## Elements of Natural Philosophy, Volume 1 |

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Page 15

... we consider the motion to be confined to a plane passing through the fixed

point , the angle which the joining line makes with a fixed line in the plane is

continually altering , and its rate of alteration at any instant is called the

Velocity ...

... we consider the motion to be confined to a plane passing through the fixed

point , the angle which the joining line makes with a fixed line in the plane is

continually altering , and its rate of alteration at any instant is called the

**Angular**Velocity ...

Page 16

We may also speak of the

fixed one , as the rate of increase of the angle contained by them ; but unless

their line of intersection remain fixed , or at all events parallel to itself , a

somewhat ...

We may also speak of the

**angular**velocity of a moving plane with respect to afixed one , as the rate of increase of the angle contained by them ; but unless

their line of intersection remain fixed , or at all events parallel to itself , a

somewhat ...

Page 17

acceleration in the orbit , varies inversely as the square of the radius - vector ;

and therefore ( $ 59 ) directly as the

described in any time , is proportional to the corresponding angle - vector in the

orbit , i . e ...

acceleration in the orbit , varies inversely as the square of the radius - vector ;

and therefore ( $ 59 ) directly as the

**angular**velocity . Hence the arc of Pl ,described in any time , is proportional to the corresponding angle - vector in the

orbit , i . e ...

Page 20

... comes to its greatest elongation in the direction reckoned as positive , from its

mean position or the middle of its range . Epoch in

described on the circle of reference in the period of time defined as the epoch .

... comes to its greatest elongation in the direction reckoned as positive , from its

mean position or the middle of its range . Epoch in

**angular**measure is the angledescribed on the circle of reference in the period of time defined as the epoch .

Page 22

resultant of the motions P and P . But CS , the diagonal of the parallelogram , is

constant ( since the

angle QCQ is constant ) , and revolves with the same

resultant of the motions P and P . But CS , the diagonal of the parallelogram , is

constant ( since the

**angular**velocities of CQ and CQ are equal , and therefore theangle QCQ is constant ) , and revolves with the same

**angular**velocity as CQ or ...### What people are saying - Write a review

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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.