Amazingly, when Montpelier's archaeologists heard about the Restoration Team's problem, they remembered that they had found a fragment of marble directly underneath the fireplace during their excavation of the cellar.  The white fragment of stone measured approximately 1-1/4 inch and had a rough, hand-hewn bottom surface but a smooth, well-finished top that was similar to a hearth stone.  But how to definitively prove it was part of the hearth President Madison had installed in the room?