Referee's report by James Joseph Sylvester, on a paper 'Researches on the theory of invariants' by William Spottiswoode Recommended for publication in the 'Philosophical Transactions of the Royal Society'. Suggests that the author be asked if an abstract in the Proceedings would be sufficient until such a times their researches are fuller and more complete for publication in the Transactions. Discusses the merits and otherwise of the reviewing process and the tasks of the referee. Subject: Mathematics [Published in the 'Proceedings of the Royal Society of London'] 26 April 1855