Elements of Natural Philosophy, Volume 1 |
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Page 24
... harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 , the epochs being ... harmonic motions of one period , and of the same phase , superimposed , produce a single simple harmonic motion of ...
... harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 , the epochs being ... harmonic motions of one period , and of the same phase , superimposed , produce a single simple harmonic motion of ...
Page 25
... harmonic motion of P ' , in B'A ' , a quarter of a period behind that of the motion of P in BA . But , since A'OA , QPO , and QP'O are right angles , the figure QP'OP is a parallelogram , and therefore Q is in the position of the ...
... harmonic motion of P ' , in B'A ' , a quarter of a period behind that of the motion of P in BA . But , since A'OA , QPO , and QP'O are right angles , the figure QP'OP is a parallelogram , and therefore Q is in the position of the ...
Page 26
... harmonic motions of different kinds and in different lines . In general , whether these lines be in one plane or not , the line of motion returns into itself if the periods are commensurable ; and if not , not . This is evident without ...
... harmonic motions of different kinds and in different lines . In general , whether these lines be in one plane or not , the line of motion returns into itself if the periods are commensurable ; and if not , not . This is evident without ...
Page 27
... harmonic motions in one plane , such that the resultant of each group is uniform circular motion . If their periods are equal , we have a case belonging to those already treated ( § 80 ) , and conclude that the resultant is , in general ...
... harmonic motions in one plane , such that the resultant of each group is uniform circular motion . If their periods are equal , we have a case belonging to those already treated ( § 80 ) , and conclude that the resultant is , in general ...
Page 28
... harmonic motions , we must enunciate Fourier's Theorem , which 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 ...
... harmonic motions , we must enunciate Fourier's Theorem , which 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 ...
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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.