Rutherglen in Lanarkshire was a royal burgh that returned one commissioner to the Parliament of Scotland and to the Convention of Estates.
After the Acts of Union 1707, Rutherglen, Dumbarton, Glasgow and Renfrew formed the Glasgow district of burghs, returning one member between them to the House of Commons of Great Britain.
References
Rutherglen (Parliament of Scotland constituency) Wikipedia(Text) CC BY-SA