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'. Subject: Mathematics [Published in the Philosophical Transactions of the Royal Society, 1864] 28 April 1864