Mathematical tracts on the lunar and planetary theories [&c.]. |
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Page 1
... Multiply the equation by cos no * , d'u then cos no . de + n2 cos no . u + cos no . → = 0 ; * sin n 0 , sin ( n 0 + D ) , or cos ( n 8 + D ) , would have served as well for multiplier . * A. M. T. 1 integrate the first term by parts ...
... Multiply the equation by cos no * , d'u then cos no . de + n2 cos no . u + cos no . → = 0 ; * sin n 0 , sin ( n 0 + D ) , or cos ( n 8 + D ) , would have served as well for multiplier . * A. M. T. 1 integrate the first term by parts ...
Page 4
... multiplying by cos ne , multiply by sin ( n0 + D ) , ( which will do equally well ) + n2 sin ( n0 + D ) . u + .u + sin ( 2n0 + 2D ) = 0 . Integrating by parts , as in ( 1 ) , b 2 du b sin ( no + D ) . n cos ( no + D ) . u cos ( 2n0 + 2D ) ...
... multiplying by cos ne , multiply by sin ( n0 + D ) , ( which will do equally well ) + n2 sin ( n0 + D ) . u + .u + sin ( 2n0 + 2D ) = 0 . Integrating by parts , as in ( 1 ) , b 2 du b sin ( no + D ) . n cos ( no + D ) . u cos ( 2n0 + 2D ) ...
Page 10
... $ ( ≈ ) } = ( 2 sin ≈ — sin 2z ) 3 4 3e Зе = 22 cos 2z - COS 2+ cos 32 ; 2 2 in which it is not necessary to include higher powers of e , be- cause it will be multiplied by e2 . d Зе 9e .. dz { $ ( z ) 10 LUNAR AND PLANETARY THEORIES .
... $ ( ≈ ) } = ( 2 sin ≈ — sin 2z ) 3 4 3e Зе = 22 cos 2z - COS 2+ cos 32 ; 2 2 in which it is not necessary to include higher powers of e , be- cause it will be multiplied by e2 . d Зе 9e .. dz { $ ( z ) 10 LUNAR AND PLANETARY THEORIES .
Page 14
... multiplied дов E 2012 M by , and by E + ME + M and which , in the lunar 20729 theory , ( where = 7 ° 1 400 M nearly , and = E + M 10 ) is quite in- sensible . In the same manner we find the accelerating force perpendicular to Gm ' m ' 3 ...
... multiplied дов E 2012 M by , and by E + ME + M and which , in the lunar 20729 theory , ( where = 7 ° 1 400 M nearly , and = E + M 10 ) is quite in- sensible . In the same manner we find the accelerating force perpendicular to Gm ' m ' 3 ...
Page 21
... multiplying each side by p2 or 2 do d ( 2 p2 dt ・ dt 1 d 1 d dt ( de 2 de dt de dt 2 = = 20 dt Tp at Тра de dt ; do ... multiply both sides dt by it becomes ᏧᎾ or or d / dp de dt 2 2 + p2 2 ( d ) " } = − 2p do + 2Tp , dt 9 ] de ...
... multiplying each side by p2 or 2 do d ( 2 p2 dt ・ dt 1 d 1 d dt ( de 2 de dt de dt 2 = = 20 dt Tp at Тра de dt ; do ... multiply both sides dt by it becomes ᏧᎾ or or d / dp de dt 2 2 + p2 2 ( d ) " } = − 2p do + 2Tp , dt 9 ] de ...
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Mathematical Tracts on the Lunar and Planetary Theories George Biddell Airy No preview available - 2019 |
Mathematical Tracts on the Lunar and Planetary Theories George Biddell Airy No preview available - 2019 |
Common terms and phrases
2π λ analyzing plate angle angular velocity attraction axis bright Cambridge cloth co-ordinates coefficient Consequently constant cos² Crown 8vo crystal curve depending different colours differential direction displacement distance disturbing force dR dR dt dt Earth elliptically polarized ellipticity equal equation expression extraordinary ray Fcap front function ƒ² glass h²)² Hence inclined integration intensity investigation length longitude mean anomaly Moon motion multiplied nearly node Nutation ordinary ray parallel particles perigee perihelion perpendicular plane of incidence plane of polarization plane of reflection point of Aries principal plane produced PROP proportion quantity radius vector refraction rhombohedron rings shew sin² spheroid Sun's suppose surface tangent tion tourmaline undulation vibration wave