 The law of free fall—i.e., a body in free fall from rest traverses a distance proportional to the square of the time elapsed—was discovered by Galileo through the inclined plane experiments (Drake 1999, v. 2). At first, Galileo attempted to represent this phenomenon with a velocity-distance relation, and the equivalent mean proportional relation. His later and correct definition of natural acceleration dependent on time was an insight gained through recognizing the physical significance of that mean proportional relation (Machamer and Hepburn 2004; for a different analysis of Galileo’s discovery of free fall see Renn, et al. 2000). Yet Galileo would not publish anything making time central to his analysis of motion until 1638, in the Two New Sciences.