Elements of Natural Philosophy, Volume 1 |
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Page 3
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
Page 15
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in YS produced , so that YS SU is constant , the locus of U is easily seen to be a circle ...
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in YS produced , so that YS SU is constant , the locus of U is easily seen to be a circle ...
Page 16
... turned through by its radius - vector in the same time . 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
... turned through by its radius - vector in the same time . 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
Page 17
... turned . Hence ( § 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely ...
... turned . Hence ( § 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely ...
Page 18
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
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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.