Referee's report by Henry Frederick Baker, on a paper 'The theory of the double gamma function' by Ernest William Barnes Sectional committee: Mathematics Recommended for publication in Philosophical Transactions. The first 69 pages could be reduced by the omission or condensation of demonstrations. The paper should be preceded by a very full statement of the notations adopted and a table of contents, and as far as possible be made independent of the references to the author's previous publications. He cannot understand it in entirety but is happy to undertake a thorough examination if desired. From what he has examined of this and other papers by the author, he does not expect any tangible criticism would arise from a more detailed study of the paper. [Published in Philosophical Transactions A , 1901]. Endorsed on verso as received 7 May 1900. 5 May 1900