That point in a body revolving about a fixed axis into which the whole force or motion is collected; it is, therefore, that point of a revolving body which would strike an obstacle with the greatest effect, and from this property it has received the name of the centre of percussion. The centres of percussion and of oscillation are generally treated separately, but the two centres are in the same point, and therefore their properties are the same. As in bodies at rest the whole weight may be considered as collected in the centre of gravity, so in bodies in motion, the whole force may be considered as concentrated in the centre of percussion; therefore, the weight of the rod multiplied by the distance of the centre of gravity from the point of suspension, will be equal to the force of the rod divided by the distance of the centre of percussion from the same point. For example: suppose a rod, 12 feet long, and weighing 2 lbs. per foot, with two balls of 3 lbs. each, one fixed 6 feet from the point of suspension, and the other at the end of the rod; what is the distance between the points of suspension and of percussion 1

12x 2x6

=144

momentum of rod.

3X6

= 18

ditto of first ball.

3x12

= 36

ditto of second ball.

198

momentum of balls and rod:

and the weight of the rod multiplied by the square of its length, and divided by 3 = to the force of the rod; and the weight of the balls multiplied by the square of their distance from the point of suspension=to the force of the ball. Therefore -

24x144

3 =1152 the force of the rod and 1692 /198=8.545 feet from the point of suspension. In a slender rod, of small breadth as compared with its length, the distance of the centre of percussion is nearly two-thirds of its length from the point of suspension. In an isoceles triangle, suspended by its apex, and vibrating in a plane perpendicular to itself, the distance of the centre of percussion is three-fourths of its altitude; and the same thing holds with regard to fly-wheels, or wheels in general.

3X36 =

108

ditto of the first ball

3 X 144=

432

ditto of the second ball

1692

=force of balls and rod,