Andrew Kuntz's The Fiddler's Companion, which should always be your first port of call when looking for information on dance tunes, has the following entry for Colonel Hamilton's Delight:
"Composed by Joseph Reinagle (1762-1836) around 1783 or earlier. Reinagle, born in Portsmouth, was the son a an Austrian father and Scottish mother and spent his childhood and young adulthood in Edinburgh, becoming leader of the orchestra in the Theatre Royal. Later he moved to Dublin, London, and finally settled in Oxford where he taught the cello. The tune appears in Niel Gow's Strathspey Reels, the Sharpe Manuscript, and Davie's Caledonian Repository. Johnson (Scottish Fiddle Music in the 18th Century), 1984; No. 87, pg. 230. Neil (The Scots Fiddle), 1991; No. 3, pg. 6 (appears as "Hamilton House")."
There is also a list of printed and recorded examples available at the DanceData World-Wide-Web Interface, which is an online database specialising in Scottish Country Dance:
As Hamilton House, the tune itself may be found through J C's Tunefinder.