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 5
... dt ( Whewell on the Free Motion of Points , Art . 24 ; Earnshaw's Dynamics , Art . 87 ; or Art . 32 below , if T = 0 , ) we must put for P the attraction of the Sun on the planet , and by solving the equation , we should find u in terms ...
... dt ( Whewell on the Free Motion of Points , Art . 24 ; Earnshaw's Dynamics , Art . 87 ; or Art . 32 below , if T = 0 , ) we must put for P the attraction of the Sun on the planet , and by solving the equation , we should find u in terms ...
Page 7
... dt Art . 24 ; Earnshaw's Dynamics , Art . 87 ; or Art . 32 below , if T = 0 , ) we must put for P the attraction of the Sun on the planet , and by solving the equation , we should find u in terms of e , and the form of the orbit which ...
... dt Art . 24 ; Earnshaw's Dynamics , Art . 87 ; or Art . 32 below , if T = 0 , ) we must put for P the attraction of the Sun on the planet , and by solving the equation , we should find u in terms of e , and the form of the orbit which ...
Page 9
... dt cos 3.0 B + & c - & c . } . 15 . Hence ( 12 ) , = d Ꮎ ' M + M ' 2e2 ( 1 + 2√1 - e2 ) { 1-2e cos 0 - B + ( 1 + √1 − e2 ) 2 - cos 2.0 - B - & c . } . Integrating and correcting , so as to make nt + c - B = 0 , when B = 0 , e being ...
... dt cos 3.0 B + & c - & c . } . 15 . Hence ( 12 ) , = d Ꮎ ' M + M ' 2e2 ( 1 + 2√1 - e2 ) { 1-2e cos 0 - B + ( 1 + √1 − e2 ) 2 - cos 2.0 - B - & c . } . Integrating and correcting , so as to make nt + c - B = 0 , when B = 0 , e being ...
Page 17
... dt dt dt2 Z , are changed into the following , d2 x dt2 d2 y dt2 d2 z = dt P 00 -- py S. P TY + T P + The three fore in the relative of the Earth ? 2-2 l'ovn dx d2x dy dy 2 P Hence 2 +2 dt DIFFERENTIAL EQUATIONS FOR THE MOON'S MOTION . 19 S ...
... dt dt dt2 Z , are changed into the following , d2 x dt2 d2 y dt2 d2 z = dt P 00 -- py S. P TY + T P + The three fore in the relative of the Earth ? 2-2 l'ovn dx d2x dy dy 2 P Hence 2 +2 dt DIFFERENTIAL EQUATIONS FOR THE MOON'S MOTION . 19 S ...
Page 17
... dt dt dt dt ( + ) ρ ( de ) " } dy_dp = dt dt dp sine + pcos e de dt But 2 . d dt dx d'x dt dť 2 + p2 +2 . 2 dy d'y dt dt2 since = + T +27 ( ady - da ) . y P dt dt 2 d [ da ( dy ) " } { ( d ) dt dt dx dp = cos + - dy dt de sin 0 dt P = dp ...
... dt dt dt dt ( + ) ρ ( de ) " } dy_dp = dt dt dp sine + pcos e de dt But 2 . d dt dx d'x dt dť 2 + p2 +2 . 2 dy d'y dt dt2 since = + T +27 ( ady - da ) . y P dt dt 2 d [ da ( dy ) " } { ( d ) dt dt dx dp = cos + - dy dt de sin 0 dt P = dp ...
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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
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