Equilibrium and *explanation in 18th century *mechanics

The received view of the Scientific Revolution is that it was completed with the publication of Isaac Newton's (1642-1727) Philosophiae Naturalis Principia Mathematica in 1687. Work on mechanics in the century or more following was thought to be merely filling in the mathematical details of Newton's program, in particular of translating his mechanics from its synthetic expression into analytic form. I show that the mechanics of Leonhard Euler (1707--1782) and Joseph-Louis Lagrange (1736--1813) did not begin with Newton's Three Laws. They provided their own beginning principles and interpretations of the relation between mathematical description and nature. Functional relations among the quantified properties of bodies were interpreted as basic mechanical connections between those bodies. Equilibrium played an important role in explaining the behavior of physical systems understood mechanically. Some behavior was revealed to be an equilibrium condition; other behavior was understood as a variation from equilibrium. Implications for scientific explanation are then drawn from these historical considerations, specifically an alternative account of mechanical explanation and unification. Trying to cast mechanical explanations (of the kind considered here) as Kitcher-style argument schema fails to distinguish legitimate from spurious explanations. Consideration of the mechanical analogies lying behind the schema are required.