Referee's report by George Ballard Mathews, on a paper 'Quaternions and projective geometry' by Charles Jasper Joly Sectional Committee: Mathematics Recommended for publication in Philosophical Transactions, in full. He has no modifications to suggest. He has had no time, and shall have none in the near future, for a thorough study of the paper and has read only a small part of it, glancing over the rest. He has however convinced himself that it is of considerable interest. It connects the theory of quarternions with a number of other branches of mathematics and this lifts it out of the somewhat isolated position which it has hitherto occupied, and largely extends the scope of its applications. The paper, though long, is of a concise style. [Published in Philosophical Transactions A, 1903]. Endorsed on verso as received 12 December 1902. December 1902