This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

**Composition Of Forces** is the finding a single force which shall be equal to two or more given forces when acting in given directions, the principles of which may be thus illustrated. If two forces, moving in the direction of the two adjacent sides of a parallelogram with velocities proportional to the length of the sides of the said parallelogram, impinge upon a body, it will cause that body to move over the diagonal of the parallelogram in the same time that either of the forces singly would have impelled it along its corresponding side. This may be demonstrated experimentally by an ingenious apparatus, designed and executed by Mr. C. Holtzapfell, of Charing-cross, and which is exhibited in the annexed engraving. The apparatus consists of a rectangular board, with a perpendicular brass pillar fixed in one corner. Two guide steel wires extend from the flanch at the bottom to the cap at the top, and sufficiently distant from the pillar to allow the two ivory balls a and b to descend upon them without touching the pillar. The board is made perfectly flat, varnished, and polished, and when used, must be placed perfectly level. At the point where two straight lines from the bottom of the guide wire3 would meet and make a right angle, a small hollow is made to receive a ball c.

The weights of the balls a and b are adjusted to correspond with the length of the sides of the board; so that when the ball a is dropped, it will give an impulse to the ball c, and send it to the end of the board in the direction of the line d in the same time that the ball b would send it to the edge of the board in the direction e. If now both balls be dropped at the same instant from the same height, they will propel the ball in the diagonal c f of the parallelogram in the same time that one of them singly would have impelled it along one of the sides.

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