To confirm that the plaster fragment dated to the Madisons’ occupation of Montpelier, paint analyst Dr. Susan Buck analyzed a small sample of its yellowish coating.  Specifically she was looking to see if the pigments (which gives the coating its color) or the binder (which keeps the coating from falling apart) could be dated to President Madison’s time.  Like nails and screws, paint pigments and binders have evolved over time.  By knowing the dates when pigments and binders were used in historic paints an analyst can accurately determine the latest possible date for a paint (much like an archaeologist's TPQ dating technique).  In this case, if the pigments and binders used in the yellow paint were available in the late 18th and early 19th century, then the plaster fragment most likely dated to the Madison-era.