The Bold Princess Royal songs aren't sung to the "Princess Royal" tune (which is by Carolan), but the Arethusa is one of three songs to this tune. You can find them all on Lesley Nelson's Contemplator website, which I think is in Mudcat Links.

There are also over a dozen versions of the tune as a Morris Dance, collected from various English villages. Usually (but not always) in a major key for a set dance (6 men),and in minor for a jig (solo dance).

Wassail! V