Inherent and Centrifugal Forces in Newton

Abstract

Over the last few years a resurgence of Newtonian studies has led to a deeper understanding of several aspects of his Philosophiae naturalis principia mathematica. Besides the new translation of Newton's masterpiece, these contributions touched on his mathematical style, investigative method, experimental endeavors, and conceptual systematization of key notions in mechanics and the science of motion (I. Newton, The `Principia'. A new translation by I. Bernard Cohen and Anne Whitman assisted by Julia Budenz (Berkeley: University of California Press, 1999), hereafter New translation. Readers can find a useful bibliography on Newton in I.B. Cohen and G. Smith, eds, The Cambridge Companion to Newton (Cambridge: Cambridge University Press, 2002, hereafter Cambridge Companion), 465–80.). With regard to the last topic, recent works have identified two notions where Newton's choices look unclear and scholarly opinion is divided. These notions are materiae vis insita or vis inertiae, namely the inherent force of matter or force of inertia, and vis centrifuga or centrifugal force. It is my conviction that the two notions became inter-related in Newton's thought starting from the time of composition of the Principia and that a new look at them will simultaneously clarify matters about both. Newton's beliefs about the nature of centrifugal force did not affect his calculations of planetary and cometary orbits in the Principia, but they are none the less of considerable intellectual interest.

After a brief introduction on Huygens and the early Newton, Sect. 2 focuses on Newton's views in the Principia and its preliminary manuscripts. Section 3 presents a summarized account of Leibniz's views, which are necessary for understanding Newton's criticism of them. This is the subject of Sect. 4, where we find his views most fully spelled out.