Everyone needs to know a little marble maintenance, right? Maybe. But you never know when this will come in handy. As taken from “The Household Encyclopedia; or, Family Dictionary of Everything Connected with Housekeeping and Domestic Medicine.” By an association of Heads of Families and Men of Science. Volume II. London: 1859
The following will usually remove stains from them: Wash the marble well with soap and water, and then apply this mixture: Powdered whitning, 1/4 lb.; a tea-spoonful of stone blue, powdered; 1 oz. of soda dissolved in a little water; and 1/2 lb. of soft soap. Boil these together till thoroughly mixed and put it whilst hot on the marble with a paste brush; let it remain on for an hour, then wash it off, and rub the marble dry.
As best I can tell, powdered whitning is the name of powdered and washed white chalk (calcium carbonate), used in metal polish, putty, and whitewash, and sometimes added to paint to improve the paint’s opacity. And stone blue, powdered is copper sulphate. I would try this on a small inconspicuous area to make sure that those folks back 1859 knew what they were talking about.