Newton's numerator in 1685: A year of gestation

Abstract

In his “‘From the Phenomena of Motions to the Forces of Nature’: Hypothesis or Deduction?” of 1990 Howard Stein reinvigorated a centuries-old dispute over whether Newton had derived his law of gravity from phenomena. More specifically, Stein – like such notables before him as Euler – challenged whether any phenomenon involving gravity served as a basis for Newton inferring that his third law of motion applies to gravity, and with it for inferring that the mass of the attracting body belongs in the numerator of the law. Stein ends up conjecturing that Newton's conception of forces of nature as forces of interaction “was actually developed by Newton at the same time that he was discovering the law of gravitation.” This paper assesses this conjecture by examining the manuscripts – including deletions and insertions – that we have from 1685, the year during which the theory of gravity emerged and the Principia took shape. The conclusion is not merely that the manuscript evidence supports Stein's conjecture, but more significantly that the driving consideration behind both the Newtonian conception of forces of nature as forces of interaction and the inclusion of the mass of the attracting body in the numerator of the law was that the mass of the attracted body, as inferred from phenomena, must be included in the numerator – that is, the phenomena establishing that gravitational forces, unlike any other kind of forces, somehow “proportion themselves” to the individual bodies on which they act.