## 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 homogeneous body . Then M = Vp ; if we so take our units that unit ...

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 homogeneous body . Then M = Vp ; if we so take our units that unit ...

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 becomes body called centre centre of inertia circle cloth 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 period perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain 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

### 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 9 - Persius. The Satires. With a Translation and Commentary. By John Conington, MA, late Corpus Professor of Latin in the University of Oxford. Edited by H. Nettleship, MA Second Edition.

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 10 - Crown 8vo. cloth, 7s. 6d. A Treatise on Electricity and Magnetism. By J. Clerk Maxwell, MA, FRS, Professor of Experimental Physics in the University of Cambridge.

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 9 - An Elementary Treatise on Quaternions. By PG TAIT, MA, Professor of Natural Philosophy in the University of Edinburgh ; formerly Fellow of St Peter's College, Cambridge. Second Edition. Demy 8vo. 14*.

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.