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 4
... we might assume u = - a 22 + A cos ( no + C ) + D cos me + B + Ecos q0 + Q , and , substituting this series in the equation , determine the values of D and E. 7. When m does not differ much from n , 4 LUNAR AND PLANETARY THEORIES .
... we might assume u = - a 22 + A cos ( no + C ) + D cos me + B + Ecos q0 + Q , and , substituting this series in the equation , determine the values of D and E. 7. When m does not differ much from n , 4 LUNAR AND PLANETARY THEORIES .
Page 6
... Substituting this for P in the equation above , t d2 u d02 M + M ' + u 0 , h2 the solution of which , by ( 3 ) , is u = M + M ' h9 + A cos 0 - B , tion 1 the rela ! or r = M + M ' h2 2 1 + A cos - B 9 which is the general polar equation ...
... Substituting this for P in the equation above , t d2 u d02 M + M ' + u 0 , h2 the solution of which , by ( 3 ) , is u = M + M ' h9 + A cos 0 - B , tion 1 the rela ! or r = M + M ' h2 2 1 + A cos - B 9 which is the general polar equation ...
Page 25
... Substituting these values , putting E + M = My panding P = ( 1 - 3 2 1 3 1 ( 1 + s2 ) 20 + 15 ( 881 ) as far as s1 , E - M ρ and ex- ( 0-0 ) + cos 3. ( 0 ( 0-0 ) ) } , -m { ( + cos2 . ( 0-0 ) ) + ( cos ( 9-0 ) + coss . ( 9- ρ 13 3 ль ...
... Substituting these values , putting E + M = My panding P = ( 1 - 3 2 1 3 1 ( 1 + s2 ) 20 + 15 ( 881 ) as far as s1 , E - M ρ and ex- ( 0-0 ) + cos 3. ( 0 ( 0-0 ) ) } , -m { ( + cos2 . ( 0-0 ) ) + ( cos ( 9-0 ) + coss . ( 9- ρ 13 3 ль ...
Page 26
... substituting these values in the equation ( d ) , it will be reduced to this form , d2 u d Ꮎ ? : + u + II = 0 , ПI being a complicated function of u , 8 , and 0. No method of directly solving such an equation is known but we have seen ...
... substituting these values in the equation ( d ) , it will be reduced to this form , d2 u d Ꮎ ? : + u + II = 0 , ПI being a complicated function of u , 8 , and 0. No method of directly solving such an equation is known but we have seen ...
Page 40
... becomes - C 3 m2 a { cos ( 2 − 2 m ) 0 − 2 ß − 2 e cos ( 2 − 2 m − c ) 0 − 2 ß + a } . 54. PROP . 19 . - - To form the differential equation for u . Collecting the terms , and substituting them in the equa- 40 LUNAR THEORY .
... becomes - C 3 m2 a { cos ( 2 − 2 m ) 0 − 2 ß − 2 e cos ( 2 − 2 m − c ) 0 − 2 ß + a } . 54. PROP . 19 . - - To form the differential equation for u . Collecting the terms , and substituting them in the equa- 40 LUNAR THEORY .
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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
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