Richard

I did start looking at sheet music with Man In The Moon in the title, but without finding Scan's tune so far (there are a lot of Men in the Moon!).

The Irish Washerwoman mentioned by Steve for the Glasgow Poet's Box edition is the only tune mentioned in the sources I've found. The Alfred Williams copy (the only one listed in Roud at VWML, and with a copy there) is text only.

Mick