the parishes of Biggar, Carluke, Carmichael, Carnwath, Carstairs, Covington and Thankerton, Crawford, Crawfordjohn, Culter, Dolphinton, Douglas, Dunsyre, Lamington and Wandel, Lanark, Lesmahagow, Liberton, Pettinain, Symington, Walston, Wiston and Roberton, Moffat, Avondale, Stonehouse, Glasford, and East Kilbride; so much of the parish of Cathcart as adjoins East Kilbride, and so much of the parish of Kirkpatrick juxta as may be in the county of Lanark.