In　the　case　of　metal-carbon　eutectics,　with　transition　temperatures　above　1000　degrees　C,　the　liquidus-point　temperature,　associated　with　melting,　serves　as　a　prime　reference　temperature.　Factors　influencing　the　shape　of　the　melting　curve　and　how　to　deal　with　them　when　specifying　the　liquidus　temperature　are　the　main　subject　of　this　paper.　Influence　factors　investigated　are　the　impurity　factor,　the　furnace-temperature　gradient,　and　a　factor　not　considered　before:　the　thermal　inertia　of　the　furnace　and　the　associated　transient　in　furnace　temperature　during　melting.　These　investigations　resulted　in　an　improved　method　for　determining　the　liquidus　point,　demonstrated　for　Co-C,　which　implicitly　corrects　for　the　post-melting　effect,　if　any.　In　addition,　a　new　method,　the　step-shift　method,　is　proposed　for　the　determination　of　the　solidus　point　by　direct　observation.　As　shown,　there　is　a　clear　justification　for　establishing　reference　methods　to　determining　the　solidus　and　liquidus　points　of　M-C　eutectics　along　the　lines　set　out　in　this　paper.