This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in (...) their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics. (shrink)

Leibniz’s argument against Descartes’s conservation principle in the Brevis demonstratio (1686) has traditionally been read as passing from the premise that motive force must be conserved to the conclusion that motive force is not identical to quantity of motion and, finally, that quantity of motion is not conserved. In a lesser-known draft of the same year, Christiaan Huygens claimed that Descartes had in fact never held the view that Leibniz was attacking. Huygens is right as far as the traditional reading (...) is concerned. However, if the Brevis demonstratio is seen, as it should be, in the context of Leibniz’s attempt to ground mechanics in the foundational metaphysical axiom of the equivalence of full cause and entire effect, then Huygens’s objections can be answered. Leibniz may have committed Descartes to the foundational axiom because of the Traité de la méchanique, which was available to Leibniz at that time. Leibniz had used the equivalence of full cause and entire effect both in discovering the conservation of vis viva earlier and in various arguments for it later. Thus, the Brevis demonstratio should be viewed with Leibniz’s broader foundational mission in mind. (shrink)

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

It has been suggested in the literature that, although Willem Jacob ‘s Gravesande occasionally treated Newton's doctrines in a selective manner, he was nevertheless an unremitting follower of Newton's methodology. As part of a reassessment of ‘s Gravesande's Newtonianism, I argue that, although ‘s Gravesande took over key terms of Newton's methodological canon, his methodological ideas are upon close scrutiny quite different from and occasionally even incongruent with Newton's views on the matter.