Mechanism of the HeavensJ. Murray, 1831 - 621 pages |
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Page 7
... co - or- dinate planes are generally assumed to be perpendicular to each other , so that xoy , xoz , yoz , are right R B Q fig . 3 . fig . 4 . angles . The position of or , oy , oz , the axes of the co - ordinates ... co - ordinate plane be ...
... co - or- dinate planes are generally assumed to be perpendicular to each other , so that xoy , xoz , yoz , are right R B Q fig . 3 . fig . 4 . angles . The position of or , oy , oz , the axes of the co - ordinates ... co - ordinate plane be ...
Page 8
... co - ordinates . If the co - ordinates be rectangular , a is the tangent of the angle moA , for mB = oA , and oAm is a b right angle ; hence oA : Am :: 1 : tan Aom ; whence mA = oA x tan Aom = mB . tan Aom . As this relation is the same ...
... co - ordinates . If the co - ordinates be rectangular , a is the tangent of the angle moA , for mB = oA , and oAm is a b right angle ; hence oA : Am :: 1 : tan Aom ; whence mA = oA x tan Aom = mB . tan Aom . As this relation is the same ...
Page 11
... co- ordinates ; a , b , c , the co - ordinates of o , and x , y , z those of m ; the dia- gonal om , which may be represented by r , will be r = √ ( x − a ) 2 + ( y − b ) 2 + ( x − c ) 2 P fig.11 . But F , the whole force in om , is ...
... co- ordinates ; a , b , c , the co - ordinates of o , and x , y , z those of m ; the dia- gonal om , which may be represented by r , will be r = √ ( x − a ) 2 + ( y − b ) 2 + ( x − c ) 2 P fig.11 . But F , the whole force in om , is ...
Page 12
... co - ordinates ; hence δι F = Σ.F δι Sr Sx ' Su ; F dr Su = Σ.Γ Sr -Σ.F бу бу 02 Sz be or if the sums of the component forces parallel to the axis x , y , z , represented by X , Y , Z , we shall have Su F ' Su = X ; F = Y ; F , ( 2 ) бу ...
... co - ordinates ; hence δι F = Σ.F δι Sr Sx ' Su ; F dr Su = Σ.Γ Sr -Σ.F бу бу 02 Sz be or if the sums of the component forces parallel to the axis x , y , z , represented by X , Y , Z , we shall have Su F ' Su = X ; F = Y ; F , ( 2 ) бу ...
Page 13
... co - ordinates , that is to X = 0 , Y = 0 , Z = 0 , = for it is evident that if the resulting force be zero , its component forces must also be zero . On Pressure . 43. A pressure is a force opposed by another force , so that no motion ...
... co - ordinates , that is to X = 0 , Y = 0 , Z = 0 , = for it is evident that if the resulting force be zero , its component forces must also be zero . On Pressure . 43. A pressure is a force opposed by another force , so that no motion ...
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Common terms and phrases
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