An Elementary Treatise on the Lunar Theory: With a Brief Sketch of the History of the Problem Up to the Time of Newton |
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Page v
... explanation of her disturbances ; and his Eleventh Section is the first attempt at a theoretical investigation of the Lunar inequalities . The results he obtained were found to agree very nearly with those de- termined by observation ...
... explanation of her disturbances ; and his Eleventh Section is the first attempt at a theoretical investigation of the Lunar inequalities . The results he obtained were found to agree very nearly with those de- termined by observation ...
Page 51
... explained in Art . ( 34 ) . 29 2 51. The preceding equations U2 , S2 , give the reci- procal of the radius vector , the latitude and the time in terms of the true longitude ; but the principal object of the analytical investigations of ...
... explained in Art . ( 34 ) . 29 2 51. The preceding equations U2 , S2 , give the reci- procal of the radius vector , the latitude and the time in terms of the true longitude ; but the principal object of the analytical investigations of ...
Page 60
... explained how the numerical values of the coefficients in these equations may be determined from observation ; and we ... explain those inequalities or departures from uniform circular motion which ancient astronomers had observed , but ...
... explained how the numerical values of the coefficients in these equations may be determined from observation ; and we ... explain those inequalities or departures from uniform circular motion which ancient astronomers had observed , but ...
Page 62
... explaining the elliptic inequality and the evection , Arts . ( 66 ) and ( 70 ) ; but in the remaining inequalities each term of the expression will form a correction to be considered by itself . 65. Neglecting all the periodical terms ...
... explaining the elliptic inequality and the evection , Arts . ( 66 ) and ( 70 ) ; but in the remaining inequalities each term of the expression will form a correction to be considered by itself . 65. Neglecting all the periodical terms ...
Page 63
... the expression of Art . ( 13 ) is here omitted ; a proper assumption for the origin of t , as explained in Art . ( 34 ) , enabling us to avoid the ε . 7 and the orbit will have taken the position indicated MOTION OF THE APSE . 63.
... the expression of Art . ( 13 ) is here omitted ; a proper assumption for the origin of t , as explained in Art . ( 34 ) , enabling us to avoid the ε . 7 and the orbit will have taken the position indicated MOTION OF THE APSE . 63.
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3m²e accelerating forces Algebra angle angular velocity annual equation anomaly apogee apse line astronomers attraction bodies BROOKE FOSS WESTCOTT calculated Cambridge centre cloth coefficient considered correct cos2 Crown 8vo determined differential equations distance disturbing force E-Ma E+Ma earth eccentricity ecliptic ELEMENTARY TREATISE elliptic inequality epicycle equal evection expression Fcap fixed plane fourth order h²u³ higher order Hipparchus hu³ integration John's College Lunar Theory MACMILLAN AND CO'S Mathematical mean anomaly mean longitude mean motion mean value method moon moon's mean moon's motion moon's orbit nearly neglected Newton node numerous observations obtained order of approximation parallax particle perigee periodical terms position Ps-S Ptolemy quadrature quantity radius vector revolution Schools Second Edition second order shew sidereal month sin2 solution sphere student substituted syzygy third order true anomaly true longitude Tycho variation že²
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