Referee's report by Arthur Cayley, on a paper 'Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c' by James Joseph Sylvester Recommended for publication in the 'Philosophical Transactions of the Royal Society'. Considers the manuscript to be of poor quality, the writing is nearly illegible, and makes the work of reviewing the paper very difficult. Subject: Mathematics [Published in the Philosophical Transactions of the Royal Society, 1864] 2 October 1864