Second referee's report by Henry John Stephen Smith, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock Not recommended for publication in the 'Philosophical Transactions of the Royal Society'. Encloses a memorandum [RR/5/194] clearly stating his disagreement with the demonstration. Has not communicated with Arthur Cayley. Addendum, dated 12 November 1863. Has received the letter from George Gabriel Stokes containing a note from Arthur Cayley. Agrees with Arthur Cayley regarding the doubtful points of the paper. Has sent Alexander John Ellis' paper to Price [Bartholomew Price?], who will respond in a few days. Suggests Ellis be discouraged from publishing criticisms of other mathematicians, including Julius Plücker ['On an application of the theory of scalar and clinant radical loci', Proceedings, doi:10.1098/rspl.1860.0030 Vol.11 1862]. Refers to work by George Salmon and Carnot [?], August Ferdinand Möbius and Michel Chasles, the last of which the Committee has decided not to publish. Subject: Mathematics [Published in the Proceedings of the Royal Society of London, 1864] 10 November 1863