OS THE MOTIONS OF CONNECTED BODIES. 85 



nitude, is made to revolve round a centre, it is sometimes necessary to in- 

 quire, into what point their masses might be supposed to be concentrated, so 

 as to preserve the same rotatory power, with the same angular velocity. This 

 point is called the centre of gyration* In a circle, or any portion of a circle, 

 turning round its centre, the square of the distance of this point, from the 

 centre, is half the square of the semidiameter ; and the whole eftect of the mo- 

 mentum of the circle, upon an obstacle at its circumference, is exactly half 

 as. great as that of an equal quantity of matter, striking the obstacle with the 

 velocity of tlie circumference.- 



There is another point, of which the determination is of considerable utility 

 in manv meclianical problems: this is the centre of percussion ; or the point 

 at which an obstacle nuist be applied, in order to receive the whole eftect of a 

 stroke of a body, which is revolving round a given centre, without producing 

 any pressure,, or strain, on the centre, or axis of motion. In a straight line, 

 or a slender, rod, iixed at one extremity, the distance of this point, from the 

 centre of motion, is two thirds of the whole length. 



The same point is also the centre of oscillation, the distance of which de- 

 termines the time of oscillation, or vibration, of the body, suspended as a 

 pendulum, upon the given centre, of motion. It may easily be shown, that 

 a rod a yard long, and of equable thickness, suspended at one extremity, vi- 

 brates in the same time as a ball suspended by a ducd< , of which the length 

 is two feet. But if the rod were suspended on a centre, at some point 

 within its extremities, the time of its vibration would be prolonged, so as to • 

 become equal to that of a simple pendulum of much greater length. This 

 may be illustrated by two balls, fixed at the end of a rod, with a centre of 

 suspension moveable to any part of the rod, for as the centre approaches the 

 middle of the rod, the vibrations are rendered extremely slow. -(Plate V. 

 Fig 75.) 



The rotatory motion of bodies, not fixed on an axis, might be considereol 

 in, this place, but the subject involves in its whole extent some intricacy of 

 calculation, and, except in astronomy, the investigation is scarcely applicable 

 to any problems which occur in practice. We may, however, examine a few 

 of the simplest cases. If two bodies be supposed to be connected by an in- 



