Elements of Natural Philosophy, Volume 1 |
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Page 49
... density bears to the density , at any instant , the same ratio as the rate of increase of the volume of an infinitely small portion bears to the volume of this portion at the same instant . 164. To find the differential equation of ...
... density bears to the density , at any instant , the same ratio as the rate of increase of the volume of an infinitely small portion bears to the volume of this portion at the same instant . 164. To find the differential equation of ...
Page 52
... Density conjointly . In reality , the definition gives us the meaning of density rather than of mass ; for it shows us that if twice the original quantity of matter , air for example , be forced into a vessel of given capacity , the density ...
... Density conjointly . In reality , the definition gives us the meaning of density rather than of mass ; for it shows us that if twice the original quantity of matter , air for example , be forced into a vessel of given capacity , the density ...
Page 53
... density , the mass or quantity is proportional to the volume or space it occupies . Let M be the mass , p the density , and V the volume , of a homo- geneous body . Then M = Vp ; if we so take our units that unit of mass is that.of unit ...
... density , the mass or quantity is proportional to the volume or space it occupies . Let M be the mass , p the density , and V the volume , of a homo- geneous body . Then M = Vp ; if we so take our units that unit of mass is that.of unit ...
Page 54
... density , we have taken no account of the dimensions of the moving body . This is of no consequence so long as it does not rotate , and so long as its parts preserve the same relative positions amongst one another . In this case we may ...
... density , we have taken no account of the dimensions of the moving body . This is of no consequence so long as it does not rotate , and so long as its parts preserve the same relative positions amongst one another . In this case we may ...
Page 56
... density of the earth , may be employed to calculate the most probable value of the apparent force of gravity , being the resultant of true gravitation and centrifugal force , in any locality where no pendulum observation of sufficient ...
... density of the earth , may be employed to calculate the most probable value of the apparent force of gravity , being the resultant of true gravitation and centrifugal force , in any locality where no pendulum observation of sufficient ...
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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.