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 10
... described at the end of the time t , if , commencing with the angle e – B , it had moved uniformly with such an angular velocity , that it would have performed a revolution in the same time in which it does perform it . It is therefore ...
... described at the end of the time t , if , commencing with the angle e – B , it had moved uniformly with such an angular velocity , that it would have performed a revolution in the same time in which it does perform it . It is therefore ...
Page 11
... called the mean longitude . The aggregate of the terms following nte is called the equation of the center . * x time try- LUNAR THEORY . PERTURBATION OF THE EARTH'S MOTION . 20. LONGITUDE DESCRIBED IN GIVEN TIME . 11.
... called the mean longitude . The aggregate of the terms following nte is called the equation of the center . * x time try- LUNAR THEORY . PERTURBATION OF THE EARTH'S MOTION . 20. LONGITUDE DESCRIBED IN GIVEN TIME . 11.
Page 12
... described , the following theorem will be useful . 21. PROP . 5. The center of gravity of the Earth and Moon describes about the Sun , very nearly , an ellipse in one plane , and the area passed over by its radius vector is very nearly ...
... described , the following theorem will be useful . 21. PROP . 5. The center of gravity of the Earth and Moon describes about the Sun , very nearly , an ellipse in one plane , and the area passed over by its radius vector is very nearly ...
Page 47
... a ( 1 + 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.
... a ( 1 + 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 66
... described if undisturbed : dr the perturbation of the radius vector : then r + dr = r . Substituting this in the last equation , ď2 ( r + dr ) 2 dť 2C + == 2 μ r + dr d ( R ) d R - 4 · −2 . ( r + dr ) . dt dr , Now or is supposed to be ...
... described if undisturbed : dr the perturbation of the radius vector : then r + dr = r . Substituting this in the last equation , ď2 ( r + dr ) 2 dť 2C + == 2 μ r + dr d ( R ) d R - 4 · −2 . ( r + dr ) . dt dr , Now or is supposed to be ...
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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...