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 co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point 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 normal section P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular 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 theory tion torsion uniform unit vertical whole wire