## Elements of Natural Philosophy, Volume 1 |

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Page 7

... in the latter case , the direction of motion continually changes , the mere

must have in every such case additional data to thoroughly specify the motion , In

such ...

... in the latter case , the direction of motion continually changes , the mere

**amount**of the velocity is not sufficient completely to describe the motion , and wemust have in every such case additional data to thoroughly specify the motion , In

such ...

Page 9

... becomes the tangent at P . Hence the direction of acceleration is that of the

tangent to the curve thus described . The

change of velocity , and is therefore measured by the velocity of P in the curve PQ

. 36 .

... becomes the tangent at P . Hence the direction of acceleration is that of the

tangent to the curve thus described . The

**amount**of acceleration is the rate ofchange of velocity , and is therefore measured by the velocity of P in the curve PQ

. 36 .

Page 10

Hence the velocity of P is to that of A as OP to CA , i . e . as V to R ; and is

therefore equal to V . . v or ' R ' and this ( § 35 ) is the

in the circular path ABD . 37 . The whole acceleration in any direction is the sum

of the ...

Hence the velocity of P is to that of A as OP to CA , i . e . as V to R ; and is

therefore equal to V . . v or ' R ' and this ( § 35 ) is the

**amount**of the accelerationin the circular path ABD . 37 . The whole acceleration in any direction is the sum

of the ...

Page 14

... the change of velocity of the moving point during the corresponding time ; and

also that the tangent to the hodograph is parallel to the direction , and the velocity

in the hodograph is equal to the

... the change of velocity of the moving point during the corresponding time ; and

also that the tangent to the hodograph is parallel to the direction , and the velocity

in the hodograph is equal to the

**amount**of the acceleration of the moving point . Page 22

To find the time and the

phase , let CA be equal to the greater half - amplitude . From A as centre , with AB

the less halfamplitude as radius , describe a circle . CB touching this circle ...

To find the time and the

**amount**of the maximum acceleration or retardation ofphase , let CA be equal to the greater half - amplitude . From A as centre , with AB

the less halfamplitude as radius , describe a circle . CB touching this circle ...

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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.