influxion

Influxion is a historical term with two principal senses in English. In the context of the history of calculus, influxion (often spelled fluxion) designates the instantaneous rate at which a quantity changes with respect to time, equivalent to what is now called the derivative. In Newtonian rhetoric, a quantity that varies is a fluent, and the rate of change of a fluent is its influxion; the common modern notation is the derivative ẋ or dx/dt. Problems were framed as relating the influxion of a quantity to its fluent via algebraic relations, with infinitesimals and limits providing the grounding ideas. The term fell out of use as calculus matured and the language of derivatives and integrals replaced fluxions and fluents.

A second, rarer sense of influxion is as a general noun meaning the act or process of flowing in or entering; an inflow. This usage is largely archaic or literary and is typically replaced by influx or inflow in contemporary writing. The word can be found in older scientific, medical, or descriptive texts to describe, for example, the influxion of blood, fluid, or people into a region.

Etymology: influxion derives from late Latin influxio or French influxion, from in- “into” plus fluxio “a flowing.” In modern usage, the more common term for the mathematical concept is derivative or rate of change; influxion survives mainly in historical discussions of Newtonian calculus.