Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 11
... less as the space passed over in a given time is greater or less : and it may be uniform , i.e. , the same at every instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in ...
... less as the space passed over in a given time is greater or less : and it may be uniform , i.e. , the same at every instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in ...
Page 12
... less the interval is , the more nearly does the average velocity coincide with the actual velocity at any instant of the interval . Or again , we define the exact velocity at any instant as the space which the point would have described ...
... less the interval is , the more nearly does the average velocity coincide with the actual velocity at any instant of the interval . Or again , we define the exact velocity at any instant as the space which the point would have described ...
Page 23
... less fore - shortened catenary ( § 580 ) if from the plane . As in case c , perpendicular to at any instant . d2z dt = dz 0 , dt 0 , and z = 0 , if the axis of z be the acceleration and to the direction of motion Also , if we choose the ...
... less fore - shortened catenary ( § 580 ) if from the plane . As in case c , perpendicular to at any instant . d2z dt = dz 0 , dt 0 , and z = 0 , if the axis of z be the acceleration and to the direction of motion Also , if we choose the ...
Page 29
... less than , that of the second . The figures in the text below represent the curves in these cases , the velocities of the pur- suer being , 1 , and of those of the pursued , respectively . In the second and third cases the second point ...
... less than , that of the second . The figures in the text below represent the curves in these cases , the velocities of the pur- suer being , 1 , and of those of the pursued , respectively . In the second and third cases the second point ...
Page 35
... less than that of the water , it never reaches the other bank , and is carried indefinitely down stream . The compari- e = 1 -4-4 € = 2 son of the figures in § 40 with those in the present section cannot fail to be instructive . They ...
... less than that of the water , it never reaches the other bank , and is carried indefinitely down stream . The compari- e = 1 -4-4 € = 2 son of the figures in § 40 with those in the present section cannot fail to be instructive . They ...
Contents
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - 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.