Referee's report by Henry John Stephen Smith, on a paper 'On the calculus of symbols.— Fourth memoir. With applications to the theory of non-linear differential equations' by William Henry Leighton Russell Not recommended for publication in the 'Philosophical Transactions of the Royal Society'. The paper is very different in style and structure to the earlier papers in the series, and can be considered for publication on it's own merits without reference to the earlier papers. As such, the paper is recommended for publication in the Proceedings. Subject: Mathematics [Published in the 'Proceedings of the Royal Society of London', 1864] 10 April 1864