Elements of Natural Philosophy, Volume 1 |
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Page 35
... determined in magnitude , and the direction . of its axis is found , as follows : -The square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are ...
... determined in magnitude , and the direction . of its axis is found , as follows : -The square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are ...
Page 36
... determine the position of the body in space after a given time . But the general solution of this problem demands higher analysis than can be admitted into the present treatise . 112. We shall next consider the most general possible ...
... determine the position of the body in space after a given time . But the general solution of this problem demands higher analysis than can be admitted into the present treatise . 112. We shall next consider the most general possible ...
Page 44
... determined by a simple geometrical construction . 146. With the same data the alteration of angle between any two planes of the body may also be easily determined , geometrically . 147. Let the ellipse of the annexed diagram represent ...
... determined by a simple geometrical construction . 146. With the same data the alteration of angle between any two planes of the body may also be easily determined , geometrically . 147. Let the ellipse of the annexed diagram represent ...
Page 50
... determine the position of the body . Thus if six points properly chosen on the barrel and stock of a rifle be made to rest on six convex portions of the surface of a fixed rigid body , the rifle may be replaced any number of times in ...
... determine the position of the body . Thus if six points properly chosen on the barrel and stock of a rifle be made to rest on six convex portions of the surface of a fixed rigid body , the rifle may be replaced any number of times in ...
Page 51
... determination of the degrees of freedom or constraint in any case that may present itself . 170. One degree of constraint of the most general character , is not producible by constraining one point of the body to a curve surface ; but ...
... determination of the degrees of freedom or constraint in any case that may present itself . 170. One degree of constraint of the most general character , is not producible by constraining one point of the body to a curve surface ; but ...
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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.