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 124
... , whence OP - EG , or EH - EG , = 2 CK = CK + CL . 5. PROP . 4. The vertical solid angle of a homogeneous pyramid being given , its attraction upon a particle placed at the vertex , is proportional to its length , 124 FIGURE OF THE EARTH .
... , whence OP - EG , or EH - EG , = 2 CK = CK + CL . 5. PROP . 4. The vertical solid angle of a homogeneous pyramid being given , its attraction upon a particle placed at the vertex , is proportional to its length , 124 FIGURE OF THE EARTH .
Page 125
... particle ∞ be divided into an indefinitely great number of strata of the same thickness , by sections perpendicular to its axis : the homologous sides of these sections will be as the dis- tance from the vertex ; therefore the areas of ...
... particle ∞ be divided into an indefinitely great number of strata of the same thickness , by sections perpendicular to its axis : the homologous sides of these sections will be as the dis- tance from the vertex ; therefore the areas of ...
Page 126
... particle placed at its pole . Let B , ( fig . 4 ) , be the pole of the spheroid , BD the axis ; let the spheroid be divided into wedges , by planes passing through BD , two of which are BPD , BQD , making with each other the very small ...
... particle placed at its pole . Let B , ( fig . 4 ) , be the pole of the spheroid , BD the axis ; let the spheroid be divided into wedges , by planes passing through BD , two of which are BPD , BQD , making with each other the very small ...
Page 128
... particle at its equator . Let ARM , fig . 5 , be the equator of the spheroid ; AZ a perpendicular to it from the attracted point 4 ; suppose the spheroid divided into wedges , by planes passing through AZ ; let two of these planes ...
... particle at its equator . Let ARM , fig . 5 , be the equator of the spheroid ; AZ a perpendicular to it from the attracted point 4 ; suppose the spheroid divided into wedges , by planes passing through AZ ; let two of these planes ...
Page 134
... particle at X. But , by Prop . 6. , the at- traction of the spheroid XY , on a particle at X = 4πk . WX . √ ( 1 − e2 ) - sin e3 therefore the attraction of the larger spheroid on E , in a direction parallel to its axis , is 4πk.EC ...
... particle at X. But , by Prop . 6. , the at- traction of the spheroid XY , on a particle at X = 4πk . WX . √ ( 1 − e2 ) - sin e3 therefore the attraction of the larger spheroid on E , in a direction parallel to its axis , is 4πk.EC ...
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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...