 We turn now to a modern-day attempt to implement Mach-heavy known as ‘shape dynamics’. (In fact, shape dynamics is just one theory within this tradition, as we will see below.) This approach was initiated – albeit not under that name – by Barbour and Bertotti (1977, 1982). In tackling the problem of implementing Mach-heavy, rather than formulating a revised law of gravity/inertia using relative quantities, Barbour and Bertotti used the framework of Lagrangian mechanics, replacing elements of the mathematics referring to absolute quantities of motion with new terms invoking only relative distances, velocities, etc. In this section, we presuppose a basic familiarity with the Lagrangian framework. For a non-technical introduction to shape dynamics, see Barbour (1999); for an up-to-date review of recent work in the field, see Mercati (2018).