Princess Augusta of Saxe-Gotha ( 30 November 1719 â `` 8 February 1772 ) was Princess of Wales between 1736 and 1751 , and Dowager Princess of Wales thereafter . Princess Augusta of Saxe-Gotha-Altenburg ( 30 November 1719 â `` 8 February 1772 ) was Princess of Wales between 1736 and 1751 , and Dowager Princess of Wales thereafter .