Elements of Natural Philosophy |
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Page 10
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
Page 11
... proportional to its dis- tance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( S $ 66 , 78 ) ...
... proportional to its dis- tance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( S $ 66 , 78 ) ...
Page 13
... proportional to the times employed . Evidently there is no acceleration perpendicular to the plane con- taining the fixed point and the line of motion of the moving point at any instant ; and there being no velocity perpendicular to ...
... proportional to the times employed . Evidently there is no acceleration perpendicular to the plane con- taining the fixed point and the line of motion of the moving point at any instant ; and there being no velocity perpendicular to ...
Page 14
William Thomson Baron Kelvin, Peter Guthrie Tait. by the radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence ...
William Thomson Baron Kelvin, Peter Guthrie Tait. by the radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence ...
Page 15
... proportional to the velocity at P. Also SZ is perpendicular to the direction of motion PY , and thus the circular locus of Z is the hodograph turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is ...
... proportional to the velocity at P. Also SZ is perpendicular to the direction of motion PY , and thus the circular locus of Z is the hodograph turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is ...
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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 co-ordinates component configuration consider constant cord corresponding cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external finite fixed point flexure fluid forces acting formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel parallelogram particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular relative 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 tion torsion uniform unit vertical vibrations weight whole wire
Popular passages
Page 149 - 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 38 - We cannot, of course, give a definition of matter which will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force. The latter, and indeed the former also, of these definitions involves the idea of force, which, in point of fact, is a direct object of sense ; probably of all our senses, and certainly of the
Page 11 - 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 149 - 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 118 - 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.
Page 45 - The Component of a force in any direction, sometimes called the Effective Component in that direction, is therefore found by multiplying the magnitude of the force by the cosine of the angle between the directions of the force and the component The remaining component in this case is perpendicular to the other. It is very generally convenient to resolve forces into components parallel to three lines at right angles to each other; each such resolution being effected by multiplying by the cosine of...
Page 40 - Matter has an innate power of resisting external influences, so that every body, as far as it can, remains at rest, or moves uniformly in a straight line.
Page 95 - Herschel, regards what are called re-sidual phenomena. When, in an experiment , all known causes being allowed for, there remain certain unexplained effects (excessively slight it may be), these must be carefully investigated, and every conceivable variation of arrangement of apparatus, etc., tried ; until, if possible, we manage so to exaggerate the residual phenomenon as to be able to detect its cause.
Page 51 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.