Source : Webster's Revised Unabridged Dictionary (1913)

Madam \Mad"am\, n.; pl. {Madams}, or {Mesdames}. [See {Madame}.]
   A gentlewoman; -- an appellation or courteous form of address
   given to a lady, especially an elderly or a married lady; --
   much used in the address, at the beginning of a letter, to a
   woman. The corresponding word in addressing a man is Sir.