Elements of Natural Philosophy, Volume 1 |
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Page 4
... problems occur in connexion with it . We shall say nothing here about such cases as knots , knitting , weaving , etc. , as being exces- sively difficult in their general development , and too simple in the ordinary cases to require ...
... problems occur in connexion with it . We shall say nothing here about such cases as knots , knitting , weaving , etc. , as being exces- sively difficult in their general development , and too simple in the ordinary cases to require ...
Page 16
... problem of finding the hodograph ( § 35 ) for any case of motion in which the acceleration is directed to a fixed point , and varies inversely as the square of the distance from that point . The velocity of P , in the hodograph PQ ...
... problem of finding the hodograph ( § 35 ) for any case of motion in which the acceleration is directed to a fixed point , and varies inversely as the square of the distance from that point . The velocity of P , in the hodograph PQ ...
Page 28
... problem , —to find a complex harmonic function expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the reso- lution is determinate ...
... problem , —to find a complex harmonic function expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the reso- lution is determinate ...
Page 30
... problems of Mechanics . - Thus in any Lever , turning in the plane of its arms- -the rate of motion of any point is proportional to its distance from the fulcrum , and its direction of motion at any instant perpendicular to the line ...
... problems of Mechanics . - Thus in any Lever , turning in the plane of its arms- -the rate of motion of any point is proportional to its distance from the fulcrum , and its direction of motion at any instant perpendicular to the line ...
Page 36
... problem : -From the given angular velocities of the body about three rectangular axes attached to it to determine the position of the body in space after a given time . But the general solution of this problem demands higher analysis ...
... problem : -From the given angular velocities of the body about three rectangular axes attached to it to determine the position of the body in space after a given time . But the general solution of this problem demands higher analysis ...
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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 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 P₂ 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 theorem 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.