If the said Universities of Edinburgh and Aberdeen, of Glasgow and Saint Andrew's respectively, shall not be able to agree upon some One Person to represent them in the Council, it shall be lawful for each One of the said Universities to select One Person; and thereupon it shall be lawful for Her Majesty, with the Advice of Her Privy Council, to appoint One of the Persons so selected to be a Member of the said Council for the said Universities.