## Elements of Natural Philosophy, Volume 1 |

### From inside the book

Results 1-5 of 59

Page 10

... and equal to the acceleration of the velocity ; the other towards the centre of

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is

... and equal to the acceleration of the velocity ; the other towards the centre of

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is

**proportional**to the square of the velocity and also to the curvature of the path . Page 11

( 6 ) If a point moves in a plane , and its component velocity parallel to each of

two rectangular axes is

ellipse or hyperbola whose principal diameters coincide with those axes ...

( 6 ) If a point moves in a plane , and its component velocity parallel to each of

two rectangular axes is

**proportional**to its distance from that axis , the path is anellipse or hyperbola whose principal diameters coincide with those axes ...

Page 12

When the acceleration is directed to a fixed point , the path is in a plane passing

through that point ; and in this plane the areas traced out by the radius - vector

are

When the acceleration is directed to a fixed point , the path is in a plane passing

through that point ; and in this plane the areas traced out by the radius - vector

are

**proportional**to the times employed . This includes the case of a satellite or ... Page 13

This is the case of a motion in which the acceleration is directed to a fixed point ,

and we thus prove the second theorem of $ 45 , that in the case supposed the

areas described by the radius - vector are

This is the case of a motion in which the acceleration is directed to a fixed point ,

and we thus prove the second theorem of $ 45 , that in the case supposed the

areas described by the radius - vector are

**proportional**to the times ; for , as we ... Page 14

Produce YS to cut the circle again in Z . Then YS SZ is constant , and therefore

SZ is inversely as SY , that is , SZ is

the A SZ is perpendicular to the direction of motion PY ,. | Proc . R . S . 1865 .

Produce YS to cut the circle again in Z . Then YS SZ is constant , and therefore

SZ is inversely as SY , that is , SZ is

**proportional**to the velocity at P . Also B letthe A SZ is perpendicular to the direction of motion PY ,. | Proc . R . S . 1865 .

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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.