leibniz

Dynamics

In 1686 Leibniz published the article Brevis demonstratio erroris memorabilis Cartesii (Short demonstration of a remarkable error by Descartes) in the journal Acta Eruditorum, thus unleashing a dispute that lasted for a good half a century over the true measure of force. Descartes had considered the quantity of motion (measured as the product of mass and speed) to be constant and the cause of changes in nature. Leibniz chose as a model case of his argument not elastic collision but rather free fall. Only that physical quantity can be conserved and referred to as force which, at least in terms of the calculation, is able to restore the initial state. Leibniz assumed that the force needed to lift a weight can be determined by the product of weight and height. However, according to Galileo's law of falling bodies, a fourfold increase in the height of fall results in a doubling of the speed. Thus the motive force must be made proportional to mv². For this doctrine of the conservation of force, Leibniz coined the term "Dynamik" (dynamics), which however we associate today with the Newtonian concept of force (the product of mass and acceleration). Newton interpreted friction phenomena as experimental refutations of a principle of conservation; he even postulated that God would have to add fresh motive forces to the universe from time to time, as otherwise everything would come to a standstill. In Leibniz's view, friction phenomena are to be understood as transformations of motion, that are perceptible to the senses, into molecular motion. Leibniz's law of conservation of force differs from the law of conservation of energy, formulated in the nineteenth century, in that he was not able to provide a mechanical equivalent of heat. Moreover, Leibniz certainly was aware that a law of conservation could be formulated for momentum; this was not, however, the issue in the dispute with the Cartesians.

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