## Elements of Natural Philosophy, Volume 1 |

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Page 36

Let S

the body from its first position , without rotation , in a direction perpendicular to S ,

till S comes into the plane of its - C planes be second position . Then to get 36 ...

Let S

**denote**a plane of the body , the two positions of which are parallel . Movethe body from its first position , without rotation , in a direction perpendicular to S ,

till S comes into the plane of its - C planes be second position . Then to get 36 ...

Page 38

What we have

sometimes called , the rate of precession . The angular motions W , 12 are to one

another inversely as the distances of a point in the axis of the rolling cone from ...

What we have

**denoted**by 12 is the angular velocity of the precession , or , as it issometimes called , the rate of precession . The angular motions W , 12 are to one

another inversely as the distances of a point in the axis of the rolling cone from ...

Page 82

Hence at the instant when their velocities are equalized they move as one mass

with a momentum equal to the sum of the momenta of the two before impact .

That is to say , if v

v ...

Hence at the instant when their velocities are equalized they move as one mass

with a momentum equal to the sum of the momenta of the two before impact .

That is to say , if v

**denote**the common velocity at this instant , we have ( M + M ' )v ...

Page 83

( M + M ' ) v = MV + M ' V ' , MV + M ' y or v = MIM if M , M '

the two bodies , and V , V ' their velocities before impact . During this first period

of the impact the bodies have been , on the whole , coming into closer contact

with ...

( M + M ' ) v = MV + M ' V ' , MV + M ' y or v = MIM if M , M '

**denote**the masses ofthe two bodies , and V , V ' their velocities before impact . During this first period

of the impact the bodies have been , on the whole , coming into closer contact

with ...

Page 99

... where a

radius of the circular cross section of the ring . This is proved by remarking that an

infinitely narrow band from the outermost part of the ring has , at each point , a ...

... where a

**denotes**the radius of that circle , w the angular velocity in it , and b theradius of the circular cross section of the ring . This is proved by remarking that an

infinitely narrow band from the outermost part of the ring has , at each point , a ...

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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.