A muffle furnace is built around a separate inner chamber, the muffle itself, made of a heat-resistant material such as fired clay or later ceramic, which sits inside an outer firebox but is fully enclosed on every side except a small opening for loading. The fire burns in the space around the muffle, never inside it, so heat has to pass through the muffle's walls to reach whatever is placed within, rather than reaching it directly as flame or hot gas. This indirect path costs some efficiency compared to an open fire, but it buys something assaying and fine metallurgical work could not do without: a working chamber completely free of ash, soot, sulfur fumes and other combustion byproducts that would otherwise settle on or react with the material inside.
Because the heat reaching the muffle's interior comes evenly through its walls rather than from one direction as a flame does, the temperature inside stays far more uniform than an open hearth could manage, which mattered enormously for a process like cupellation, where a cupel holding a tiny, precisely weighed sample of metal needed steady, even, contamination-free heat to oxidize away its base-metal content cleanly and leave an accurate button of pure gold or silver behind.