## Elements of Natural Philosophy |

### From inside the book

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Page 10

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

curvature ( perpendicular therefore to the direction of mo . tion ) , whose

magnitude is

the path .

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

curvature ( perpendicular therefore to the direction of mo . tion ) , whose

magnitude is

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

Page 11

7 ( 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 ; and the

...

7 ( 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 ; and the

...

Page 13

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

vector are

perpendicular to the plane containing the fixed point and the line of motion of the

...

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

vector are

**proportional**to the times employed . Evidently there is no accelerationperpendicular to the plane containing the fixed point and the line of motion of the

...

Page 14

William Thomson Baron Kelvin, Peter Guthrie Tait. by the radius - vector are

double the area traced out by the radius - vector in unit of time . 48. Hence in this

case ...

William Thomson Baron Kelvin, Peter Guthrie Tait. by the radius - vector are

**proportional**to the timess for , as we have seen , the moment of the velocity isdouble the area traced out by the radius - vector in unit of time . 48. Hence in this

case ...

Page 15

... of the perpendicular with the tangent lies in the circle S YAZ , whose diameter

is the major axis . Produce YS to cut the circle again in 2. Then YS . SZ is

constant ; and therefore SZ is inversely as SY , that U is , SZ is

velocity ...

... of the perpendicular with the tangent lies in the circle S YAZ , whose diameter

is the major axis . Produce YS to cut the circle again in 2. Then YS . SZ is

constant ; and therefore SZ is inversely as SY , that U is , SZ is

**proportional**to thevelocity ...

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### Common terms and phrases

acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium expression figure fixed fluid force friction give given gravity harmonic Hence 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 produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire