ACTION, in Mechanics, implies either the effort which a body or power makes against another body or power, or the effect itself of that effort.
All power is nothing more than a body actually in motion, or which tends to move itself; that is, a body which would move itself if nothing opposed it. The action therefore of a body is rendered evident to us by its motion only; and consequently we must not fix any other idea to the word
action than that of actual motion, or a simple tendency to motion. The famous question relating to vis viva and vis mortua owes its existence, in all probability, to an inadequate idea of the word action; for had Leibnitz and his followers observed that the only precise and distinct idea we can give to the word force or action reduces it to its effect, that is, to the motion it actually produces or tends to produce, they would never have made that curious distinction.
Quantity of ACTION, a name given by M. de Maupertuis, in the Memoirs of the Parisian Academy of Sciences for 1744, and those of Berlin for 1746, to the product of the mass of a body by the space which it runs through, and by its celerity. He lays it down as a general law, that "in the changes made in the state of a body, the quantity of action necessary to produce such change is the least possible." This principle he applies to the investigation of the laws of refraction, of equilibrium, &c. and even to the ways of acting employed by the Supreme Being. In this manner M. de Maupertuis attempts to connect the metaphysics of final causes with the fundamental truths of mechanics.