FIRED GUN-POWDER. ' 7$

the pendulum, a stylette F is fastened in E, to trace uponthe fine dust, with which the circumferene G K H iscovered, the arch described by the first vibration of thependulum. Instead of the arch of the circle, RoeinSused a ribband attached to E, which the motion of thependulum drew between two iron plates fixed to a woodenbar that was between the legs of the frame, and mea-sured the arch described by the pendulum, by thelength of the ribband drawn between the plates.

161. The instrument being placed as above directed, ifwe know;

1. The weight P of all the parts of the pendulum.

2. The distance from the point C in the axis ofsuspension or motion to the centre of gravity L, orCL = *.

3. The distance from C to the centre of oscillationM, or CM=d.

4. The length C F — b of the radius with whichthe arch G K H is described.

5. The weight of the ball =q.

6. The chord of the arch — c described by thefirst vibration of the pendulum, and measured uponG K H ; then the motion communicated to the pendu-lum, and consequently the velocity with which the ballimpinged on it will be found.

Find the distances C L, CM: it is proved, (Philos. Instit.)that the vis inertiæ of a body moving freely round its axis,is equal to the product of its weight multiplied by thedistance from the centre of gravity to the axis of motion,and by the distance from the centre of oscillation to the sameaxis ; and the quantity of its motion is equal to the productof the vis intertiæ multiplied by the velocity of the pendulum,which is equal to the square root of the versed sine of thearch described by the centre of oscillation.

Fire a ball against the centre of oscillation M. To findthe velocity communicated to this point, make the propor-

tion b:c::d: the last term is the chord of the arch de-

scribed by this point: The versed sine of which is C ~ 4 , and

2 b

the uniform velocity of M during one second will be

/bq. 36. c*d