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The Newtonian Equivalence Principle: How the Relativity of Acceleration Led Newton to the Equivalence of Inertial and Gravitational Mass

Published online by Cambridge University Press:  01 January 2022


From late 1684 through mid-1685, Isaac Newton turned to developing and refining the conceptual foundations presupposed by his emerging physics. Analysis of his manuscripts from this period reveals that Newton’s understanding of the relativity of acceleration led him to seek a spatiotemporally invariant quantity of matter. He found two such quantities and then designed an experiment to discover their relationship. Interpreting the experiment, however, required distinguishing a new notion of force. Others have recognized the conceptual distinction between inertial and gravitational mass. I show here that Newton clearly saw this distinction and that he provisionally established their equivalence.

Newtonian Relativity
Copyright © The Philosophy of Science Association

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I am deeply indebted to George Smith for countless discussions related to this project and for his support and encouragement. I am also grateful to Robert DiSalle and Chris Smeenk, with whom I have had many fruitful discussions. I also thank Howard Stein for his insightful commentary on my talk given during the PSA symposium, Newtonian Relativity. I also thank Stathis Psillos, William Demopoulos, William Harper, Ryan Samaroo, and the anonymous referees for helpful comments on an earlier draft. This research was supported by the Rotman Institute of Philosophy. This article is dedicated to the memory of my father, William Fox.


Biener, Zvi, and Smeenk, Chris. 2012. “Cotes’ Queries: Newton’s Empiricism and Conception of Matter.” In Interpreting Newton: Critical Essays, ed. Janiak, Andrew and Schliesser, Eric. Cambridge: Cambridge University Press.Google Scholar
Carus, Titus Lucretius. 1937. De Rerum Natura. Trans. Rouse, W. H. D.. Cambridge: Cambridge University Press.Google Scholar
Casini, Paolo. 1984. “Newton: The Classical Scholia.” History of Science 22 (1): 158.CrossRefGoogle Scholar
Friedman, Michael. 2012. “Newton and Kant: Quantity of Matter in the Metaphysical Foundations of Natural Science.” Southern Journal of Philosophy 50 (3): 482503.CrossRefGoogle Scholar
Fox, Craig W. Forthcoming. “Newtonian Relativity and Quantity of Matter.”Google Scholar
Harper, William L. 2011. Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Cosmology. Oxford: Oxford University Press.CrossRefGoogle Scholar
Kochiras, Hylarie. 2013. “The Mechanical Philosophy and Newton’s Mechanical Force.” Philosophy of Science 80 (4): 557–78.CrossRefGoogle Scholar
Newton, Isaac. 1684a. De motu corporum in gyrum. Cambridge University Library, MS Add. 3965 fols. 55r–62*r. Scholar
Newton, Isaac 1684b. De motu sphæricorum corporum in fluidis. Cambridge University Library, MS Add. 3965 fols. 40r–54r. Scholar
Newton, Isaac 1685a. De motu corporum in medijs regulariter cedentibus. Cambridge University Library, MS Add. 3965 fols. 25r, 25v, 26r, 23r, 23v, 24r. Scholar
Newton, Isaac 1685b. De motu corporum—Liber Secundus. Trans. Smith, George E. and Whitman, Anne. Cambridge University Library, MS Add 3990 fols. 1r–56r. Scholar
Whitman, Anne 1999. The Principia: Mathematical Principles of Natural Philosophy; A New Translation. Berkeley: University of California.Google Scholar
Stein, Howard. 1990. “On Locke, ‘the Great Huygenius, and the Incomparable Mr. Newton.’” In Philosophical Perspectives on Newtonian Science, ed. Bricker, Phillip and Hughes, R. I. G.. Cambridge, MA: MIT Press.Google Scholar
Wilson, Curtis. 1999. “Re-doing Newton’s Experiment for Establishing the Proportionality of Mass and Weight.” St. John’s Review 45 (2): 6473.Google Scholar