Elements of Natural Philosophy, Volume 1 |
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Page 2
... unit of length of the curve , is called the Curvature . To exemplify this , suppose two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the points of contact . The angle between the tangents is the change of direction ...
... unit of length of the curve , is called the Curvature . To exemplify this , suppose two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the points of contact . The angle between the tangents is the change of direction ...
Page 3
... unit length of the curve . The simplest illustration of a tortuous curve is the thread of a screw . Compare § 41 ( d ) . 14. The Integral Curvature , or whole change of direction , of an arc of a plane curve , is the angle through which ...
... unit length of the curve . The simplest illustration of a tortuous curve is the thread of a screw . Compare § 41 ( d ) . 14. The Integral Curvature , or whole change of direction , of an arc of a plane curve , is the angle through which ...
Page 6
... unit velocity a point describes unit of space in unit of time . 25. It is well to observe here , that since , by our formula , we have generally $ v = " and since nothing has been said as to the magnitudes of s and t , we may take these ...
... unit velocity a point describes unit of space in unit of time . 25. It is well to observe here , that since , by our formula , we have generally $ v = " and since nothing has been said as to the magnitudes of s and t , we may take these ...
Page 9
... unit of time . If we choose as the unit of acceleration that which adds a unit of velocity per unit of time to the velocity of a point , an acceleration measured by a will add a units of velocity in unit of time — and , therefore , at units ...
... unit of time . If we choose as the unit of acceleration that which adds a unit of velocity per unit of time to the velocity of a point , an acceleration measured by a will add a units of velocity in unit of time — and , therefore , at units ...
Page 13
... unit of time . 48. Hence in this case the velocity at any point is inversely as the perpendicular from the fixed point to the tangent to the path or the momentary direction of motion . For the product of this perpendicular and the ...
... unit of time . 48. Hence in this case the velocity at any point is inversely as the perpendicular from the fixed point to the tangent to the path or the momentary direction of motion . For the product of this perpendicular and the ...
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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.