## Elements of Natural Philosophy, Part 1 |

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Page 2

If the path be not straight the direction of motion changes from point to point , and

the rate of this change , per unit of

exemplify this , suppose two tangents PT , QU , drawn to a circle , T and radii ...

If the path be not straight the direction of motion changes from point to point , and

the rate of this change , per unit of

**length**of the curve , is called the Curvature . Toexemplify this , suppose two tangents PT , QU , drawn to a circle , T and radii ...

Page 3

The rate of torsion , or the tortuosity , is therefore to be measured by the rate at

which the osculating plane turns about the tangent , per unit

The simplest illustration of a tortuous curve is the thread of a screw . Compare $

41 ...

The rate of torsion , or the tortuosity , is therefore to be measured by the rate at

which the osculating plane turns about the tangent , per unit

**length**of the curve .The simplest illustration of a tortuous curve is the thread of a screw . Compare $

41 ...

Page 16

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the centre of a circle an arc whose

radius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly . 56. The

angular ...

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the centre of a circle an arc whose

**length**is equal 180 ° to theradius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly . 56. The

angular ...

Page 18

Then , as the form of the relative GO À B path depends only upon the

direction of the line joining the two points ... And with regard to G and G ' it is

evident that the directions remain the same , while the

given ...

Then , as the form of the relative GO À B path depends only upon the

**length**anddirection of the line joining the two points ... And with regard to G and G ' it is

evident that the directions remain the same , while the

**lengths**are altered in agiven ...

Page 19

... mechanical applications , the following method is preferable :CF and ED are

rods of equal

middle point E of each - CA , AD , EB , and BF are rods of B half the

...

... mechanical applications , the following method is preferable :CF and ED are

rods of equal

**length**moving freely round a pivot at P , which passes through themiddle point E of each - CA , AD , EB , and BF are rods of B half the

**length**of the...

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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 evidently experience 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 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