Elements of Natural Philosophy, Volume 1 |
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Page 24
... expression in Fourier's Theorem , to be presently enunciated . We give below a graphic representation of the composition of two simple harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 ...
... expression in Fourier's Theorem , to be presently enunciated . We give below a graphic representation of the composition of two simple harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 ...
Page 28
... expression , in mathematical language , for any arbitrary periodic function ; and consequently can express any ... expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have ...
... expression , in mathematical language , for any arbitrary periodic function ; and consequently can express any ... expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have ...
Page 35
... expressing in two ways the area of the parallelogram IpOq , we have Hence Oq.IB = Op.Ia . Oq : Op :: w1 : w . In words , if on the axes OA , OB , we measure off from O lines Op , Oq , proportional respectively to the angular velocities ...
... expressing in two ways the area of the parallelogram IpOq , we have Hence Oq.IB = Op.Ia . Oq : Op :: w1 : w . In words , if on the axes OA , OB , we measure off from O lines Op , Oq , proportional respectively to the angular velocities ...
Page 55
... expressions . The method is not correct unless it be specified at what part of the earth's surface the pound , or other definite quantity of matter named , is to be weighed ; for the weight of a given quantity of matter differs in ...
... expressions . The method is not correct unless it be specified at what part of the earth's surface the pound , or other definite quantity of matter named , is to be weighed ; for the weight of a given quantity of matter differs in ...
Page 63
... expressions together , we find , as we might expect , that the amount of work required is unchanged by the substitution of the oblique for the vertical path . 205. Generally , for any force , the work done during an indefinitely small ...
... expressions together , we find , as we might expect , that the amount of work required is unchanged by the substitution of the oblique for the vertical path . 205. Generally , for any force , the work done during an indefinitely small ...
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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.