I think you have it correct as Birniebog. It also comes up as Birnybog from other google entries. Have a look at this old post http://news.rootsweb.com/th/read/LANARK/2006-03/1141826573If you remember from the other post on the Thomson family we were trying to get the links to Corehouse and the family. If you look at the link above, you will see also effectively the enumerator's walk from 1841 which links Corehouse Estate and Brinybog.Monica