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 |
From inside the book
Results 1-5 of 52
Page 10
... velocity , that it would have performed a revolution in the same time in which it does perform it . It is therefore called the mean anomaly . fust putting 1 - 1⁄2 e2 ja 17. If we expand these coefficients as far as e3 , e3 - nt + c = 0 ...
... velocity , that it would have performed a revolution in the same time in which it does perform it . It is therefore called the mean anomaly . fust putting 1 - 1⁄2 e2 ja 17. If we expand these coefficients as far as e3 , e3 - nt + c = 0 ...
Page 26
... * By the term mean motion is meant , the velocity with which the mean longi- tude increases . The mean motion varies therefore inversely as the periodic time . : + assumed that p3 not very twall of the fish 26 LUNAR THEORY ,
... * By the term mean motion is meant , the velocity with which the mean longi- tude increases . The mean motion varies therefore inversely as the periodic time . : + assumed that p3 not very twall of the fish 26 LUNAR THEORY ,
Page 48
... velocity which is to the whole angular velocity of M as 1 - c : 1. The perigee of the Moon's orbit therefore is not fixed , but ( while we neglect the other terms of the parallax ) moves almost uniformly in the direction of the Moon's ...
... velocity which is to the whole angular velocity of M as 1 - c : 1. The perigee of the Moon's orbit therefore is not fixed , but ( while we neglect the other terms of the parallax ) moves almost uniformly in the direction of the Moon's ...
Page 80
... long time ) , the velocity of the planet may be increased so that it describes a larger orbit than before , and its periodic time will therefore be increased , and that by a quantity proportional to the time of 80 PLANETARY THEORY .
... long time ) , the velocity of the planet may be increased so that it describes a larger orbit than before , and its periodic time will therefore be increased , and that by a quantity proportional to the time of 80 PLANETARY THEORY .
Page 84
... velocity , with the values of A ' and B ' that we have found , is nA'sin ( nt -B ' ) : that is , that the velocity of the body also is expressed by the same formula as if its vibration were not disturbed by the additional force ...
... velocity , with the values of A ' and B ' that we have found , is nA'sin ( nt -B ' ) : that is , that the velocity of the body also is expressed by the same formula as if its vibration were not disturbed by the additional force ...
Other editions - View all
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...