not only is the force altered in the direction of the radius vector , but a force also acts perpendicular to it . And as the Moon's orbit is inclined to the ecliptic , the disturbing force draws the Moon from the ...
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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...