Referee's report by William Burnside, on a paper 'The asymptotic expansion of integral functions defined by Taylor's series' by Ernest William Barnes Sectional Committee: Mathematics Recommended for publication in Philosophical Transactions. Some compression is desirable. Strongly thinks the title should be modified by the introduction of 'certain' or some other qualifying word before 'integral'. The figures should be reproduced. Notes the paper raises a serious general question. He understands that the author contends that no general treatment can be attempted of the question of the behaviour of integral functions for large values of the variable. There could be an endless discussion of special cases to which some limit must be put. Burnside thinks that in the present paper this limit has been overpassed. Burnside knows from experience that the recommendation that the paper should not be printed is regarded as too drastic, but he thinks the author may be fairly called upon to shorten it. Provides examples of redundant material from sections of the paper he has read closely, noting he has not read the whole thing closely. It might be made clear in the title of the paper that it deals only with specially chosen functions; as otherwise it is bound to mislead people who are looking up references on the subject. [Published in Philosophical Transactions A, 1906]. Endorsed on verso as received 30 March 1905. May 1905