## Elements of Natural Philosophy, Volume 1 |

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Page 13

Their half - moments round the point 0 are

Now OCA , together with half the area of the parallelogram CABD , is equal to

OBD . Hence the sum of the two half - moments together with half the area of the

...

Their half - moments round the point 0 are

**respectively**the areas OAB , OCA .Now OCA , together with half the area of the parallelogram CABD , is equal to

OBD . Hence the sum of the two half - moments together with half the area of the

...

Page 22

... of P , and falling short of that of the motion of P ' , by the angles QCS and SCQ

the resultant of two simple harmonic motions , whether of the same period or not .

... of P , and falling short of that of the motion of P ' , by the angles QCS and SCQ

**respectively**. 76 . [ The construction described in the preceding section exhibitsthe resultant of two simple harmonic motions , whether of the same period or not .

Page 35

Let OA , OB be two axes about which a body revolves with angular velocities w ,

w ,

Draw la , Iß perpendicular to OA , OB

Let OA , OB be two axes about which a body revolves with angular velocities w ,

w ,

**respectively**. With radius unity describe the arc AB , and in it take any point I .Draw la , Iß perpendicular to OA , OB

**respectively**. Let the rotations about the ... Page 45

Let OX and OZ be the directions of maximum elongation and maximum

contraction

and A , the same point of the altered body , so that OA , = a . OA . Now , if we take

OC = 0A ...

Let OX and OZ be the directions of maximum elongation and maximum

contraction

**respectively**. Let A be any point of the body in its primitive condition ,and A , the same point of the altered body , so that OA , = a . OA . Now , if we take

OC = 0A ...

Page 46

The principal axes of a shear are the lines of maximum elongation and of

maximum contraction

construction ( 5 150 ) , thus : - In the plane of the shear bisect the obtuse and

acute angles ...

The principal axes of a shear are the lines of maximum elongation and of

maximum contraction

**respectively**. They may be found from the precedingconstruction ( 5 150 ) , thus : - In the plane of the shear bisect the obtuse and

acute angles ...

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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.

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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.