The popular conception of force is something that produces motion, but its true definition is “that which tends to produce _or resist_ motion.” There are forces in existence when there is no motion. When you hold a weight in your hand there is a force tending to pull the weight to the earth, but this force is opposed by an equal force exerted by your muscles in holding up the weight. There is no motion because the two forces are perfectly balanced. If they were unbalanced, there would be motion in the direction of the greater force. If the pull of the arm is greater than that of gravity, the weight will be lifted, and if the weight is too heavy for the arm to support, it will go down despite muscular efforts to prevent it. In one case the force of gravity will endeavor to destroy motion by opposing the lift of the arm, and in the other case the arm will endeavor to resist motion by opposing the pull of gravity. A book on a table is motionless and yet it is acted upon by two forces which are opposed to each other and hence balanced. The table furnishes a force which resists and balances the force exerted by gravity. If the book were heavy enough, in other words, if the force directed downward were great enough, the table would be crushed. When two forces are in perfect balance they must be equal and opposite. Unless the directions of the two forces are exactly opposite, there will be motion in some new direction. Suppose we use an apparatus such as shown in Fig. 56 to study the result of three coacting forces. It consists of a T-shaped frame with a pulley _P_ at each end of the cross arm. These pulleys turn very freely on their axes, so that we need not be concerned with any appreciable amount of friction. Two fine cords running over these pulleys are knotted at _O_ to a third short cord. Each cord is provided with a hook on which weights may be hung. Now if we put a pound weight on each cord the two _A_ and _B_ will raise the weight _C_ until the angles between the cords at _O_ are all equal. In other words each force of one pound is balanced by two other forces of one pound each pulling at an angle of 120 degrees to it and to each other. If we put a 3-pound weight at _A_, a 4-pound weight at _B_ and a 5-pound weight at _C_, the cords will come to rest in the position shown in Fig. 57. The weight _B_ being heavier than weight _A_ will pull the knot _O_ to the right until the angle between the cords running to these weights is a right angle. [Illustration: FIG. 56.--BALANCED FORCES--EQUAL WEIGHTS] PARALLELOGRAM OF FORCES