Robert Dundas, the 3rd Lord Arniston (also known as Robert Dundas the Elder), was the second son of Robert Dundas, the 2nd Lord Arniston (died 1726). He inherited the Arniston estate because his elder brother, James, died before their father.
Sources:
Richard Scott, ‘Dundas, Robert, Lord Arniston (1685-1753)', Oxford Dictionary of National Biography (Oxford: Oxford University Press, 2004) <http://www.oxforddnb.com/view/article/8257> [accessed 7 April 2008]
http://www.historic-scotland.gov.uk/index/heritage/gardens/gardenssearchsummary.htm?s=Arniston&r=&bool=1&PageID=2309 [accessed 7 April 2008]