Sometimes it is necessary to express or measure a force or forces graphically, that is, by means of lines. This is particularly true in the building of machinery and structures, where the results of the application of force and skill may be obtained with less labor than by calculation. Graphic expression also gives accuracy sufficiently near for good practice. Force is measured in this way by considering the beginning of a line to be the point at which the force is applied, the length of the line to be its magnitude, and the direction of the line to be the direction of the force.

To illustrate: If a force of 10 lbs. is applied at a certain point A in an easterly direction, it would be represented by the line AB drawn 10 units in length. If there are two forces acting on a body at A and at right angles, one with an easterly direction of 10 lbs. and another with a northerly direction of 5 lbs., the actual direction of the motion of the body may be represented by the following parallelogram, the lines of which are parallel to each other (Fig. 39). If AC represents a force of 5 lbs. (called a component force) and AB represents a component force of 10 lbs., AD will represent the resultant of the two forces. To maintain the forces AB and AC in equilibrium a force must be applied at A equal to AD and acting in the opposite direction AF.

AF = AD

AF is called the equilibrant.

The above principle may be worked backwards. For example: If one force is given, it is always possible to find two others in given directions which will balance it.

FIG.39.   Parallelogram of Forces.

FIG.39. - Parallelogram of Forces.