## Elements of Natural Philosophy, Volume 1 |

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Page 14

The invention of this construction is due to Sir W . R . Hamilton ; and one of the

most beautiful of the many

Hodograph for the motion of a planet or comet is always a circle , whatever be the

...

The invention of this construction is due to Sir W . R . Hamilton ; and one of the

most beautiful of the many

**remarkable**theorems to which it leads is this : TheHodograph for the motion of a planet or comet is always a circle , whatever be the

...

Page 47

From this follows the

after another , in any piece of matter , each without rotation , may be so adjusted

as to leave the body unstrained , but rotated through some angle about some ...

From this follows the

**remarkable**corollary that three pure strains produced oneafter another , in any piece of matter , each without rotation , may be so adjusted

as to leave the body unstrained , but rotated through some angle about some ...

Page 65

But it is

explain what may be called directional rest . Also , as will be seen farther on , a

perfectly smooth spherical body , made up of concentric shells , each of uniform ...

But it is

**remarkable**that the first law of motion enables us ( § 215 , below ) toexplain what may be called directional rest . Also , as will be seen farther on , a

perfectly smooth spherical body , made up of concentric shells , each of uniform ...

Page 67

A

. Since forces are measured by the changes of motion they produce , and their

directions assigned by the directions in which these changes are produced ; and

...

A

**remarkable**consequence follows immediately from this view of the second law. Since forces are measured by the changes of motion they produce , and their

directions assigned by the directions in which these changes are produced ; and

...

Page 69

In the scholium appended , he makes the following

introducing another specification of actions and reactions subject to his third law ,

the full meaning of which seems to have escaped the notice of commentators :Si

...

In the scholium appended , he makes the following

**remarkable**statement ,introducing another specification of actions and reactions subject to his third law ,

the full meaning of which seems to have escaped the notice of commentators :Si

...

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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.