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 3
... fore PQ is parallel and equal to PP . 1 Hence the projection of the whole disturbance PQ on any straight line , being equal to the algebraical sum of the pro- jections of PP , and P , Q , will B 2 SUPERPOSITION OF SMALL MOTIONS . 3.
... fore PQ is parallel and equal to PP . 1 Hence the projection of the whole disturbance PQ on any straight line , being equal to the algebraical sum of the pro- jections of PP , and P , Q , will B 2 SUPERPOSITION OF SMALL MOTIONS . 3.
Page 4
... whole disturbance equals the sum of the three separate disturbances . This reasoning can evidently be extended to any number of forces ; and if x , y , z be the coordinates of the disturbed particle , ( x , y , z ) any function of x , y ...
... whole disturbance equals the sum of the three separate disturbances . This reasoning can evidently be extended to any number of forces ; and if x , y , z be the coordinates of the disturbed particle , ( x , y , z ) any function of x , y ...
Page 5
... whole sphere be divi- ded into circular laminæ by planes perpendicular to OP . Let SQ be P one of these . PS = x , PQ = z , and thickness of lamina = dx . Next , let this lamina be divided into concentric rings ATTRACTIONS . 5.
... whole sphere be divi- ded into circular laminæ by planes perpendicular to OP . Let SQ be P one of these . PS = x , PQ = z , and thickness of lamina = dx . Next , let this lamina be divided into concentric rings ATTRACTIONS . 5.
Page 6
... whole ring will clearly be the sum of the resolved parts along PO of the attractions of its constituent elements ; therefore , attraction of ring - 2πρη.δι.δι x2 sec2 0 cos = 2πp sine dx.80 ; Ꮖ rcos - 1 名 therefore , attraction of whole ...
... whole ring will clearly be the sum of the resolved parts along PO of the attractions of its constituent elements ; therefore , attraction of ring - 2πρη.δι.δι x2 sec2 0 cos = 2πp sine dx.80 ; Ꮖ rcos - 1 名 therefore , attraction of whole ...
Page 7
... whole sphere is precisely the same as if the whole mass were condensed into its centre . COR . 1. The attraction of a shell radius = c and thickness Sc will be obtained from the preceding expression by diffe- rentiating it with respect ...
... whole sphere is precisely the same as if the whole mass were condensed into its centre . COR . 1. The attraction of a shell radius = c and thickness Sc will be obtained from the preceding expression by diffe- rentiating it with respect ...
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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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