Elements of Natural Philosophy, Volume 1 |
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Page 49
The form under which the equation of continuity is most commonly given , or the
differential equation of continuity , as we may call it , expresses that the rate of
diminution of the density bears to the density , at any instant , the same ratio as
the ...
The form under which the equation of continuity is most commonly given , or the
differential equation of continuity , as we may call it , expresses that the rate of
diminution of the density bears to the density , at any instant , the same ratio as
the ...
Page 52
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 will be doubled , and so on .
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 will be doubled , and so on .
Page 53
shows us that , of matter of uniform 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- , géneous body . Then M = Vp ; if we so take our units that ...
shows us that , of matter of uniform 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- , géneous body . Then M = Vp ; if we so take our units that ...
Page 54
It is to be observed that , in what precedes , with the exception of the definition of
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 ...
It is to be observed that , in what precedes , with the exception of the definition of
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 ...
Page 56
The formula , deduced by Clairault from observation , and a certain theory
regarding the figure and density of the earth , may be employed to calculate the
most probable value of the apparent force of gravity , being the resultant of true ...
The formula , deduced by Clairault from observation , and a certain theory
regarding the figure and density of the earth , may be employed to calculate the
most probable value of the apparent force of gravity , being the resultant of true ...
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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain remarkable respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire