Elements of Natural Philosophy, Volume 1 |
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Page 10
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
Page 11
... proportional to its dis- tance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( §§ 66 , 78 ) ...
... proportional to its dis- tance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( §§ 66 , 78 ) ...
Page 12
... proportional to the times employed . This includes the case of a satellite or planet revolving about its primary , according to Kepler's first law . Evidently there is no acceleration perpendicular to the plane con- taining the fixed ...
... proportional to the times employed . This includes the case of a satellite or planet revolving about its primary , according to Kepler's first law . Evidently there is no acceleration perpendicular to the plane con- taining the fixed ...
Page 13
... proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as the perpendicular ...
... proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as the perpendicular ...
Page 14
... . Then YS SZ is constant , and therefore SZ is inversely as SF , that is , SZ is proportional to the velocity at P. Also 1 Proc . R. S. 1865 . A S P U -B SZ is perpendicular to the direction of motion PY , 14 PRELIMINARY .
... . Then YS SZ is constant , and therefore SZ is inversely as SF , that is , SZ is proportional to the velocity at P. Also 1 Proc . R. S. 1865 . A S P U -B SZ is perpendicular to the direction of motion PY , 14 PRELIMINARY .
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular cloth co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance elements ellipse ellipsoid elongation equal equations equilibrium external point Extra fcap finite flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving Natural Philosophy normal section Oxford P₁ parallel particle path pendulum perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular resultant right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theory tion torsion uniform unit vertical whole wire
Popular passages
Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.
Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.