Hertz's Mechanics and a unitary notion of force

Heinrich Hertz dedicated the last four years of his life to a systematic reformulation of mechanics. One of the main issues that troubled Hertz in the customary formulation of mechanics was a 'logical obscurity' in the notion of force. However, it is unclear what this logical obscurity was, hence it is unclear how Hertz took himself to have avoided it. In this paper, I argue that a subtle ambiguity in Newton's original laws of motion lay at the basis of Hertz's concerns; an ambiguity which led to the development of two slightly different notions of force. I then show how Hertz avoided this ambiguity by deriving a unitary notion of force, thus dispelling the obscurity that lurked in the customary representation of mechanics.