The Folk Music Journal did and article (by Wilf Darlington) on this tune (1992 Vol 6 No3), complete with a Captain Pugwash sketch on the front cover. The article covers the harmony of the tune in detail and investigates the descending chromatic part, which seems only to have come into the tune in the early part of the 20th century and to have been introduced via the popular commercial bands (like Jimmy Shand's).

(This is from memory - I'd have to reread the article to be certain of the details)

Mick