Mach's principle has been an important inspiration for the construction of general relativity, but the physical interpretation of Einstein's formulation of general relativity still requires external clocks and rods and thus fails to be manifestly relational. Mach's principle would be fully implemented if the predictions of general relativity were independent of the choice of clocks and rods. Barbour and Bertotti conjectured that Jacobi's principle and a mechanism they called "best matching" were construction principles for a fully Machian theory. Barbour implemented these principles in collaboration with Niall Ó Murchadha, Edward Anderson, Brendan Foster and Bryan Kelleher to derive the ADM formalism in constant mean curvature gauge. This did not implement Mach's principle, because the predictions of general relativity in constant mean curvature gauge depend on the choice of clocks and rods. Mach's principle was successfully implemented in 2010 by Henrique Gomes, Sean Gryb and Tim Koslowski who drew on the work of Barbour and his collaborators to describe gravity in a fully relational manner as the evolution of the conformal geometry of space.