Mechanism of the HeavensJ. Murray, 1831 - 621 pages |
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Page 12
... preceding equation could be of no use . 41. When the particle is in equilibrio , the resulting force is zero ; consequently Xộc + Yông + Z = 0 ( 3 ) , which is the general equation of the equilibrium of a free particle . 42. Thus , when ...
... preceding equation could be of no use . 41. When the particle is in equilibrio , the resulting force is zero ; consequently Xộc + Yông + Z = 0 ( 3 ) , which is the general equation of the equilibrium of a free particle . 42. Thus , when ...
Page 14
... equation of the radius of curvature is formed from the equation of the curve , or surface . If r be the radius of ... preceding equation to Xôn + Yông + Zồi = 0 . But this equation is no longer equivalent to three equations , but to two ...
... equation of the radius of curvature is formed from the equation of the curve , or surface . If r be the radius of ... preceding equation to Xôn + Yông + Zồi = 0 . But this equation is no longer equivalent to three equations , but to two ...
Page 24
... preceding equation becomes sy Sz 0 = ( x - dr ) & x + ( Y - dy ) by + ( Z - A ) dz dt2 + R1ds - λόκ and this is true whatever A may be . ( 8 ) But A being thus left arbitrary , we are at liberty to determine it by any convenient ...
... preceding equation becomes sy Sz 0 = ( x - dr ) & x + ( Y - dy ) by + ( Z - A ) dz dt2 + R1ds - λόκ and this is true whatever A may be . ( 8 ) But A being thus left arbitrary , we are at liberty to determine it by any convenient ...
Page 31
... preceding equation ; and when the forces are functions of the distance , the integral is and 2f ( x , y , z ) + c = v2 , A2 — v2 = 2ƒ ( x , y , z ) – 2f ( a , b , c ) , - as before . Hence , if the particle be urged by accelerating ...
... preceding equation ; and when the forces are functions of the distance , the integral is and 2f ( x , y , z ) + c = v2 , A2 — v2 = 2ƒ ( x , y , z ) – 2f ( a , b , c ) , - as before . Hence , if the particle be urged by accelerating ...
Page 40
... equation to a straight line , it follows that the projection of the curve in ... equations become ds dx d2z dex ( a ) = -h . dt • ; g h - • dt dt dt2 the integral of the first is ds dt ... preceding integral 40 [ Book I. VARIABLE MOTION .
... equation to a straight line , it follows that the projection of the curve in ... equations become ds dx d2z dex ( a ) = -h . dt • ; g h - • dt dt dt2 the integral of the first is ds dt ... preceding integral 40 [ Book I. VARIABLE MOTION .
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A₁ action angle ascending node attraction axes axis B₁ becomes c'mv centre of gravity centrifugal force co-ordinates coefficients comets computed conic sections consequently cosines curve density depending determined differential direction disturbing forces dR dR dt dt earth eccentricity ecliptic elements epoch equal equilibrium equinoxes expression fixed plane fluid functions give hence inclination indefinitely small integral Jupiter latitude mass mean anomaly mean distance mean longitude mean motion moon moon's move nearly observation omitted orbit of Jupiter oscillations parallax particle perigee perihelion periodic inequalities perturbations planets preceding equation preceding values radius vector ratio regard rotation satellites Saturn secular inequalities secular variations sidereal sine spheroid square substituted surface system of bodies terrestrial theory tion true longitude Uranus velocity whence zero