Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page vi
... corresponding divisions of Dynamics are thus conveniently entitled Statics and Kinetics . One object which we have constantly kept in view is the grand principle of the Conservation of Energy . According to modern experimental results ...
... corresponding divisions of Dynamics are thus conveniently entitled Statics and Kinetics . One object which we have constantly kept in view is the grand principle of the Conservation of Energy . According to modern experimental results ...
Page 4
... corresponding property is conveniently called Tortuosity . 8. The nature of this will be best understood by consider- ing the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane ...
... corresponding property is conveniently called Tortuosity . 8. The nature of this will be best understood by consider- ing the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane ...
Page 6
... corresponding to that of OZ relatively to OX and OY . Then , using ( 8 ) and ( 9 ) , with ( 7 ) , in ( 5 ) and ( 6 ) respectively , we have d dz ds dx d dy d ds ds a == p'ds ' B = Y = p - 1 ds ' dz , dx d dx , dz d d d ( 10 ) ; dy , dz ...
... corresponding to that of OZ relatively to OX and OY . Then , using ( 8 ) and ( 9 ) , with ( 7 ) , in ( 5 ) and ( 6 ) respectively , we have d dz ds dx d dy d ds ds a == p'ds ' B = Y = p - 1 ds ' dz , dx d dx , dz d d d ( 10 ) ; dy , dz ...
Page 26
... corresponding interval of time , to find the velocity at its end . Hence the velocity in the hodo- graph is equal to the acceleration in the path ; and the tangent to the hodograph is parallel to the direction of the acceleration in the ...
... corresponding interval of time , to find the velocity at its end . Hence the velocity in the hodo- graph is equal to the acceleration in the path ; and the tangent to the hodograph is parallel to the direction of the acceleration in the ...
Page 28
... corresponding arc of the hodograph . From this it is easy to see , for example , that if a comet move in a parabola , the amount of heat it receives from the sun in any interval is pro- portional to the angle through which its direction ...
... corresponding arc of the hodograph . From this it is easy to see , for example , that if a comet move in a parabola , the amount of heat it receives from the sun in any interval is pro- portional to the angle through which its direction ...
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acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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