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: Designed for the Use of Students in the University |
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Page 12
... plane , and the area passed over by its radius vector is very nearly proportional to the time . Let E and M , ( fig . 1. ) be the Earth and Moon , m ' the Sun ; G the center of gravity of the Earth and Moon ; join m'E , m'G , m'M ; and ...
... plane , and the area passed over by its radius vector is very nearly proportional to the time . Let E and M , ( fig . 1. ) be the Earth and Moon , m ' the Sun ; G the center of gravity of the Earth and Moon ; join m'E , m'G , m'M ; and ...
Page 14
... is the same as that of a mass = E + M ; that is , it will very nearly describe an ellipse in one plane , making the areas proportional to the times . 23 . COR . The Sun's apparent longitude , therefore 14 PHYSICAL ASTRONOMY . 1 ...
... is the same as that of a mass = E + M ; that is , it will very nearly describe an ellipse in one plane , making the areas proportional to the times . 23 . COR . The Sun's apparent longitude , therefore 14 PHYSICAL ASTRONOMY . 1 ...
Page 15
... plane in which she is moving , and thus the plane of her orbit is perpetually changing . There appears to be no better mode of estimating the disturbing force , than by resolving it into three parts , one in the direction of the ...
... plane in which she is moving , and thus the plane of her orbit is perpetually changing . There appears to be no better mode of estimating the disturbing force , than by resolving it into three parts , one in the direction of the ...
Page 16
... plane of the ecliptic . The force of m ' direction Mm ' , which is equivalent to MG , and m ' Gm ' 12 y ૫ m ' upon M is in the y ' 12 m ' MG 12 · y y in direction parallel to Gm ' . Resolving the force in direction into one parallel to ...
... plane of the ecliptic . The force of m ' direction Mm ' , which is equivalent to MG , and m ' Gm ' 12 y ૫ m ' upon M is in the y ' 12 m ' MG 12 · y y in direction parallel to Gm ' . Resolving the force in direction into one parallel to ...
Page 17
... plane of the ecliptic , and per- pendicular to the projection of the radius vector . The only force which acts in ... plane of the ecliptic . The only force on M , perpendicular to the plane of the ecliptic , is the resolved part of the ...
... plane of the ecliptic , and per- pendicular to the projection of the radius vector . The only force which acts in ... plane of the ecliptic . The only force on M , perpendicular to the plane of the ecliptic , is the resolved part of the ...
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Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the ... George Biddell Airy No preview available - 2018 |
Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the ... George Biddell Airy No preview available - 2015 |
Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the ... George Biddell Airy No preview available - 2018 |
Common terms and phrases
analyzing plate angle angle of incidence angular velocity attraction axes axis bright co-ordinates coefficient common light Consequently cos² crystal curve density different colours differential direction displacement distance disturbing force dR dR dt dt dx dx Earth ellipticity equal equation expression extraordinary ray Fresnel's rhomb front function ƒ² glass Hence integration intensity investigation length longitude lunar Moon Moon's motion multiplied nearly Newton's rings nutation orbit ordinary ray parallel particles perigee perihelion perpendicular plane of incidence plane of polarization plane of reflection precession principal plane produced PROP proportion quantity refraction rhombohedron rings shews sin² spheroid suppose surface true anomaly undulation vibration vt-x wave
Popular passages
Page 12 - The centre 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 proportional to the time.
Page 285 - We have every reason to think that a part of the velocity of sound depends on the circumstance that the law of elasticity of the air is altered by the instantaneous developement of latent heat on compression, or the contrary effect on expansion. Now if this heat required time for its developement, the quantity of heat developed would depend on the time during which the particles remained in nearly the same relative state; that is, on the time of vibration. Consequently...
Page 286 - 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 339 - On considering this presumption in conjunction with the second and third conclusions, 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...
Page 343 - ... that there are three directions^" at right angles to each other, in which if a particle be disturbed, the resultant of the forces * M.
Page 343 - To explain the separation of common light into two pencils by doubly refracting crystals : and to account for the polarization of the two rays in planes at. right angles to each other.
Page 255 - I* when a single undulation' only is considered. It is to be observed that a is the maximum vibration of any particle. PROP. 5. To explain the interference of undulations. 9. By interference is meant the co-existence of two undulations in which the length of a wave is the same. The conception of interference is not in any circumstances...
Page 284 - ... and this will cause a reflected wave. Thus when light passes through glass there will be reflection at both surfaces. But there is this difference between th'e two reflections : one is caused by a vibration in the same direction as that of the incident ray, and the other by a vibration in the direction opposite to that of the incident ray. We shall find this distinction important in explaining a fundamental experiment (65). The same thing may be thus shewn. If we suppose a mass of glass to be...