I have recently bought Nancy's excellent book, and indeed even sat next to her at Edinburgh Folk Club tonight (how's that for name-dropping?) "The Mistress" is in the book, and apart from Nancy using a lot more Scots words in the published version, I can probably clear up some of the debates above re correct lyrics. (Ed Miller may, of course, have made his own changes!)
In the chorus, it's:
THAT siren of the ocean streams
Who whispers in A seaman's dreams.
"No mistress have but me".

Verse 1, second line:
He claimed as freend the tide and wind, as brither named the wave.

Verse 2, first line:
My brither jined a merchantman to traivel foreign lands,

Verse 3, final line:
I see the new moon SAILIN' wi' the auld moon in her airm.

When I get time I'll maybe post the complete lyrics!