## 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

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 asthe ...

Page 52

In reality , the definition gives us the meaning of

shows us that if twice the original quantity of matter , air for example , be forced

into a vessel of given capacity , the

In reality , the definition gives us the meaning of

**density**rather than of mass ; for itshows 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

to the volume or space it occupies . Let M be the mass , p 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 proportionalto the volume or space it occupies . Let M be the mass , p the

**density**, and V thevolume , 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

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 isof 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

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 themost probable value of the apparent force of gravity , being the resultant of true ...

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### Common terms and phrases

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