Referee's report by Henry John Stephen Smith, on a paper 'A Memoir on the Single and Double Theta-Functions' by Arthur Cayley Recommended for publication in the 'Philosophical Transactions of the Royal Society'. Refers to work of Goessul [?] and Johann Georg Rosenhain. The work is valuable for the great number of formulae included. Subject: Mathematics [Published in the Philosophical Transactions of the Royal Society, 1880] 13 March 1880