"The Princess Royal", in Gaelic "Bean-Priunsa Riogda" or "Beanphrionsa Rioghamhuil", is also known as "Miss MacDermott" ("Inion Nic Diarmada").
The air under the title "Princess Royal" or "Miss MacDermott" is attributed to O'Carolan by collector Edward Bunting (The Ancient Music of Ireland, 1840), with the note “composed by Carolan for the daughter of MacDermott Roe, the representative of the old princes of Coolavin.” O'Sullivan, however, notes there were two branches of the County Roscommon family; the MacDermotts of Alderford, usually known by the title MacDermott Roe, and the MacDermotts of Coolavin. The head of the latter branch was known in O'Carolan's time as the Prince of Coolavin and O'Sullivan believes it probable that the Princess Royal was his eldest daughter and not of the MacDermott Roes.
I learned it from Miles Krassen's edition of O'Neill's Music of Ireland.