From what has been just stated it follows, that the energy of the weight of S to move the body on its axis, does not depend alone upon the actual amount of that weight, but also upon the distance of the string from the axis. If, while the position of the string remains unaltered, the weight of S be increased or diminished, the resisting weight W must be increased or diminished in the same proportion. But if, while the weight of S remains unaltered, the distance of the string P R from the axis G be increased or diminished, it will be found necessary to increase or diminish the resisting weight W in exactly the same proportion. It therefore appears that the increase or diminution of the distance of the direction of a force from the axis has the same effect upon its power to give rotation as a similar increase or diminution of the force itself. The power of a force to produce rotation is, therefore, accurately estimated, not by the force alone, but by the product found by multiplying the force by the distance of its direction from the axis. It is frequently necessary in mechanical science to refer to this power of a force, and, accordingly, the product just mentioned has received a particular denomination. It is called the _moment_ of the force round the axis. (185.) The distance of the direction of a force from the axis is sometimes called the _leverage_ of the force. The _moment_ of a force is therefore found by multiplying the force by its leverage, and the energy of a given force to turn a body round an axis is proportional to the leverage of that force. From all that has been observed it may easily be inferred that, if several forces affect a body moveable on an axis, having tendencies to turn it in different directions, they will mutually neutralise each other and produce equilibrium, if the sum of the moments of those forces which tend to turn the body in one direction be equal to the sum of the moments of those which tend to turn it in the opposite direction. Thus, if the forces A, B, C, ... tend to turn the body from right to left, and the distances of their directions from the axis be _a_, _b_, _c_, ... and the forces A′, B′, C′, ... tend to move it from left to right, and the distances of their directions from the axis be _a′_, _b′_, _c′_, ...; then these forces will produce equilibrium, if the products found by multiplying the ounces in A, B, C, ... respectively by the inches in _a_, _b_, _c_, ... when added together be equal to the products found by multiplying the ounces in A′, B′, C′, ... by the inches in _a′_, _b′_, _c′_, ... respectively when added together. But if either of these sets of products when added together exceed the other, the corresponding set of forces will prevail, and the body will revolve on its axis.